Tunable and narrow linewidth mm-wave generation through monolithically integrated phase-locked DFB lasers
1. Universit`a degli Studi di Pavia
Dipartimento di Elettronica
Corso di Dottorato in Ingegneria Elettronica,
Informatica ed Elettrica - XXIV ciclo
Tunable and narrow linewidth
mm-wave generation through
monolithically integrated
phase-locked DFB lasers
Design, Fabrication and Characterization
Advisor:
Prof. Guido Giuliani
Co-Advisor:
Dr. Michael J. Strain
PhD Thesis by
Marco Zanola
Anno accademico 2011
5. CONTENTS 5
5.3.4 RF signal linewidth vs. RF signal frequency . . . . . . 143
5.3.5 RF signal linewidth vs. injected power . . . . . . . . . 144
5.3.6 High-frequency measurements . . . . . . . . . . . . . . 148
Conclusions 152
Bibliography 159
Acknowledgements 173
6. Introduction
During the last couple of decades, the generation of high electrical fre-
quency signals (with frequencies from a few GHz up to the THz domain) has
been the subject of exhaustive research studies. Despite the wide range of
potential applications, the THz range is currently poorly developed due to
difficulties encountered in the generation of these signals. In fact, this range
of frequencies lies right in between the well-developed microwave and optical
domains.
Applications such as high-speed telecommunications, radio astronomy, spec-
troscopy, tomography and homeland security could be remarkably improved
by the availability of sources capable to emit efficiently in this range. The
range 40-60 GHz represents the next unlicensed frequency band, which can
used to offer a wide number of new services for indoor wireless communi-
cations. Local oscillators for radio astronomy and spectroscopy applications
are also required, with emission frequencies of a few hundred GHz and stable
and narrow linewidth. THz- waves can be successfully employed in novel
tomography spectroscopy and screening applications, thanks to their non-
ionising energies intrinsically safe for human beings. Finally, these waves
offer a high-contrast penetration of non-conductive (such as clothes) and
conductive (metals) materials, which can be used for homeland security ap-
plications (like mm- and THz- wave scanners).
Both electronics and optoelectronic approaches have been explored aiming
the generation of mm- and THz- waves, obtaining encouraging results. How-
ever, so far none of the available techniques has proven to be able to generate
7. CONTENTS 7
signals in the above-mentioned frequency range, by means of a single, effi-
cient, compact and reliable device. Such a device is required to generate
signals with high spectral purity (narrow linewidth and low phase noise)
that can be continuously tuned over the whole range of frequencies; the de-
mand for field-deployment requires stable room-temperature operation and
the control of a limited number of its parameters.
A promising optoelectronic technique has been recently proposed [1], which
represents an improvement of the basic Photomixing technique. It is based
on the mutual injection of three single mode lasers, which are all-optically
phase-locked via a Four Wave Mixing non-linear process. The beating of the
three lasers on a high speed photodetector is expected to generate a spec-
trally pure RF signal. Wide tunability of the generated RF signal can be
achieved by tuning the driving currents of the lasers, thus changing their
relative frequency separation.
Aim of the present work
The photomixing technique assisted by mutual injection locking and Four
Wave Mixing gave promising results using an experimental setup composed
of discrete optical components [1]. Three Distributed FeedBack (DFB) lasers
have been mutually injected using single mode optical fibres and couplers,
and an effective phase-locking between the lasers has been achieved.
The present work, funded by Fondazione Cariplo (Project 2007-
5263, ”Semiconductor lasers with nanostructured gratings for wire-
less application signal generation”), aims at the integration of that
complex discrete setup into a single monolithic optoelectronic chip,
followed by the demonstration and characterisation of the mutual
injection locking using the integrated device.
The monolithic integration entails multiple advantages but also severe tech-
nological challenges. The full integration into a single Photonic Integrated
Circuit (PIC) is desirable in terms of reduced size, cost and power consump-
8. CONTENTS 8
tion, together with a higher reliability of the final device. Moreover, in order
to achieve a high yield and reliable fabrication process, the techniques em-
ployed by the optical telecommunication industry to produce semiconductor
lasers can be borrowed. In particular, Indium Phosphide (InP) based semi-
conductor material compounds can be used, thanks to their well-developed
fabrication technologies.
To reach this goal many design and technological challenges have to be solved,
since the development of PICs, which consists in the integration of different
optical structures and functions on the same active semiconductor substrate,
is still in its infancy. Different device geometries are to be investigated, with
the goal of assessing the best configuration that ensures an output RF sig-
nal that well matches the specifications set above. For each configuration,
different optical structures need to be designed and optimised for a reliable
fabrication. The three DFB lasers, which represent the core of the devices,
must exhibit high Side Mode Suppression Ratio (SMSR), and precise and
predictable lasing wavelength. Couplers, attenuators and output waveguides
are needed to guide and couple the output field of the lasers, to adjust the
levels of mutual injection and to allow the extraction of the generated optical
signals.
The fabrication of the device has to be as simple as possible. In fact, a simple
fabrication process reduces costs and enhances the yield of the process and
the reliability of the devices. In view of this, the use of a post-growth fabri-
cation process is highly advisable because it does not require active material
regrowth, and it can thus reduce the technological complexity.
A thorough experimental characterisation of the devices is mandatory in or-
der to assess the different design/technological solutions, and to investigate
the complex dynamics that develops when optical oscillators are mutually
coupled. The DFB lasers have to be fully characterised, as well as the FWM
process that allows the mutual locking of the lasers. Once the feasibility of
the mutual injection locking technique on the integrated device is demon-
strated, the locking regime and the generated RF signal have to be analysed
9. CONTENTS 9
with respect to the operating conditions of the device.
Thesis outline
In this thesis the full development process of the device for the RF signal
generation is described, starting from the description of the innovative lock-
ing technique (Chapter 1), to the design of the monolithic device (Chapter
2), its fabrication (Chapter 3) and characterisation (Chapter 4 and 5).
Chapter 1 starts from the description of the potential applications of high
frequency signals, and the available techniques to generate those signals are
analysed. Particular attention is paid to the optoelectronics techniques pro-
posed so far, with respect to their potential of integration into a single mono-
lithic device. The improved photomixing technique based on the mutual
injection locking assisted by FWM is described in details, and the results
previously obtained using the experimental setup composed by discrete op-
tical components are analysed.
In Chapter 2, four different device geometries are presented. The design of
the basic building blocks is described, taking into account the limitations
set by the fabrication process technology. Starting from the analysis of the
available semiconductor material, the design of the optical waveguides is pre-
sented. The design of the DFB lasers is one of the most relevant sections,
including the review of the theory of their operation and the description of the
design strategies that have been devised in order to obtain a pure single-mode
operation together with precise and predictable lasing wavelength. Finally,
the design of the optical couplers employed in the different geometries is de-
scribed.
In Chapter 3 the fabrication of the device is presented. The full fabrication
process, personally carried out in the cleanrooms of the James Watt Nanofab-
rication Centre of the University of Glasgow, U.K., required state-of-the-art
techniques which are described in detail. All the main fabrication steps are
10. CONTENTS 10
described, starting from the design of the lithography masks. In particular,
the etching effect called RIE-lag is analysed aiming a reliable fabrication of
the designed optical structures.
Chapter 4 focuses on the characterisation of the DFB lasers. Starting from
the L-I curves, optical spectrum and optical linewidth, the optical properties
of the lasers are analysed. Particular attention is given to the characterisation
of the precise wavelength spacing achievable with the employed fabrication
process. Finally, a characterisation of the stability of the basic lasing prop-
erties over the time is briefly presented.
In Chapter 5 the mutual injection locking of two and three lasers is de-
scribed, together with the characterisation of the efficiency of the FWM pro-
cess needed to achieve the phase-locking of the lasers. The experimental lock-
ing of two DFBs operating at the same frequency is firstly reported. Then,
the locking of three DFBs operating at different frequencies is demonstrated,
and three different parameters are found as indicators of the occurrence of
the locking. It is shown that the generated RF signal has a narrow linewidth
which can be tuned over a wide range of frequencies. The Chapter closes
with a preliminary demonstration that the mutual injection locking can be
achieved up to several hundreds of GHz.
11. Chapter 1
Photonic techniques for
high-frequency signal
generation
High frequency signals lie in the highest radio frequency band, in the
range of frequencies from 3 to 300 GHz (Extremely High Frequency, EHF,
also called mm-waves), and above, up to the THz range. In recent years
the interest in generating mm- and THz- waves increased exponentially, due
to their potential applications in several fields. This chapter starts with
the description of the most promising applications of high frequency signals.
In fact, mm- and THz- waves find interesting applications in several fields,
such as the next unlicensed band for ultrafast wireless communications (40-
60 GHz), in anti-collision radar systems, spectroscopy and radio astronomy,
medicine and homeland security. Then, an overview on the most common
techniques for the generation of high frequency signal is given, focusing in
particular on the photonic techniques. Finally, the recently proposed tech-
nique of Photomixing assisted by mutual injection locking and Four Wave
Mixing is detailed, with a view to the issues related to its integration into a
single monolithic device.
12. 1.1 Applications of mm- and THz- waves 12
1.1 Applications of mm- and THz- waves
Spectrally pure frequency carriers for the 40-60 GHz communication band
are required. This band is currently essentially undeveloped, and therefore
available for a wide number of services, such as high-speed point-to-point
wireless local area networks, radio-over-fibre and broadband Internet access
[2].
Slightly higher carrier frequencies (70-80 GHz) can be used in millimetre
wave radar sensors, used in adaptive cruise control (ACC) applications [3].
Spectroscopy and radio astronomy applications require local oscillators to
operate from a few tens of GHz up to several hundreds of GHz. The main
interest is the detection of the so-called cold universe, the portion of universe
optically dark but very bright in the mm-wave region [4]. This detection
employs large telescopes, to be placed both on earth (project CARMA1
) or
floating in space (project SWAS2
).
Interesting spectroscopy applications come from the gas recognition via re-
mote sensing, using a terahertz time-domain spectroscopy technique [5–7].
Medical related applications are the most promising, due to the wide number
of benefits that mm- and THz- waves bring compared with the other tech-
nologies. The main feature of these waves is their non-ionising energy: their
photon energy is much smaller than X-rays’, making these frequencies safer
for in-vivo applications. Non-destructive imaging of biological tissue repre-
sents a huge research field, headed by THz tomography [8–10]. Advanced
techniques are able to scan biological samples in order to obtain high resolu-
tion 2D and 3D images, providing powerful information to diagnostic a wide
number of different diseases (Figure 1.1).
High frequency signals find promising applications also in the homeland
security, as shown by the TeraHertz Scanners recently installed in the most
important airports all around the world. Those devices exploit a second very
important feature of THz waves: they can penetrate non-conductive mate-
1
http://www.mmarray.org/
2
http://www.cfa.harvard.edu/swas/swas.html
13. 1.1 Applications of mm- and THz- waves 13
Figure 1.1: Oesophagus cancer from a horse; left: real image; right: THz-
image recorded at 480 GHz. Courtesy of University of Stuttgart, Germany.
rials, such as clothes, wood and plastic, but they cannot penetrate metals
and are strongly absorbed by water. Together with their harmless levels of
ionisation, these waves can be used to scan the passenger’s body in order to
detect concealed weapons [11, 12](Figure 1.2).
Figure 1.2: Image from an advanced prototype of airport THz scanner.
Harmful substances and gases can be detected too, thanks to their ab-
sorption lines in the THz domain [13].
The THz imaging is finally used also in industrial application for packaging
inspection and monitoring of integrated circuits quality [14, 15], and in the
analysis of cultural heritage objects (Figure 1.3) [16, 17].
14. 1.2 Generation of mm- and THz- waves 14
Figure 1.3: 3D THz computed tomography. a) Foam cube with plastic and
metallic oblique bars, b) Russian doll matryoshka, c) Egyptian pottery from
the 18th Dynasty. Courtesy of the museum of Aquitaine, France.
1.2 Generation of mm- and THz- waves
The typical requirements of the above mentioned applications are high
spectral purity, which means a narrow linewidth (< 100 kHz) and a low
phase noise (< 100 dBc @ 100 kHz offset), and a wide frequency tunability.
The spectral purity is crucial when generating carrier frequencies for com-
munication applications, but also in order to ensure high definition imaging
and good signal to noise ratio, necessary to detect the generated waves. The
wide frequency tunability is mainly required by the spectroscopy and medical
applications, since they are based on the frequency sweep of the incoming
electromagnetic wave.
Despite the large number of potential applications, this portion of the elec-
tromagnetic spectrum was substantially unexploited for long time, due to the
absence of appropriate sources. This range of frequency is often referred as
THz gap, since it lies between the well known microwave and optical worlds
(Figure 1.4).
The lower end of the THz gap is covered by the high-speed electronic
circuitry, while the higher end is covered by infra-red laser sources. The gen-
eration of mm- and THz- waves is a very broad research field, that includes
both electronic and photonic techniques.
The different techniques can be reviewed with respect to some important
characteristics. The ideal mm- and Thz- wave source would be integrable
into a monolithic chip, tunable over a wide range of frequencies and able to
15. 1.2 Generation of mm- and THz- waves 15
Figure 1.4: Electromagnetic spectrum. The THz gap lies between the well
known microwave and optical worlds.
reach the THz domain.
The firstly proposed electronic techniques are based on the use of impact
avalanche transit time (IMPATT) diodes, Gunn diodes and frequency multi-
pliers [18–20]. Although they are able to reach the THz domain (through the
use of frequency multipliers), they do not satisfy any of the other previously
listed requirements. Modern electronic techniques are based on high-speed
transistor oscillators: they can be easily integrated into monolithic chips,
obtaining an efficient generation of high frequencies with excellent spectral
characteristics [21, 22]. These devices can indeed generate frequencies up to
a few hundreds of GHz, but with a very limited tunability and very difficult
scalability to other frequency ranges. In fact, the operating frequency of
an electronic oscillator can be tuned only by a few GHz around its nominal
value. For operation at slightly different frequencies, devices with the same
design architecture can be used, but for operate in very different ranges of
frequencies totally different designs have to be considered.
Approaching the THz gap from the upper frequency end, a large number of
photonic techniques have been investigated, showing different performances
in terms of the discussed requirements. In the next section the most promis-
ing photonic techniques are briefly described.
16. 1.3 Photonic techniques for mm- and THz- wave generation 16
1.3 Photonic techniques for mm- and THz-
wave generation
Photonic systems generate radiations at very high frequencies, of the or-
der of hundreds of THz and higher. However, by employing traditional optical
sources in some particular configurations lower frequencies can be generated
[23, 24].
A purely photonic technique is based on mode locked laser, where several
modes of a multimode laser are phase-locked together, and their interference
forces the laser to work in a pulsed regime. Depending on the properties
of the laser, the pulses may be extremely short (few femtoseconds), while
the repetition rate is set by the frequency spacing between the modes and
therefore by the cavity length (f = c/2L). The electrical signal is produced
by the beating of the locked modes on a high speed photodiode.
Semiconductor lasers can be mode locked, and both active and passive ap-
proaches are available. Active mode-locking technique requires a modulator
inside the laser cavity [25], such as a standing wave acousto-optic, electro-
optic modulator or a semiconductor electro-absorption modulator. It pro-
duces a sinusoidal amplitude modulation of the light in the cavity, which
turns in the generation of sidebands sideways each lasing mode of the cav-
ity. When the modulator is driven at the same frequency of the cavity-mode
spacing, the sidebands superimpose the lasing modes, phase locking them.
The output frequency is therefore synchronised with the Radio Frequency
(RF) signal applied to the modulator.
Passive mode-locking techniques do not require any external RF signal to
produce pulses. A saturable absorber is added as intracavity element, which
modifies the dynamic of the cavity making the pulsed operation favourable
[26]. Mode locking frequencies up to 1 THz have been demonstrated, ex-
hibiting a linewidth of the generated electrical signal of a few kHz. However,
these schemes do not allow the frequency tunability of the generated signal,
since its frequency depends on the cavity length. Moreover, the active mode
17. 1.3 Photonic techniques for mm- and THz- wave generation 17
locking does not allow a monolithic integration of the system, since an ex-
ternal RF source is required.
A very versatile photonic technique is the Photomixing [27–29]. This tech-
nique is based on a coherent detection scheme of two monochromatic optical
signals, which are made beating on a non-linear material such as a high speed
photodetector (Figure 1.5a). The two optical sources emit at the frequencies
ν1 and ν2, where
|ν2 − ν1| ν1, ν2 (1.1)
The photocurrent generated by the photodetector can be described as:
iph = R P1 + P2 + 2 P1P2cos((ν2 − ν1)t + φ2 − φ1) (1.2)
where R is responsivity of the photodetector, (P1, P2) and (φ1, φ2) are
respectively the optical powers and phases of the incident optical signals.
Assuming a sufficiently high bandwidth of the photodetector, it is clear that
the generated signal can be tuned over a very wide range of frequencies,
only limited by the tunability of the optical sources. By using commercial
semiconductor lasers and by tuning both their temperature and their current
(tunability of ∼10 GHz/K and ∼3 GHz/mA) a tunability of up to 1 THz
can be achieved. This approach can be easily integrated, fabricating the two
lasers into a monolithic semiconductor device. However, this technique offers
a limited spectral purity of the generated signals, since the lasers are in a
free-running regime and the fluctuations of their output frequencies ν1 and
ν2 are not correlated. By integrating them into a single monolithic device
the two modes can exhibit a better correlation, since any thermal fluctuation
is now common to the two lasers. However, the spectral purity offered by
this approach is still poor.
Interesting improvements of this technique have been proposed, such as
Photomixing assisted by Optical PLL and Photomixing assisted by Side Band
Injection Locking. The first method is realised by applying a phase-locked-
loop (PLL) at the basic photomixing scheme, in order to lock the phase of the
two optical sources (Figure 1.5b) [30–32]. Using a mixer as phase detector,
18. 1.3 Photonic techniques for mm- and THz- wave generation 18
Figure 1.5: a) Photomixing; b) Photomixing assisted by Optical PLL; c)
Photomixing assisted by Side Band Injection Locking. The insets show the
techniques operation in the optical domain.
the phase of the beating signal is compared with the phase of a reference
RF signal. By cascading the mixer with an amplifier and a low pass filter,
an error signal can be generated. This error signal is proportional to the
phase difference of the two optical waves. By coupling it back into one of the
lasers, it can be used to lock the phase of the beating signal to the phase of
the RF reference. Although high levels of spectral purity are achievable, the
19. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 19
complexity of the system makes it impossible to be integrated into a single
monolithic chip. Not only a RF seed signal is required, but also electronic
mixer and amplifier have to be used. Moreover, the presence of electronic
components limits the tunability of the generated signal, making the THz-
range difficult to achieve.
In the Photomixing assisted by Side Band Injection Locking the two free
running lasers (ν1 and ν2) are phase locked by the injection of a third laser
(ν3) [33–35]. The additional master laser is directly modulated by a RF seed
signal at the frequency νRF (Figure 1.5c). The applied modulation creates
several sidebands around the central frequency of the master laser. Each
sideband is located at the frequency ν3 ± n · νRF , where n is the order of the
sidebands. The master laser is then injected into the two free running lasers.
By choosing the wavelengths of the two slave lasers to be ν1 = ν3 − n · νRF
and ν2 = ν3 + n · νRF , they can be injection locked by the nth
sidebands
of the master laser. Their beating on a high speed photodiode produces
a spectrally pure signal. However, also in this case the spectral purity is
achieved at the expense of an external RF seed signal. The need for the
external RF signal prevents the system from being integrated into a single
monolithic chip, offering a limited tunability of the generated mm- wave
signal and making the THz- range not achievable.
Although all the techniques so far described are very promising and used in
different applications, they do not satisfy the requirements of integrability,
tunability and spectral purity at the same time.
1.4 Photomixing assisted by mutual injection
locking and Four Wave Mixing
An alternative improvement of the photomixing technique has been re-
cently proposed [1], based on the Photomixing assisted by mutual injection
locking and Four Wave Mixing. Previous experiments demonstrated the ca-
pability of this technique of satisfying all the discussed requirements. This
20. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 20
technique is a further improvement of the photomixing techniques previously
described. It is based on an all-optical phase locking of three single mode
lasers, and it allows to achieve wide tunability and high spectral purity of
the photomixing signal, without the need for an external spectrally pure RF
seed signal. The simultaneous locking of three lasers is achieved via the sum
of two locking effects: mutual injection locking and injection locking assisted
by Four Wave Mixing (FWM).
The description of the locking mechanism can start from considering two
mutually optically coupled single mode lasers, operating at two distinct fre-
quencies ν1 and ν2 (Figure 1.6).
Figure 1.6: Mutual injection locking through modulation sidebands.
In each laser diode, the carrier density is sinusoidally modulated in time at
the beating frequency ν12 = |ν1 −ν2|. As consequence, modulation sidebands
arise on both upper and lower sides of the optical carrier generated by each
laser, specifically at frequencies ν = ν1 ± ν12 inside the laser 1 and ν =
ν2 ± ν12 inside the laser 2. Due to the mutual injection configuration, the
two lasers can exchange their phase information through these modulation
sidebands, achieving a stable reciprocal phase relation. Therefore, as already
demonstrated in [36], the two lasers can be phase locked through their self-
produced modulation sidebands. However, this situation does not ensure
the stability of their lasing frequencies, since the sidebands are generated
(and mutually injected) whatever is the instantaneous frequency separation
21. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 21
between the lasers. The beating of the two lasers on a photodiode would
exhibit only a very small improvement from the basic photomixing technique,
preventing from the generation of a spectrally pure RF signal.
An improved frequency stability of the system can be achieved by introducing
a feedback effect on the instantaneous emission frequencies of the lasers. This
can be done by adding to the previously described configuration a third laser,
operating at the frequency ν3, as show in Figure 1.7.
Figure 1.7: Mutual injection locking assisted by Four Wave Mixing. The
colour of the FWM clones in the figure indicates the lasers which interaction
generated each clone.
In the new configuration laser 1 and laser 2 are injected into a third laser,
placed between them. Both the laser pairs 1 - 3 and 2 - 3 are mutually
coupled. Moreover, a FWM process takes place inside the laser 3, producing
22. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 22
two clones of the injected lasers 1 and 2, respectively at the frequencies
ν1 = 2ν3 − ν1 and ν2 = 2ν3 − ν2. When the laser 3 is operating at the
frequency
ν3 =
ν1 + ν2
2
(1.3)
a double locking mechanism occurs. First of all, the lasers 1 and 2 phase
lock to laser 3 thanks to the sideband locking mechanism already described.
Secondly, the FWM clones ν1 and ν2 have respectively frequencies ν1 = ν2
and ν2 = ν1. Due to the mutually coupled configuration, these FWM clones
generated inside laser 3 are injected into lasers 1 and 2, thus locking their
instantaneous frequency difference.
Figure 1.8: Mutual injection locking assisted by Four Wave Mixing, with the
full mutual locking mechanism illustrated.
As shown in Figure 1.8, the three lasers now constitute a three coupled
oscillators system, where all the oscillators are coupled to the others. The
lasers pairs 1 - 3 and 2 - 3 are coupled through their modulation sidebands,
while the laser pair 1 - 2 is coupled by the FWM process that takes place
in laser 3. This multiple locking mechanism ensures an improved stability
23. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 23
of the system, locking the frequency difference between the lasers. There-
fore, when the locking condition represented by the Eq. (1.3) is satisfied,
the electrical beating signal generated by photomixing on a high speed pho-
todiode is expected to exhibit improved spectral characteristics. The FWM
process represents the most convenient way to lock lasers operating at dif-
ferent frequencies, thanks to its capability to generate optical modes at new
frequencies.
This recently proposed technique is potentially capable to satisfy all the dis-
cussed requirements. Thanks to the all-optical locking method, this system
can produce spectrally pure photomixing signals without the need of an ex-
ternal RF seed signal. By increasing the frequency spacing between the lasers
(while satisfying the locking condition), the generated RF signal can also be
widely tuned from a few GHz up to the THz domain, thanks to the high
efficiency of the FWM process. As reported in [37], in semiconductor medi-
ums the FWM for detuning values larger than a few tens of GHz is due to
the spectral hole burning, which acts as non-linear suppression of the opti-
cal gain. The spectral hole burning is governed by the intraband relaxation
processes, which can be extremely fast, in order of less than a picosecond.
As consequence the FWM process can take place for pump-probe detuning
up to ∼1 THz. However, at large detuning the FWM efficiency decreases
[37], and consequently higher level of optical power have to be injected into
laser 3. For small detunings, the FWM process is very efficient, and therefore
an attenuation between the lasers is necessary in order to avoid an unsta-
ble regime of operation of the injected laser. On the other hand, for large
detuning the FWM efficiency strongly decreases, requiring lower level of at-
tenuation or even the amplification of the FWM clones.
Experiments using a setup with discrete components have been previously
carried out [1]. Figure 1.9 shows the experimental setup used to demon-
strate the mutual locking, where three DFB lasers without optical isolator
were mutually injected through optical fibres.
DFB-1 and DFB-2 were mutually coupled with DFB-3, where the FWM
24. 1.4 Photomixing assisted by mutual injection locking and Four
Wave Mixing 24
Figure 1.9: Experimental discrete setup for the mutual injection locking
assisted by FWM.
process took place. The clones generated inside the DFB-3 cavity were then
back injected to the lasers 1 and 2 following a different path, in order to
allow a better control on the injection levels. Attenuators were inserted, to
adjust the injection levels and avoid unwanted complex dynamic regimes of
operation. Moreover, the attenuators prevented from a strong self optical
feedback the may be generated from the amplification of each laser when
injected into the others.
Promising experimental results were obtained, achieving stable locking for
detuning up to 100 GHz. However, excessive optical feedback from the var-
ious optical fibre components leaded to a narrowing of the laser linewidths
with respect to the ideal unperturbed case. As consequence, the linewidth
and phase noise of the beating RF signal could not be measured reliably.
In order to assess the phase noise reduction, additional drive-current noise
was applied to one of the lasers. Figure 1.10 shows the RF beating when the
three lasers are unlocked and locked.
A clear suppression of the noise was achieved, thanks to the mutual injec-
tion locking mechanism that strongly enhanced the stability of the system.
Since no external RF signal was used to lock the lasers, this all-optical lock-
ing technique had the potential to be fully integrated into a single monolithic
device. The aim of this work was the integration of the hybrid setup previ-
25. 1.5 Integration into a single optoelectronic device 25
Figure 1.10: RF beating signal with drive-current noise applied to one of the
lasers, in unlocked and locked condition.
ously reported into a single monolithic chip, followed by the demonstration
of the mutual injection locking using the integrated device.
1.5 Integration into a single optoelectronic
device
The integration of several discrete optical components into a single mono-
lithic chip entails multiple advantages and technological challenges at the
same time. First of all, the final device would have a mm-scale size and a
strongly reduced power consumption, allowing its use for a wide number of
applications, up to portable mm- and Thz- wave sources for spectroscopy and
tomography. Moreover, the fabrication of a single multifunction chip would
decrease the final cost of the system: the most expensive processes, such as
packaging and fibre coupling, have to be done only once. Finally, by using an
Indium Phosphide (InP) based semiconductor material, the well-established
technology developed for optical telecommunication devices could be used.
Such device would be able to provide the required performance in terms of
26. 1.5 Integration into a single optoelectronic device 26
frequency stability, tunability, efficiency and reliability.
At the same time, the monolithic integration of different optical devices
brings several technological and design challenges. The fabrication process
have to be optimised in order to define all the different optical structures in
few lithography steps. The use of a post-growth fabrication process would
be preferable, since a material regrowth would increase the fabrication com-
plexity and costs, decreasing at the same time the final yield of the working
devices. The yield is particularly important in complex multi-section devices,
since their correct operation is achieved only when all the optical structures
of the device are fully working. Finally, the mutual injection of lasers may
lead to unstable or chaotic regimes of operation if the injection levels are
not optimised. Complex multi-section devices have to be designed, where
attenuators and couplers have to be fully integrated with the lasers. Due to
the complexity of the mutual injection scheme, different geometries, coupling
and attenuation levels have to be investigated in order to find out the best
design solution.
27. Chapter 2
Device Design
This chapter details the design of the monolithic devices where the mu-
tual injection locking of three lasers is exploited, aiming at the generation
of mm-waves. Different geometries were investigated, requiring the dedi-
cated design of several optical structures. First of all, the different device
geometries are presented, describing their operating principle. The chapter
continues with the detailed description of the semiconductor material that
will be used to fabricate the devices, since the layout of each optical structure
strongly depends from its characteristics. Then the design of each compo-
nent is detailed: the waveguides are firstly introduced, also describing their
utilisation as integrated spot size converters. A complete analysis of the
Distributed FeedBack (DFB) lasers follows, starting from the mathematical
theory used to model their behaviour, to the design choices that have been
made in order to guarantee single mode operation and precise determination
of the lasing wavelength. Finally, the chapter closes with the design of the
different optical couplers used in the devices. It will be also shown the im-
portance of properly taking into account the fabrication limits and tolerances
during the design stage, in order to define structures that can be fabricated
obtaining a high yield.
28. 2.1 Device geometries 28
2.1 Device geometries
As described in the previous chapter, three lasers can be phase-locked via
mutual injection assisted by a Four Wave Mixing process. When appropriate
locking conditions are satisfied (Figure 2.1a), the beating of the locked lasers
on a high-speed photodiode generates spectrally pure mm-waves. Since this
method does not require the use of any RF seed signal, it can be fully inte-
grated on a single optoelectronic device.
The mutual injection locking at different frequencies is ensured by the genera-
tion of optical clones at new frequencies, followed by a subsequent re-injection
of these new signals back into the original optical sources. Therefore, the in-
tegrated devices required three fundamental elements:
• Three single mode lasers operating at the frequencies ν1, ν2 ν3
• A non-linear section where the two Four Wave Mixing clone signals can
be generated
• A feedback mechanism to allow the re-injection of the newly generated
clone signals into the original lasers.
Starting from these fundamental elements, different geometries were con-
ceived and investigated (see Figure 2.1b).
As single mode sources, DFB lasers represented the best option. Thanks
to a very flexible design of their optical properties (Section 2.4), they can
stably operate in a single-mode regime with high SMSR and precisely de-
fined lasing wavelength.
The Designs 1, 2, 3 share the same principle of operation. DFB-1 (oper-
ating at ν1) and DFB-2 (ν2) are coupled into DFB-3 (ν3), where, due to
the high non-linearity of the active material, Four Waves Mixing clones at
the idler frequencies ν1 and ν2 are generated. The DFB-3 also provide the
feedback mechanism necessary for the mutual locking, by reflecting back /
transmitting the newly generated clones towards the original lasers. The new
optical frequencies are generated into the cavity of DFB-3, where they also
29. 2.1 Device geometries 29
Figure 2.1: a) Mutual injection scheme. b) Conceptual scheme of the different
device geometries investigated.
30. 2.1 Device geometries 30
get amplified thanks to the active cavity resonance. The signals are finally
re-emitted from DFB-3, and coupled back to the DFB-1 and DFB-2 through
an optical coupler.
Design 1, 2, 3 differ for the coupling strength between the lasers. It is
highly important that this aspect be investigated, because the locking prop-
erties of mutually injected lasers strongly depend on the strength of their
mutual coupling. High levels of injected power might lead to an unwanted
unstable regime of operation. On the other hand, too low levels of injection
might be not sufficient to ensure the locking between the lasers. In order to
gain more insight into this issue, in Design 1 evanescent couplers are used to
couple low levels of power: a value of 1% was chosen. In Design 2 a Multi
Mode Interference coupler is used to achieve a coupling of 50% with a short
coupler. In Sections 2.5 the design of these couplers is discussed. Finally,
in Design 3 the lasers are coupled through direct injection, with a coupling
factor of 100%. The yellow sections in Figure 2.1b represent optically active
waveguides, which can be used as Semiconductor Optical Amplifiers (SOA)
or as attenuator, depending on whether they are operated under direct or
reverse bias respectively. These sections can be used to further adjust the
injection levels of optical power.
Design 4 strongly differs from the previous ones. The three single mode
lasers are injected through a MMI coupler into an auxiliary non-linear active
section, where the Four Wave Mixing process occurs. The optical signals
are then reflected by a straight-cleaved facet at the edge of the device. The
semiconductor-air interface reflects 30% of the incident optical power, thus
providing the feedback mechanism. The reflected signals are further ampli-
fied during the second transit through the SOA, and finally injected in the
DFB lasers.
Besides the mentioned optical structures, single mode waveguides were used
to distribute the optical signals along the chip. Tilted and tapered output
waveguides were used to collect the generated optical signals using lensed
optical fibres. Finally, inverse tapered waveguides were used in Design 1 to
31. 2.2 Material description 31
disperse the uncoupled light, avoiding backreflections that could negatively
affect the proper operation of the device. The waveguide design is discussed
in Section 2.3.
2.2 Material description
The device design starts from the study of the semiconductor material
that will be used for the fabrication. The design is strongly related to the
material, since different compounds have different layer structures and opti-
cal characteristics (refractive index, gain spectrum, etc.), according to which
the geometrical characteristics of the devices have to be varied. The pho-
tomixing effect used to generate the mm-waves works on the frequency differ-
ence between the optical signals rather than their absolute frequency. This
makes every optically active semiconductor suitable for the fabrication of the
devices. However, the choice fell on a material with a gain spectrum cen-
tred around the C-band wavelength range (1530-1565 nm), normally used
for telecommunications devices. This choice is mainly due to the maturity of
the growth techniques used for producing such material and also to the avail-
ability of a wide range of instruments to characterise the devices. Moreover,
state-of-the-art fabrication techniques for this material were available in the
institution chosen for the fabrication of the devices (described in Chapter 3).
The material used is a commercially available1
AlGaInAs/InP compound,
with a multiple quantum well (MQW) structure. Figure 2.2 shows the struc-
ture of the epitaxial wafer.
Recently, several theoretical and experimental studies focussed on the
Al-quaternary material, due to its attractive band discontinuity properties.
It was shown that the conduction band offset of AlGaInAs/InP material
(∆Ec=0.72∆Eg) is larger compared to that of the traditional InGaAsP/InP
material (∆Ec=0.40∆Eg), leading to improved electron confinement and
higher characteristic temperature [38–40].
1
IQE Ltd, Cardiff, U.K. (www.iqep.com)
32. 2.2 Material description 32
200 nm GaInAs cap
60 nm AlGaInAs
1720 nm InP cladding
60 nm AlGaInAs GRINSCH
MQW and barriers
60 nm AlGaInAs GRINSCH 60 nm AlGaInAs
800 nm InP cladding
n-type InP substrate
}Waveguide
core
Figure 2.2: Layer structure of the commercial material IQE-IEGENS-13-17,
used for the fabrication of the devices.
The material was grown by Metal Organic Chemical Vapour Deposition
(MOCVD), and consists of five compressively strained (12000 ppm) 6nm
thick Al0.07Ga0.22In0.71As wells with six tensiley strained (-3000 ppm) 10nm
thick Al0.224Ga0.286In0.71As barriers. The QWs and barriers are situated be-
tween two 60nm AlGaInAs graded index separate confinement heterostruc-
ture (GRINSCH, GRaded INdex Separate Confinement Heterostructure) lay-
ers. The GRINSCH section is included to prevent electrons and holes from
escaping the QW region. Moreover, it allows for a lower threshold current
density and larger differential gain as compared to standard SCH structures
[41]. Finally, the structure is completed by an 800nm InP lower cladding,
1720nm InP upper cladding and a 200nm highly doped (1.5 x 1019
cm−3
)
GaInAs contact layer. All layers (except the wells and barriers) are lattice
matched to a n-doped InP substrate with Zn and Si used as the p-type and
n-type dopants respectively.
33. 2.3 Waveguides 33
2.3 Waveguides
The described layer structure ensures the photon confinement in the ver-
tical direction, since the core’s refractive index is higher than that of the top
and bottom cladding layers. However, in order to achieve the guiding effect,
lateral confinement of photons is also needed. This is provided by etched
ridge waveguide technique that produces lateral index guiding and transver-
sal current confinement. There are two commonly used structures for achiev-
ing such index guiding: shallow-etched and deep-etched ridge waveguides, as
shown in Figure 2.3.
Figure 2.3: Schematic of a shallow etched and a deep etched waveguides.
The shallow-etched waveguides are defined by etching the ridge down to
the upper edge of the active region, but not through it. They ensure a rel-
atively low lateral photon confinement, since the effective refractive index
difference (∆neff = neff - nc) between the non etched and etched areas is
small, typically smaller than 0.1. However, the amount of lateral confine-
ment is large enough to fabricate waveguides which sustain a single transver-
sal mode, and becomes problematic only for curved waveguides with small
radius. On the other hand, as the etching does not penetrate into the core,
the shallow-etched waveguides provide a reduced carrier recombination rate
at the sidewall, and the sidewall roughness induces negligible back-reflections
because the optical mode does not overlap with the ridge sidewall regions.
Deep-etched waveguides are defined by etching the ridge down through the
34. 2.3 Waveguides 34
core. They ensure a stronger lateral confinement of the optical mode, as there
is a much larger difference between the refractive indices of the waveguide and
the surrounding medium (usually air). This allows the fabrication of low-loss
curved waveguides with a small radius. However, the increased interaction
of the optical mode with sidewalls may lead to large back-reflections and
scattering losses if the sidewall roughness is not sufficiently small. Moreover,
non-radiative recombination is more likely to occur since the quantum wells
are exposed to the atmosphere. This might lead to the generation of phonons
and heating, negatively affecting device performance and lifetime.
For the above reasons, the shallow-etch approach was chosen for the fabri-
cation of the optical structures; this approach requires the material to be
etched down for 1920 nm, i.e. until the first Al-containing layer placed at the
top edge of the core is reached. Moreover, as it will be widely discussed in the
next chapter, the Al-containing layer may be used as a dry etch stop layer,
allowing a very precise and repeatable definition of the optical structures.
The number of the guided TE polarised modes depends on the waveguide
width. In order to guide only the fundamental TE mode, it is necessary to
determine the waveguide width below which the higher order modes are sup-
pressed. A set of simulations was carried out using the commercial software
RSoft BeamPropTM
, based on the beam propagation method (BPM). The
refractive indices of the different layers were calculated using [42] and the
dedicated website Luxpop2
. The results indicated that, for waveguide width
of 2.6 µm and below, only the fundamental mode is supported. A value of 2
µm was then chosen, in order to increase the losses of the non-fundamental
modes and avoid any power transfer to them. Figure 2.4 shows the simulated
optical field density of a 2 µm width waveguide, etched down till the edge of
the active layers (etch depth of 1920 nm); the dashed lines reveal the position
of the core inside the material.
As shown in Figure 2.1, the devices require also curved waveguides. The
shallow etched ridges are able to effectively guide the optical mode also for
2
www.luxpop.com
35. 2.3 Waveguides 35
Figure 2.4: Simulated optical field density of a 2 µm width and 1920 height
ridge; the solid line represents the etched ridge profile, while the dashed lines
underline the position of the core inside the material.
curved guides, as long as the radius of curvature is larger than a certain
value. Extensive studies on this material were previously carried out, while
aiming the fabrication of ring and micro-ring lasers for all-optical process-
ing3
[43, 44]. Using this material, it was shown that a curved shallow etched
ridge waveguide 2 µm wide and 1920 high exhibits negligible curvature losses
provided the bend radius larger than 250 µm. Therefore, all the curved
waveguides used in the devices had a radius of curvature of 300 µm.
Some considerations are due about the output waveguides. Proper operation
of the devices requires low back-reflection from the output cleaved facets, in
order to not spoil the single mode operation of the DFBs (Section 2.4) and
to avoid the creation of sub Fabry-Perot/etalon cavities. There are two well
known methods to reduce reflections of a cleaved facet: the application of
an antireflection (AR) coating and the tilting of the ouput waveguides with
respect to the cleaving plane. AR requires the deposition of a multilayer thin
3
www.iolos.org
36. 2.3 Waveguides 36
film on the facet, where the semiconductor-air interface creates the backre-
flections. The refractive index and thickness of these layers has to be accu-
rately designed to produce destructive interference in the light reflected from
the interfaces, and constructive interference in the corresponding transmitted
light. However, in order to not add further fabrication steps, the tilting of
the output waveguides was preferred. With this method the reflected power
coupled back to the waveguide can be strongly reduced, although the reflec-
tivity at the interface does not change significantly. Marcuse in [45] shows
that the reflected power already decreases of 25 dB by tilting the output
waveguides by an angle of only 5 degrees. Larger angles provide even lower
backreflections, but the wide refraction angle of the free space beam may
make the light collection troublesome. A trade-off was found by tilting the
output waveguides 10◦
: this produces a transmission angle of 33◦
.
A further improvement of the output waveguides was made in order to max-
imise the coupling efficiency between the chip and the lensed fibre. The idea
was to create an integrated spot-size converter, which adiabatically trans-
forms the waveguide mode and reduces the modal mismatch with the lensed
fibre. This was easily done by up-tapering the output waveguides from the
standard width of 2 µm to 12 µm. This transformation occurs over a length
of 100 µm. The modal spot was optimised aiming an efficient coupling with
the available lensed fibre4
. The use of tapered output waveguides also im-
proves the alignment tolerances and, in case of tilted waveguides, it further
reduces the back coupled optical power [45].
Finally, down-tapered waveguides were also used. The Design 1 requires only
a small amount of optical power to be coupled between the different lasers.
The uncoupled power has to be dispersed in order to avoid back reflections
and/or subsequent coupling with other waveguides. By down-tapering the
standard 2 µm waveguide to a nanometer-sized tip, the propagating mode is
pushed down into the substrate where it is scattered away due to the absence
of a guiding structure. The smooth down-shift of the mode ensures very low
4
OZ optics TSMJ-3A-1550-9/125-0.25-7-5-26-2-AR
37. 2.4 DFB design 37
back reflections of optical power. Figure 2.5 shows how the inverse taper
spreads the mode into the substrate.
Figure 2.5: Propagating mode is dispersed into the substrate by down-
tapering the standard 2 µm waveguide down to a nanometer-sized tip.
2.4 DFB design
The DFB lasers represent the core of the devices, where the optical signals
are generated. As discussed in the previous chapter, the mutual injection-
locking assisted by FWM requires single mode lasers, with high SMSR.
A conventional Fabry-Perot laser exhibits multiple longitudinal modes be-
cause the reflectivity of its mirrors is not wavelength-selective, and conse-
quently a large number of modes are close or above the lasing threshold.
The most common way to achieve single mode operation in integrated lasers
is the use of periodic structures such as Bragg gratings. They act as mir-
rors with a wavelength-dependent reflectivity, increasing the gain difference
between the dominant mode and the side modes. In this section, the theory
behind the Bragg reflectors is briefly reviewed; different design solutions will
38. 2.4 DFB design 38
be discussed in order to fabricate DFB lasers which operate in a single mode
regime and with a well defined and predictable lasing wavelength.
2.4.1 Coupled-wave equations
As discovered by W.L. Bragg [46], it is possible to induce coupling be-
tween orthogonal modes of a waveguide by introducing a refractive index
perturbation; by making this perturbation periodic in the propagating direc-
tion, the forward and backward propagating modes of the waveguide can be
coupled. This effect, known as backward Bragg scattering, produces coherent
coupling only between fields that propagate at specific wavelengths, defined
by the Bragg condition:
mλb = 2neff Λ0 (2.1)
where m is the order of the grating response, λb is the free space wavelength
of the mode satisfying the Bragg condition, neff is the effective index of the
relevant waveguide mode and Λ0 is the grating period.
The effects of this refractive index perturbation over the fields involved have
been studied in several papers and books [47–51]. They can be described
starting from the general wave equation for the electric field propagating
with a wavelength λb and free space propagation constant k0 = 2π/λb:
d2
E
dz2
+ β2
0E = 0 (2.2)
where E is given by the sum of the forward and backward propagating fields
and β0 = n(z)k0 is the Bragg propagation constant, with n(z) the refractive
index along the propagating direction. The general solution can be written
in the form:
E(z) = R(z)e(−jβ0z)
+ S(z)e(jβ0z)
(2.3)
where the electric filed is described as sum of right- and left- propagating
39. 2.4 DFB design 39
fields. The functions R(z) and S(z) vary comparatively slow with z because
the rapidly varying phase factor is included in the exponential functions. By
considering an index perturbation with rectangular profile and 50% of duty
cycle (Figure 2.6), the coupling coefficient of the system is expressed by the
parameter:
κ =
(n2
1 − n2
2)Γx,y
2n2
eff Λ0
(2.4)
which accounts the coupling between the two counter-propagating fields.
neff , n1 and n2 are the refractive indices of the propagating mode, the waveg-
uide and the grating recess respectively, while Γx,y represents the confinement
factor of the mode to the grating area.
Figure 2.6: Schematic of refractive index perturbation in a waveguide struc-
ture
The set of equations that relate the counter-propagating waves is known
as coupled-wave equations:
dR
dz
+ j∆βR = −jκS (2.5)
dS
dz
+ j∆βS = −jκR (2.6)
where ∆β is the detuning around β0, with ∆β β0. It is clear as for
vanishing coupling (κ = 0) the two equations become decoupled, leading to
just a pair of independent counter-propagating waves.
A more physical interpretation of the coupling coefficient κ is reported in
40. 2.4 DFB design 40
[48]. By considering the periodic structure shown in Figure 2.6, the field
reflection coefficient r of the first discontinuity follows the Fresnel formula:
r =
∆n
2neff
(2.7)
where ∆n = n1−n2. The field reflection of the next discontinuity is -r because
now the field goes from a high to a low index. When the wavelength is equal
to the Bragg wavelength, the phase change for a round-trip in a subsection
is β0Λ0 = π, corresponding to a factor -1. Therefore, all reflections add
in phase, and the field reflectivity per unit length (with two reflections per
period) is:
κ =
2r
Λ0
=
∆n
neff
2neff
λb
=
2∆n
λb
(2.8)
giving a clear idea that the coupling coefficient of a periodic structure can
be interpreted as the amount of reflection per unit length.
By knowing the functions R and S at a given point, for example z = 0, the
general solution of the coupled-wave equations can be written as [48]:
R(z) = cosh(γz) −
j∆β
γ
sinh(γz) R(0) −
jκ
γ
sinh(γz)S(0) (2.9)
S(z) =
jκ
γ
sinh(γz)R(0) + cosh(γz) +
j∆β
γ
sinh(γz) S(0) (2.10)
where γ2
= κ2
− ∆β2
. The solutions given in (2.9) and (2.10) can be written
in a matrix form:
R(z)
S(z)
= M(z)
R(0)
S(0)
(2.11)
where M(z) is:
M(z) =
cosh(γz) − j∆β
γ
sinh(γz) −jκ
γ
sinh(γz)
jκ
γ
sinh(γz) cosh(γz) + j∆β
γ
sinh(γz)
(2.12)
41. 2.4 DFB design 41
In the literature, the Bragg laser analysis is often carried out by using the
transfer matrix theory, since it represents a powerful tool to model grating
lasers as well as for structures consisting of several different periodic sections
in the longitudinal direction.
2.4.2 Grating design
The coupled-wave equations give the mathematical tool to design a Bragg
grating as a wavelength-dependent mirror. The design starts by choosing
the Bragg wavelength of the grating, followed by the design of its reflectivity
spectrum.
From (2.1), the Bragg wavelength λb is designed by varying the grating period
Λ0 and the grating order m; the minor effects of a neff variation will be
described in Section 2.4.4. A period Λ0 of 242 nm was chosen in order to
target the gain peak of the available semiconductor material (centred around
1550 nm), considering a first order grating with a neff 3.20. By defining
an index profile as shown in Figure 2.6, the first order grating with 50% of
duty cycle D is the one that gives the highest coupling coefficient. For other
grating shapes or orders the coupling coefficient has to be reduced as follow
[48]:
κ(mth−order) = κ(1st−order) · fred (2.13)
with:
fred =
1
m
· |sin(πmD)| (2.14)
Figure 2.7 shows the effect of (2.14).
The first order not only allows the highest coupling factor for a given
index profile, but it also ensures the smallest dependence of κ on the duty
42. 2.4 DFB design 42
Figure 2.7: Reduction factor fred as a function of duty cycle D, for different
grating orders m.
cycle. This is important in order to minimise the fabrication tolerances when
defining the index profile.
The second design step is the definition of the reflectivity spectrum of the
grating. The key spectrum properties that can be designed are the width of
the reflectivity spectrum ( also called stop band of the grating) and the peak
of reflectivity at the Bragg wavelength. From the coupled-wave equations
(2.9) and (2.10), and considering ∆β =
2πneff
λ
−
2πneff
λb
and γ2
= κ2
− ∆β2
,
the behaviour of a Bragg grating as a wavelength-dependent reflector can be
described by its power reflectivity R(λ) [48]:
R(λ) =
κ2
sinh2
(γL)
∆β2sinh2(γL) + γ2cosh2(γL)
(2.15)
It is clear that the spectral properties of the grating strongly depend on the
coupling coefficient κ and interaction length L (which represents the grating
length). It is interesting to investigate how κ and L can affect the reflectivity
spectrum. Figure 2.8 shows the reflectivity spectrum as a function of λ, for
different coupling coefficients κ and interaction lengths L. It appears that
when κ increases, both the stop band width and reflectivity peak at λ = λb
43. 2.4 DFB design 43
Figure 2.8: Reflectivity spectrum Vs wavelength for different grating lengths
(a,c) and coupling coefficient (b,d).
increase, up to saturate at R = 1 for a wide range of wavelengths. On the
other hand, when the grating length L increases the stop band narrows, while
the reflectivity increases. This can be simply summarised as:
κ ⇑ −→ StopBand ⇑, Reflectivity ⇑
L ⇑ −→ StopBand ⇓, Reflectivity ⇑
By increasing κ, the coupling between the counter-propagating modes in-
creases, thus the grating is able to couple light at sitting further from the
44. 2.4 DFB design 44
Bragg wavelength. By increasing the length L, more grating periods partici-
pate in the backward Bragg scattering, enhancing the wavelength selectivity
of the grating.
The stop band can be conveniently defined as the separation in wavelength
between the first two zeros of the reflectivity spectrum. From (2.15), it is
readily found that (for ∆βL > κL) the first zeroes of R are found as:
∆βL = (κL)2 + (π)2 (2.16)
Moreover, again from (2.15), the power reflectivity for λ = λb reduces to:
R = tanh2
(κL) (2.17)
From (2.16) and (2.17), Figure 2.9 shows how the stop band width and
reflectivity peak depend on the coupling coefficient κ and grating length
L. The graphical visualisation of the relations between κ and L and the
grating properties represents a very powerful tool when designing gratings
with precise requirements of stop band width and reflectivity at the same
time. It shows how different combinations of coupling coefficient and grating
length give the same stop band width, allowing a free choice of their values
in order to ensures the required reflectivity.
Equation (2.17) shows that the magnitude of reflection at λb is determined
only by the κL product. This dimensionless parameter, known as normalised
coupling coefficient κL, determines the performances of the whole grating,
allowing the generalisation of the results for gratings with different coupling
coefficients and lengths. Figure 2.10 shows the curve describing the peak
power reflectivity R(λb) as a function of κL.
As it will be described in Chapter 4, some preliminary tests were per-
formed in order to find out the value of κL that ensures the best characteris-
tics for the DFB lasers in terms of threshold current and SMSR. Satisfactory
results were obtained by fabricating 400 µm long gratings with a κ of 75
45. 2.4 DFB design 45
Figure 2.9: Stop band width and reflectivity peak as a function of the cou-
pling coefficient κ and grating length L.
Figure 2.10: Peak power reflectivity R(λb) as a function of κL.
46. 2.4 DFB design 46
cm−1
, which gives κL = 3. These values ensure a stop band of about 3 nm
and a reflectivity close to unity.
2.4.3 DFB for single mode operation
The analysis carried out so far did not take into account the gain of the
material. Depending on the relative position of active region and grating,
different types of lasers can be obtained. In a Distributed Bragg Reflector
(DBR) lasers the active region and the grating are separated longitudinally.
The mathematical analysis can be carried out using the equations previously
reported, since the grating acts as a passive wavelength selective reflector. In
a Distributed FeedBack (DFB) laser the grating is superimposed on the active
region, combining the grating reflection with the optical amplification in the
same volume. Historically, DFB lasers preceded the development of DBRs,
mainly because DFBs are easier to fabricate, since no longitudinal integration
of active and passive region is required. However, the mathematical analysis
of DFBs is slightly more complicated, since the gain and phase conditions
cannot be separated.
The simplest DFB structure is formed by a grating defined just below or
above the active material, and by neglecting Fabry-Perot reflections arising
from the end facets. The analysis of this structure can still be based on the
coupled-wave equations (2.9 and 2.10), but the gain has to be considered by
replacing ∆β with (∆β +jg0), where g0 represents the gain for the field. The
intensity gain is represented by 2g0. As discussed in [47–49], the oscillation
condition is found by taking into account the boundary conditions for the
system. This devices differ from the normal Fabry-Perot cavities, where the
boundary conditions for internal waves are determined by outcoming waves,
incident onto the mirrors. A distributed feedback structure represents a self-
oscillating system: as shown in Figure 2.11, the internal waves start from
zero amplitude at the boundaries, receiving their energy via scattering from
the counter-propagating waves.
From this observation, the boundary conditions S(0) = R(L) = 0 fol-
47. 2.4 DFB design 47
Figure 2.11: a) Laser oscillation in a periodic structure. b) Plot of the am-
plitudes of left travelling wave (S) and right travelling wave (R) Vs distance.
Image from [47]
.
low, where L represents the grating length. Considering the coupled-wave
equations written with the matrix formalism (2.11), the boundary conditions
require the term M22 to be set at zero:
cosh(γL) +
j(∆β + jg0)
γ
sinh(γL) = 0 (2.18)
where the parameter:
γ2
= κ2
− (∆β + jg0)2
(2.19)
now includes the gain. Re-writing the oscillation condition (2.18) as:
γLcoth(γL) = −j(∆βL + jg0L) (2.20)
a complex transcendental equation is obtained. It determines, for a given
product κL, the possible values of (∆βL, g0L). Each solution gives the wave-
length (in terms of ∆β) and the required threshold gain (in terms of g0) for
the possible lasing modes. It is clear how, in contrast to the situation for
Fabry-Perot or DBR lasers, the gain and phase conditions do not separate
but are determined together from the complex number (∆βL + jg0L) [48].
48. 2.4 DFB design 48
Generally, the solutions of (2.20) have to be found numerically. Figure 2.12
shows some numerical solutions obtained for different values of κL, expressed
as amplitude threshold gain g0L as a function of the normalised detuning fac-
tor ∆βL.
Figure 2.12: Threshold gain of DFB modes for different values of κL; for
clarity, the point corresponding the same mode are joined. Image from [49]
As expected, gratings with high values of κL have a lower threshold gain,
since a stronger grating ensures an efficient feedback, allowing more optical
power travelling in the cavity. On the other hand, for low values of κL (and
for bigger detuning ∆βL from the Bragg wavelength) the feedback is less
efficient, leading to a higher threshold gain. However, from Figure 2.12 it
is also clear that a DFB structure with a uniform grating and no reflections
from the end facets does not allow the presence of a lasing mode at the Bragg
wavelength (∆βL = 0), where the threshold gain goes to infinity. This para-
dox arises because, although reflection and gain are very strong at λb, the
feedback is in antiphase, preventing the lasing action. This can be explained
by looking at the field reflections from the centre of the grating. Moving both
backward or forward, the field reflectivity has a π/2 phase shift at the Bragg
49. 2.4 DFB design 49
wavelength. This entails a total round-trip phase over the grating of π. Since
the resonance round-trip phase change must be a multiple integer of 2π, this
phase condition cannot be satisfied at the Bragg wavelength, but only at a
certain wavelength separation from it. With no oscillation conditions satis-
fied for λ = λb, a stop band region is formed between first two lasing modes,
conventionally called +1 (placed on the left side of λb) and -1 (on the right
side) modes. The stop band width increases with increasing values of κL,
and can be calculated with excellent approximation using (2.16).
Figure 2.12 also shows that the lasing modes are symmetrically distributed
around the Bragg wavelength. This degeneracy causes the first lasing modes
to have the same threshold gain, although they are located at different wave-
lengths. Therefore, the structure described so far will not work as a single
mode laser, since the ±1 modes have the same chance to lase once the lasing
condition is reached.
The simplest way to achieve the single mode operation is to break the sym-
metry, i.e. by adding some reflectivity at one or both the end facets by
cleaving the edge of the gratings [52]. This solution modifies the oscillation
condition (2.18), because the discrete reflection from the facet interferes with
the distributed reflection along the grating. This method is capable to break
the symmetry of the uniform grating previously described, decreasing the
threshold gain of the -1 mode that becomes the main lasing mode (Figure
2.13). However, the result depends on a phase angle, which is determined
by the position of the cleaved facet with respect to the grating period. The
mode selectivity, represented by the threshold gain difference between the
± 1 modes, strongly depends on this phase angle. In order to increase the
SMSR of the laser, it is crucial to achieve a high mode selectivity. Unfortu-
nately, it is technologically impossible to control the facet-to-grating phase.
In fact, the cleaving creates a random phase angle, and the yield of single
mode lasers fabricated using this method is rather low [53]. Moreover, this
solution does not ensure lasing conditions for λ = λb, a condition that is
crucial to achieve a good control on the lasing wavelength. This structure
50. 2.4 DFB design 50
Figure 2.13: Relationship between the amplitude threshold gain and the
detuning coefficient of a DFB with finite reflectivity at the facets. Image
from [49]
will typically lase with two longitudinal modes symmetrically placed at the
borders of the stop band.
In order to improve the single mode operation and ensure the lasing at the
Bragg wavelength, a phase discontinuity or phase-shift must be introduced
along the corrugation. This solution, firstly proposed in [54] and [55], consists
in creating a ∆L = λ/4 section in the center of the grating. For a first order
grating, this can be done by simply adding half grating period in the center
of the grating. Since it corresponds at an additional π/2 phase shift along
each direction of propagation, now the round-trip phase over the grating is
2π, and consequently the oscillation condition can be satisfied exactly for λb.
With this method the phase angle is precisely defined by the phase-shifting
section, which is fabricated together with the rest of the grating. As conse-
quence the achievable yield of single mode operation is very high, without
the need of a very precise cleaving position. It has to be noticed that now
the facets reflectivity has to be as low as possible, in order to avoid any phase
51. 2.4 DFB design 51
interferences caused by backreflections at the facets. In [56] it is suggested
that the residual facet reflectivity should be lower than 1% in order to get a
high single mode yield.
The structure is conveniently modelled using the matrix formalism, consid-
ering two L/2 long gratings separated by the λ/4 section. The oscillation
condition follows [48]:
γLcoth
γL
2
+ j(∆βL + jg0L) = ±κL (2.21)
Figure 2.14 shows the numerical solutions for the oscillation condition. The
graph shows the solutions compared to the uniform grating case, for a 500
µm long grating with κ = 40 cm−1
(κL = 2). It is clear that the phase
Figure 2.14: Allowed resonance modes for DFB lasers with different grating
structures: a) Uniform grating; b) λ/4 shifted grating. Image from [49]
degeneracy has been removed by the λ/4 shifting section, since the mode
with the lowest threshold gain is now placed exactly at the Bragg wavelength.
Moreover, only one mode is allowed at the lowest threshold gain, ensuring
single mode operation. Finally, the large difference in threshold gain between
52. 2.4 DFB design 52
the fundamental mode and the ± 1 modes turns into a high SMSR also when
the laser is pumped at high power.
The effect of the phase shifting section can be also observed on the reflectivity
spectrum of the grating, which modifies by creating a deep notch in the center
of the stop band (Figure 2.15).
Figure 2.15: Spectrum reflectivity of a) uniform grating and b) λ/4 phase
shifted grating.
The phase-shifted gratings were chosen to be used in the devices for the
mm-wave generation, thanks to their single mode operation at the designable
Bragg wavelength.
2.4.4 Side-etched gratings for post-growth fabrication
As previously described, Bragg gratings are formed by producing a peri-
odic modulation of the refractive index seen by the propagating mode. In
DFB lasers, the conventional way to define gratings relies on the etch of the
material on the top of the active region, followed by a subsequent material
regrowth. However, the regrowth over a grating structure greatly compli-
cates the epitaxial growth process and increases fabrication time and cost.
Moreover, the devices for the mm-wave generation require the integration of
other optical structure such as couplers, tapers and attenuators, which fur-
ther increases the fabrication challenges. In order to remove the necessity of
a regrowth fabrication process, laterally-coupled Bragg gratings can be used.
53. 2.4 DFB design 53
Figure 2.16: Lateral coupled grating.
As shown in Figure 2.16, a grating can be fabricated by laterally etching
the active waveguide. This structure, firstly proposed in [57], combines the
lateral optical confinement of the ridge waveguide with distributed feedback
from gratings etched along the side of the waveguide. A laterally-coupled
grating is simply formed by a waveguide of width W, where lateral recesses
of depth d and period Λ0 create the rectangular refractive index profile previ-
ously described. The periodic lateral corrugation of the waveguide interacts
with the evanescent tails of the propagating waves, producing a reflection of
the field that satisfy the Bragg condition. This approach offers a very high
flexibility in designing the coupling coefficient κ, since its value can be de-
fined by either varying the recess depth d or the waveguide width W : higher
values of the ratio W/d lead to lower values of κ, and vice versa.
This type of grating can be fabricated using a fully post-growth technology,
allowing an easier integration with the other optical structures. The gratings
are defined together with the rest of the device in a single lithographic step,
with a mask defined by Electron Beam Lithography. This technology allows
a superb control on the geometrical dimension of the structures, which turns
into a very precise definition of their optical characteristics.
Laterally-coupled gratings allow a very high flexibility also in the design of
their Bragg wavelength. From the Bragg condition λb = 2neff Λ0, it turns
out that both the effective refractive index neff and grating period Λ0 can
54. 2.4 DFB design 54
be changed.
By varying the grating period Λ0, only a discrete tuning of the Bragg wave-
length is achievable. The typical resolution of the electron beam lithography
tools does not allow a wavelength tuning resolution better than around 3
nm, since a small variation of the grating period leads to a big change in λb.
The range of tuning is very wide, and it is only limited by the material gain
band.
On the other hand, a fine quasi-continuous tuning can be obtained by chang-
ing neff , through the variation of waveguide width W or recess depth d.
A small variation of W or d corresponds to a small variation of λb, and
therefore, under normal fabrication tolerances, a spacing resolution of 100
pm (12.5 GHz) is achievable. However, the maximum allowed variation of
W and d limits the tuning bandwidth to a few nanometres. The waveguide
width W is limited by the fact that the grating has to sustain only the fun-
damental mode; the recess depth d is limited by the RIE-lag, a fabrication
issue that will be widely discussed in Chapter 3.
The optimal solution is the combination of the variation of the two effects.
It can be obtained by jointly modifying both the grating period Λ0 and the
refractive index neff , thus achieving a fine tuning of λb over a wide range of
wavelengths (Figure 2.17).
Figure 2.17: Wide quasi-continuous tuning bandwidth achievable using lat-
eral coupled gratings.
The devices for the mm-wave generation required only a small variation
of Bragg wavelength between the different DFBs within the same chip. Since
55. 2.4 DFB design 55
the frequency range of interest for the generated mm-wave signals was up to
40 GHz, a Bragg wavelength spacing of 20 GHz was designed. It was achieved
by changing only the waveguide width, by steps of 25 nm from 2.375 µm to
2.425 µm, while all the DFBs had a period Λ0 of 242 nm and recess depth d
of 400 nm.
However, further studies on the wide quasi-continuous tunability were car-
ried out, in order to use this technology to fabricated multi-wavelength laser
arrays suitable for Dense Wavelength Division Multiplexing (DWDM) ap-
plications. The post-growth fabrication ensures low production costs and
allows for a further monolithic integration with other optoelectronic devices
on the same chip. It was found that it is possible to obtain a notable wave-
length tunability for a single grating period while maintaining an optimal κL
product. By choosing the right values of waveguide width and recess depth,
the coupling coefficient κ can be kept close to the one that ensures the best
performances in terms of threshold current and SMSR [58, 59].
In order to tune the Bragg wavelength, action on the variation of the waveg-
uide width W is more advisable rather than changing the recess depth d.
This approach allows to obtain more constant κ values over a wide Bragg
wavelength range. It avoids fabrication problems that could affect the fine
control of the lateral etch depth between the grating teeth (intended as the
space between the laterally not etched parts of the grating), with a subse-
quent modification of the expected wavelength spacing. Figure 2.18 shows
the Bragg wavelength as a function of the waveguide width W, for different
recess depths d; the gray bands on the background represent different ranges
of the product κL.
In the given range of waveguide width W, a high value of recess depth
(i.e. d = 0.5 µm) ensures a wide range of wavelength tunability, at the
expense of a large variation in the κL. On the other hand, a low value of d
(i.e. d = 0.1 µm) allows an almost constant κL product, but it only allows
for a limited tuning of the Bragg wavelength. A trade-off can be found by
56. 2.5 Couplers 56
Figure 2.18: Bragg wavelength as a function of the waveguide width W,
for different recess depths d; the gray bands on the background represent
different ranges of the coupling coefficient κL.
fabricating gratings with a recess depth of 0.3 µm: a range of wavelength
tunability of 3.5 nm is achievable, while keeping 2≤ κL ≤4. As it will be
discussed in Chapter 4, such a κL range ensures values of SMSR larger than
40 dB, since it avoids spatial hole burning effects that could perturb the
single longitudinal mode operation. The promising approach outlined here
is demonstrated to be capable of producing a DFB laser array with a quasi-
continuous tunability over a wide range of wavelength, always ensuring high
values of SMSR. Moreover, thanks to the post-growth fabrication process,
the fine frequency spacing can be precisely fixed by manufacture, without
a critical adjustment of operating conditions of the laser such as injected
current or temperature.
2.5 Couplers
The mutual injection in the devices Design 1 and Design 2 (Figure 2.1)
is achieved through optical couplers. As it has been discussed in Section 2,
the devices differed in the type of optical coupler used. In order to achieve a
57. 2.5 Couplers 57
low coupling factor, an evanescent field coupler was used in the Design 1. A
Multi Mode Interference (MMI) coupler was used in the Design 2, in order
to couple 50% of the optical power while keeping down the coupler size. This
section details the design of the couplers, also analysing their fabrication
tolerances.
2.5.1 Evanescent field coupler
Evanescent field couplers, also called directional couplers, transfer the op-
tical power between two parallel running waveguides through the overlapping
tails of their evanescent fields. In case of identical waveguides, the propaga-
tion constants are matched, and the power is periodically transferred from
one waveguide into the other. This transfer can be formulated as [60]:
P1(z) = P1(0)cos2
(ηz) (2.22)
P2(z) = P1(0)sin2
(ηz) (2.23)
where P1(0) is the input power, P1(z) and P2(z) are the optical powers
travelling respectively in the first and in the second waveguide. η represents
the coupling factor, which strongly depends on the width of the gap g between
the waveguides. It is clear that an evanescent coupler is able to transfer any
desired fraction of optical power, just by tuning the length of interaction or
the gap between the waveguides. At the distance z = Lπ all optical power is
coupled into the second waveguide: the parameter Lπ is called beating length,
and it is inversely proportional to the coupling factor η.
The basic idea can be reiterated in order to couple the power travelling in a
waveguide into other two, symmetrically placed beside it. BPM simulations
were performed aiming the definition of the optimal interaction length and
gap width g to achieve 1% of coupling, as required by the design 1.
Figure 2.19a shows how the optical power is exchanged between the
waveguides along the propagation. At the beginning the central waveguide
58. 2.5 Couplers 58
Figure 2.19: a) BPM simulations of three parallel identical waveguides, gap
width g = 1 µm. b) Contour map of the propagating optical fields after
different length z of propagation.
carriers all the optical power. During the propagation it is coupled into the
lateral waveguides, till when at Lπ = 680 µm it is fully and equally trans-
ferred into them. Then, as the propagation continues, the optical power
is transferred back into the central waveguide, following the periodical be-
haviour predicted by the theory. Figure 2.19b shows the cross section of the
waveguides after different length z of propagation: the contour map of the
propagating fields tells how the propagating mode is split between the three
waveguides.
From Equation 2.23, the amount of transferred power does not depends only
on the length of interaction, but also on the coupling factor η. Since it
strongly depends on the gap width g, simulation were performed also for
different values of g (Figure 2.20).
The simulations were carried out for the already discussed standard 2 µm
59. 2.5 Couplers 59
Figure 2.20: Coupled power into one of the lateral waveguides as a function
of the coupler length, for different gap width g.
width waveguides, and the distance between them was varied between 500
nm to 1250 nm. As expected, the power is more effectively coupled when
the waveguides are closer. For g = 500 nm, Lπ is only 230 µm, while as the
gap increases the power is fully transferred after several hundreds of microns.
Despite the coupling factor required (1%) is low and can be achieved through
short interaction lengths, in order to reduce the size of the coupler one would
choose the smallest gap possible. However, fabrication tolerances have to be
kept into account, since a non-optimal etch can strongly affect the coupling
factor. Figure 2.21 shows how the etch depth can affect the coupled power.
The simulation refers to a coupler 50 µm long, for different gap widths. The
coupled power is shown as a function of the etch distance from the core’s top
edge: negative values represent an over-etch of the material, while positive
values represent an under-etch.
It is clear that evanescent couplers are very sensitive to fabrication tol-
erances: a depth inaccuracy of few tens of nm can cause huge changes in
the coupled power. An over etch may lead to a total absence of coupling,
while an under etch may several increase the coupled power. The effects of
60. 2.5 Couplers 60
Figure 2.21: Coupled power as a function of the etch distance from the core’s
top edge. The simulation refers to a coupler 50 µm long, for different gap
widths.
an inaccuracy in the etch depth are stronger in case of under etch and small
gaps g. Moreover, the technology used to fabricate the devices (Chapter 3,
Section 3.5.2) makes an under etch more likely to happen than an over etch,
especially for small values of g. For these reasons a trade off between the
coupler compactness and fabrication tolerances had to be found. In order to
couple 1% of power a gap width g of 1 µm was chosen: it ensured acceptable
fabrication tolerances while keeping down the total length of the coupler; the
interaction length required was 50 µm.
2.5.2 MMI
The Design 2 requires a coupling factor of 50% between the lasers, which
means all the output power of the DFB-3 is split between DFB-1 and DFB-
2. Such high value of coupling makes the use of an evanescent coupler un-
favourable. As shown in Figure 2.20, in order to split the input power into
the lateral waveguides a coupler 700 µm long would be needed5
. Different
5
Using a gap width g of 1000 nm for a reliable fabrication.
61. 2.5 Couplers 61
structures can be used to couple high levels of optical power, while keeping
the coupler compact. The most common geometries are Y-junction couplers
[61] and MultiMode Intereference (MMI) couplers [62]. Both of them ensure
a low device size but also create intra-cavity back reflections, which are un-
desired here. However, since these back reflections can be minimised in a
MMI coupler, this structure was preferred.
The theory behind MMI couplers operation and properties is well under-
stood and numerous papers have been published, dealing with their design
and fabrication issues. MMI couplers are based on the self-imaging nature
of multimode waveguides. Self-imaging is a property by which an input field
profile is reproduced in single or multiple image at periodic intervals along
the propagation direction of the guide [63]. Depending on the application,
MMI couplers can be designed to have several input and output waveguides;
a simple and effective design outline can be found in [64] for NxN, 1xN and
2xN couplers, and alternatively in [65] for 1xN couplers. Figure 2.22 shows
an 1xN coupler, used in the design 2 (N = 2) and design 4 (N = 3).
Figure 2.22: 1xN MultiMode Interference coupler. The wide central area
represents the multimode waveguide where the interference occurs. The input
waveguide is placed at W/2, while the output waveguides are equally spaced
of W/N.
The central waveguide is designed to support several lateral modes, typ-
ically more than three. Depending on the ratio L/(W)2
and on the lateral
62. 2.5 Couplers 62
positions of the input and output waveguides, different self-imaging arrange-
ments can be obtained [66]. As the self-imaging depends on the interference
between the different modes, the coupling length Lc between the first two
lowest order modes can be used as a characteristic dimension:
Lc ≡
4neff W2
eq
3λ
(2.24)
where neff and Weq are respectively the effective refractive index and
the equivalent width if the waveguide. Weq takes into account the lateral
penetration depth of each mode’s field, considerable in case of low contrast
waveguides, and can be calculated as [62]:
Weq W +
λ
π
n2
eff − n2
c
(−1/2)
(2.25)
where nc is the effective refractive index of the cladding. It is clear as
for strongly guiding structures Weq W. If the input waveguide is placed
in the center of the multimode waveguide (Figure 2.22), the self-imaging is
obtained by linear combination of the symmetric modes. The self-images
appears at distances
L =
M
N
·
3Lc
a
(2.26)
where N is the number of images. M is an integer without common
divisors with N, that define the different distances where the N self-images
appear. The integer parameter a characterise the type of MMI coupler [64]:
in case of 1xN coupler a = 4, and output waveguides have to be symmetrically
located with equal spaces of W/N (Figure 2.22).
L represents the length of the multimode waveguide; it indirectly depends on
the square of the waveguide width W. In order to keep the coupler compact,
W has to be chosen the smallest possible. However, two conditions have to
be satisfied: the multimode waveguide has to be able to sustain at least N+1
lateral mode, in order to obtain a low-loss and well-balanced splitting of the
input field, and has to allow an adequate output waveguides separation, to
63. 2.5 Couplers 63
prevent their cross talking due to evanescent field coupling.
The coupler 1x2 was designed to be 8 µm wide, since this value allowed a good
multimode operations and an output waveguide separation of 2 µm, enough
to avoid cross-talking. From Equations 2.24 and 2.26, and considering nc =
3.1662 and neff = 3.2071, the coupler length L was calculated to be 84 µm.
Following the same design flow, the coupler 1x3 was 13 µm wide and 138 µm
long.
In order to verify this result, a BPM simulations were also carried out (Figure
2.23).
Figure 2.23: BPM simulation of an 1x2 MMI coupler.
The simulation confirmed the theoretical values, and only a small optimi-
sation of the coupler length was necessary in order to maximise the output
power. The optimised coupler length were respectively 87 µm and 143 µm
for the 1x2 and 1x3 couplers.
Another important factor in the design of MMI couplers is the understanding
and elimination of undesirable back reflections arising from the coupler itself
[67]. By inspecting the optical field pattern inside the multimode waveguide,
it is clear that the field is absent from the areas next to the input and output
waveguides. However, those areas represent a source of reflections due to
64. 2.5 Couplers 64
the step-like refractive index transition. It has been demonstrated that by
bevelling off all of the right-angled edges of the coupler corners, the return
loss can be reduced up to -30 dB [68].
Figure 2.24: Schematic of a 1x2 MMI coupler optimised for low back reflec-
tions.
Following this approach, the input/output waveguides were tapered by
an angle θ = 20◦
, as shown in Figure 2.24. The angle θ was chosen to be
twice as large as compared to the divergence angle of the light entering in
the MMI section, that was estimated to be 10◦
from the BPM simulation.
Since the optical fields do not interact immediately with the side-walls of the
MMI coupler, the multimodal interference properties were not affected. BPM
simulations confirmed the optimal physical dimensions previously obtained.
As during the mutual injection the couplers are also used in the reverse
direction as power combiners (DFB-1 and DFB-2 are injected into DFB-3),
a second type of reflection was taken into account. An efficient combining
operation requires input fields with equal phase and amplitude. If the two
inputs are 180◦
out of phase, in the output waveguide the optical power is
minimum since it is mostly reflected back, creating a perfect imaging of the
input guides back to themself. To solve this issues the SOA/attenuators
were placed next to the input/output waveguides: they acted also as phase
adjusting sections, allowing for the optimisation of the input signals.
The effect of fabrication tolerances was investigated in order to address their
effect on the device performances. BPM simulations were carried out, by
varying the calculated optimal physical dimensions. The couplers exhibited
a very good immunity to fabrication tolerances: this characteristic is due
65. 2.5 Couplers 65
to the multi-modal interference effect which can be surprisingly effective also
for non-optimal physical dimension of the multimode waveguide. Figure 2.25
shows the effect of an inaccuracy in defining the waveguide width, length and
height on the output coupled power.
Figure 2.25: Effect of fabrication inaccuracies in defining the multimode
waveguide width, length and height on the output coupled power.
First of all, the output power was always balanced between the two output
waveguides, independently from the fabrication tolerances. Moreover, the
MMI couplers showed a much stronger tolerance to fabrication inaccuracies
than evanescent couplers. Inaccuracies of up to 200 nm around the designed
value of waveguide width and length do not considerably change the optical
power coupled in the output waveguides. Slightly larger changes may occur in
case of inaccuracy in the waveguide height (over/under etch of the material).
However, since the technology used to fabricate the devices ensures a planar
resolution of a few nanometers and a vertical resolution of a few tens of
nanometers, this issue did not require any further design optimisation.
66. 2.6 Design summary 66
2.6 Design summary
For a clear overview of the devices, in the following tables the geometrical
characteristics of the previously described optical structures are reported.
The designed height of all the structures is 1920 nm.
Table 2.1: Waveguide and tapers
Structure Width [µm] Length [µm] Bend radius [µm] Tilting [◦
]
Waveguides 2 - 300 -
Spot size converter 2 to 12 100 - 10
Inverse taper 2 to 0 100 - 10
Table 2.2: Gratings
Structure Width [µm] Recess [µm] Length [µm] Period [nm]
DFB-1 2.375 0.4 400 242
DFB-2 2.4 0.4 400 242
DFB-3 2.425 0.4 400 242
Table 2.3: Couplers
Structure Length [µm] Width [µm] gap [µm]
Evanescent 50 2 1
MMI - 1x2 87 In/Out: 2; MM:8 -
MMI - 1x3 143 In/Out: 2; MM:13 -
67. Chapter 3
Fabrication
The fabrication of the devices required the state-of-the-art techniques for
the manufacture of optoelectronic devices on III-V material, which were not
available at the University of Pavia. For this reason, a visiting research period
at the University of Glasgow (U.K.) allowed for the design and fabrication
of the devices in the newly built James Watt Nanofabrication Centre1
.
The centre, one of the most advanced in the U.K. and member of EPSRC Na-
tional Centre for III-V Technologies2
, offered the necessary state-of-the-art
facilities, like an Ultra-High resolution Electron beam lithography tool, dry
etching and metal evaporation tools and high resolution scanning electron
microscopes (SEM).
In the following sections, the whole fabrication process is presented, focus-
ing on its most critical steps. First of all, the mask realisation issues will
be briefly described, followed by the detailed description of fabrication tech-
niques used in this work. Special attention will be given to the electron
beam lithography and Reactive Ion Etching issues, such as the RIE lag ef-
fect. Isolation and quasi-planarisation, contact windows opening and final
metallisation processes will also be also described in details.
1
www.jwnc.gla.ac.uk
2
www.epsrciii-vcentre.com/Home.aspx
68. 3.1 Mask realisation 68
3.1 Mask realisation
The very first step of the fabrication process was the design of the lithog-
raphy masks, which contain all the different patterns to be transferred onto
the material by the electron beam lithography tool. The masks were drawn
using the commercial software Tanner L-Edit, which allows a multi-layer and
cell structured design. A multi-layer mask was necessary, since several subse-
quent steps of lithography patterning were used to fabricate the devices; the
cell-structured software allowed a simpler and more flexible design in case of
repeated basic building blocks in the different devices.
During the mask design, all the subsequent fabrication steps had to be kept
in mind, in order to be able to compensate for some of the technology limits
with a smarter design. As shown in the Section 3.5.2, a typical example
comes from the fabrication of gratings and evanescent couplers, where the
RIE lag effect plays an important role. Finally, other smaller layout solu-
tions were devised to ease the characterisation of the devices, such as output
waveguides orientation, contact pads size, etc.
Figure 3.1 shows a complete lithography mask: the devices lie in the central
zone and are organised in six bars, which will be cleaved and mounted on
separate supports.
3.2 Electron Beam Lithography
The fabrication process used to fabricate the devices required several
lithography steps, which were carried out using the High Resolution Elec-
tron Beam Lithography (EBL) tool available in the JWNC. This kind of
tool works in a different way compared to the usual photolithography tools
of the CMOS industry, where the whole pattern is written on the material
with a single exposition using a pre-formed lithography mask. Although also
this approach has the capability to produce micro- and nano- sized patterns,
the need of a pre-formed mask sensibly reduces the flexibility of the process,
since a specific mask has to be produced for each pattern. This fact makes
69. 3.2 Electron Beam Lithography 69
Figure 3.1: Example of a full lithography mask.
the high resolution photolithography sustainable only when used for mass-
production.
For both high levels of resolution and pattern flexibility, required for device
research and prototyping, Electron Beam Lithography (EBL) is the best al-
ternative. EBL is currently the main form of non-optical lithography used
for research regarding nanotechnology applications. The EBL tool used in
this work is a state of the art Vistec VB6-UHR-EWF 100 keV machine, ca-
