3. Optical Filters
Optical filters are used for example to separate a single of
multiple optical signals from a WDM signal
Optical filters are also widely used to reject out-of-band ASE
noise imposed on the desired signals
Some of the desirable features of an optical filter are:
1. A high out-of-band signal rejection,
2. Temperature independent operation,
3. Low insertion loss,
4. Compact size and
5. low cost
4. Optical Filters
In this course, we will discuss the four most common optical
filters used in communications namely:
1. Grating Based Filter
2. Arrayed Waveguide Grating Filter
3. Fabry-Perot Filters
4. Fiber Bragg Grating Filter
5. Grating Filters
Grating filters exploit the phenomenon of light-diffraction to
different wavelengths of an input optical signal
It uses a diffraction grating, which is essentially a glass having
a rectangular cross-section and multiple slits or groves
When light composed of different wavelengths impinges on
such a grating, it passes through the narrow slits and spreads
out at the output due to diffraction
Hence each slit effectively acts like a separate source of light
7. Grating Filters
An important quality of diffraction grating is that for a unique set
of discrete angles, the light diffracted from the multiple slits
facing in different directions are in phase
This coherent phase relationship results in constructive
interference among various diffracted wavefronts at spatially
separate points at the opposite side of the diffraction grating
The condition for constructive interference to occur for a grating
having a uniform slit spacing of d between two consecutive slits
and an incident light of wavelength λ is given by:
8. Grating Filters
Where m is the diffraction order and θ is the diffraction angle
The operating principle of a grating filter based on a diffraction
grating can be understood from the simplified diagram
The optical signal to be filtered impinges on a diffraction
grating, which results in a diffraction pattern at the opposite side
The diffraction pattern is composed of multiple bright spots of
light at different wavelengths separated spatially
9. Grating Filters
The spatial distance among the different bright spots depends
both upon:
1. The slit spacing of the grating and
2. The distance of the screen used for observing the pattern
A narrow bandwidth of light can be filtered out by using an exit
slit located at some distance from the diffraction grating
The bandwidth retained depends upon the size of the exit slit
10. Grating Filters
In order to construct a tunable grating filter, the diffraction
grating is mounted on a mechanical structure that can be
rotated externally
When the diffraction grating rotates, the diffraction pattern on
the screen also shifts, resulting in different retained
wavelengths exiting the exit slit
11. Arrayed Waveguide Grating Filter
The grating filter described in the previous section uses a
diffraction grating for achieving spatial dispersion of the input
optical signal
Now we discuss the Arrayed Waveguide Grating (AWG) filter,
which uses optical waveguides for achieving a spatial
separation similar to the grating filter
AWG filters rely on the principle of optical interferometers
12. Arrayed Waveguide Grating Filter
The simplest interferometer is the Mach-Zehnder
Interferometer (MZI)
MZI is composed of two optical couplers connected by two
separate waveguides in order to filter a single wavelength, in a
fashion that is reminiscent of the MZM
Similarly, the AWG is composed of two optical couplers that are
connected by more than two waveguides in order to filter
multiple wavelengths
14. Arrayed Waveguide Grating Filter
Observe that the AWG consists of input and output
waveguides, two slab waveguides and a set of arrayed
waveguides, which are made up of silica
When the optical signal passing through the input waveguide
enters the first slab waveguide, it diverges in the free
propagation region of the slab waveguide
The signal that spreads in the first slab waveguide is captured
by the set of arrayed waveguides which function as dispersive
elements and are arranged to have a constant length-difference
between the adjacent waveguides
15. Arrayed Waveguide Grating Filter
The length of each waveguide is chosen by ensuring that a
particular wavelength undergoes the same dispersion in each
waveguide
Therefore, after travelling through the free propagation region
of the second slab waveguide, all the optical signals having a
particular wavelength constructively focus their output on a
single output waveguide
16. Arrayed Waveguide Grating Filter
The length-difference △L of the adjacent arrayed waveguides
required for achieving the constructive focusing of all the optical
signals having a particular wavelength can be written as:
Where m is the order and ng is the effective refractive index of
the arrayed waveguide
The central wavelength of the incident optical signal is
represented by λ𝑐
17. Fiber Bragg Grating Filter - Concept
From a practical standpoint, a diffraction grating is defined as
any optical element capable of imposing a periodic variation in
the amplitude or phase of light incident on it
Clearly, an optical medium whose refractive index varies
periodically acts as a grating since it imposes a periodic
variation of phase when light propagates through it
Such gratings are called index gratings
18. Bragg Diffraction
The diffraction theory of gratings shows that when light is
incident at an angle θi (measured with respect to the planes of
constant refractive index), it is diffracted at an angle θr such
that:
Λ is the grating period,
λ is the wavelength of the light inside the medium
𝑛 is the average refractive index
m is the order of the Bragg diffraction
19. Fiber Bragg Grating Filter
In the case of single-mode fibers, the incident and diffracted
light lie along the fiber axis
As a result, the diffracted light propagates backward
Therefore:
If m = 1, the period of the grating is related to the vacuum
wavelength as:
This condition is known as the Bragg condition
20. Fiber Bragg Grating Filter
A fiber grating acts as a reflector for a specific wavelength of
light for which the phase-matching condition is satisfied
21. Fiber Bragg Grating Filter
Gratings satisfying Bragg condition are referred to as Bragg
gratings
Physically, the Bragg condition ensures that weak reflections
occurring throughout the grating add up in phase to produce a
strong reflection
For a fiber grating reflecting light in the wavelength region near
1550 nm, the grating period is:
22. Fabry-Perot Filter
A Fabry-Perot (FP) filter exploits the interference of light in a
resonating cavity
The resonating cavity of the FP filter consists of two highly
reflective mirrors that are placed parallel to each other at a
distance L
The input light enters into the cavity through the left mirror and
after traveling a distance of L it falls on the reflective side of the
right mirror
23. Fabry-Perot Filter
A part of the light exits through the right mirror, while a part of it
is reflected back into the cavity
The percentage of light refracted or reflected depends upon the
reflectivity of the mirrors
The resonating cavity structure of the FP filter can be used to
filter out a particular wavelength by choosing the length of the
cavity to be an integer multiple of half the wavelength
That is L = mλ/2, where m is an integer and λ is the wavelength
to be retained
25. Fabry-Perot Filter
Light having a particular wavelength λ interferes constructively
after going through a round-trip inside the cavity, the resultant
high intensity light exits through the right facet
The power transfer function PTF of the filter in terms of
wavelength is given by:
A and R are the absorption loss and reflectivity of the each
mirror’s respectively and n is the refractive index of the cavity
