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EE-566 Presentation
Topic: Fiber Bragg Gratings
Presented By: Eric Glauber
Date: 10/29/03

Fiber Bragg Grating: Introduction
• The Fiber Bragg Grating (FBG) is a fiber optic passive component
exhibiting basic functional attributes of reflection and filtering.
• FBG’s are relatively simple to manufacture, small in dimension,
low cost and exhibit good immunity changing ambient conditions
and EM radiation.
• FBG’s have replaced bulk optic mirrors & beam splitters in
equipment which increases system stability and portability.

Fiber Bragg Grating: Introduction
Telecommunications
 Fiber Lasers
 Fiber Amplifiers
 Fiber Filters
 Dispersion Compensators
 Optical Fiber Phase Conjugator
 WDM
– Multiplexers
– Demultiplexers
Sensors
Strain Sensors
Temperature Sensors
Chemical Sensors
Accelerometers
FBG’s are commercially used in the areas of Telecommunications and Sensors:

Fiber Bragg Grating: Theory
1978 – Hill et. all
• Phenomenon of photosensitivity in optical
fibers
• Exposed Ge-doped core fibers to intense
light at 488 or 514 nm
• Induced permanent refractive index changes
to the core.

• FBG is a longitudinal periodic variation of the index of
refraction in the core of an optical fiber.
• The spacing of the variation is determined by the
wavelength of the light to be reflected.
Bragg
Bragg

The Bragg Condition is the result of two requirements:
1. Energy Conservation: Frequency of incident radiation and reflected radiation is the
same.
2. Momentum Conservation: Sum of incident wave vector and grating wave vector
equal the wave vector of the scattered radiation. K + ki = kf
The resulting Bragg Condition is: B = 2L neff
• The grating reflects the light at the Bragg wavelength (B)
• B is a function of the grating periodicity (L) and effective index (neff).
• Typically; B= 1.5 mm, L = 0.5mm

• The spectral component reflected (not transmitted) typically has a bandwidth of 0.05 –
0.3 nm.
 A general expression for the approximate Full Width Half Maximum
bandwidth of a standard grating is given by (S = grating parameter (.5 to
1), N = numbers of grating pains):
Δλ =λ B S( (Δn/2n0)2 + (1/N)2 )1/2
1570 1572 1574 1576 1578
-40
-30
-20
-10
0
Loss
in
dB
Wavelength in nm
Reflection
Transmission

• The shift in Bragg Wavelength with strain and temperature can be
expressed using:
DB = 2nL({1-(n2/2)[P12 – n(P11 + P12)]}e
+ [a + (dn/dT)/n]DT
Where:
e = applied strain
Pi,j = Pockel’s coef. of the stress-optic tensor
n = Pisson’s ratio
a = coef. of thermal expansion
DT = temperature change
[P12 – n(P11 + P12)] ~ 0.22
• The shift in Bragg Wavelength is approximately linear with
respect to strain and temperature.

• The measured strain response at a constant
temperature is found to be:
(1/B)dB/ de = 0.78 x 10-6me-1
• Sensitivity Rule of thumb at B = 1300nm:
0.001nm/me

• The measured temperature response at a
constant strain is found to be:
(1/B)dB/ dT = 6.67 x 10-6 oC-1
• Sensitivity Rule of thumb at B = 1300nm:
0.009nm/ oC

Fiber Bragg Grating: Theory – Blazed Grating
• Bragg grating planes are tilted at an angle to the fiber axis.
• Light which otherwise would be guided in the fiber core, is coupled
into the loosely bound, guided cladding or radiation modes.
• The bandwidth of the trapped out light is dependent on the tilt angle of
the grating planes and the strength of the index modulation.
• As shown above, the vector diagram is a result of the conservation of
momentum and conservation of energy requirement. The results of
applying the law of cosines yealds: Cos(θb) = ‫׀‬K‫׀‬/2v

Fiber Bragg Grating: Theory – Chirped Grating
• Bragg grating has a monotonically varying period as illustrated above.
• These gratings can be realized by axially varying either the period of
the grating or the index of refraction of the core or both.
• The Bragg Condition becomes: λB = 2neff(z)Λ(z)
• The simplest type of chirped grating is one which the grating period
varies linearly with axial length: Λ(z) = Λ0 + Λ(z)

Fiber Bragg Grating: Manufacturing
1989 Meltz et. all.
• Grating written into core by holographic
side exposure method
• Exposure with two beam interference
pattern of UV light at 244nm
• Focal spot is approx. rectangular, 4mm L X
125 mm W.

Split Beam Interferometer Method

Interference pattern
Grating
Core
ø 9µm
Cladding
ø 125µm
Laser
Beam
Laser
Beam
L
Fiber

Novel interferometer
technique using a right
angled prism.
Inherently more stable -
because beams are
perturbed similarly by
any prism vibration.

Phase Mask
Technique.
• UV is diffracted into –1,0,1
orders by relief grating.
• Input mask is wavelength
specific.
• Different B require
different phase masks.

Fiber Bragg Grating: Manufacturers
Manufacturers:
• Advanced Optics Solutions GMBH
• Blue Road Research
• 3M Optical OEM Systems
• Alcatel Optronics
• Boeing
• Gould Fiber Optic
• MPB Communications
• OZ Optics Limited
• TeraXion Inc.
• Oxford Lasers Inc.
• Thorlabs Inc.

FBG custom design software:

FBG
order
form:

Fiber Bragg Gratings - Application
Mach-Zehnder interferometric Band Pass Filter:
• This arrangement has two identical FBG’s.
• The relative phases of the two transmitted signals is adjusted to maximize the output
from either port 3 or 4 and thus avoiding the 3-db loss of the couplers.
• This arrangement is difficult to manufacture because the performance of the filter is
strongly affected by the spectral characteristics of the two couplers. Also affecting
the filter performance is any imbalance int the power splitting of the couplers or the
relative phases of the signals.

Chirped Grating used for Dispersion Compensation:
• The operating principle is that the grating reflects different wavelength components
of the signal from different sections along the grating.
• As shown below, short wavelengths are reflected first at the near end and longer
wavelengths are reflected at a later time at the far end of the grating.
• Shown below is a simple expression for the group delay dispersion of a linear chirped
grating of length L.

Chirped Grating used for Dispersion Compensation:
• Shown below is a system which transmits a 2 pico-second pulse which is
compensated using a linearly chirped Bragg grating.
• Shown to the lower right is a graph of the compensated and uncompensated
signal.
Other more complicated grating structures are avaliable. For
example cubic dispersion compensation is important in long
distance, high bit rate transmission systems.

Mach-Zehnder DWM – Multiplexer / Demultiplexer:
• This is the Mach-Zehnder arrangement for a WDM application.
Extraction of channel λk Insertion of channel λk

Frustrated Coupler Drop Add Multiplexer:
• This is composed of a mismatched coupler with a Bragg Grating written into one of
the cores.
• Power would not normally be transferred due to the mismatch of the core. With the
Bragg grating, power transfer of the guided mode from port 1 to port 4 can happen if
the sum of the propagation constants of the LP01 modes of each core satisfies the
Bragg condition: (β01(λ12,1) +β01(λ12,2)) = 2Π/Λ
• This cross coupling transfers the guided optical power at λ12 in core 1 into back
propagating optical power in core 2.

Chemical Sensor:
• FBG is blazed into the core at a tilt angle y.
• The FBG Tap radiates a beam out of the core and cladding at an
angle gB.

Chemical Sensor (Continued):
• FBG Tap excites fluorescent layer which in turn emits
light which is in turn collected by the core (f1).

Fiber Bragg Gratings – Application, WDM
• In WDM, each FBG sensor is assigned a
portion of the source spectrum.
• Enables quasi-distributed sensing of strain,
temperature, chemical, etc….
• No. of FBG is a function of:
– Source profile width
– Grating operational bandwidth

• Approx 20 strain sensors can be
multiplexed along a single fiber (peak
strains of +1000me)

Time & Wavelength Division Multiplexing:

Fiber Bragg Gratings – References
Othonos, Andreas and Kalli, Kyriacos, “Fiber Bragg Gratings – Fundamentals and Applications in Telecommunications and
Sensing”, Artech House, Inc, 1999.
Hill, K.O., et al., “Photosensitivity in Optical Fiber Waveguides: Application to Reflection Filter Fabrication,” Appl. Phys.
Letter, Vol.32 (647-651) 1978.
Kersey, Alan D., et al., “Fiber Grating Sensors,” Journal of Lightwave Technology, Vol. 15, No. 8, August 1997.
Maher, M.H. and E.G. Nawy, “Evaluation of Fiber Optic Bragg Grating Strain Sensor in High Strength Concrete Beams,”
Fiber Optic Sensors for Construction Materials and Bridges, pp. 120-133, Farhad Ansari, editor, Technical Publishing
Company, Inc., 1998.
Pallas-Areny, R. and J.G. Webster, Sensors and Signal Conditioning, second Ed., John Wiley & Sons, Inc., 2001.
Meltz, G., W.W. Morey and W.H. Glenn, “Formation of Bragg Gratings in Optical Fibers by a Transverse Holographic
Method,” Opt. Lett, 14, (823-825) 1989.
Webster, J.G., The Measurement Instrumentation and Sensors Handbook, RC Press, 1999.
http://www.photonics.com/directory/bg/xq/asp/url.viewcat/bgpsa.30125/qx/categories.html
http://www.aos-fiber.com/

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