Bragg and fiber gratings

Mikko Saarinen 27.10.2009

Bragg grating

- Bragg gratings are periodic perturbations in the propagating medium,

usually periodic variation of the refractive index

- like diffraction gratings, refractive index variations scatter light

- multiple scatterings can be approximated as two waves propagating in

opposite directions with propagation constant 𝛽0 =2𝜋𝑛𝑒𝑓𝑓

𝜆0

- energy is coupled from one wave to the other if 𝛽0 − −𝛽0 =2𝜋

𝛬 where

Λ is the period of the grating, usually around 0.5 µm

- grating reflects Bragg wavelength λ0=2neffΛ

- reflectance decreases as the incident wavelength differs from Bragg

wavelength -> only one wavelength is reflected

- the high-index regions also scatter light at other wavelengths, but the

scattered waves differ in phase so they cancel each other by destructive

interference

- uniform refractive index pattern change has unwanted side lobes caused

by abrupt start and end of grating

- side lobes can be eliminated with apodized grating, where the refractive

index change is made smaller towards the edges of the grating

- bandwidth is inversely proportional to the length of the grating

Fabrication

- Fiber Bragg gratings are created by "writing" the periodic variation of

refractive index into the core of optical fiber using an ultraviolet source

- typical material is a conventional silica fiber doped with germanium which

makes it extremely photosensitive

- only small refractive index changes needed (Δn≈10-4)

- one manufacturing method is to expose fiber to two interfering UV

beams, which causes the radiation intensity to vary periodically along the

fiber

- requires very high coherence length (amplitude splitting) or spatial

coherence across beam width (Lloyd mirror)

- single – frequency gratings only

- another way is to illuminate phase mask with UV light, which will diffract

light in two directions

- low – coherence UV sources can be used

- arbitrary Λ(z) profiles possible, depends only on the mask

Grating structures - Structures of Fiber Bragg Gratings vary via refractive index (uniform or

apodized) or grating period

- the refractive index profile of the grating may be modified to add linear

variation in the grating period, called a chirp. The reflected wavelength

changes with the grating period, broadening the reflected spectrum

- chirped Bragg gratings can be used to compensate dispersion by making

the grating so that segments which reflect different wavelengths are in

different positions along the length of the grating

Applications - Fiber gratings have low loss (0.1 dB), high wavelength accuracy (0.05 nm),

ease of coupling with other fibers and high adjacent channel crosstalk

suppression (40 dB)

- cheap all-fiber devices with small packing and polarization insensitivity

- typical temperature coefficient 1.25*10-2 nm/○C caused by variation in

fiber length with temperature. This can be compensated with by packing

the grating with a material that nas negative thermal expansion

coefficients

- Bragg wavelength is dependent on strain and temperature

𝛥𝜆𝐵 = 2 𝛬𝜕𝑛𝑒𝑓𝑓

𝜕𝑙+ 𝑛𝑒𝑓𝑓

𝜕𝛬

𝜕𝑙 𝛥𝑙 + 2 𝛬

𝜕𝑛𝑒𝑓𝑓

𝜕𝑇+ 𝑛𝑒𝑓𝑓

𝜕𝛬

𝜕𝑇 𝛥𝑇

- gratings can be used as a sensing element in optical fiber sensors

- Fiber Bragg Gratings have variety of uses in WDM systems: filters, optical

add/drop elements and dispersion compensation

- cascading multiple optical add/drop elements will create a optical

multiplexer/demultiplexer

Long-Period Fiber Gratings - operation is based on energy transfer from the forward propagating

mode in the core onto the forward propagating in the cladding

- coupling occurs between core mode at given wavelengths and pth-order

cladding mode

- phase-matching condition dictates that 𝛽 − 𝛽𝑐𝑙𝑝=

2𝜋

𝛥

- the difference between propagation modes are quite small -> typical

values for Λ are typically from hundred micrometers to few millimeters

- cladding modes are very lossy -> energy will decay along the fiber

- losses are caused by absorption and scattering

- wavelength at which energy will be coupled from can be written as a

function of effective indices 𝜆 = 𝛬 𝑛𝑒𝑓𝑓 − 𝑛𝑒𝑓𝑓𝑝

- wavelength is proportional to grating length -> grating acts as a

wavelength-depending loss element

- loss can be controlled by controlling the UV exposure time during

fabrication

- more complicated transmission spectra can be obtained by cascading

multiple gratings with different wavelengths and exposures

- applications as an efficient band rejection filters and spectral

shaping devices include ASE filtering, removal of undesirable

Stokes’ lines in cascaded Raman lasers and most importantly gain

flattening in EDFA

References

Optical Networks: A Practical Perpective, second edition, R. Ramaswami, K. Sivarajan, 2002, Academic Press

http://en.wikipedia.org/wiki/Fiber_Bragg_grating

http://zone.ni.com/devzone/cda/ph/p/id/90

http://en.wikipedia.org/wiki/Long-period_fiber_grating

Fiber Grating Sensors, A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, E. Friebele,

Journal of Lightwave Technology, 1997

Long period fiber gratings, A. Vengsarkar, Optical Fiber Communications, 1996. OFC '96

Long-period fiber-grating-based gain equalizers, A. Vengsarkar, J. Pedrazzani, J. Judkins, P. Lemaire, Vol. 21,

No. 5, March 1, 1996, Optics Letters