Bragg and fiber gratings. Mikko Saarinen

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1 Bragg and fiber gratings Mikko Saarinen

$variation of the refractive index - like diffraction gratings, refractive index variations scatter$

2 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 β 0 = 2πn eff λ0 - energy is coupled

3 - multiple scatterings can be approximated as two waves propagating in opposite directions with propagation constant β 0 = 2πn eff λ0 - energy is coupled from one wave to the other if β 0 β 0 = 2π Λ where Λ is the period of the grating, usually around 0.5 µm - grating reflects Bragg wavelength λ 0 =2n eff Λ

4 - 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

$- uniform refractive index pattern change has unwanted side lobes caused by abrupt start and end of grating - side lobes can be eliminated with apodized$

5 - 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

6 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 )

7 - 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

8 - 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

9 Grating structures - Structures of Fiber Bragg Gratings vary via refractive index (uniform or apodized) or grating period

10 - 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

11 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 Δλ B = 2 Λ n eff l + n eff Λ l Δl + 2 Λ n eff T + n eff Λ T ΔT

12 - 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

13 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 β cl p = 2π Δ - the difference between propagation modes are quite small -> typical values for Λ are typically from hundred micrometers to few millimeters

14 - 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 n eff n eff - 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 p

15 - 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

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

Optical Communications and Networking 朱祖勍. Sept. 25, 2017

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