Fiber Bragg Grating and Its Application As Sensor

Term Paper Leading To Thesis

On

Fiber Bragg Grating and its application as sensor

Submitted by

Pratyay Masanta

Registration No. 101040410027 of 2010-2011

Roll No. 10409010009

Under supervision of

Prof. Dr. Asim Kar

Head of the Department

Department of Electronics & Communication Engineering

Institute of Engineering & Management

Introduction:

The fiber optics field has undergone a tremendous growth and advancement over last 40 years. Among the reasons why optical fibers are such an attractive are their low loss, high bandwidth, EMI immunity, small size, lightweight, safety, relatively low cost, low maintenance etc. Asopticalfiberscementedtheirpositionin the telecommunications industry and its technology and commercial markets matured, parallel efforts were carried out by a number of different groups around the world to exploit some of the key fiber featuresandutilizethem insensingapplications.Today opticalfibersensingmechanism isinvolvedinbio-medicallaserdelivery systems,military gyrosensors, aswellasautomotivelighting and control-tonamejustafew.Opticalfibersensoroperationand instrumentation havebecomewell understoodanddeveloped.Andavarietyofcommercialdiscretesensors basedonFabry-Perot(FP)cavitiesandFiberBraggGratings(FBGs),as well as distributed sensors based on Raman and Brillouin scattering methods, are readily available along with pertinent interrogation instruments. Amongallofthese, FBGbased sensorshavebecomewidely known, researched andpopular withinand outthephotonicscommunity.

Diffraction Grating:

A diffraction grating is an optical component with a regular pattern. The form of the light diffracted by a grating depends on the structure of the elements and the number of elements present, but all gratings have intensity maxima at angles θm which are given by the grating equation

d (sinθm + sinθi) =mλ

where θi is the angle at which the light is incident, d is the separation of grating elements and m is an integer which can be positive or negative.

The light diffracted by a grating is found by summing the light diffracted from each of the elements, and is essentially a convolution of diffraction and interference patterns.

Operation of diffraction grating:

The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation.

An idealized grating is considered here which is made up of a set of long and infinitely narrow slits of spacing d. When a plane wave of wavelength λ is incident normally on the grating, each slit in the grating acts as a point source propagating in all directions. The light in a particular direction, θ, is made up of the interfering components from each slit. Generally, the phases of the waves from different slits will vary from one another, and will cancel one another out partially or wholly. However, when the path difference between the light from adjacent slits is equal to the wavelength, λ, the waves will all be in phase. This occurs at angles θm which satisfy the relationship dsinθm/λ=|m| where d is the separation of the slits and m is an integer. Thus, the diffracted light will have maxima at angles θm given by

dsinθm=mλ

It is straightforward to show that if a plane wave is incident at an angle θi, the grating equation becomes

d (sinθm + sinθi) =mλ

This derivation of the grating equation has used an idealised grating. However, the relationship between the angles of the diffracted beams, the grating spacing and the wavelength of the light apply to any regular structure of the same spacing, because the phase relationship between light scattered from adjacent elements of the grating remains the same. The detailed distribution of the diffracted light depends on the detailed structure of the grating elements as well as on the number of elements in the grating, but it will always give maxima in the directions given by the grating equation.

Fiber Bragg Grating:

AfiberBragggratingisaperiodicoraperiodicperturbationoftheeffectiverefractive indexinthecoreofanopticalfiber.Typically,theperturbationisapproximatelyperiodic overacertainlengthofe.g.afewmillimetersorcentimeters,andtheperiodisofthe orderofhundredsofnanometers.Thisleadstothereflectionoflight(propagatingalong the fiber) in a narrow rangeofwavelengths,for whicha Bragg condition is satisfied.This basically means thatthewavenumberofthegrating matchesthe difference ofthewave numbersoftheincidentandreflectedwaves.(Inotherwords,thecomplexamplitudes correspondingtoreflectedfieldcontributionsfromdifferentpartsofthegratingareallin phasesothat canaddupconstructively;thisisakindofphasematching.)Other wavelengthsarenearlynotaffectedbytheBragggrating,exceptforsome side lobes which frequently occur in the reflection spectrum.AroundtheBraggwavelength,evenaweak indexmodulation(withan amplitudeofe.g.10^-4)issufficienttoachievenearlytotalreflection,ifthe gratingis sufficiently long (e.g.a fewmillimeters).Thereflectionbandwidthofafibergrating,whichistypicallywellbelow1nm,depends onboththelengthandthestrengthoftherefractiveindexmodulation.

Figure 1: A Fiber Bragg Grating structure, with refractive index profile and spectral response

Theory:

Figure 2:FBGsreflectedpowerasa functionof wavelength

Thegratingwilltypicallyhavea sinusoidalrefractiveindexvariationoveradefined length.The reflectedwavelength(λB),calledtheBraggwavelength,isdefinedbythe relationship,

WherenistheeffectiverefractiveindexofthegratinginthefibercoreandΛisthegratingperiod.

Inthiscase,i.e.itistheaveragerefractiveindexinthe grating.

Thewavelengthspacingbetweenthefirstminimums(nulls),orthebandwidth(Δλ),is givenby,

whereδn0 isthevariationintherefractiveindex(n3 − n2),andηisthefractionofpower in the core.

The peak reflection (PB(λB))isapproximately given by,

WhereNisthenumberofperiodicvariations.Thefullequationforthereflectedpower (PB(λ)),is givenby,

where,

Fiber Bragg Grating Sensors:

Asthewavelengthofmaximumreflectivitydepends notonlyon theBragggratingperiod but also on temperature and mechanical strain, Bragg gratings can be used in temperatureandstrainsensors.Transversestress,asgeneratede.g.bysqueezinga fiber grating between two flat plates, induces birefringence and thus polarization- dependentBraggwavelengths.

As well as being sensitive to strain, the Bragg wavelength is also sensitive to temperature.ThismeansthatfiberBragggratingscanbeusedassensingelementsin opticalfibersensors.Ina FBGsensor,themeasurandcausesashiftintheBragg wavelength,ΔλB.TherelativeshiftintheBraggwavelength,ΔλB/ λB,duetoanapplied strain (ε) anda change intemperature (ΔT) is approximatelygiven by,

or,

Here,CS isthecoefficientofstrain,whichisrelatedtothestrainopticcoefficientpe. Also,CT isthecoefficientoftemperature,whichismadeupofthethermalexpansion coefficientoftheoptical fiber, αΛ,andthethermo-optic coefficient,αn.

Fiber Bragg gratings can then be used as direct sensing elements for strain and temperature.Theycanalsobeusedastransductionelements,convertingtheoutputof anothersensor,whichgeneratesastrainortemperaturechangefromthemeasurand, forexamplefiberBragggratinggas sensorsuseanabsorbentcoating,whichinthe presenceofagasexpandsgeneratingastrain,which ismeasurablebythegrating. Technically,theabsorbentmaterialisthesensingelement,converting the amountof gas toastrain. The Bragg grating then transduces the strain to the change in wavelength.