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`Fiber Bragg Grating Technology
`Fundamentals and Overview
`
`Kenneth O. Hill and Gerald Meltz, Member, IEEE
`
`(Invited Paper)
`
`Abstract— The historical beginnings of photosensitivity and
`fiber Bragg grating (FBG) technology are recounted. The basic
`techniques for fiber grating fabrication, their characteristics, and
`the fundamental properties of fiber gratings are described. The
`many applications of fiber grating technology are tabulated, and
`some selected applications are briefly described.
`
`Index Terms—Bragg gratings, optical fiber devices, optical fiber
`dispersion, optical fiber filters, optical fiber sensors, optical planar
`waveguides and components, photosensitivity.
`
`I. INTRODUCTION
`
`AFIBER Bragg grating (FBG) is a periodic perturbation
`
`of the refractive index along the fiber length which
`is formed by exposure of the core to an intense optical
`interference pattern. The formation of permanent gratings
`in an optical fiber was first demonstrated by Hill et al.
`in 1978 at the Canadian Communications Research Centre
`(CRC), Ottawa, Ont., Canada, [1], [2]. They launched intense
`Argon-ion laser radiation into a germania-doped fiber and
`observed that after several minutes an increase in the reflected
`light intensity occurred which grew until almost all the light
`was reflected from the fiber. Spectral measurements, done
`indirectly by strain and temperature tuning of the fiber grating,
`confirmed that a very narrowband Bragg grating filter had been
`formed over the entire 1-m length of fiber. This achievement,
`subsequently called “Hill gratings,” was an outgrowth of
`research on the nonlinear properties of germania-doped silica
`fiber. It established an unknown photosensitivity of germania
`fiber, which prompted other inquires, several years later,
`into the cause of the fiber photo-induced refractivity and
`its dependence on the wavelength of the light which was
`used to the form the gratings. Detailed studies [3] showed
`that the grating strength increased as the square of the light
`intensity, suggesting a two-photon process as the mechanism.
`In the original experiments, laser radiation at 488 nm was
`reflected from the fiber end producing a standing wave pattern
`that formed the grating. A single photon at one-half this
`wavelength, namely at 244 nm in the ultraviolet, proved
`to be far more effective. Meltz et al. [4] showed that this
`radiation could be used to form gratings that would reflect
`any wavelength by illuminating the fiber through the side of
`
`the cladding with two intersecting beams of UV light; now, the
`period of the interference maxima and the index change was
`set by the angle between the beams and the UV wavelength
`rather than by the visible radiation which was launched into
`the fiber core. Moreover, the grating formation was found to
`be orders-of-magnitude more efficient.
`At first, the observation of photo-induced refractivity in
`fibers was only a scientific curiosity, but over time it has
`become the basis for a technology that now has a broad and
`important role in optical communications and sensor systems.
`Research into the underlying mechanisms of fiber photosen-
`sitivity and its uses is on-going in many universities and
`industrial laboratories in Europe, North and South America,
`Asia, and Australia. Several hundred photosensitivity and fiber
`grating related articles have appeared in the scientific literature
`and in the proceedings of topical conferences, workshops,
`and symposia. FBG’s are now commercially available and
`they have found key applications in routing, filtering, control,
`and amplification of optical signals in the next generation of
`high-capacity WDM telecommunication networks.
`This article contains an introduction to the fundamentals
`of FBG’s, including a description of techniques for grating
`fabrication and a discussion of those fiber photosensitivity
`characteristics which underlie grating formation. We highlight
`the salient properties of periodic, optical waveguide structures
`that are used in the design of grating filters and conclude with
`an overview of key applications in optical telecommunications
`and quasidistributed, thermophysical measurement. Other arti-
`cles and reviews of the technology that have appeared include
`a recent comprehensive article by Bennion et al. [5] and survey
`papers that discuss the physical mechanisms that are believed
`to be important in photosensitivity [6] and applications of
`gratings to fiber optic sensors [7].
`
`II. PHOTOSENSITIVITY AND GRATING FORMATION
`Fiber photosensitivity was first observed in the experimental
`arrangement showed in Fig. 1. Continuous wave blue (488
`nm) light from an Argon ion laser is launched into a short
`piece of nominally monomode optical fiber and the intensity
`of the light reflected back from the fiber is monitored. Initially,
`the reflected light
`intensity is low, but after a period of
`few minutes, it grows in strength until almost all the light
`launched into the fiber is back-reflected. The growth in back-
`reflected light was explained in terms of a new nonlinear effect
`called “photosensitivity” which enables an index grating to be
`0733–8724/97$10.00 ª
`
`Manuscript received May 13, 1997; revised May 19, 1997.
`K. O. Hill is with the Communications Research Center, Ottawa, Ont. K2H
`8S2 Canada.
`G. Meltz is with OFT Associates, Avon, CT 06001 USA.
`Publisher Item Identifier S 0733-8724(97)05932-X.
`
`1997 IEEE
`
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`488 nm, the wavelength of the blue Argon laser line used to
`produce the “Hill gratings.” The two overlapping ultraviolet
`light beams interfere producing a periodic interference pattern
`that writes a corresponding periodic index grating in the
`core of the optical fiber. The technique called the transverse
`holographic technique is possible because the fiber cladding
`is transparent to the ultraviolet light whereas the fiber core is
`highly absorbing to the ultraviolet light.
`The holographic technique for grating fabrication has two
`principal advantages. Bragg gratings could be photoimprinted
`in the fiber core without removing the glass cladding. Fur-
`thermore, the period of the photoinduced grating depends on
`the angle between the two interfering coherent ultraviolet light
`beams. Thus even though ultraviolet light is used to fabricate
`the grating, Bragg gratings could be made to function at much
`longer wavelengths in a spectral region of interest for devices
`which have applications in fiber optic communications and
`optical sensors.
`
`III. CHARACTERISTICS OF PHOTOSENSITIVITY
`When ultraviolet light radiates an optical fiber, the refractive
`index of the fiber is changed permanently; the effect is termed
`photosensitivity. The change in refractive index is permanent
`in the sense that it will last for decades (life times of 25
`years are predicted) if the optical waveguide after exposure
`is annealed appropriately, that is by heating for a few hours
`at a temperature of 50 C above its maximum operating
`temperature [10]. Initially, photosensitivity was thought to be
`a phenomenon associated only with germanium doped optical
`fibers. Subsequently, it has been observed in a wide variety of
`different fibers, many of which did not contain germanium as a
`dopant. Nevertheless, optical fiber having a germanium doped
`core remains the most important material for the fabrication
`of devices.
`The magnitude of the refractive index change (
`) obtained
`depends on several different factors such as the irradiation
`conditions (wavelength, intensity, and total dosage of irradi-
`ating light), the composition of glassy material forming the
`fiber core and any processing of the fiber prior to irradiation.
`A wide variety of different continuous wave and pulsed
`laser light sources with wavelengths ranging from the visible
`to the vacuum ultraviolet have been used to photo-induce
`refractive index changes in optical fibers. In practice, the most
`commonly used light sources are KrF and ArF excimer lasers
`that generate, respectively, 248 and 193 nm optical pulses
`(pulsewidth 10 ns) at pulse repetition rates of 50–75 pulses/s.
`The typical irradiation conditions are an exposure to the laser
`light for a few minutes at intensities ranging for 100–1000
`mJ/cm2. Under these conditions
`is positive in germanium
`doped monomode fiber with a magnitude ranging between
`10 5 to 10 3. Techniques such as “hydrogen loading” [11] or
`“flame brushing” [12] are available which can used to process
`the fiber prior to irradiation in order to enhance the refractive
`index change obtained on irradiation. By the use of hydrogen
`as high as 10 2 has been obtained.
`loading a
`Irradiation at intensity levels higher than 1000 mJ/cm2 mark
`the onset of a different nonlinear photosensitive process that
`
`Fig. 1. Schematic of original apparatus used for recording Bragg gratings
`in optical fibers. A position sensor monitored the amount of stretching of the
`Bragg grating as it was strain-tuned to measure its very narrow-band response.
`
`written in the fiber. The reasoning is as follows. Coherent
`light propagating in the fiber interferes with a small amount
`of light reflected back from the end of the fiber to set up a
`standing wave pattern which through photosensitivity writes
`an index grating in the fiber core. As the strength of grating
`increases the intensity of the back-reflected light increases until
`it saturates near 100%. In these first experiments, permanent
`index gratings (Bragg gratings) with 90% reflectivity at the
`Argon laser writing wavelength were obtained. The bandwidth
`of the Bragg grating which was measured by stretching the
`fiber, is very narrow ( 200 MHz) indicating a grating length
`of
`1 m.
`it was recognized that gratings in optical
`the time,
`At
`waveguides would have many potential applications in the
`fabrication of devices for use in fiber optic communications.
`In fact, it was shown that “Hill gratings” could be used as
`a feedback mirror for a laser and as a sensor for strain by
`stretching the fiber. Although photosensitivity appeared to
`be an ideal means for fabricating gratings in optical fibers,
`the “Hill gratings” unfortunately functioned only at
`light
`wavelengths in the visible close to the wavelength of the
`writing light. This limitation on photosensitivity was overcome
`about ten years later in an experiment by Meltz et al. [4]
`who recognized from the work of Lam and Garside [3] that
`photosensitivity was a two photon process that could be
`made much more efficient if it were a one photon process
`at a wavelength in the 5 eV (245 nm) germania oxygen-
`vacancy defect band [8], [9]. In their experiment, the fiber
`is irradiated from the side with two intersecting coherent
`ultraviolet light beams (see Fig. 2). The wavelength of the
`ultraviolet light is 244 nm which corresponds to one half of
`
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`HILL AND MELTZ: FBG TECHNOLOGY FUNDAMENTALS
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`Fig. 2. Two-beam interferometer arrangement for side-writing fiber Bragg gratings (FBG’s).
`
`enables a single irradiating excimer light pulse to photoin-
`duce a large index changes in a small localized region near
`the core/cladding boundary. In this case the refractive index
`changes are sufficiently large to be observable with a phase
`contrast microscope and have the appearance of damaging
`physically the fiber. This phenomenon has been used for the
`writing of gratings using a single excimer light pulse.
`Another property of
`the photoinduced refractive index
`change is anisotropy. This characteristic is most easily
`observed by irradiating the fiber from the side with ultraviolet
`light polarized perpendicular to the fiber axis. The anisotropy
`in the photoinduced refractive index change results in the
`fiber becoming birefringence for light propagating through the
`fiber. The effect is useful for fabricating polarization mode
`converting devices or rocking filters [13].
`The physical mechanisms underlying photosensitivity are
`not very well understood but are associated with the color
`centers in glassy materials. For example, UV photoexcitation
`of oxygen-vacancy-defect states [9] in Ge–SiO2 fiber forms
`paramagnetic GeE¢ centers that contribute to the index change
`[14]. There is also evidence that structural rearrangement of the
`glass matrix, possibly densification, is also correlated with the
`index increase [15]. The net result of the photoinduced changes
`is a permanent change in the refractive index of the glassy
`material at wavelengths far removed from the wavelength of
`the irradiating ultraviolet light.
`
`IV. GRATING FABRICATION TECHNIQUES
`Historically, Bragg gratings were first fabricated using the
`internal writing [1] and the holographic technique [4]. Both
`these methods, which have been described already, have been
`
`largely superseded by the phase mask technique [16], [17]
`which is illustrated in Fig. 3. The phase mask is made from
`flat slab of silica glass which is transparent to ultraviolet light.
`On one of the flat surfaces, a one dimensional periodic surface
`relief structure is etched using photolithographic techniques.
`The shape of the periodic pattern approximates a square wave
`in profile. The optical fiber is placed almost in contact with the
`corrugations of the phase as shown in Fig. 3. Ultraviolet light
`which is incident normal to the phase mask passes through
`and is diffracted by the periodic corrugations of the phase
`mask. Normally, most of the diffracted light is contained in
`the
`,
`1, and
`1 diffracted orders. However, the phase
`mask is designed to suppress the diffraction into the zero-
`order by controlling the depth of the corrugations in the phase
`mask. In practice the amount of light in the zero-order can be
`reduced to less than 5% with approximately 40% of the total
`1 orders. The two
`1
`light intensity divided equally in the
`diffracted order beams interfere to produce a periodic pattern
`that photoimprints a corresponding grating in the optical fiber.
`If the period of the phase mask grating is
`, the period
`of the photoimprinted index grating is
`. Note that this
`period is independent of the wavelength of ultraviolet light
`irradiating the phase mask; however, the corrugation depth
`required to obtain reduced zeroth-order light is a function of
`the wavelength and the optical dispersion of the silica.
`The phase mask technique has the advantage of greatly
`simplifying the manufacturing process for Bragg gratings, yet
`yielding gratings with a high performance. In comparison with
`the holographic technique, the phase mask technique offers
`easier alignment of the fiber for photoimprinting, reduced
`stability requirements on the photoimprinting apparatus and
`lower coherence requirements on the ultraviolet laser beam
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`Fig. 3. Bragg grating fabrication apparatus based on a zero-order nulled diffraction phase mask. The duty cycle of the phase mask is chosen to be 50%.
`The amplitude of the phase mask groves is chosen to reduce the light transmitted in the zero-order beam to less than 5% of the total throughput. These
`choices result typically in more than 80% of the throughput being in the 1 diffracted beams.
`
`thereby permitting the use a cheaper ultraviolet excimer laser
`source. Furthermore, there is the possibility of manufacturing
`several gratings at once in a single exposure by irradiating
`parallel fibers through the phase mask. The capability to
`manufacture high-performance gratings at a low per unit
`grating cost is critical for the economic viability of using
`gratings in some applications. A drawback of the phase
`mask technique is that a separate phase mask is require for
`each different Bragg wavelength. However, some wavelength
`tuning is possible by applying tension to the fiber during the
`photoimprinting process; the Bragg wavelength of the relaxed
`2 nm.
`fiber will shift by
`The phase mask technique not only yields high performance
`devices but is very flexible in that it can be used to fabricate
`gratings with controlled spectral response characteristics. For
`instance, the typical spectral response of a finite length grating
`with a uniform index modulation along the fiber length has
`secondary maxima on both sides of the main reflection peak.
`In applications like wavelength division multiplexing this type
`of response is not desirable. However, if the profile of the
`index modulation along the fiber length is given a bell-like
`functional shape, these secondary maxima can be suppressed
`[18]. The procedure is called apodization. Apodized fiber
`
`gratings have been fabricated using the phase masks technique
`and suppressions of the sidelobes of 30–40 dB have been
`achieved [19]–[21].
`The phase mask technique has also been extended to the
`fabrication of chirped or aperiodic fiber gratings. Chirping
`means varying the grating period along the length of the
`grating in order to broaden its spectral response. Aperiodic
`or chirped gratings are desirable for making dispersion com-
`pensators [22]. A variety of different methods have be used
`to manufacture gratings that are chirped permanently or have
`an adjustable chirp.
`Another approach to grating fabrication is the point-by-
`point technique [23] also developed at CRC. In this method
`each index perturbations of the grating are written point-
`by-point. For gratings with many index perturbations,
`the
`method is very not very efficient. However, it has been used
`to fabricate micro-Bragg gratings in optical fibers [24], but
`is most useful for making coarse gratings with pitches of
`the order of 100 m that are required LP01 to LP11 mode
`converters [23] and polarization mode converters [13]. The
`interest in coarse period gratings has increased lately because
`of their use in long period fiber grating band-rejection filters
`[25] and fiber amplifier gain equalizers [26], [27].
`
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`Fig. 4. Bragg resonance for reflection of the incident mode occurs at the wavelength for which the grating pitch along the fiber axis is equal to one-half
`of the modal wavelength within the fiber core. The back scattering from each crest in the periodic index perturbation will be in phase and the scattering
`intensity will accumulate as the incident wave is coupled to a backward propagating wave.
`
`V. FUNDAMENTAL PROPERTIES OF GRATINGS
`The index perturbation in the core is a periodic structure,
`similar to a volume hologram or a crystal lattice, that acts as
`a stop-band filter. A narrow band of the incident optical field
`within the fiber is reflected by successive, coherent scattering
`from the index variations. The strongest interaction or mode-
`coupling occurs at the Bragg wavelength
`given by
`
`(1)
`
`is the grating period. Each
`is the modal index and
`where
`reflection from a crest in the index perturbation is in phase with
`the next one at
`, as shown in Fig. 4, and any change in fiber
`properties, such as strain, temperature, or polarization which
`varies the modal index or grating pitch will change the Bragg
`wavelength. The grating is an intrinsic sensor which changes
`the spectrum of an incident signal by coupling energy to other
`fiber modes. In the simplest case, the incident wave is coupled
`to a counterpropagating like mode and thus reflected.
`The grating filter characteristics can be understood and mod-
`eled by several approaches [28]–[32]. Coupled-mode theory
`is often the foundation for many of these computations. In its
`simplest form, this analysis leads to a single Ricatti differential
`equation for a modified local reflectivity
`, which is easily
`integrated by standard numerical methods. In the most general
`takes the form of a phase
`case, the index perturbation
`and amplitude-modulated periodic waveform
`
`Fig. 5. Comparison of computed and measured transmission spectra for a
`moderate reflectivity Gaussian-apodized fiber grating. The grating length is
`about 10 mm as determined from measurements of the approximately Gaussian
`UV beam width; the grating strength (n=n = 9  105) was inferred from
`the measured minimum transmittance.
`
`is an apodization function, typically a Gaussian or
`where
`raised-cosine weighting, and
`is a modal overlap factor. In
`the case of bound-mode reflection from an unblazed grating,
`it is simply the fraction of modal power in the photosensitive
`region of the fiber index profile. If the grating has low
`reflectivity, then (3) can be linearized and the reflectivity
`spectrum
`will be proportional to the Fourier
`transform of
`. A good guide to choosing a suitable
`amplitude weighting for a given filter characteristic is to begin
`) is
`with this relationship. The reflectivity at line center (
`
`(2)
`
`(5)
`
`Both the average refractive index and the envelope of
`the grating modulation, and therefore the modal index
`,
`usually vary along the grating length. The contrast, which is
`determined by the visibility of the UV fringe pattern, is given
`by the parameter
`.
`The local reflectivity
`is the complex ratio of the
`forward and backward going wave amplitudes. It is related
`by a multiplicative phase factor
`. The modified
`to
`reflectivity satisfies an equation of the form
`
`subject to the boundary condition
`coefficient
`is given by
`
`(3)
`
`. The coupling
`
`(4)
`
`, or
`where we neglected the chirping introduced by
`taken it to be a constant which offsets the line center, and
`adjusted the grating length by the average value
`of the
`envelope weighting function. The reflectivity spectrum of
`a uniform grating can also be obtained from an analytic
`solution of (3) [3], [28]. It can be used to model an arbitrary
`grating by considering it to be a concatenated set of piecewise
`uniform sections and deriving a matrix transfer function for
`each section. The reflectivity spectrum is given by the matrix
`product of the set of transfer function approximations. Either
`modeling approach provides an accurate prediction of the
`reflectivity and the grating spectrum. Fig. 5 shows an example
`of the good agreement between the measured and computed,
`[in this case by integration of (3)], transmittance spectra.
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`(a)
`
`(b)
`
`Fig. 6. A strongly reflecting grating with a large index change (a) becomes saturated and (b) after a long exposure and the spectrum broadens because the
`incident wave is completely reflected before reaching the end of the grating. A strongly saturated grating is no longer sinusoidal, the peak index regions are
`flattened and the valleys in the perturbation index distribution are sharpened. As a result, second order Bragg reflection lines (c) are observed at about one-half
`the fundamental Bragg wavelength and at other shorter wavelength for higher order modes. Computed second-order wavelength is shown in parenthesis.
`
`(c)
`
`When a grating is formed with a saturated exposure, then
`the effective length will be reduced as the transmitted signal is
`depleted by reflection. As a result, the spectrum will broaden
`appreciably and depart from a symmetric sinc or Gaussian-
`shape spectrum whose width is inversely proportional to the
`grating length. This is illustrated in Fig. 6(a) and (b). In
`addition, the cosinusoidal shape of the grating will distort into
`a waveform with steeper sides. A second-order Bragg line
`[Fig. 6(c)] will appear from the new harmonics in the Fourier
`spatial spectrum of the grating.
`Another feature which is observed in strongly reflecting
`gratings with large index perturbations are small sharp spectral
`resonances on the short wavelength side of the grating line
`center. They are due to the self-chirping from
`. These
`features do not occur if the average index change is held
`constant or adjusted to be constant by a second exposure of
`the grating [19], [21].
`A Bragg grating will also couple dissimilar modes in reflec-
`tion and transmission provided two conditions are satisfied:
`1) phase synchronism and 2) sufficient mode overlap in the
`region of the fiber that contains the grating. The phase-
`matching condition, which ensures a coherent exchange of
`energy between the modes, is given by
`
`(6)
`
`where
`is the modal index of the incident wave and
`is the modal index of the grating-coupled reflected (a negative
`
`Fig. 7. Phase-matching conditions to achieve synchronous mode coupling
`with a fiber Bragg grating. The ratio of the wavelength  and the grating pitch
` z along the fiber axis determines which type of mode (cladding or bound,
`backward or forward-propagating) is excited by the forward-propagating,
`incident LP01 fundamental mode.
`
`quantity) or transmitted wave. Note, that we have explicitly
`allowed for a tilt or blaze in the grating by using the grating
`in this equation. A useful way
`pitch along the fiber axis
`to understand this requirement and its importance is to show
`the mode-coupling, phase-matching requirement graphically
`(Fig. 7).
`In this illustration, we show five different types of interac-
`tions that can occur, depending on the ratio of the wavelength
`and pitch of the grating. Ordinary bound-mode propagation
`occurs when the effective index of the wave lies between
`the cladding and core values. A grating that reflects a like
`mode couples waves between the upper, forward-propagating
`
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`Fig. 8. Transmission spectrum of a grating in a single mode de-
`pressed-cladding fiber (AT&T Accutether) showing the fine-structure, cladding
`mode resonances on the short-wavelength side of the LP01–LP01 Bragg line.
`
`branch of the dispersion relation, to its lower negative-going,
`mirror image. This situation occurs when the grating has a
`pitch sufficiently fine that the Bragg condition (1) is obeyed.
`However, this same grating will also couple to other modes at
`shorter wavelengths; some will be reflected and or absorbed,
`and others will be radiated away from the fiber. The dotted line
`(not to scale) is a locus of wave-coupling between a forward-
`going fundamental mode and modes within the cladding. These
`interactions are seen as a series of many transmission dips
`in the spectrum at wavelengths that are less than the Bragg
`wavelength (Fig. 8) [31], [33]. No cladding modes are excited
`in a single mode-fiber unless the effective index of the excited
`mode is less than the cladding
`(with a simple matched
`cladding profile).
`Another, quite useful situation arises if the grating period is
`much coarser. Now the fundamental mode exchanges energy
`in a resonant fashion with a forward-going cladding mode.
`The effect is similar to mode coupling in a two-core fiber or
`between modes in a multimoded waveguide. These gratings
`can be made easily with a simple transmission mask because
`the required pitch is a few hundred microns, as contrasted with
`the fine submicron pitch that is required to reflect a bound
`mode [25].
`If the grating is tilted or radially nonuniform, then inter-
`actions will take place between symmetric and asymmetric
`modes (Fig. 9) [33]. For example, the grating can be used to
`couple the fundamental to the next lowest order mode (Fig. 10)
`[34], [35], as shown on the right side of Fig. 7.
`
`VI. APPLICATIONS
`The characteristics of photosensitivity technology and its
`inherent compatibility with optical fibers has enabled the
`fabrication of a variety of different Bragg grating fiber devices
`including novel devices that were not possible previously. The
`FBG dispersion compensator is a good example of this latter
`type device. FBG’s have also been incorporated in optical
`devices simply to act as a reflector thereby transforming the
`device into a practical component with enhanced performance.
`The semiconductor laser with a pigtail containing an FBG
`is an example of this type of application. Although research
`has concentrated on the development of Bragg grating-based
`
`Fig. 9. Transmission spectrum of blazed grating (4.36 effective tilt angle
`within the core) in depressed-cladding fiber showing pronounced coupling
`into the asymmetric LP16 backward-propagating cladding mode. A tilt in the
`grating index profile also reduces the strength of the LP01–LP01 reflection and
`produces a series of additional higher order asymmetric cladding-mode lines.
`
`Fig. 10. Transmission spectrum of a fiber grating formed with a tilted (0.9
`from normal to fiber axis) fringe pattern.
`
`fiber devices for use in fiber optic communications or fiber
`optic sensor systems, there are other potential applications
`in lidars, optical switching, optical signal processing, and
`optical storage. In the following, we list in table format the
`applications that have employed fiber Bragg gratings. Only a
`few of the applications are described in more detail.
`Table I lists a number potential applications for fiber Bragg
`gratings in fiber optic communications. A particularly exciting
`application is the Bragg grating dispersion compensator. As a
`light pulse propagates down an optical fiber, it is dispersed,
`that is the width of the pulse broadens because the longer
`wavelength light lags the shorter wavelength light. Conse-
`quently, at sufficiently high data rates and/or fiber lengths,
`the pulses in a data stream will begin to overlap. In this
`way, fiber dispersion limits the maximum data that can be
`transmitted through a fiber. The principles underlying the
`operation of the FBG dispersion compensator are as follows.
`A dispersed light pulse with the longer wavelengths lagging
`the shorter wavelengths is incident on a chirped fiber grating.
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`TABLE I
`TELECOMMUNICATION APPLICATIONS
`
`APPLICATION
`
`Dispersion compensation
`Wavelength selective devices
`Band-rejection filters, long-period gratings
`Fiber taps
`Fiber erbium amplifiers
`Network monitoring and optical fiber identification
`Cascaded Raman amplification at 1.3 m
`Fiber lasers
`Semiconductor lasers with external Bragg grating reflector
`
`REFERENCES
`[22], [36], [37], [38], [39], [40]
`[41]–[47]
`[25]
`[48]
`[49]–[56]
`[57]–[59]
`[60]
`[61]–[72]
`[73]–[76]
`
`TABLE II
`OTHER APPLICATIONS
`
`APPLICATION
`Optical fiber mode converters; spatial mode converters, polarization mode converters
`Grating-based sensors
`Optical single processing; delay line for phased array antennas, fiber grating compressor
`Nonlinear effects in fiber Bragg gratings; optical Switching, electrooptic devices, wavelength
`conversion devices
`Optical storage; holographic storage, direct writing
`
`REFERENCES
`[23], [13], [76]
`[7]
`[77]–[81]
`[82], [83]
`
`[84], [85]
`
`The longer wavelength light is reflected near the front of the
`grating whereas the shorter wavelength light is reflected near
`the back. Thus, the short wavelengths are delayed relative to
`the longer wavelengths. The chirped grating can be designed
`so that all wavelengths in the light pulse exit the reflector
`at the same time and the dispersion in the optical pulse in
`equalized. This picture is actually too simple. In reality, the
`relative light pulse delay as a function of wavelength is not
`linear but has an oscillatory behavior [36]. However, this
`delay characteristic can be linearized by suitably profiling or
`apodizing the amplitude profile of the grating [37]. In order
`to make a practical device, the chirped Bragg grating must be
`operated in the reflection mode. This can be accomplished by
`incorporating the chirped grating in an optical circulator or a
`Mach–Zehnder (MZ) interferometer. The use of chirped Bragg
`gratings for dispersion compensation have been demonstrated
`in several laboratories [38]–[41].
`There are several possible applications for fiber gratings that
`are not related to telecommunications; some of these are listed
`in Table II. The most promising application FBG is in the field
`of optical fiber sensors. In fact, the number of fiber gratings
`that are used in this application may exceed that of all other
`applications. In the following, we describe in more detail the
`application of fiber gratings to sensors. We also discuss mode
`converters because of their potential use in FBG sensors.
`
`VII. MODE AND POLARIZATION CONVERTERS
`A resonant interaction that produces efficient bound-mode
`conversion within a fiber is enabled by a periodic index
`perturbation with a pitch that satisfies the Bragg condition
`for backward or forward synchronous interaction and the cor-
`rect azmuthial variation to couple symmetric and asymmetric
`modes. A simple example is the reflection of the LP11 mode
`by a grating which is slightly tilted (Fig. 10) [34], [35].
`In a fiber with a depressed index cladding, very efficient
`mode conversion is observed (Fig. 9) between an incident
`fundamental mode and a higher-order cladding mode which
`
`Fig. 11. Radial field distributions of the LP16 cladding mode and LP11
`isolated “core” mode at the LP01–LP16 resonance wavelength.
`
`Fig. 12. Bragg wavelength shift due to UV-induced birefringence (data
`provided by D. R. Huber). The resonances for two orthogonal polarizations,
`oriented parallel and perpendicular to the polarization of the UV beam, are
`displaced by about 0.025 nm.
`
`has a field distribution within the core that approximates an