Long-Period Fiber Gratings as Band-Rejection Filters

Special 30th Anniversary 

Long-Period Fiber Gratings as Band-Rejection Filters 

Ashish M. Vengsarkar, Paul J. Lemaire, Justin B. Judkins, Vikram Bhatia, 

Turan Erdogan, and John E. Sipe 

Reprint of most cited article from Journal of Lightwave Technology - Vol. 14, No. 1, pp 58-65 

ω = ω 1 

ω = ω 2 , ω 2 < ω 1 

Short-Period Grating 

2π/A 

−β 01 0 β (2) β (1) n cl 

ω β 01 

C 

2π/A 

−β 01 0 β (2) β (1) β 01 

Figure 1: Phase matching considerations for short- and longperiod 

gratings. 

Wavelength (nm) 

1600 

1500 

1400 

1300 

1200 

1100 

1000 

900 

150 200 250 300 350 400 450 500 550 600 

Grating Period (μm) 

Figure 2: Theoretical determination of the relationship between 

grating periodicity and wavelengths where guided-to-cladding 

mode coupling takes place for an AT&T dispersion shifted fiber. 

MANUSCRIPT RECEIVED APRIL 21, 1995; REVISED MAY 30, 1995. 

A.M. VENGSARKAR AND P.J. LEMAIRE ARE WITH AT&T BELL 

LABORATORIES, MURRAY HILL, NJ 07974 USA. 

J.B. JUDKINS WAS WITH THE DEPARTMENT OF ELECTRICAL 

ENGINEERING, UNIVERSITY OF ARIZONA, TUCSON, AZ 85723 USA. HE 

IS NOW WITH AT&T BELL LABORATORIES, MURRAY HILL, NJ 07974 USA. 

V. BHATIA IS WITH THE BRADLEY DEPARTMENT OF ELECTRICAL 

ENGINEERING, VIRGINIA TECH, BLACKSBURG, VA 24061 USA. 

T. ERDOGAN IS WITH THE INSTITUTE OF OPTICS, UNIVERSITY OF 

ROCHESTER, ROCHESTER, NY 14627 USA. 

J.E. SIPE IS WITH THE DEPARTMENT OF PHYSICS, UNIVERSITY OF 

TORONTO, ONT. M5S 1A7, CANADA. 

PUBLISHER ITEM IDENTIFIER: S 0733-8724(96)00701-3. 

Abstract 

We present a new class of long-period fiber gratings that can be 

used as in-flber, low-loss, band-rejection filters. Photoinduced 

periodic structures written in the core of standard communication-grade 

fibers couple light from the fundamental guided 

mode to forward propagating cladding modes and act as spectrally 

selective loss elements with insertion losses < 0.2 dB, 

backreflections < −80 dB, polarization-mode-dispersions < 

0.01 ps and polarization-dependent-losses < 0.02 dB. 

Introduction 

Optical fiber communications systems that use optical amplifiers 

are increasingly seeking high-performance devices that 

function as spectrally selective filters. For example, ASE filters 

that improve noise figure in erbium doped fiber amplifiers and 

band-rejection filters used to remove unnecessary Stokes’ 

orders in cascaded Raman amplifiers should have low insertion 

losses and low back-reflections. In addition, they must be relatively 

inexpensive to mass-produce and should be compact 

after packaging. While bulk-optic filters and short-period 

Bragg gratings [1] can be used for some of the applications, all 

the aforementioned requirements are rarely met. In this paper, 

we present photoinduced, long-period fiber gratings that can 

be used as low-loss, in-fiber band-rejection filters. 

The fabrication principle is based on the ability to induce 

large index changes in hydrogen loaded germanosilicate fibers 

by exposing the cores to ultraviolet (UV) light, typically, in the 

242–248 nm range [2]. This technology has been successfully 

used for making Bragg-type fiber gratings [3] (periodicities 

less than a micron) that are increasingly being used as reflectors 

and in the fabrication of high-efficiency fiber lasers [4], [5]. 

Long-period fiber gratings with periodicities in the hundreds 

of microns have been used in the past for coupling from one 

guided mode to another. For example, a blazed grating in a 

two-mode fiber has been used to induce an LP 01 ↔ LP 11 mode 

conversion [6], LP 01 ↔ LP 02 mode converters have been 

demonstrated [7], and rocking filters have been written in single-mode 

fibers for polarization mode conversion [8], [9]. 

In this paper, we describe periodic structures that couple the 

guided fundamental mode in a single-mode fiber to forwardpropagating 

cladding modes. These modes decay rapidly as they 

propagate along the fiber axis owing to scattering losses at the 

cladding-air interface and bends in the fiber. Since the coupling 

is wavelength-selective, the fiber grating acts as a wavelengthdependent 

loss element. In the subsequent sections, we describe 

the principle of operation of such gratings, develop a theory and 

present experimental results. We also evaluate their stability to 

strain, temperature, recoating, and bends. 

12 IEEE LEOS NEWSLETTER June 2007

Principle of Operation 

Consider a single-mode fiber with the propagation constant of 

the fundamental mode, LP 01 , denoted by β 01 and the propagation 

constants of the cladding modes given by β (n) 

cl , where 

the superscript denotes the order of the mode. The relative 

positions of the propagation constants (for a given 

ω, ω = ω 1 ) are shown in Figure 1. The hatched region 

extending from 0 to n cl ω/c represents the continuum of radiation 

modes that exist for an infinite cladding. We restrict this 

analysis to a purely rectangular index modulation along the 

fiber with the periodic index structure being perpendicular to 

the fiber axis. These assumptions exclude blazed gratings and 

as a result modal overlap conditions dictate that the fundamental 

guided mode can couple only to those cladding modes 

that are azimuthally symmetric with a central peak at r = 0. 

The ordinals of β (n) 

cl reflect this assumption. 

In order to couple from a forward propagating guided 

mode to backward propagating (guided or radiation) modes 

the phase matching K-vector is large, thus requiring a shortperiod 

grating. Examples of these gratings are Bragg-reflectors 

(for coupling to a back-propagating guided mode, denoted 

by −β 01 ) or blazed/tilted gratings (for coupling to backpropagating 

radiation modes). 

The phase matching condition between the guided mode 

and the forward propagating cladding modes is given by 

β 01 − β (n) 

cl 

= 2π 

(1) 

fiber at a specific wavelength. We then obtain a set of periodicities 

(n) that will meet the phase-matching condition given 

by (1). This step is then repeated for several different wavelengths; 

the resulting plot of coupling-wavelength versus 

grating-period is shown for an AT&T dispersion-shifted fiber 

(DSF) in Figure 2. One can choose a grating period such that 

mode coupling takes place at any desired wavelength. Further, 

the choice of ’s also allows the designer to vary the separation 

between two cladding modes, denoted by δλ. 

The AT&T DSF was modeled by using an exact refractive 

index profile in the mode-parameter calculation program 

developed by Lenahan [10]. The method of solution 

involved a finite element approach that reduced Maxwell’s 

equations to standard eigenvalue equations and an eigensystem 

package (EISPACK) computed the desired propagation 

parameters for the guided mode. The cladding mode propagation 

constants were calculated using the eigenvalue equa- 

Broadband 

Source 

PC 

Fiber 

KrF Laser 

Fiber 

Optical 

Spectrum 

Analyzer 

Figure 3: Experimental setup for long-period grating fabrication. 

AM: Amplitude mask. PC: Polarization controller. 

AM 

where is the grating periodicity required to couple 

the fundamental mode to the nth-cladding mode. In 

this case, the phase matching vector is short resulting 

in a long , typically on the order of hundreds of 

microns. For another ω, (ω = ω 2 where ω 2 ω 1 ) one 

can visualize the K-vector of the grating coupling the 

guided mode to the edge of the radiation mode continuum. 

This optical frequency ω cut corresponds to a 

minimum wavelength, λ cut , at which the grating can 

couple the fundamental mode to the radiation 

modes. This parameter is used to describe grating 

behavior in the subsequent analysis. 

Theory 

One can now predict the wavelengths at which 

mode-coupling will be enabled by a particular grating 

period. The first step in our modeling approach 

involves the calculation of the propagation constants 

of the guided and the various cladding modes of a

0 

−4 

A 

B 

C 

0 

−5 

Transmission (dB) 

−8 

−12 

−16 

D 


−10 

−15 

−20 

−25 

−20 

1520 1540 1560 1580 1600 1620 


Figure 4: Growth of a long-period grating as a function of time. A: 

1 min, B: 2 min, C: 3 min, D: 4 min, E: 5 min. 

E 

−30 

−35 

1475 1492 1509 1526 1543 1560 


Figure 6: Transmission spectrum of a band-rejection filter. 

1670 

0 

1640 

−5 

Peak Wavelength (nm) 

1610 

1580 

1550 


−10 

−15 

1520 

1490 

0 1 2 3 4 

Time (h) 

Figure 5: Effect of annealing (@ 150°C) on peak wavelengths of a 

long-period grating. 

tions [11] for a simple multimode step-index structure (of 

diameter 125 μm) ignoring the effect of the core. The 

curves in Figure 2, thus, are not accurate indicators of the 

exact wavelengths at which coupling occurs and are to be 

used merely as a guideline. They summarize the behavior of 

the grating peak wavelengths and separation and their 

dependence on different periodicities. For example, to 

obtain a δλ > 100 nm for a grating peaked at 1550 nm one 

would use a period of 200 μm, while for a δλ < 50 nm a 

grating period of 500 μm may be desirable. The curves are 

highly sensitive to small variations in effective indexes of 

the different modes. The wavelength difference δλ between 

the modes can also be calculated using a simplified approximation, 

as described below. The minimum wavelength, 

−20 

900 1000 1100 1200 1300 1400 


Figure 7: Transmission spectrum over a broad wavelength range 

shows the various LP 0m cladding modes to which the fundamental 

guided mode couples. 

λ cut , at which guided-to-radiation mode coupling is possible 

(for an infinite cladding) was calculated from the phasematching 

condition of (1) and the procedure outlined in 

[12] using an equivalent step-index model for the DSF. The 

result is given by the dashed curve in Figure 2, which shows 

that for any given periodicity, λ cut is less than the wavelengths 

at which the cladding-mode coupling takes place. 

This observation is consistent with the phase-matching diagrams 

of Figure 1. 

Another method of calculating the wavelength separation 

between the different cladding modes makes use of the wavelength 

λ cut . We consider the transverse component of the 

propagation constant of the cladding mode κ. This component 

satisfies the condition 


βcl 2 + κ2 = ω2 n 2 cl 

(2) 

c 2 

where n cl is the refractive index of the cladding. Assuming a 

simple step-index profile, the axially symmetric cladding 

modes that are nonzero at the origin are described by Bessel 

function of order zero, namely, J 0 (κ a cl ) where a cl is the 

cladding radius. The difference in the wavelengths at which 

the guided mode couples to the different cladding modes, δλ, 

correspond to the separation of the zeros of the Bessel function 

[13]. Since the difference in the zeroes of J 0 (x), denoted by 

δx 0 , can be approximated by δx 0 ≈ π [14], the δλ’s will correspond 

to the condition κ a cl = πp where p is an integer. The 

expression for δλ is obtained in an indirect manner, as follows. 

We first find the separation in wavelength between the 

pth-cladding mode and λ cut . Using (1) and (2), we arrive at the 

expression 

λ p λ 2 cut 

(λ p − λ cut ) ≈ 

8n cl (n eff − n cl ) . p2 

a 2 (3) 

cl 

where n eff is the effective index of the guided LP 01 mode 

(β 01 = 2πn eff /λ). In deriving (3), we have assumed that the 

effective index of the fundamental mode at λ p and λ cut is the 

same. For an AT&T DSF, this approximation leads to an error 

< 2%. For the first few cladding modes one can further simplify 

the expression by assuming that λ p and λ cut are in close 

proximity. The wavelength separation between the pth and the 

(p + 1)th-mode can then be approximated by 

λ 3 cut + 1) 

δλ p, p+1 ≈ 

.(2p 

8n cl (n eff − n cl ) a 2 . (4) 

cl 

As an example, we consider a DSF with a long-period grating 

with the following properties: = 550 μm, λ cut = 1.41 μm 

and predict the wavelength separation between the first two 

cladding modes δλ 1 to be 65 nm. Our experiments show that 

the separation of wavelengths between the first and second 

modes, δλ 1 for the above example is 57 nm. 

The spectral dependence of the grating transmission can be 

approximately determined by using expressions derived in the 

literature [15] for codirectional mode-coupling. The ratio of 

power coupled into the nth-cladding mode to the initial power 

contained in the guided LP 01 [ mode √ is then given ] by [16] 

( ) 2 

sin 2 κ 

P (n) 

g L 1 + δ 

κ 

cl 

(L) 

g 

P 01 (0) = 

where δ is the detuning parameter 

δ = 1 2 

( ) 2 

(5a) 

1 + δ 

κ g 

{ 

β 01 − β (n) 

cl 

− 2π } 

 

(5b) 

κ g is the coupling constant for the grating and L is the grating 

length. The coupling constant κ g is proportional to the UVinduced 

index change and is typically increased to maximize the

1600 

0 

1500 

−5 


1400 

1300 

1200 

1100 


−10 

−15 

−20 

1000 

−25 

900 

150 200 250 300 350 400 450 500 550 600 

Grating Period (μm) 

−30 

1230 1260 1290 1320 1350 1380 


Figure 8: Experimentally obtained template to determine choice of 

grating periodicities for transmission dips at various wavelengths. 

Plot is for annealed gratings. 

Backreflection (dB) 

−88 

−91 

−94 

−97 

190 195 200 

Distance (mm) 

Figure 9: Optical coherence domain reflectometer (OCDR) trace 

showing the low back-reflection properties of the grating. 

power transfer to the cladding mode. Thus, n (and hence, κ g ) 

is increased until the condition κ g L = π/2 is met. Assuming 

complete transfer, the full width at half maximum (FWHM) λ 

of the spectral resonance defined by (5) is given approximately by 

λ = 

205 210 

0.8λ 2 

L(n eff − n cl ) . (6) 

Using the earlier example of a DSF with a grating with 

= 550 μm, L = 2.54 cm, and λ cut = 1.41 μm, we obtain 

from (6) a value of λ = 23 nm. Experimental results show 

this value to be in the 20–30 nm range for gratings with 

≈ 550–600 μm. 

Figure 10: Band rejection filter used in Raman amplifiers. 

Experiments 

Fabrication 

The experimental setup for grating fabrication is shown in Figure 

3. Hydrogen loaded germanosilicatc fibers were exposed to a KrF 

laser (λ = 248 nm) through an amplitude mask made of chromeplated 

silica. The optical threshold level for mask damage was 

≈100 mJ/cm 2 per pulse. Each grating imprint on the mask was 

one inch long, the duty cycle of the modulation structure was 

50% and grating periodicities ranged from 60 μm to 1 mm. 

Typical exposure conditions of energy = 250 mJ/pulse, pulse repetition 

frequency = 20 Hz and beam area = 2.6 × 1.1cm 2 were 

used. The transmission spectrum of the grating was actively monitored 

as the grating was being written. The peak loss and the 

peak wavelength increased as a function of time, as shown in 

Figure 4. Fabrication times were in the 5–10 min range for fibers 

with 2–3% H 2 /D 2 and the number of gratings that could be 

batch-produced was limited primarily by beam dimensions. 

Annealing 

UV-induced index changes in D 2 /H 2 loaded fibers occur when 

dissolved D 2 /H 2 reacts to form index-raising defects at Ge sites 

in the fiber core. After the UV-writing it is necessary to anneal 

the grating in order to stabilize its optical properties [17]. The 

anneal serves two purposes: 1) to outgas unreacted D 2 /H 2 which 

otherwise would raise the average index of the fiber and temporarily 

shift the grating peaks to longer wavelengths, and 2) to 

anneal out that portion of the UV-created sites which would be 

thermally unstable over long periods of time at normal operating 

temperatures. Appropriate anneal conditions will depend on 

the fiber and grating type, as well as on the anticipated operating 

temperature and the required stability of the grating device. 

Figure 5 shows results for the 150°C anneal of a grating written 

in a H 2 sensitized fiber. The rapid wavelength shift in the first 

several hours is primarily associated with the outgassing of 

residual H 2 , while the more subtle long term changes are caused 

by the gradual decay of UV-induced defects. 


Properties 

In Figure 6, we show the transmission spectrum of a strong 

grating of length 2.54 cm written with a grating period 

= 402 μm. The maximum loss is 32 dB at a peak wavelength 

λ p = 1517 nm, the 20 dB isolation point is 

4 nm wide, the 3 dB point (λ) is 22 nm, and the 

insertion loss is < 0.20 dB for wavelengths < 1480 

nm and > 1545 nm. Viewed over a broader wavelength 

range, a typical spectrum is shown in Figure 

7 (for a FLEXCOR fiber with = 198 μm) which 

clearly indicates the different cladding modes. 

Several different gratings with periodicities in the 

150–600 μm range were fabricated and the different 

peaks in the spectrum were categorized according to 

the different cladding mode orders. The experimental 

results of the complete DSF characterization are 

shown in Figure 8. One of the key features that distinguishes 

the long-period gratings from their shortperiod 

blazed counterparts is the ultra-low backreflection 

properties. An optical coherence domain 

reflectometer trace for a long-period grating is 

shown in Figure 9. The backreflection numbers 

are consistent with our estimate (based on detailed 

growth and annealing experiments) of maximum 

UV-induced n of 5 × 10 −4 . A measurement of 

polarization properties of these devices shows the 

polarization mode dispersion (PMD) < 0.01 ps and 

polarization dependent loss (PDL) < 0.02 dB. 

Applications 

The most common use of the long-period gratings is 

as a band-rejection filter and several applications 

have been explored. The grating of Figure 6 can be 

used as an ASE suppressor, presenting a near-transparent 

path to the pump (1480 nm) and signal 

wavelengths (> 1545 nm) in erbium-doped amplifiers. 

A band-rejection filter is also used to remove 

unnecessary Stokes’ orders in a cascaded Raman 

amplifier/laser [18]. For example, the grating of 

Figure 10 is used to reject extraneous 1310 nm light 

while simultaneously allowing the 1240 nm pump 

wavelength to be transmitted with minimum loss. 

The band-gap filling effect [19] seen in Bragg-grating 

stabilized 980 nm pump-diodes can also be 

countered using a small band-rejection filter at 

∼ 1 μm. This effect is shown in 

Figure 11, where the tendency of the laser to split its 

spectrum and lase at λ >980 nm (thus rendering it 

ineffective for erbium pumping applications) is 

curbed by the addition of the filter whose transmission 

spectrum is shown in the inset [20]. In coarse 

WDM applications, it is often critical to insert a 

cleanup filter after the demultiplexer (at the receiver 

end) to remove vestiges of the channel that is not 

being monitored. For a 1310/1550 nm system, we 

can fabricate this filter by splicing two gratings separated 

by a few nanometers in peak wavelength. 

Output Power (dBm) 

Output Power (dBm) 

−30 

−40 

−50 

−60 

−70 

With concatenation, we have fabricated devices with a 15 dB 

bandwidth of 20 nm, a 20 dB bandwidth of 10 nm 

(centered around 1555 nm), with an insertion loss < 0.20 dB 

at 1310 nm. 

−80 

950 975 1000 1025 

−35 

−45 

−55 

−65 

Wavelength(nm) 

Figure 11: Effect of band-rejection filters on grating-stabilized 

980 nm pump diodes. (a) Bragg-grating stabilized semiconductor pump diode 

shows a split in the spectrum. (b) The addition of a long-period grating moves 

the peak lasing wavelength toward 980 nm. Inset shows transmission spectrum 

of long-period grating [20]. 

June 2007 IEEE LEOS NEWSLETTER 17 


(a) 

0 

−1 

−2 

−3 

−4 

−5 

950 975 1000 1025 1050 


−75 

950 975 1000 1025 

Wavelength(nm) 

(b)

1590 

1588 

1.5 

1560 

1557 

1586 

1554 

A 


1584 

1582 

1580 

1530 

1528 

1526 

1524 

1522 

1520 

1.0 

2.0 

2.5 

0 20 40 60 80 100 120 140 

Temperature (°C) 


1551 

1548 

1545 

1273 

1270 

1267 

1264 

1261 

1258 

1255 

B 

0.0 0.2 0.4 0.6 0.8 1.0 

Strain (%) 

Figure 12: Effect of grating length on temperature dependence. 

Numbers indicate lengths of gratings in centimeters. 

Environmental Effects 

The characteristics of long-period fiber gratings are affected 

by external perturbations such as strain, temperature and 

bends. The effect is primarily due to a differential change 

induced in the two modes. More specifically, since the propagation 

constants β 01 and β (n) 

cl undergo dissimilar changes 

owing to a change in the external conditions, the difference 

between the two modes, β, is altered. For a fixed periodicity 

one has to shrink or stretch the β-axis of Figure 1, 

implying a shift in the wavelength of resonant coupling 

between the two modes. 

The temperature dependence of the peak wavelength in 

the transmission spectrum for four different lengths of 

gratings written in DSF’s is shown in Figure 12. The slope 

is found to vary from 0.04–0.05 nm/°C. We see that neither 

the length of the grating nor the peak wavelength significantly 

affects the temperature sensitivity and may further 

imply that the predominant factor responsible for the 

effect is the differential-mode propagation constant. By 

means of comparison, a Bragg grating peak wavelength 

shifts by about 1.1 nm for a 100°C change (slope ≈0,01 

nm/°C). The effect of strain on the grating is more 

dependent on the type of fiber. The variations in peak 

wavelengths with strain for two different fibers are plotted 

in Figure 13. Grating A exhibits a slope of −0.7 nrn/mε, 

while grating B has a slope of +1.5 nrn/mε. This dramatic 

dependence on the fiber type is currently being studied. 

In comparison, Bragg gratings Show a strain dependence 

of +1.0 to +1.8 nrn/mε. 

The effect of bending and recoating on long-period gratings 

is important from a practical viewpoint since it directly 

determines the packaging method of choice. Small bends 

in the fiber gratings can completely wash out the grating 

properties, with the peak isolation falling to less than 3 dB 

(from 20 dB) and the peak wavelength shifting to the shorter 

side. The loss and shift in the transmission dip is thought 

Figure 13: Effect of strain on the peak wavelength of two different 

gratings. 

to be due to two causes: 1) Bending the fiber destroys the 

constant reinforcement in the coupling between the core and 

the cladding modes since the cladding mode is being forced 

out at the cladding-air interface, and 2) Bending changes the 

effective cladding mode index thus tending to alter the 

wavelength characteristics. As a consequence, the package 

design should be chosen with no allowance for slack. This 

may also imply that these gratings cannot be routinely 

recoated and spooled, as may be desirable in some applications 

where packaging real-estate is at a premium. Recoating 

the gratings adds to the complexity of design, as we show 

below. 

Recoating the grating with a conventional polymer (used 

for recoating splices) reduces the peak isolation by as much as 

10 dB. The change in grating characteristics is ascribed to the 

absorptive nature of the coating which affects the cladding 

mode properties. One can use low-index polymer coatings currently 

being developed for cladding-pumped laser applications 

to maintain the guiding properties of the cladding. A 

low-index (n = 1.38) polymer coating was applied to a grating 

whose transmission spectrum had three peaks at 

λ 1 = 1479.0 nm, λ 2 = 1510.2 nm, and λ 3 = 1564.2 nm, 

corresponding to the coupling of the LP 01, core , to the LP 01, cl , 

LP 02, cl , and LP 03, cl modes, respectively. After recoating, the 

three peaks shifted by −0.4, −1.2, and −2.4 nm, respectively. 

The shift to shorter wavelengths is expected since the application 

of the coating raises the effective index of the cladding 

modes and from Figure 1, we can see that the β-axis needs to 

be stretched (ω ↑, λ↓) to match the grating vector to the 

differential propagation constants. The relative amplitudes of 

these shifts are consistent with the relative mode confinement. 

For example, it is reasonable to expect that the polymer coating 

will have a greater effect on the LP 02, cl mode (with two 

intensity peaks spread further into the cladding) than the 

more tightly confined LP 01, cl mode. These observations add 

another consideration to grating design if recoating is a neces- 


sary step during packaging. For minimum 

spectral shifts after recoating, one 

should choose the grating periodicity 

such that the LP 01, core mode couples to 

the first cladding mode. 

Conclusion 

We have presented a new class of 

long-period gratings that function as 

spectrally selective loss elements. 

Natural extensions of these gratings 

are in spectral shape-shifting applications, 

whereby the spectrum of an 

existing system can be modified with 

the use of these in-fibe’r devices. 

Gain-flattening devices for erbiumdoped 

liber amplifiers, and sensors 

for measuring strain, temperature, 

and refractive index have been 

demonstrated. Other applications 

such as switching and power monitoring 

are currently being explored. 

In summary, these all-fiber fillers are 

versatile devices with low insertion 

losses (< 0.2 dB), low back-reflections 

(< −80 dB), excellent polarization 

insensitivity (PMD < 0.01 ps, 

PDL < 0.02 dB) and midband peak 

losses (band rejection) reaching as 

high as 30 dB. 

Acknowledgment 

The authors would like to thank V. 

Mizrahi, K.L. Walker, and I.A. 

White for useful discussions, W.A. 

Reed for help in modeling fiber-dispersion 

curves, G. Jacobovitz- 

Veselka for providing the data in 

Figure 11, D.S. Gasper for 

PMD/PDL measurements, and S.G. 

Kosinski for recoating gratings. 

We are grateful to Photonetics, Inc., 

for the use of the high-sensitivity 

OCDR. 

References 

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and D.C.J. Reid, “Broadband 

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487–489, 1992. 

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“Tilted fiber phase gratings,” J. 

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Long-Period Fiber Gratings as Band-Rejection Filters

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