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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
Abstract
ω = ω1
Short-Period Grating
2π/A
−β01
0
β(2) β(1)
ncl ω
C
β01
ω = ω2, ω2 < ω1
2π/A
−β01
0
β(2) β(1)
β01
Figure 1: Phase matching considerations for short- and longperiod gratings.
1600
Wavelength (nm)
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.
12
IEEE LEOS NEWSLETTER
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 LP01 ↔ LP11 mode
conversion [6], LP01 ↔ LP02 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.
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Principle of Operation
Consider a single-mode fiber with the propagation constant of
the fundamental mode, LP01 , denoted by β01 and the propagation constants of the cladding modes given by β cl(n) , where
the superscript denotes the order of the mode. The relative
positions of the propagation constants (for a given
ω, ω = ω1 ) 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 cl(n) 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 −β01 ) 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
β01 − β cl(n) =
2π
(1)
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 = ω2 where ω2 < ω1 )
the axis now shrinks [Figure 1] and the original periodicity that coupled the LP01 mode to the first
cladding mode now supports the phase matching
condition for the second cladding mode. This pictorial description implies that for a given periodicity one can induce mode-coupling between the fundamental mode and several different cladding modes, a
property that manifests itself as a set of spiky losses
at different wavelengths in the transmission spectrum. For another frequency, ωcut (ωcut > ω1 ) one
can visualize the K-vector of the grating coupling the
guided mode to the edge of the radiation mode continuum. This optical frequency ωcut corresponds to a
minimum wavelength, λcut , 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
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-
KrF Laser
Broadband
Source
AM
PC
Fiber
Fiber
Optical
Spectrum
Analyzer
Figure 3: Experimental setup for long-period grating fabrication.
AM: Amplitude mask. PC: Polarization controller.
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0
0
A
B
−5
C
Transmission (dB)
Transmission (dB)
−4
−8
D
−12
−16
−10
−15
−20
−25
−30
E
−20
1520
1540
1560
1580
1600
−35
1475
1620
Wavelength (nm)
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.
1492
1509
1526
Wavelength (nm)
1543
1560
Figure 6: Transmission spectrum of a band-rejection filter.
0
1670
−5
Transmission (dB)
Peak Wavelength (nm)
1640
1610
1580
1550
−10
−15
1520
−20
900
1490
0
1
2
Time (h)
3
4
1000
1100
1200
1300
1400
Wavelength (nm)
Figure 5: Effect of annealing (@ 150°C) on peak wavelengths of a
long-period grating.
Figure 7: Transmission spectrum over a broad wavelength range
shows the various LP0m cladding modes to which the fundamental
guided mode couples.
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,
λcut , 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, λcut 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 λcut . We consider the transverse component of the
propagation constant of the cladding mode κ. This component
satisfies the condition
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β cl2 + κ 2 =
ω2 n2cl
c2
(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, J0 (κ acl ) where acl 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 J0 (x), denoted by
δx0 , can be approximated by δx0 ≈ π [14], the δλ’s will correspond to the condition κ acl = 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 λcut . Using (1) and (2), we arrive at the
expression
(λp − λcut ) ≈
λp λ2cut
p2
. 2
8n cl (neff − n cl ) acl
(3)
where neff is the effective index of the guided LP01 mode
(β01 = 2πneff /λ). In deriving (3), we have assumed that the
effective index of the fundamental mode at λp and λcut 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 λp and λcut are in close
proximity. The wavelength separation between the pth and the
(p + 1)th-mode can then be approximated by
δλp, p+1 ≈
(2p + 1)
λ3cut
.
.
8n cl (neff − n cl )
a2cl
(4)
As an example, we consider a DSF with a long-period grating
with the following properties: = 550 μm, λcut = 1.41 μm
and predict the wavelength separation between the first two
cladding modes δλ1 to be 65 nm. Our experiments show that
the separation of wavelengths between the first and second
modes, δλ1 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 LP01 mode
given
by [16]
is then
2
δ
2
sin κ gL 1 + κg
P(n)
cl (L)
(5a)
=
2
P01 (0)
δ
1 + κg
where δ is the detuning parameter
δ=
1
2π
β01 − β cl(n) −
2
(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
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Page 16
1600
0
1500
−5
1400
Transmission (dB)
Wavelength (nm)
21leos03.qxd
1300
1200
1100
−10
−15
−20
−25
1000
900
150 200 250 300 350 400 450 500 550 600
−30
1230
Grating Period (μm)
1260
1290
1320
1350
1380
Wavelength (nm)
Figure 8: Experimentally obtained template to determine choice of
grating periodicities for transmission dips at various wavelengths.
Plot is for annealed gratings.
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/cm2 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 × 1.1 cm2 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% H2 /D2 and the number of gratings that could be
batch-produced was limited primarily by beam dimensions.
Backreflection (dB)
−88
−91
−94
−97
190
195
200
205
Distance (mm)
210
Annealing
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 =
0.8λ2
.
L(neff − n cl )
(6)
Using the earlier example of a DSF with a grating with
= 550 μm, L = 2.54 cm, and λcut = 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.
16
IEEE LEOS NEWSLETTER
UV-induced index changes in D2 /H2 loaded fibers occur when
dissolved D2 /H2 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 D2 /H2 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 H2 sensitized fiber. The rapid wavelength shift in the first
several hours is primarily associated with the outgassing of
residual H2 , while the more subtle long term changes are caused
by the gradual decay of UV-induced defects.
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Properties
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.
Output Power (dBm)
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 λp = 1517 nm, the 20 dB isolation point is
4 nm wide, the 3 dB point (λ) is 22 nm, and the
−30
insertion loss is < 0.20 dB for wavelengths < 1480
>
1545
nm and
nm. Viewed over a broader wavelength range, a typical spectrum is shown in Figure
7 (for a FLEXCOR fiber with = 198 μm) which
−40
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
−50
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 short−60
period 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
−70
are consistent with our estimate (based on detailed
growth and annealing experiments) of maximum
UV-induced n of 5 × 10−4 . A measurement of
−80
polarization properties of these devices shows the
950
<
0.01
polarization mode dispersion (PMD)
ps and
polarization dependent loss (PDL) < 0.02 dB.
Applications
June 2007
1000
1025
Wavelength(nm)
(a)
−35
Transmission (dB)
0
−45
Output Power (dBm)
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.
975
−1
−2
−3
−4
−5
950
−55
975 1000 1025 1050
Wavelength (nm)
−65
−75
950
975
1000
1025
Wavelength(nm)
(b)
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].
IEEE LEOS NEWSLETTER
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1590
1560
1.5
1588
1557
1586
1584
1551
1.0
1582
Wavelength (nm)
Wavelength (nm)
A
1554
1580
1530
1528
2.0
1526
1548
1545
1273
1270
1267
B
1264
1524
1261
2.5
1522
1258
1255
1520
0
20
40
60
80
100
120
140
Temperature (°C)
0.0
0.2
0.4
0.6
Strain (%)
0.8
1.0
Figure 12: Effect of grating length on temperature dependence.
Numbers indicate lengths of gratings in centimeters.
Figure 13: Effect of strain on the peak wavelength of two different
gratings.
Environmental Effects
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
λ1 = 1479.0 nm, λ2 = 1510.2 nm, and λ3 = 1564.2 nm,
corresponding to the coupling of the LP01, core , to the LP01, cl ,
LP02, cl , and LP03, 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 LP02, cl mode (with two
intensity peaks spread further into the cladding) than the
more tightly confined LP01, cl mode. These observations add
another consideration to grating design if recoating is a neces-
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 β01 and β cl(n) 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
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Page 19
sary step during packaging. For minimum spectral shifts after recoating, one
should choose the grating periodicity
such that the LP01, c o re 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. JacobovitzVeselka 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
[1]
[2]
M.C. Parries, C.M. Ragdale,
and D.C.J. Reid, “Broadband
chirped fiber Bragg filters for
pump rejection and recycling in
erbium doped fiber amplifiers,”
Electron. Lett., vol. 28, pp.
487–489, 1992.
P.J. Lemaire, R.M. Atkins, V.
Mizrahi, and W.A. Reed, “High
pressure hydrogen loading as a
technique to achieving ultrahigh uv-photosensitivity and
June 2007
thermal sensitivity in GeO 2
doped optical fibers,” Electron.
Lett., vol. 29, pp. 1191–1193,
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[3] G. Meltz, W.W. Morey, and
W.H. Glenn, “Formation of
Bragg gratings in optical fibers
by transverse holographic
method,” Opt. Lett., vol. 14, pp.
823–825, 1989.
[4] G.A. Ball and W.W. Morey,
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[5] V. Mizrahi, D.J. DiGiovanni,
R.M. Atkins, S.G. Grubb, Y.K. Park, and J.-M. Delavaux,
“Stable single mode erbium
fiber grating laser for digital
communication,” J. Lightwave
Technol.,
vol.
11,
pp.
2021–2025, 1993.
[6] K.O. Hill, B. Malo, K.
Vineberg, F. Bilodeau, D.
Johnson, and I. Skinner,
“Efficient mode-conversion in
telecommunication fiber using
externally written gratings,”
Electron. Lett., vol. 26, pp.
1270–1272, 1990.
[7] F. Bilodeau, K.O. Hill, B. Malo,
D. Johnson, and L. Skinner,
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