otf

ft

~wcw

Rdflttt

Design and tolerance analysis of a router with anamplified resonator and Bragg gratings

Carmen Vazquez, Salvador Vargas, and Jose Manuel Sanchez Pena

A novel ring resonator configuration with Bragg gratings is presented. The stability of this configurationis studied by a z-transform technique. A router design with a FWHM of 17 MHz, a 240-dB rejectionratio, and a 15-dB gain at the output port is reported. The influence of temperature and of fabricationtolerance on parameters of this router configuration implemented with fiber technology is reviewed.Deviations in design specification owing to parameter variations are studied and compensated for witha gain control of 2.4% in a specific design. © 2000 Optical Society of America

OCIS codes: 060.1810, 060.0060, 060.2340, 060.2320, 060.2360, 070.4340.

7

Bawvaran

1. Introduction

Nowadays ring resonators ~RR’s! are widely used inptical communication systems. Several applica-ions of RR’s, including routers in self-routingrequency-division multiple-access networks,1 as fil-

ters in optical frequency-division multiplexing trans-mission systems,2–4 and as converters fromrequency-shift to amplitude-shift keying modula-ion,5 have been reported. RR’s have also been used

with Bragg gratings2,6 as tuning filters.In Ref. 2 a RR with gain and Bragg gratings

RRGB! was proposed; its fundamental behavior as aavelength demultiplexer was analyzed and a spe-

ific design that uses integrated optics technologyas proposed.In this paper we study the general properties of the

RGB by the z-transform technique and analyze inetail its behavior as a wavelength router. The in-uence of parameter variations on design specifica-ions for a device based mainly on fiber opticechnology is also studied. The RRGB operates inhe coherent regime, so Tc .. t, where Tc is the source

coherence time and t is the loop transit time.The main features of this novel device are the ways

The authors are with Departamento Ingenierıa Electrica,Electronica y Automatica, Area Tecnologıa Electronica, Uni-versidad Carlos III, Avenida Universidad 30, Leganes 28911,Madrid, Spain. The e-mail address for C. Vazquez iscvazquez@ing.uc3m.es.

Received 28 July 1999; revised manuscript received 3 January2000.

0003-6935y00y121934-07$15.00y0© 2000 Optical Society of America

1934 APPLIED OPTICS y Vol. 39, No. 12 y 20 April 2000

in which RR periodicity is avoided because of theBragg grating transfer function8 and in which theFWHM is improved. These two features imply anincremental increase of free spectral range ~FSR! inthis device compared with a simple RR, so the num-ber of channels to be multiplexed is increased. An-other advantage is flexibility through gain variation,allowing deviations from device specifications to beovercome.

In this paper, Section 2 is devoted to explaininggeneral device performance; stability conditions arederived and a detailed study of transfer-function be-havior is carried out. Configurations of the deviceboth as a router and as a demultiplexer are consid-ered.

In Section 3 we describe the ways in which designspecifications depend on K ~an input-coupler couplingfactor! and H ~a parameter that takes into account

ragg grating reflectivity, the coupler inside the loop,nd amplifier gain!. In Section 4 we describe theays in which parameter deviations that are due toariances in temperature and component size toler-nces influence the performance of a RRGB as aouter. Most critical parameters are identified, andcompensation for the global effect is proposed. Fi-ally, the tuning process is also studied.

2. General Theory

In this section we derive a device transfer functionand use it to study the stability and influence of var-ious parameters on device performance. A sche-matic of the RRGB under study is shown in Fig. 1. Itis a simple RR with new transfer functions embeddedwithin the loop. To describe a generic device with N

sIm

g

E

B

transfer functions inside the loop, we can use thefollowing expressions:

E3

E15 ~1 2 g!1y2

Î1 2 K 2 H exp~2jbL!

1 2 HÎ1 2 K exp~2jbL!, (1)

E4

E15

jÎ~1 2 g! K

1 2 HÎ1 2 K exp~2jbL!, (2)

where E1 is the input amplitude to the coupler at port1 ~P1; Fig. 1!, E3 is the output amplitude at port 3~P3!, and E4 is the amplitude at port 4 ~P4!. K andg are the intensity coupling coefficient and the excessloss in intensity of coupler A, b is a propagation con-stant, L is the loop length, and H is defined as

H 5 ~1 2 g!1y2 exp~2aL!)i51

N

Fi, (3)

so it includes the loss factor ~1 2 g!1y2 exp~2aL!,where a is the amplitude loop attenuation coefficient,and the product of all functions of concatenated ele-ments inside the loop. Only forward transmission isconsidered, because, in Subsection 4.A below, we es-timate that backward reflections inside the loop ~ow-ing to inaccuracies in the intensity couplingcoefficient of coupler B! and backward amplifiedpontaneous emission of the amplifier are negligible.n any case, we can avoid them in a practical imple-entation by placing an isolator inside the loop,9

before transfer function F2.In the device proposed in this paper, only two func-

tions, gain and Bragg grating transmission through a3-dB coupler, are considered inside the loop. Thosefield transfer functions, Fi, are given by

F1 5 G1y2, (4)

F2 5 j2~1 2 g2!@K2~1 2 K2!#1y2r~l!, (5)

where G is the optical amplifier intensity gain and K2and g2 are the intensity coupling coefficient and theexcess loss in intensity of coupler B; r~l! is the Braggrating reflectivity, given by10

r 52jk sinh~gb Lb!

~ap 1 jDb!sinh~gb Lb! 1 g cosh~gb Lb!, (6)

Fig. 1. Configuration of the RRGB. Abbreviations are defined intext.

where k, ap, and Lb are the coupling factor, the losscoupling, and the length of the Bragg gratings, re-spectively, Db is the propagation constant’s deviationwith respect to its value at the main reflection point,and gb

2 5 k2 1 ~ap 1 jDb!2. To determine the de-vice’s stability we can apply the z-transform tech-nique if its transfer function generates constantdelays in the wavelength range of interest. This isaccomplished if the transfer-function phases are lin-ear functions of frequency. The first transfer func-tion, G, follows this rule. In the case of F2, the Bragggrating phases are linear at the central peak,10 sophase F2 is almost linear in the working range, as canbe seen from Fig. 2, with k 5 110 m21, ap 5 0, andLb 5 0.01 m. The principal effect of attenuation, ap,within transfer function F2 is a reduction in reflec-tivity in the central wavelength and less-distinct re-flectivity in the sidelobes. The first effect,attenuation of reflectivity at the central wavelength,has been considered in the device that we designedbecause we chose a nonideal value at a central wave-length of 0.8. The other effect, less-distinct reflec-tivity in the sidelobes, would improve the ratio ofrejection of adjacent channels, so is no restriction onusing the parameter ap 5 0. Commercially avail-able devices, however, have the other specificationslisted above.

The basic delay time, t, of the RRGB is equal to tr 1tb, where tr is the loop delay time and tb is the delaytime of F2, which includes a Bragg grating. Once afundamental delay time is defined, one can apply thez-transform technique to determine the stability ofthe system. To do so, we substitute exp@2j~bL 2/H!# 5 z21 into Eqs. ~1! and ~2! ~where /H is thephase of H!. After doing so, we find that poles of the

3yE1 and E4yE1 functions are located at zp 5 uHu~1 2K!1y2 and that the E3yE1 function also has a zero atzc 5 uHuy~1 2 K!1y2.

The system is stable if the transfer-function polesare located inside the unit circle, so it must followthat uHu , ~1 2 K!21y2 or K . 1 2 uHu22. So it can

Fig. 2. Intensity transfer function F2, with a maximum value ofragg grating reflectance of 0.65, K2 5 0.5, and g2 5 0.05.

20 April 2000 y Vol. 39, No. 12 y APPLIED OPTICS 1935

pwbd.iptwt ~

g

1

be inferred that the maximum and the minima arelocated as follows: At port P4 the maxima are lo-cated where exp@2j~bL 2 /H!# 5 11, so the optical

ath lengths are equal to integer multiples of theavelength. At port P3 the situation is different,ecause the locations of the maxima and the minimaepend on the value of uHu at that wavelength. If uHu1, the maxima are located at the same positions as

n port P4, but, if uHu , 1, the maxima are located inlaces where exp@2j~bL 2 /H!# 5 21. At this porthe transition from maximum to minimum happensith uHu 5 1, which is the point where transfer func-

ion E3yE1 has a constant amplitude.In our device the uHu value is a function of fre-

quency because the Bragg grating transfer functionalters the magnitude of F2, as can be seen from Eq.~5!. That is the reason for the aperiodicity of trans-fer functions at ports P3 and P4.

Previously it was shown that the RRGB can beused as a router1 if we work with uHu , 1 or as ademultiplexer with uHu . 1, with a FSR greater thana simple RR FSR. It is important to note that, forhigher rejection ratios between adjacent channels,the RR FSR must be at least a third of the Bragggrating’s FWHM; see Fig. 3.

The new FSR in our ideal device would be infinitebecause transfer function F2 attenuates all the chan-nels, apart from the device’s central wavelength. Ina real device the RRGB FSR is restricted by the tun-ing range of the Bragg gratings. In conventionalcommunication-grade fibers, their spectra typicallyshift by 3–10 nm for each 100 °C change in temper-ature. Newly designed long-period gratings, withair rings that have inside claddings made from poly-mer, can provide a tuning range of 50 nm when thetemperature is cycled from 20 to 80 °C.11 Thereforea 50-nm FSR is possible.

In the design analyzed in this paper, whose trans-fer functions are plotted in Fig. 4, a loop length of0.055 m is considered, with a RR FSR of 0.03 nm ~3.75GHz! and a Bragg grating FWHM of 0.09 nm. The

Fig. 3. Normalized intensity transfer functions: solid curve,Bragg grating; dotted curve, RR.

936 APPLIED OPTICS y Vol. 39, No. 12 y 20 April 2000

FSR of the RRGB is limited to the Bragg gratingtuning range, as indicated above.

The behavior of the RRGB as a router is illustratedin Fig. 4~a!, with uHu 5 0.993 ~a specific optical carrieris rejected!. If uHu 5 1 @Fig. 4~a!, inset#, all opticalcarriers pass through. The demultiplexer’s behav-ior is shown in Fig. 4~b!. From Fig. 4~b! it can beseen how the dependence of uHu on frequency causesa decrement in maxima adjacent to the central max-imum at port P3, even these can be transformed intominima.

3. Implementation of the RRGB Router

In what follows, we describe the design of the RRGBas a router, which means that it selects a specificoptical carrier when it is turned on, at port P4, whilethe other carriers pass through port P3 without at-tenuation. Device behavior is controlled by two pa-rameters, H and K. As we mentioned above, theRRBG behaves as a router if uHu , 1; if we also wantto have a reasonable opportunity to reject a selectedchannel at port P3, parameters must be chosen tolocate port P3 zero close to the port P4 pole. Thiscondition is accomplished at values of K3 0. Figure

Fig. 4. RRGB output power at port P3 ~solid curves! and port P4dotted curves! with K 5 0.014, a maximum reflectance of 0.65, g 5

2 5 0.05, and K2 5 0.5: ~a! router with G 5 1.7956 ~inset, uHu 51; G 5 1.8188!; ~b! demultiplexer with G 5 1.8442.

wramzgcaAalusb

FK

m

a

5, shows uHu values when zp and zc are equal to 1,designated uHpu and uHcu, respectively. Pole effectsthat cancel to zero at port P3, which is the case whenuHu 5 1, should be avoided. uHu, when it is modifiedwith amplifier gain G, can be used as the controlparameter. If we modify the value of uHu at theworking wavelength we can compensate for vari-ances from specified tolerances in design specifica-tions and select the device functionality ~router ordemultiplexer!. Design specifications of interest arethe FWHM and the output power of the rejected–selected channel at the working wavelength.

From Fig. 6 we can observe the FWHM and thepeak value at the working wavelength versus uHu,with K 5 0.014 and uHpu 5 1.007, which is the max-imum allowed value for a stable system. At port P3,when uHu 5 1 the central peak has a 0-dB value,

hereas for lower values of uHu this wavelength isejected @Fig. 6~b!#. The lowest output power valuet port P3 @Fig. 6~b!# is related to the uHu value thatakes the output power at port P3 become nearly

ero at the central wavelength. At port P4 the peakain increases monotonically while the FWHM de-reases monotonically. If we now fix the value of uHund change K, the device behaves analogously.gain, two distinct functions appear, as a router ands a demultiplexer. The value of K does not alter theocations of the maxima and the minima but it can besed to control device specifications. The only re-triction on the value of K is related to system sta-ility.From Fig. 7 we can see the dependence of the

WHM and the peak value at ports P3 and P4 on thevalue with uHu 5 0.993 ~with G 5 1.7956!. At the

design point, the RRBG operates as a router. In Fig.7~a! the FWHM at port P4 increases monotonicallyand the system is always stable for any K value,because as a router uHu , 1. However, at port P3,while the K value increases, a maximum FWHM isreached. Then the FWHM decreases until it disap-

Fig. 5. uHpu ~solid curve! and uHcu ~dotted curve! versus K, with aaximum reflectance of 0.65, g2 5 0.05, and K2 5 0.5. Inset,

zoom view of the figure.

pears, because the value of the minimum of the func-tion is greater than the half-maximum value. FromFig. 7~b! it can be observed that there are values of uHuat port P4 of constant output power. This propertyhas been used in designing a RR with tuning finesseand constant loss.3

In summary, it has been shown that device perfor-mance depends on the value of uHu.

For a router

uHu must be less than 1.K should tend to 0, which helps the device to move

nearer poles and zero location, defined by Eqs. ~1! and~2!, permitting greater gains at port P4 and highrejection ratios at port P3.

Graphic representations in Figs. 6 and 7 allow fil-ters to be designed with the desired specifications.

The RR FSR is must be at least equal to a third ofthe FWHM of Bragg gratings to permit reasonableratios of rejection between adjacent channels.

Once the device’s functionality is defined, its FWHMand its value at the working wavelength can be con-trolled through manipulation of K and uHu values.

Fig. 6. RRGB as a router with K 5 0.014 at port P3 ~solid curves!nd port P4 ~dotted curves!: ~a! FWHM versus uHu, ~b! peak value

versus uHu.

20 April 2000 y Vol. 39, No. 12 y APPLIED OPTICS 1937

t

udt

olK

op

Io

1

4. Device Tolerances

This device can be implemented with either of twotechnologies: integrated optics or optical fibers. Inthis section we study ways in which parameter vari-ations alter device specifications. Afterward, the de-pendence of the working wavelength on temperatureis also reported.

A. Parameter Variations

First we analyze the ways in which uHu depends onparameter variations when the device operates as arouter. Then we estimate the maximum deviationthat is due to variations in component size tolerancesand temperature for each parameter, and the param-eters with a greater effect on uHu are identified. Thenext step is to determine the influence of these pa-rameters on device specifications. Finally, the worstcase is described, with the influence of all parameterstaken into account simultaneously. This procedureis also done with constant uHu and with K as theuning parameter.

The tolerance study is important because it helpss to estimate specification tolerances of fabricatedevices, depending on the basic elements of whichhey are composed. Our tolerance study is focused

Fig. 7. RRGB as a router with G 5 1.7956 at port P3 ~solid curves!and port P4 ~dotted curves!: ~a! FWHM versus K, ~b! peak valueversus K.

938 APPLIED OPTICS y Vol. 39, No. 12 y 20 April 2000

n the working design, which is defined by the fol-owing parameter values: K 5 0.014, g 5 g2 5 0.05,

2 5 0.5, G 5 1.7956, a 5 0.00002, and a fiber Braggreflectivity at a central wavelength of 0.8005. Thoseparameters are selected for optimum operation of thedevice as a router, with uHu 5 0.993. At this point ofoperation, rejection ratios as high as 40 dB at port P3and gains of 15 dB at port P4 are obtained. Devia-tions are due mainly to two effects. The first is tem-perature, which modifies fiber length, couplingcoefficients, and excess loss and gain.12–15 The sec-nd is fabrication tolerances. The output powers atorts P3 and P4 are functions of uHu and K.

1. Analysis of uHu variationsFrom Eqs. ~1! and ~2! we observe that the factor ~1 2g!1y2 does not affect the rejection ratio or the FWHMat ports P3 and P4. So it can be considered a con-stant value. However, the peak values at ports P3and P4 depend on deviations in g, but these are sosmall that their effect is not relevant. So it is a goodapproximation to consider that ~1 2 g!1y2 is a con-stant factor. From Eqs. ~3!–~5! we see that uHu isgiven by

uH~l!u 5 2~1 2 g2!exp~2aL!ur~l!u

3 @GK2~1 2 g!~1 2 K2!#1y2. (7)

Analyzing parameter values, we see that the factorexp~2aL! depends on temperature variations, whichmodify the length. Once more, those changes aresmall, so the factor is considered equal to 1.

uHu variations that are due to the other parametersnear the design point are given by

]uHu]g

5 2F~1 2 K2!K2 G~1 2 g! G1y2

~1 2 g2!uru, (8)

]uHu]G

5 F~1 2 g!~1 2 K2!K2

G G1y2

~1 2 g2!uru, (9)

]uHu]g2

5 22@~1 2 g!~1 2 K2!K2 G#1y2uru, (10)

]uHu]K2

5 ~1 2 2K2!~1 2 g2! F ~1 2 g!G~1 2 K2!K2

G1y2

uru, (11)

]uHu]uru

5 2~1 2 g2!@~1 2 g!~1 2 K2!K2 G#1y2uru. (12)

f we evaluate these terms at the point of workingperation we get the following values:

]uHu]g

5 20.5227,]uHu]G

5 0.2766,

]uHu]g2

5 21.0455,]uHu]K2

> 0,]uHu]uru

5 1.2407.

If the deviation margin were equal for all theseparameters, the dominant effects would be related to

epi

d

fi

g2 and to Bragg reflectivity r~l!. Such is not thecase, so we need to evaluate margin variations.

g and g2 Deviations. These deviations are duemainly to environmental operating conditions suchas temperature variations. For commercially avail-able couplers the temperature coefficient has a valueof 0.002 dBy°C.13 This coefficient implies an excessloss deviation equal to Dg 5 0.00044, in each coupler,if a 1 °C temperature change is considered.

K2 Deviation. These deviations are due to temper-ature changes with a worst-case variation of 0.002dBy°C ~Ref. 13! and to variations in fabrication tol-rance, typically of 60.001. For the inside loop cou-ler, a 1 °C change produces a coupling coefficientncrease of DK2 5 0.0002. So the effects of devia-

tions in fabrication tolerance dominate. K2 is a crit-ical parameter because for only a forwardcontribution of F2 this coupling coefficient should beequal to 0.5. Although a small deviation in K2 nearthe working point does not seriously affect the valueof uHu ~]uHuy]K2 5 0!, backward reflections can beavoided by use of an isolator.

Reflectivity Deviation r~l0!. This deviation is re-lated to fabrication tolerances; we accept a change of22%. This deviation changes the reflectivity as Duru5 20.01601.

Gain variation ~G!. Emission and absorptiontransversal sections depend on temperature14,15; tak-ing a 22% deviation into account, we obtain a gain

ecrement of DG 5 20.035912.These deviations, along with previously calculated

actors, produce the following changes in uHu:

Dgf DuHu 5 20.00115, Dg2 with DT

5 50 °Cf DuHu 5 20.0023,

DK2f uHu 5 0, Dr~l!f DuHu

5 20.01986, DGf DuHu

5 20.009735.

Critical parameters with a greater influence on uHuare fiber Bragg reflectivity and loop gain. Only theworst modifications in reflectivity motivate a varia-tion in uHu, which makes peak values at ports P3 andP4 change from 239.93 and 18.61 dB ~ideal values! to24.75 and 10.76 dB, respectively. The FWHM atports P3 and P4 changes from 17.93 and 15.37 MHzto 23.05 and 38.42 MHz. This effect is overcomewith a 2.4% gain correction, which means a new gainvalue of 1.888. G can be used as the control param-eter, so gain must be stabilized in the temperaturerange of operation. Considering simultaneously theworst-case variations of all parameters, we will havea uHu decrement of 20.033045, which could be cor-rected with a 7% gain variation, which means a newG value of 1.9213.

2. Analysis of K variationsThere are two factors to be considered: temperatureand fabrication tolerance. In this case a tolerancevariation of 60.001 dominates. A final K value of

0.015 when the design value is 0.014 changes thepeak values at ports P3 and P4 to 227.13 and 18.85dB, respectively, and the FWHM to 17.93 MHz inboth outputs. A K value of 0.013 makes the peakvalues at ports P3 and P4 change to 231.6 and 18.32dB, with a FWHM of 15.37 MHz. G tuning can beused to compensate for a deviation in design specifi-cation caused by K variations at any port. TheFWHM and peak values at the working wavelengthdepend less on variations in K than on variations inuHu.

B. Variations in Working Wavelength

We tune the wavelength of the device by changing theoptical path length. When we use the device as arouter, once we have tuned it to extract a certainoptical carrier, which means a certain wavelength,fluctuations can modify the working wavelength in aRR or a fiber Bragg grating. Temperature changesinduce optical path-length changes that are due tovariations in length and refractive index, which re-sult in a variation in central wavelength for a RRexpressed as

Dl0 5 l0aTDT 1l0

neffjDT, (13)

where l0 is the central wavelength, neff is the effec-tive refractive index, aT is a linear thermal expansioncoefficient of a monomode fiber ~8 3 1027y°C!, and js the thermo-optic coefficient ~1 3 1025y°C!. A tem-

perature change of 10 °C produces a change of 0.12nm, which is a significant change because at a1.55-mm window it represents 15 GHz. So temper-ature stabilization is critical if we want a stable cen-tral wavelength of operation. In the case of fiberBragg gratings, the change in central wavelength isgiven by12

Dl0 5 2Ln# aTDT 1 2LjDT, (14)

where n is the average effective refractive index of thefiber Bragg gratings. Temperature changes are crit-ical in RR and fiber Bragg gratings, so it is importantto stabilize temperature. Piezoelectric devices fixedto loop length and Bragg gratings can be used to tunedevice operation at a certain wavelength and to over-come deviations in length that are due to tempera-ture.

4. Summary

A general study of a novel device that can operate asa router and as a demultiplexer has been carried out.The periodicity of a simple ring resonator is brokenthrough a Bragg grating structure, so the device hasa high free spectral range and a selective FWHM. Itincludes a gain section that incorporates design flex-ibility while overcoming the problem of tolerance ofvariations from design specifications. Use of az-transform technique for device stability has beenstudied. Stability depends on the values of K anduHu at the working wavelength. The device can be

20 April 2000 y Vol. 39, No. 12 y APPLIED OPTICS 1939

filter of adjustable finesse using an amplified fiber ring reso-

1

1

implemented with integrated optics or with opticalfiber technology. A set of rules and graphic infor-mation for the design of routers with a specificFWHM, rejection ratio, and gain at output ports forthe working wavelength have been given.

A study of the influence of parameter variations ondesign specifications for a device implemented by fi-ber technology was carried out. Fabrication toler-ances and temperature effects were taken intoaccount. Deviations from specifications have beencompensated for by tuning of the gain value. Forexample, a reflectivity decrement of 20.01986 wasovercome with a gain change of 2.4%. For a properdevice operation, gain must be temperature stabi-lized. Temperature changes also induce variationsin working length. They can be controlled with apiezoelectric device attached to a fiber loop and tofiber Bragg gratings. A router can also be tunedwith those piezoelectric devices.

This study was supported by the Spanish ComisionInterministerial de Ciencia y Tecnologia ~TIC98-0397-C03-03!, the Comunidad Autonoma de Madrid~07Ty0003y1998!, and a grant from the Agencia Es-panola de Cooperacion Internacional.

References1. S.-L. Tsao, H.-W. Tsao, and Y.-H. Lee, “Design of a self-routing

frequency division multiple access ~SR-FDMA! network usingan optical ring filter with or without gain as a router,” J.Lightwave Technol. 13, 2168–2182 ~1995!.

2. C. Vazquez, F. Hernandez-Gil, and M. Lopez-Amo, “Tunablering resonator filter for OFDM transmission systems,” Micro-wave Opt. Technol. Lett. 8, 321–323 ~1995!.

3. Y. H. Chew, T. T. Tjhung, and F. V. Chrys Mendis, “An optical

940 APPLIED OPTICS y Vol. 39, No. 12 y 20 April 2000

nator,” J. Lightwave Technol. 15, 364–370 ~1997!.4. C. K. Madsen, “Efficient architectures for exactly realizing

optical filters with optimum bandpass designs,” Photon. Tech-nol. Lett. 10, 1136–1138 ~1998!.

5. K. Oda, S. Suzuki, H. Takahashi, and H. Toba, “An opticalFDM distribution experiment using a high finesse waveguide-type double ring resonator,” Photon. Technol. Lett. 6, 1031–1034 ~1994!.

6. S. Kim and B. Lee, “Recirculating fiber delay-line filter with afiber Bragg grating,” Appl. Opt. 37, 5469–5471 ~1998!.

7. T. Kominato, Y. Hibino, and K. Onose, “Silica-based finesse-variable ring resonator,” Photon. Technol. Lett. 5, 560–562~1993!.

8. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J.Lightwave Technol. 15, 1391–1404 ~1997!.

9. H. Okamura and K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” J. Lightwave Technol. 9, 1554–1560~1991!.

10. H. M. Stoll, “Optimally coupled GaAs-distributed Bragg reflec-tion lasers,” IEEE Trans. Circuits Syst. CAS-26, 1065–1072~1979!.

11. A. A. Abramov, A. Hale, R. S. Windeler, and T. A. Strasser,“Widely tunable long-period fiber gratings,” Electron. Lett. 35,81–82 ~1999!.

12. J. Lauzon, S. Thibault, J. Martin, and F. Ouellette, “Imple-mentation and characterization of fiber Bragg gratings lin-early chirped by a temperature gradient,” Opt. Lett. 19, 2027–2029 ~1994!.

13. 1999 Catalog, E-TEK Dynamics, Inc., 1865 Lundy Avenue,San Jose, Calif. 95131; couplers and splitters, p. 84.

14. M. Yamada, M. Shimizu, M. Horiguchi, and M. Okayasu,“Temperature dependence of signal gain in Er31-doped opticalfiber amplifiers,” IEEE J. Quantum Electron. 28, 640–648~1992!.

5. M. J. O’Mahony, “Semiconductor laser optical amplifiers foruse in future fiber systems,” J. Lightwave Technol. 6, 531–544~1988!.