4. CONCLUSION

Application of the genetic algorithm to oscillator design has beenreported for the first time. The genetic algorithm provides a sys-tematic and efficient way to optimize the circuit parameters neededin the oscillator circuit. The predicted values of phase noise(�112.6 dBc/Hz at 100 kHz from 5.3 GHz) and PFN (20.1 dB) arein excellent agreement with the experimental results (�112dBc/Hz at 100 kHz from 5.3 GHz and 21 dB) of the geneticallymodified oscillator.

ACKNOWLEDGMENT

Financial support from National Science Council under contractnos. NSC92-2212-E002-091 and 91EC17A05-S10017 and 89-E-FA-06-2-4 are appreciated.

REFERENCES

1. T.P. Liu and E. Westerwick, 5-GHz CMOS radio transceiver front-endchipset, IEEE J Solid-State Circ 35 (2000), 1927–1933.

2. M. Hershenson, A. Hajimiri, S.S. Mohan, S.P. Boyd, and T.H. Lee,Design and optimization of LC oscillators, IEEE/ACM Int Conf CAD,Beijing, China, 1999, pp 296–303.

3. R.L. Haupt, An introduction to genetic algorithms for electromagnetics,IEEE Antennas Propagat Mag 37 (1995), 7–15.

4. A. Hajimiri and T. Lee, A general theory of phase noise in electricaloscillators, IEEE J Solid-State Circ 33 (1998), 179–194.

5. D. Ham and A. Hajimiri, Concepts and methods in optimization ofintegrated LC VCOs, IEEE J Solid-State Circ 36 (2001), 896–909.

6. M. Hershenson, S. Boyd, and T.H. Lee, GPCAD: A tool for CMOSop-amp synthesis, IEEE/ACM Int Conf CAD, Beijing, China, 1998, pp296–303.

© 2004 Wiley Periodicals, Inc.

MULTIWAVELENGTH FIBER LASERUSING A MULTIMODE ELLIPTICAL-CORE ERBIUM-DOPED FIBER

Gautam Das1,2 and John W. Y. Lit1,2,3

1 Department of PhysicsAcadia UniversityNS, B4P 2R6, Canada2 Guelph-Waterloo Physics InstituteDepartment of PhysicsUniversity of WaterlooOntario, N2L 3G1, Canada3 Department of Physics and ComputingWilfrid Laurier UniversityOntario, N2L 3C5, Canada

Received 18 December 2003

ABSTRACT: This paper reports on a fiber laser constructed with anerbium-doped fiber, which has an elliptical core that is single-modedalong the minor axis and multimoded along the major axis. The lasercan simultaneously emit several stable lines at room temperatures. Themaximum number of lasing lines obtained depends on the number ofmodes supported by the erbium-doped fiber in the cavity. The separationbetween the lasing lines depends on the fiber birefringence. The princi-ple of operation is based on the anisotropic-gain effects in a polariza-tion-maintaining fiber. The stability of the lasing lines, in the presenceof anisotropic-gain effects in a polarization-maintaining fiber, has beenexplored. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett42: 124–128, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20227

Key words: multiwavelength fiber laser; polarization-maintaining fiber;birefringence; polarization dependent gain

1. INTRODUCTION

Erbium-doped fiber (EDF) lasers, which can simultaneously gen-erate multiple wavelengths, have attracted attention worldwidebecause they can serve as simple and compact sources for appli-cations in wavelength-division multiplexing (WDM) communica-tions (characterization of systems that have wavelength dependentproperties) and also as sensors. At room temperatures, an EDF haslarge homogeneous gain widths (�10 nm). There is severe modecompetition; thus, it is difficult to obtain simultaneous operationsof multiple wavelengths. Therefore, to achieve simultaneous mul-tiwavelength emission by an erbium-doped fiber laser, the first stepis to produce inhomogeneous gain. Several techniques have beenproposed to achieve this at room temperatures: using polarizationmaintaining erbium-doped fiber [1–3], acousto-optic frequencyshifter [4], spatial mode-beating filter [5], polarization hole-burn-ing effects [6], and EDF at liquid-nitrogen temperature [7].

In this work, we built a fiber laser which can lase severalwavelengths simultaneously. A PMF is used as the gain medium.Our multiwavelength fiber laser has stable outputs at room tem-peratures. We examine the threshold and stability of the differentlasing lines, the dependence of the number of lines and theirspacings on the dimensions of the PMF, and the anisotropic-gaineffect on the number of stable lasing lines.

2. EXPERIMENTAL CONFIGURATION

Figure 1 shows the resonant cavity for the laser. A polarization-independent optical isolator guarantees unidirectional propagationof waves inside the cavity in order to avoid spatial hole burning.The parameters of the PMF used as the gain medium are given inTable 1. The cavity also has a polarization controller by which wecan change the polarization of the wave inside the cavity, and

Figure 10 Figure of merit of published oscillators: power-frequency-normalized phase noise (PFN)

124 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 2, July 20 2004

thereby change the number of lasing lines emitted by the laser [1].The EDF is pumped by a laser diode at 980 nm through a980/1550-nm wavelength division multiplexer. A 1% fused fibercoupler is used to tap the output and feed it into an opticalspectrum analyzer with a resolution bandwidth of 0.06 nm.

3. THEORY AND EXPERIMENTAL RESULTS

In the ring cavity (Fig. 1), the PMF has an elliptical core. It isspliced between two pieces of single-mode fiber. The PMF issingle mode along the minor axis and multimode along the majoraxis. In the multimode region, a few modes (which interfere witheach other) are excited. This causes the transmission to becomewavelength dependent. The separation between two transmissionpeaks �� depends on the wavelengths and the length of the fiber,while the total output power is independent of the input lightpolarization [8].

When light is injected into a multimode optical fiber, its poweris distributed among the linearly polarized LPlp modes with dif-ferent azimuth l and radial p mode numbers. The LPlp polarizationmodes are combinations of the true waveguide modes which arehybrid [9], namely, HEl�1,p

e , HEl�1,po , EHl�1,p

e , and EHl�1,po . In

general, the propagation constants � of the HE and EH modes aredifferent from one another; this gives rise to the beat phenomenon,which makes the modes unstable and rotate as they propagatealong the fiber. The stability of the mode pattern is affected by thedifference ��HE � �EH� in the propagation constants of the twodifferent modes that form the LP pattern. When this value is zero,the LP mode is stable. In an elliptical core fiber, the stabilityparameter is defined as [9]:

� ��e � �o

�HE � �EH, (1)

where �e and �o are the propagation constants of the even and oddmodes in a birefringent fiber. The difference increases with theeccentricity of the elliptical core, or with the birefringence. For aweakly guiding but highly birefringent fiber, �e � �o � �HE ��EH. The stability parameter is �1; hence, the modes are stable.The PMFs shown in Table 1 have high eccentricities, so that themodes are stable.

The phase difference due to polarization or modal birefringencewhen the wave propagates along a fiber of length L is given by

��i � ��iL �i � 0, 1, x�. (2)

If we consider only the fundamental spatial mode excited at thefiber input, then the Jones matrix for the linearly birefringent fiberis given by [10]:

JPMF � � exp�i��0

2 � 0

0 exp��i��0

2 ��, (3)

where ��0 � ��0L � 2�BL/� denotes the linear relative phasedifference between the fundamental modes LP01

x and LP01y prop-

agating in the PMF of length L, and birefringence B. This gives atransmission filter with separation between two transmissionspeaks �� � �2/B L. The phase condition for maximum trans-mission is given by

��0 � 2m�; m � 0, 1, 2 . . . . (4)

Thus, the PMF acts as a filter in the cavity. With this phasecondition, the above Jones matrix for the PMF reduces to

JPMF � P�1 00 1� , (5)

where P � 1. Figure 1 shows the unidirectional ring cavity witha PMF as the gain medium. The output and circulating wavesinside the cavity are given by

E3

E1� �1 � K��1/ 2�1 � ��1/ 2

�1 �K

1 � P�1 � K �1 � � exp�i�L0 � �L0 � L� � g���L�� ,

(6)

E4

E1�

i�1 � ��1/ 2 K1/ 2

1 � P�1 � K �1 � � exp�i�L0 � �L0 � L� � g���L�,

(7)

where E1, E3, and E4 are the input, output, and circulating fieldsin the resonator, respectively, K is the coupling coefficient of thecoupler, � is the insertion loss of the coupler, � is the propagationconstant of the wave in the cavity (which differs from that of thepassive cavity by an amount caused by the population inversion), is the loss in dB/km of the fiber, L is the length of the PMF, L0

is the length of the single mode fiber, and g(�) is the gaincoefficient per unit length of the EDF. For laser oscillations,

TABLE 1 Elliptical Core Fiber Used in the Experiment withDifferent Parameters

Type ofPM-EDF

CoreDimension

(�m)NumericalAperture

ErbiumConcentration

(ppm)

1 3.8 14.8 0.15 28002 3.1 14.6 0.18 15003 3.3 14.7 0.19 4200

Figure 1 Experimental setup for the multiwavelength fiber laser (PM-EDF: erbium-doped elliptical core fiber; pump: 980-nm laser diode; PC:polarization controller; C1: 1% fused-fiber coupler; OI: polarization-inde-pendent optical isolator)

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 2, July 20 2004 125

1 � P�1 � K �1 � � exp�i�L0 � �L0 � L� � g���L� � 0.

(8)

The circulating waves inside the cavity will be in phase if

�L0 � 2m0� m0 � 0, 1, 2, 3 . . . . (9)

By using Eq. (9), which is the phase condition for laser oscilla-tions, we can obtain the amplitude condition as follows:

P�1 � K �1 � � exp���L0 � L� � g���L�) � 1. (10)

From the above equation, we obtain the threshold gain coefficient,given by

gt��� � �1 �L0

L � �1

2Lln�P2�1 � K��1 � ���. (11)

The laser oscillation starts when the amplitude [Eq. (11)] andphase conditions [Eqs. (4) and (9)] of the resonator are satisfied. InFigure 2, four lasing lines of length 6.2 m at a particular setting ofthe polarization controller are obtained with EDF1 (see Table 1).The average separation between the lasing lines is 3.28 nm and the3-dB bandwidth is 0.06 nm, the measurement of which is limitedby the resolution bandwidth of the optical-spectrum analyzer. Thenumber of lasing lines at the output may be changed by adjustingthe polarization controller in the cavity, which can introducedifferent amounts of losses to the different lasing lines. When allfour lines appear at the output, the loss is minimum for all lines.Figure 3 shows the variation of the output power for the lasinglines with pump power. The thresholds for the lasing lines are 3,12, 16, and 27 mW, respectively. By using a polarization analyzer,it is found that the lasing lines are elliptically polarized.

Our experimental observation shows that the maximum numberof lasing lines obtained from this laser depends on the number ofmodes supported by the PMF. The number of modes supported bythe EDF1 is six; however, as shown in Figure 3, we obtained onlyfour stable lasing lines because the threshold pump powers for theother lasing lines are too high. So, a stronger pump laser isexpected to produce the maximum six stable lines. Similarly,Figure 4 shows that seven stable lasing lines are obtained with

EDF2 (see Table 1), which can support a maximum of eightmodes.

The separation between the lasing lines depends on the crosssection and length of the PMF. Figure 5 shows the output of a laserusing 6.2 m of EDF3 (see Table 1). The average separationbetween two lines is 2.28 nm, which is different from that obtainedwith the same length of EDF1. Figure 6 shows the variation of theseparation between two lasing lines with fiber length for EDF2 and72-mW pump power.

By monitoring the multiwavelength oscillations for more thanan hour, the stability of the lasing lines is found to depend on thecavity birefringence, which may be exploited by the polarizationcontroller. The separations between the lasing lines are very stable,while the intensities have small fluctuations of less than 0.2 dB;these fluctuations increase with increase of erbium concentrationin the fiber.

Polarization hole-burning and polarization-dependent gain inpolarization-maintaining EDF cause polarization-anisotropic gain[11–13]. These effects originate from the anisotropic emission andabsorption cross section of the erbium ions. In the host glass,erbium-ion dipoles (with elliptical cross section) are randomlyoriented and their spatial orientations and shapes with respect to

Figure 2 Output of the laser with separation between two lasing lines(��avg � 3.28 nm, input pump power Pin � 72 mW, L � 6.2 m) forEDF1

Figure 3 Variation of the output power of the lasing lines with inputpump power for the lasing lines in Fig. 1

Figure 4 Output of the laser with separation between two lasing lines(��avg � 1.75 nm, input pump power Pin � 72 mW, L � 11.78 m) forEDF2

126 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 2, July 20 2004

the fiber-coordinate system are determined by the strength andorientation of the local field. Excited ions, whose major axes of thecross-sectional ellipse are collinear with an incident linearly po-larized optical signal, are preferentially stimulated to emit photons.This causes the polarization hole-burning, where the gain is lowerin the plane of the linearly polarized signal, relative to that in theperpendicular plane. Polarization-dependent gain causes highergain along the polarization direction of a linearly polarized pumpbeam. The above effects are more pronounced in high-birefrin-gence PEDF. Figure 7 shows the experimental setup used to studythe effect. The optical circulator guarantees the unidirectionalpropagation of the wave inside the cavity. The polarization of thelight propagating along a length of fiber to the FRM and backalong the same fiber is independent of the birefringence of the fiber[14, 15]. Thus, polarization-mode dispersion, polarization-depen-dent loss, and polarization-dependent gain, which stem from thebirefringence of the fiber, are compensated. We can prove that thepolarization of the reflected beam of light from the FRM isorthogonal to the incident beam; this removes the polarizationhole-burning effect. Hence, the anisotropic-gain effect in the po-larization-maintaining EDF is removed by introducing an FRM in

the cavity. Figure 8 shows lasing lines obtained with the setupshown in Figure 7 using EDF3. Instead of being stable for over anhour, the lasing lines are now stable only for few seconds, and theysuffer from severe intensity fluctuation of more than 5 dB. So, theanisotropic gain of the EDF is shown to stabilize the lasing lines.

4. CONCLUSION

We have shown that by using an elliptical-core erbium-doped fiberwe can build stable multiwavelength lasers at room temperatures.The number of lasing lines emitted and their separations depend onthe dimensions of the elliptical fiber. The anisotropic gain in theelliptical-core erbium-doped fiber provides the necessary inhomo-geneity in the gain spectrum. The cross-gain saturation is reducedas different lasing lines occupy different parts of the gain mediumin the fiber, thus allowing the production of stable multiwavelengthlasing lines.

ACKNOWLEDGMENTS

Financial support from the Canadian Institute for Photonic Inno-vations and the National Science and Engineering Research Coun-cil of Canada is gratefully acknowledged.

Figure 5 Output of the laser with separation between two lasing lines(��avg � 2.28 nm, input pump power Pin � 72 mW, L � 6.2 m) forEDF3

Figure 6 Variation of separation between two lasing lines with length ofEDF2

Figure 7 Experimental setup used to study the anisotropic-gain effects(CIR: optical circulator; FRM: Faraday rotator mirror)

Figure 8 Output of the laser for the configuration in Fig. 7 with EDF3

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 2, July 20 2004 127

REFERENCES

1. G. Das and J.W.Y. Lit, L-band multiwavelength erbium-doped fiberlasers using an elliptical fiber, IEEE Photon Technol Lett 14 (2002),606–608.

2. G. Das and J.W.Y. Lit, Room temperature multi-wavelength operationof an elliptical core erbium-doped fiber laser, Microwave Opt TechnolLett 33 (2002), 184–186.

3. G. Das and J.W.Y. Lit, Ring resonator for multiwavelength fiber laserusing a Sagnac loop filter, Opt Eng 42 (2003), 2257–2262.

4. A. Bellemeare, M. Karasek, M. Rochette, S. LaRochelle, and M. Tetu,Room temperature multifrequency erbium-doped fiber lasers anchoredon the ITU frequency grid, J Lightwave Technol 18 (2000), 825–831.

5. A.J. Poustie and N. Finlayson, Multiwavelength fiber laser using aspatial mode beating filter, Opt Lett 19 (1994), 716–718.

6. J. Sun, J. Qiu, and D. Huang, Multiwavelength erbium-doped fiberlasers exploiting polarization hole burning, Opt Commun 182 (2000),193–197.

7. X. Shu, S. Jiang, and D. Huang, Fiber grating Sagnac loop and itsmultiwavelength-laser application, IEEE Photon Technol Lett 12(2000), 980–982.

8. P.R. Horche, M.A. Muriel, and J.A. Martin-Pereda, Measurement oftransmitted power in untapered multifiber unions: Oscillatory spectralbehavior, Electron Lett 25 (1989), 843–844.

9. A.W. Snyder and W.R. Young, Modes in optical waveguides, J OptSpc Am 68 (1978), 297–309.

10. T.A. Eftimov, Resultant mode pattern and polarization in a LP01,LP02 two mode linearly birefringent optical fiber, Opt Quantum Elec-tron 23 (1991), 1143–1160.

11. D. Falquier, D. Lande, J.L. Wagener, M.J.F. Digonnet, and H.J. Shaw,Measurement and modeling of the output polarization of Er-dopedfiber lasers, SPIE Doped Fiber Devices Syst 2289 (1994), 24–39.

12. D.W. Hall and M.J. Weber, Polarized fluorescence line narrowingmeasurements of Nd laser glasses: evidence of stimulated emissioncross section anisotropy, Appl Phys Lett 42 (1983), 157–159.

13. B. Srinivasan, S. Gupta, R.K. Jain, and R.B. Dyott, Polarizationanisotropic gain behavior in elliptical-core rare-earth-doped fibers,SPIE Doped Fiber Devices Syst 2289 (1994), 51–55.

14. C.R. Giles, Suppression of polarization holeburning-induced gain an-isotropy in reflective EDFA’s, Electron Lett 30 (1994), 976–977.

15. A.D. Kersey, M.J. Marrone, and M.A. Davis, Polarization-insensitivefiber optic michelson interferometer, Electron Lett 27 (1991), 518–520.

© 2004 Wiley Periodicals, Inc.

IMPROVED PERFORMANCE OF EBGSON A CO-PLANAR TRANSMISSIONLINE USING TAPERED DISTRIBUTION

Shantanu Kumar PadhiIan Wark LaboratoryMolecular Science DivisionCSIROAustralia, VIC 3169

Received 17 December 2003

ABSTRACT: Conventional electromagnetic crystals or electromagneticbandgaps (EBGs) with uniform distribution show spurious ripples in thepass band and poor stop-band responses. This paper presents a detailedtheoretical investigation of the performance of EBGs on a uniplanartransmission line using tapered distribution. The nonuniform size of theEBGs is used to improve the ripple height, 20-dB rejection band, andselectivity of the filter over the pass-band and stop-band regions. Thecalculated S parameters exhibit significant improvement in ripple height

and rejection bandwidth, as compared with the conventional EBG-assisted coplanar transmission line. © 2004 Wiley Periodicals, Inc.Microwave Opt Technol Lett 42: 128–131, 2004; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20228

Key words: electromagnetic bandgap (EBG); Taylor distributions; pho-tonic bandgap; electromagnetic crystals

1. INTRODUCTION

The electromagnetic bandgap (EBG) structure is a periodic struc-ture, which exhibits a bandgap over a certain frequency range inwhich the propagation of electromagnetic waves is prohibited. Theterm bandgap is well known in semiconductor physics in relationto the propagation of optical waves [1–3]. The photonic structuresassociated with this phenomenon are named photonic bandgapstructures (PBGs) or Photonic Crystals (PCs). However, in pastyears, this concept has been scaled down to microwave and mil-limeter-wave frequency bands, thus the more appropriate terms,EBGs and electromagnetic crystals (ECs), were coined to describethe structures which control the flow and radiation of electromag-netic waves. A periodic structure (EBG) applied to a microwavecircuit can produce pass-band or stop-band characteristics for awave guided in transmission lines or for a surface wave in adielectric substrate [4–7]. By proper selection of dimensions andperiods, certain waves can be allowed to propagate through, whilethe other waves, such as surface waves, can be suppressed. Such anengineered material, where the electromagnetic propagation can becontrolled, has a wide range of applications for improving theefficiency and gain of active and passive devices at microwave andmillimeter-wave frequency ranges. The findings are very muchuseful for many applications in optoelectronics and microwaveengineering [8–12].

Planar-waveguide technology has been used widely and con-tinues to be popular in commercial applications, as compared to itscounterpart—bulky waveguide technology. This is because planarwaveguides are lightweight, low profile, compact, low cost, andeasy to integrate with MMIC fabrication technology. These char-acteristics lead to a higher demand for manufacturers to use thedevice architecture at higher-frequency bands with high levels ofintegration in MMIC technology at no additional cost. In general,EBGs can be realized as 1D, 2D, or 3D structures. With respect tomicrowave planar circuits, they can be obtained as 1D or 2Dstructures by creating holes in the dielectric substrate or by etchingin the conducting ground plane. Metallic or dielectric rods (squareor circular) can also be used to generate the bandgap at the desiredfrequency band [10].

By loading the EBGs periodically on a substrate, a bandgap iscreated at the desired frequency to stop the propagation of surfacewaves along the dielectric material. An increased amount of radi-ated power coupled to the space wave is obtained, since the surfacewave cannot propagate in the dielectric. Several configurationshave been used in the literature to realize the EBG [9–16]. And, inantenna technology, EBGs can improve the antenna performances,such as broadside gain, efficiency, and beam directivity (by sup-pressing surface waves), and the radiation pattern and beam-scanning behavior of antenna arrays [7, 8, 13]. Another importantfeature is the realization of a slow-wave structure (MIS) with lowinsertion loss by using EBGs. Such a structure has great potentialapplication in microwave circuits to reduce the dimensions ofdistributed components in integrated circuits. Slow-wave transmis-sion lines have been extensively used in Si and GaAs integratedcircuits and have the limitations of high ohmic loss and lowimpedance. However, at higher frequencies, transmission lines

128 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 2, July 20 2004