Investigation on the Multimode Dynamics of InGaAsP–InP Microring Lasers

1266 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 42, NO. 12, DECEMBER 2006

Investigation on the Multimode Dynamics ofInGaAsP–InP Microring Lasers

Ioanna Stamataki, Spiros Mikroulis, Alexandros Kapsalis, and Dimitris Syvridis

Abstract—A multimode model based on the rate equation ap-proximation is presented in order to simulate the mode dynamics of1.55- m InGaAsP–InP microring lasers. A detailed characteriza-tion is performed including calculated optical spectra, time tracesand relative intensity noise spectra. Different operation regimesare observed, bidirectional multimode with/without alternate oscil-lations, unidirectional single mode, bidirectional single mode andmode hopping. The boundaries of the above operation regimes areinvestigated with respect to the current level, bus waveguide reflec-tivity and ring radius. Varying the current level a transition frommultimode to single mode and eventually mode hopping operationis observed. Increasing the bus waveguide reflectivity a transitionfrom unidirectional to bidirectional operation is revealed, while theuse of nonequal reflectivities between the two facets, promotes uni-directional operation. Moreover, the ring radius is proved to be acritical parameter for the extent of each operation regime since itdirectly influences the modal wavelength separation.

Index Terms—Bidirectional operation, microring lasers, modehopping, nonlinear optics, unidirectional operation.

I. INTRODUCTION

SEMICONDUCTOR microring lasers are attractive candi-dates for optoelectronic integrated circuits (OEICs) as they

combine simple fabrication, small footprint, and high spectralpurity [1]. Recently, large diameter circular and triangularring laser devices have been fabricated [2]–[4], and they havebeen analyzed by considering a near single longitudinal modeoperation. This assumption is valid as long as the side-modesuppression ratio (SMSR) is greater than about 20 dB. How-ever, the SMSR is strongly dependent on the specific designand current levels used for each device. In the general case amicroring laser is expected to operate in multiple longitudinalmodes. Longitudinal mode hopping phenomena can dramati-cally increase the intensity noise of microring lasers and thuslimit the performance of a ring-based lightwave system. Anenhanced low-frequency relative intensity noise (RIN) dueto longitudinal mode hopping has been reported in 1.3- mInGaAsP–InP Fabry–Pérot (F-P) lasers [5]. Thus, a dynamicmultimode analysis is a necessity for a complete and accuratecharacterization of microring lasers.

Manuscript received June 6, 2006.I. Stamataki, A. Kapsalis, and D. Syvridis are with the Department of In-

formatics and Telecommunications, University of Athens, GR-15784 Athens,Greece (e-mail: [email protected]; [email protected]; [email protected]).

S. Mikroulis is with the Department of Informatics and Telecommunications,University of Athens, GR-15784 Athens, Greece. He is also with the Depart-ment of Physics, Division of Applied Physics, University of Athens, GR-15784Athens, Greece (e-mail: [email protected]).

Digital Object Identifier 10.1109/JQE.2006.884578

In this study a multimode model is presented based on therate equation approximation for the simulation of microringlaser’s mode dynamics including time traces, optical spectraand RIN spectra. The bus waveguide’s residual reflectivity istaken into account in the model, providing an additional opticalfeedback to the resonant microring cavity, a coupling mech-anism between the two propagating directions. A completestudy is performed varying the microring’s current, the buswaveguide’s reflectivity and the ring radius. Different operationregimes are observed; bidirectional multimode with/withoutalternate oscillations, unidirectional single mode, bidirectionalsingle mode, and mode hopping. Varying the current level, atransition from multimode to single mode and eventually modehopping operation is observed. Increasing the bus waveguidereflectivity, a transition from unidirectional to bidirectionaloperation is revealed, while the use of nonequal reflectivitiesbetween the two facets, promotes unidirectional operation.Moreover, the ring radius is proved to be a critical parameterfor the extent of each operation regime since it directly influ-ences the modal wavelength separation. Thus, the scope of thiswork is not only to examine the microring’s laser operation, ona general point of view, but also to emphasize in the influence ofkey design parameters on single mode and/or unidirectional op-eration, both being of major concern for future microring-basedlightwave system applications.

The analysis proceeds as follows. In Section II, the the-oretical model is explicated, in Section III the numericalresults are presented and the investigation is divided into foursubsections—Section III-A: influence of various current levelsat low reflectivity values; Section III-B: influence of variousreflectivity values; Section III-C: influence of nonequal reflec-tivity values on unidirectional operation, and Section III-D:influence of various microring radii. Finally, the work is con-cluded in Section IV.

II. MODEL

The electric field inside the ring cavity can be expressed asthe summation of all resonant modes

(1)

where are the mean-field slowly varying complex am-plitudes of the electric field of all modes in the ring cavity,is the mode number, and corresponds to each propagationdirection either clockwise (CW), or counterclockwise (CCW)

0018-9197/$20.00 © 2006 IEEE

STAMATAKI et al.: INVESTIGATION ON THE MULTIMODE DYNAMICS OF InGaAsP–InP MICRORING LASERS 1267

Fig. 1. Planar view of a microring laser.

(Fig. 1). The variation of the electric field , and the car-rier concentration are described by a set of multimode rateequations

(2)

(3)

(4)

where is the modal gain, the linear gain coefficient, isthe self gain suppression coefficient, and , are thesymmetric and asymmetric cross gain suppression coefficients,respectively, [6] given by the following expressions:

(5)

(6)

(7)

The symmetric cross gain suppression coefficientaccounts for the spectral hole burning effect (SHB), whilethe asymmetric cross gain suppression term accountsfor the carrier density pulsation (CDP) effect which occursdue to the electron population pulsation at the beat frequencybetween longitudinal modes [7]. Nonlinear coupling due to thefour-wave mixing (FWM) effect [4] has been neglected in theanalysis because of the relatively small ring radii resulting inlarge mode spacing and small interaction length. The nonlinearsystem of equations is solved for equal number of modes propa-gating in each direction (CW/CCW). The number of supportedmodes is determined by the gain bandwidth, and the ring’s freespectral range, . Above, is the group index,

is the ring circumference length, is the ring radius,is the differential gain coefficient, is the volume

of the active region, is the waveguide width, is the etchingdepth, is the linear gain dispersion coefficient, is the centerwavelength of the linear gain assumed to be at 1.55 m, isthe carrier concentration at transparency, is the intraband

TABLE IMICRORING LASER PARAMETERS

relaxation time, is the microring photon lifetime, is theelectron charge, is the carrier lifetime, and is the linewidthenhancement factor. The definition for the photon lifetime is

(8)

where is the ring coupling coefficient that satisfies, where is the transmission coefficient, and is

the microring’s internal loss. The parameter representslinear coupling, between counterpropagating modes at the samefrequency, due to reflection on the bus waveguide [4] and

is the time delay of the reflected light to be coupled backinto the ring

(9)

where is the facet field reflectivity, the bus waveguidenet gain per length, and the bus waveguide length. In our casethe bus waveguide is considered as a lossless section, .Assuming that the facets are antireflection (AR) coated with apower reflectivity, , varying from 20 to 60 dB, theresonant characteristics of the bus waveguide are suppressed andtherefore are not taken into account in the analysis. This residualreflectivity is taken into account in our model, providing an ad-ditional optical feedback to the resonant microring cavity, cou-pled from one direction to the other. Equations (2)–(9) are nu-merically integrated to simulate the microring’s laser operation.In the computation of laser dynamics, usual Langevin [5] noisesources are used, represented by the terms in (2).

III. RESULTS AND DISCUSSION

In the simulations we consider microring lasers with radii30-70 m coupling coefficient , equivalent to a powercoupling ratio of 25%, and bus waveguide length equal to 2r. Avariety of power reflectivities , from 60 to 20 dB hasbeen assumed for different current values from to ,where is the laser’s threshold current. The values (Table I)of parameters used in the simulations are typical for 1.55- mInGaAsP–InP lasers [6], [8], [9].


Fig. 2. Optical mode spectra for the mode 0 for CW and CCW propagationdirections at I = 1:0I and R = R = �60 dB.

A detailed characterization of the microring laser includingoptical mode spectra, time traces and RIN spectra is performed.The RIN is calculated from the intensity fluctuations over totalsimulation time from (10) and (11)

(10)

(11)

where is the total power of all modes, FFT denotes the fastFourier transform, and is the time step.

A. Influence of Injection Current for Low Reflectivity Values

A detailed characterization of the microring laser is per-formed for the case of low reflectivity values at various currentlevels. Specifically, a reflectivity value of

dB, for a radius of m, is selected. As it willbe discussed in detail in the following paragraphs, the modelpredicts a sequence of different operating regimes. At currentvalues in the order of the threshold current a bidirectional oper-ating regime combined with alternate oscillations is observed.The alternate oscillations occur between the respective modesof counter-propagating fields, i.e when mode 0 (CW) hasmaximum, mode 0 (CCW) has minimum. When the current isfurther increased a unidirectional operating regime is observed.The lasing mode in the unidirectional regime either CW orCCW, depends on the initial conditions randomly determinedby the ASE noise.

Eventually for current values greater than a mode-hop-ping operating regime combined with alternate oscillationsoccurs. The mode-hopping takes place between longitudinalmodes propagating in the same direction. The optical modespectra of the CW and CCW waves at a current value of

are observed in Fig. 2. The mode power valuesare normalized by the mean power value . The optical

spectra appear symmetric according to the homogenouslybroadened gain. In the near threshold regime mi-croring lasers exhibit a bidirectional multimode behavior due tothe strong amplified spontaneous emission (ASE) noise. Fig. 3plots the temporal evolution of the dominant mode of the

Fig. 3. Time traces for the CW and CCW propagation directions (mode 0) atI = 1:0I and R = R = �60 dB.

Fig. 4. Optical mode spectra for the CW and CCW propagation direction atI = 1:4I and R = R = �60 dB.

CW/CCW waves at . The counter-propagating fieldsappear with alternate oscillations

The optical mode spectrum at a current value ofis illustrated in Fig. 4. As the current level increases the effectof the cross gain suppression dominates while the ASE influ-ence is diminished. This phenomenon promotes single modeoperation due to the suppression of the adjacent modes by thedominant mode. A SMSR in the order of 25 dB is calculatedat a current value of . The asymmetric mode spec-trum appears due to the asymmetric cross gain suppression term

. takes a negative value for , so it sup-presses the long-wavelength nonlinear gain, resulting in an en-hancement of the long-wavelength modes [7], [10], [11]. More-over, unidirectional operation is promoted due to the directionalmode selection through cross gain suppression [2]. However theselection of either the CW or CCW propagation direction israndom, with CW and CCW having equal probability to lase.Fig. 5 plots the time variations for the modes , ofthe CW/CCW waves at . The stable operation of thelasing mode ( , CW) is evident, while the other modesare considerably suppressed.

At larger current values a transition from the stable singlemode operation to the mode-hopping operation occurs.


Fig. 5. Time traces for the CW and CCW propagation directions (modes 0,�1)at I = 1:4I and R = R = �60 dB showing the unidirectional stablesingle mode operation.

Fig. 6. Optical mode spectra for the CW and CCW propagation direction atI = 2:3I and R = R = �60 dB.

This transition appears at a current value of approximately. The optical mode spectra for are

illustrated in Fig. 6. It is worth mentioning that even thoughthe device is instantaneously under single mode operation, thespectrum appears multimode-like due to time averaging overthe total time window. Due to the asymmetric gain suppression,the longer wavelength modes are favored, so the main modehops continuously to the longer-wavelength side. However, thelinear gain of the mode decreases as the mode recedes from thegain peak, the gain of the central mode recovers, and eventuallythe main mode hops back to the central wavelength. The modehopping effect is also combined with alternate oscillationsbetween CW and CCW propagating directions. Fig. 7 plots thetime traces for the modes , 1 and 2 of the CW/CCWwave at illustrating the mode hopping describedabove. In order to justify the effect of lack of the asymmetricgain term in the model, calculations with wereperformed. The simulation without the asymmetric term of thecross gain suppression coefficient predicts unidirectional stablesingle mode operation. Fig. 8, plots the time traces of the modes

, 1 with for CW/CCW directions when

Fig. 7. Time traces for the CW and CCW propagation directions (modes 0,�1,+2) at I = 2:3I and R = R = �60 dB.

Fig. 8. Time traces for the CW and CCW propagation directions (modes 0,�1)at I = 2:3I and R = R = �60 dB, without H .

. The absence of the mode-hopping effect is evident.The transition from the stable to the hopping operation regimeis also observed through the RIN spectra. The stable multimodeand single mode operation regimes exhibit a usual peak at therelaxation frequency, while an enhanced low frequency RINis depicted at the mode hopping regime. This behavior hasalready been experimentally demonstrated in 1.55- m ridgewaveguide InGaAsP–InP microring lasers [12]. The respectiveRIN spectra at current values , , and

are illustrated in Fig. 9. A broad low frequencypeak is depicted at .

B. Influence of Various Reflectivity Values

The influence of the residual reflectivity on the microringlaser operation regimes is examined. A range of power reflec-tivity values in the area of 60 to 20 dB, for a radius of

m, is selected. As the reflectivity increases, the alreadymentioned operation regimes are observed. However, the uni-directional single mode operation regime alters to bidirectionalfor a power reflectivity of approximately 44 dB. Figs. 10 and11 show the optical spectra and time traces of the CW/CCWwaves, respectively, for a current value of and

dB. It is obvious that the microringlaser is under bidirectional stable operation. As the reflectivityincreases a greater ratio of propagating power on the CW/CCW


Fig. 9. RIN spectra for I = 1:0I , 1:4I and 2:3I with R = R =

�60 dB for r = 50 �m.

Fig. 10. Optical mode spectra of the CW/CCW propagation directions at1:6I and R = R = �30 dB.

Fig. 11. Time traces for the CW and CCW propagation directions (modes 0,�1) at I = 1:6I and R = R = �30 dB.

direction is re-injected to the opposite (CCW/CW) directionperturbing the respective modal gains acting as a driving forcefor the bidirectional operation. As the current level increases,

the microring laser transits to the mode hopping regime at a cur-rent value of approximately . A detailed mapping ofthe bus waveguide reflectivity and current level influence on themicroring operating regime for ring radius 50 m is illustratedin Fig. 12. Many typical and interesting features are extractedfrom this figure. Bidirectional multimode operation dominatesat low current values approximately up to , howeverthe reflectivity value can be a control parameter whether theoperation is bidirectional with or without alternate oscillations.Increasing the current value, and for low reflectivity values,approximately up to 42 dB, the ring laser operates, as alreadymentioned, at a unidirectional single mode operation with anequal probability of either the CW or CCW to lase. When thereflectivity increases, the ring operates at a bidirectional singlemode operation. Finally the transition to the mode-hoppingoperation regime varies accordingly to the reflectivity valueand the current level as indicated in Fig. 12. It must be notedthat the single mode operation regime is usually followed bya jittering-interim operation regime, before the ring transits tothe mode hopping regime. A small interim region is alwaysobserved at the boundary lines of all the operation regimes.

C. Influence of Nonequal Reflectivity Values on UnidirectionalOperation

Unidirectional operation described above, is an intrinsic fea-ture of the microring laser at low reflectivity values providingrandomly either a CW lasing mode or a CCW lasing mode.However accurate control of unidirectional operation can beachieved if asymmetric features are introduced on the devicedesign [13]. Therefore, we extend the previous study to thecase of nonequal reflectivities for the bus waveguide facets inorder to provide the microring laser with the required asym-metrical factors to observe possible unidirectional characteris-tics. When nonequal reflectivity values are used, a mismatch ofthe reinjected power coupled back to CW/CCW direction is in-duced. Fig. 13, shows the respective optical mode spectra of theCW/CCW waves for dB and dB at

.The enhanced reflection feedback in the CW direction results

in a domination of the respective propagating field while theCCW field is suppressed. As a result the use of different re-flectivity ratios encourages laser unidirectional operation [14].Increasing the current value unidirectionalilty is not altered butthe lasing direction transits to the mode hopping regime. Unidi-rectional single mode microring lasers are advantageous sincethey are promising candidates for applications in all-opticalswitching, gating, wavelength conversion, and optical memory.

D. Influence of Various Microring Radii

A critical parameter for an optimum microring laser perfor-mance in terms of unidirectionality and/or single mode opera-tion is the modal wavelength separation. The microring radiusdirectly affects the free spectral range (FSR) of the mode spec-trum; smaller radii give larger FSR. Thus, a detailed character-ization of the dynamic properties of the microring laser is alsoperformed for different radii. In addition to the mapping pre-sented in Fig. 12, similar mapping for the operating conditionsfor m and m is also performed. The already


Fig. 12. Detailed mapping of the bus reflectivity influence with respect to the current level for ring radius 50 �m.

Fig. 13. Optical mode spectra of the CW and CCW propagation directions atI = 1:8I and R = �60 dB R = �30 dB.

mentioned, operation regimes were observed for all three dif-ferent radii. Smaller radius rings (i.e., m) proved tohave an extended unidirectional single mode operation regime,up to current values of approximately and for facet re-flectivities up to approximately 30 dB. It is observed that forbidirectional single mode operation to occur, a 30 m radiusring needs increased reflectivity values, more than 30 dB. Themode-hopping regime is reduced and it is present only at highercurrent values, more than 2.2–2.3 as a function of the powerreflectivity value. At increased ring radii m the singlemode regimes either unidirectional or bidirectional are reducedand the mode-hopping regimes either the stable mode-hoppingor with alternate oscillations are considerably extended. The de-tailed mapping of the bus reflectivity influence with respect tothe current level for ring radius 70 m is illustrated in Fig. 14.

The differences observed are due to the dependence of the crossgain saturation coefficients on the mode’s wavelength separa-tion. Small microring radii enable larger FSRs resulting to rel-atively weak influence of the cross gain effect (6), (7), thusreducing the mode-hopping phenomenon. At larger microringradii the energy exchangeability between modes is enhancedand mode-hopping appears at lower current values. As a resultsmaller microring radii give improved characteristics with re-spect to extended single mode operation with improved SMSR.

IV. CONCLUSION

A multimode model based on the rate equation approxima-tion is presented in order to study the multimode dynamicsof microring lasers. Different operation regimes are observed;bidirectional operation with alternate oscillations close to thethreshold current, unidirectional single mode with an equalprobability of either the CW or CCW to lase, bidirectionalsingle mode operation, and finally, mode hopping. Detailedmapping of the bus reflectivity and the current level influenceon the operation regimes was performed for a variety of ringradii.

Low reflectivity values favor the unidirectional operationwhile higher values of reflectivity seem to promote bidirec-tional operation. At low current values single mode operationis observed while at higher current values the micro ring laserexhibits mode-hopping operation. Moreover, the ring radiusis proved to be a critical parameter for the extent of eachoperation regime since it directly influences the modal wave-length separation. Smaller radius rings proved to have extendedsingle mode operation either unidirectional or bidirectional,while larger radius rings promoted mode-hopping phenomena.Unidirectional operation can be controlled when nonequalreflectivity values are used for the bus waveguide facets. All


Fig. 14. Detailed mapping of the bus reflectivity influence with respect to the current level for ring radius 70 �m.

the aforementioned operation regimes were observed throughthe optical mode spectra, time traces and RIN spectra. Anenhanced low-frequency RIN is depicted at the mode hoppingregime. The observed mode interaction phenomena are due tothe nonlinear gain suppression effects. The consideration of theabove parameters is critical for design of microring lasers withoptimum performance for future lightwave system applications.

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Ioanna Stamataki received the B.S. degree in physics from the University ofCrete, Heraklion, Greece, and the M.Sc. degree in physics of laser communica-tions from the University of Essex, Essex, U.K., in 2001 and 2002, respectively.She is currently pursuing the Ph.D. degree, collaborating with the Optical Com-munications Laboratory, Department of Informatics and Telecommunications,National and Kapodestrian University of Athens, Athens, Greece, working onall-optical wavelength converters.

Her other areas of interest include microring resonators, semiconductor laserdynamics, and all-optical signal processing.

Spiros Mikroulis was born in Corfu, Greece, in 1973. He received the B.S. de-gree in physics and the M.S. degree in optoelectronics/microelectronics fromthe University of Crete, Crete, Greece, in 1998 and 2001, respectively. He iscurrently pursuing the Ph.D. degree collaborating with the Optical Communica-tions Laboratory, Department of Informatics and Telecommunications, Nationaland Kapodestrian University of Athens, Athens, Greece.

He worked in the Institute of Electronic Structure and Laser (IESL), Founda-tion of Research and Technology Hellas (FORTH) from 1999 to 2001 in growthand characterization of III–V compound semiconductors. He is author and coau-thor of more than 15 articles in international scientific journals and conferences.His present research interests are semiconductor integrated devices for all-op-tical signal processing.


Alexandros Kapsalis was born in Athens, Greece, in 1978. He received the B.S.degree in informatics and telecommunications and the M.Sc. degree in telecom-munications from the University of Athens, Athens, Greece, in 2002 and 2004,respectively. He is currently working towards the Ph.D. degree on all-opticalprocessing systems.

His other areas of interest include microring resonators, semiconductor lasers,and waveguiding properties of semiconductor materials.

Dimitris Syvridis received the B.Sc. degree in physics, the M.Sc. degree intelecommunications, and the Ph.D. degree in physics from the University ofAthens, Athens, Greece, in 1982, 1984, and 1988, respectively.

From 1990 to 1994, he was a Researcher with the Institute of Quantum Elec-tronics, Swiss Federal Institute of Technology, Zurich, Switzerland. Since 1994,he has been with the Department of Informatics and Telecommunications, Uni-versity of Athens, where he is currently an Associate Professor. He has partic-ipated in many European Research projects in the filed of optical communica-tions. He is author and coauthor of more than 70 articles in international scien-tific journals and conferences. His research interests include the areas of opticalcommunications and networks, photonic devices, and subsystems, as well asphotonic integration.

Investigation on the Multimode Dynamics of InGaAsP–InP Microring Lasers

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