JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006 2225

Coherent Kinks in High-Power RidgeWaveguide Laser Diodes

Martin Achtenhagen, Amos A. Hardy, Fellow, IEEE, Fellow, OSA, and Christoph S. Harder, Member, IEEE

Abstract—Coherent coupling of lateral modes is suggested to ex-plain the phenomena associated with beam-steering kinks, whichappear in the L−I curves of many ridge waveguide lasers. Theanalysis that is presented explains quantitatively the previouslyreported experiments.

Index Terms—Laser modes, modeling, semiconductor devicemodeling, semiconductor lasers.

I. INTRODUCTION

IN RECENT years, high-power ridge waveguide (RWG)laser diodes at λ = 980 nm have been widely used in a

variety of applications such as pump sources in Er-doped fiberamplifiers (EDFAs). These lasers are renowned for their relia-bility, beam quality, and high power output [1], [2]. Present-dayapplications, however, are limited by the maximum kink-freepower output available from these devices.

Experimental results presented in the literature [3]–[7] pro-duced L−I curves for RWG lasers of the type shown in Fig. 1.At the so-called “kink,” there is a slight beam steering [4],[8]–[11] on the order of 1◦–3◦, which can cause a significantreduction of the power available for coupling into a single-modefiber. Observations of the spontaneous emission, from the top ofthe device, showed a beat pattern along the laser ridge [9], [10].When the L−I curve measurements are made with short(< 100 ns) pulses and with a low duty cycle, the coherent kinksare shifted to higher power levels [12], [13], indicating thatindeed a temperature rise is involved.

The most common explanation for kinks is that the laseroscillates simultaneously in the two lowest order lateral modes(TE0 and TE1 at ν0 and ν1), which are both above threshold[9], [14], [15]. This explanation, however, fails to describe theobserved beam steering as well as the beat pattern in the top-side spontaneous emission. A model that assumes that the twomodes are locked in frequency and phase, on the other hand,explains the beam-steering kink and mode-beating phenomena.Since the two modes oscillate at a common frequency ν, we

Manuscript received November 9, 2005; revised February 6, 2006. The workof A. A. Hardy was supported by the Chana and Heinrich Manderman Chair inOptoelectronics at Tel-Aviv University.

M. Achtenhagen is with the Laboratory of Physics of Nanostructures, EcolePolytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland, and alsowith IBM, Ruschlikon, Switzerland (e-mail: martin.achtenhagen@epfl.ch).

A. A. Hardy is with the Laboratory of Physics of Nanostructures, EcolePolytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland, and alsowith the Department of Electrical Engineering–Physical Electronics, Tel-AvivUniversity, Tel-Aviv 69978, Israel (e-mail: hardy@eng.tau.ac.il).

C. S. Harder is with the Swiss Federal Institute of Technology, Zurich 8092,Switzerland.

Digital Object Identifier 10.1109/JLT.2006.872313

Fig. 1. Typical L−I curve for high-power RWG lasers. Kinks are observedwhen a limited aperture detector is used or when the light coupled into a fiberis measured. Usually, only one kink is observed.

shall refer to these kinks also as coherent kinks to distinguishthem from ordinary kinks [16], [17].

To illustrate the proposed mechanism, let us considerthe RWG drawn schematically in Fig. 2(a). Employing theeffective-index method, we obtain an effective lateral wave-guide, the refractive-index distribution of which is shown inFig. 2(b). Calculating the propagation constant for the twolowest order lateral modes, namely, TE0 and TE1, as a functionof frequency ν or free space wavenumber k0 = 2πν/c0, weobtain the schematic dispersion diagram depicted in Fig. 2(c).

A laser mode, oscillating at frequency ν and having apropagation constant β, must satisfy the resonance condition2Lβ = 2πq, where L is the laser length, and q is an integer.In the dispersion diagram of Fig. 2(c), we note that the TE0

mode satisfies the resonance condition at some point “A” withfrequency ν0, whereas the TE1 mode satisfies the resonancecondition at some other point “B” at frequency ν1 (where p �= qare both integers). This is the usual situation, i.e., the twomodes oscillate simultaneously at two different frequenciesν0 �= ν1, as can be verified experimentally by measuring theirbeat frequency ∆ν = ν0 − ν1. Only accidentally, the TE1 modecan oscillate exactly at the point “C” with frequency ν1 = ν0.Thus, most often, one may expect that due to spatial-holeburning, two or more modes will reach threshold and oscil-late simultaneously at different frequencies, thereby creatingordinary incoherent kinks. Nevertheless, from the experimentalevidence in the literature, one finds that many RWG lasers (notjust a few) show the beam-steering-kink phenomena (i.e., lasingin two coherent lateral modes that are locked in frequency and

0733-8724/$20.00 © 2006 IEEE

2226 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006

Fig. 2. Typical RWG laser. (a) Cross-sectional diagram. (b) Correspondinglateral effective-index distribution. (c) Schematic of the dispersion diagram, forthe three-layer symmetric slab waveguide of (b), as a function of the free-spacewavenumber k0. The ordinate is in units of 2Lβ to indicate the laser resonancesfor each mode.

phase). In addition, a similar phenomenon has been found invertical-cavity surface-emitting laser structures [18].

Furthermore, as the current density is gradually increased,the laser goes through several phases. Initially, above threshold,the L−I curve is linear, and the laser oscillates in a singlelateral mode (the TE0 mode). Then, at some specific powerlevel, the first coherent kink is observed, presumably due to theonset of the TE1 mode, which has reached threshold. With a fur-ther increase in the injected current density, the coherent kinkdisappears, and the RWG laser oscillates again in a single mode.As the current density is still further increased, quite often, asecond coherent kink is observed [7], [12] and later, for highercurrent densities, disappears. It is quite difficult to explain howthe TE1 mode could stop and start oscillating time and againonce it reached threshold at some lower current densities.

From the experimental observations, we conclude that ifcoherent kinks are created, as opposed to the incoherent ones,the TE1 mode must still be below threshold. Rather, it is drivenand constantly fed by the oscillating fundamental mode. Themechanism for this effect is an elastic scattering (i.e., same

wavelength) of light from the oscillating TE0 mode into thebelow-threshold TE1 mode by means of any type of asymmet-rically distributed imperfections and defects (e.g., hot spots,scratches, tilted mirrors, Rayleigh scattering, etc.). That is, thefundamental mode constantly feeds the TE1 mode, at the samewavelength, whether or not the latter mode is in resonance. Dueto reciprocity, a similar scattering occurs from the TE1 modeinto the TE0 mode. It is emphasized here that this scatteringshould be an elastic process. Otherwise, light scattered fromthe oscillating TE0 mode at point “A” could feed the TE1 modeat point “B,” which resonates at a different frequency. Even ifthe latter mode is not above threshold, this should result in anincoherent kink.

It is clear that as long as the driven TE1 mode at point“C” is not in resonance, it will remain negligibly small dueto destructive interference. As the current density increases,the junction temperature underneath the ridge also rises, re-sulting in an increased effective-index step (∂n/∂T > 0) andincreased ∆β = β0 − β1. Eventually the TE1 mode gets intoresonance. If elastic scattering into the TE1 mode is strongenough to overcome the extra cavity losses, the TE1 modebuilds up on the account of the driving TE0 mode and a coherentkink is generated. With a continued increase of the currentdensity, the temperature difference ∆T is further elevated, andthe driven TE1 mode gets out of resonance again.

In the next section, the mathematical equations for this phe-nomenon are presented, along with vital remarks regarding theirsolution method. Some numerical examples and discussionsare given in Section III. Finally, concluding remarks are givenin Section IV.

II. MATHEMATICAL MODEL

Although the following model can be adapted to any index-guided semiconductor laser, for definiteness, we consider aweakly index-guided single quantum-well (QW) InGaAs laser.The objective is to obtain the steady-state device characteristicsunder the influence of coherent lateral-mode coupling. There-fore, we derive a set of phenomenological equations, in whichwe include coupling terms. The equations are solved in a self-consistent manner with the effect of nonlinear gain distributiondue to the stimulated recombination.

The electric-field distribution in the cavity is representedas a superposition of forward- and backward-propagatingmodes, namely

E(y, z) =1∑

p=0

[E+

p (z) + E−p (z)

] ·Gp(y) (1)

whereGp(y), p = 0,1 are the lateral-mode profiles of the quasi-TE0 and TE1 modes, respectively, for the effective waveguideof Fig. 2(b). As a matter of convenience, these modes arenormalized to satisfy

∞∫−∞Gp(y) ·Gq(y) · dy = Qp · δpq (2)

ACHTENHAGEN et al.: COHERENT KINKS IN HIGH-POWER RIDGE WAVEGUIDE LASER DIODES 2227

where Qp, p = 0,1 is the effective width in which the modeTEp is concentrated, and δpq is the Kronecker delta function,which equals unity for p = q, and zero otherwise. The fieldcoefficients E±

p (z) then satisfy a set of four coupled equations

±dE±p (z)dz

=[iβp+

12

(Γpg(z)−α)]·E±

p (z)+iκ(z)·E±q (z)

p = 0, 1, q = 0, 1, p �= q (3)

in which β0 and β1 are the two propagation constants at thesame wavelength λ, g(z) is the local material gain per unitlength, α is the scattering loss per unit length, Γp is the powerfilling factor in the active region (Γp = ΓxΓy

p), and κ(z) is acoupling coefficient expressed by

κ(z) ∝∞∫

−∞∆n2(y, z) ·G0(y) ·G1(y) · dy (4)

where ∆n2(y, z) is the index perturbation. Note that onlyasymmetrical perturbations may couple the two lowest orderlateral modes. In the present analysis, we select some arbitrarynumerical values for κ(z). Furthermore, in this simple model,the lateral power filling factors Γy

p are constants and not affectedby current spreading, carrier diffusion, or spatial-hole burning.

In order to eliminate rapid phase variations, we define

E+p (z) =Ap · exp(iβpz), p = 0, 1 (5a)

E−p (z) =Bp · exp(−iβpz), p = 0, 1 (5b)

and (3) reduce to

d

dzU =M · U (6a)

where the transpose of U is UT = (A0, B0, A1, B1), and Mis given by (6b), shown at the bottom of the page. Note thephase terms in (6b). Since the field propagating in the cavitysees the same conditions every round trip, the coupling coef-ficient has a natural period of 2L, and the main contributionto the mode coupling comes from the Fourier component thatapproximately cancels the phase term. This is exactly the sourceof our coherent kinks. It is implicitly assumed that the TE0

mode is in resonance and oscillates at any current density abovethreshold. Thus, unless the resonance condition 2L∆β = 2πmis approximately met, there is no Fourier component of κ(z)that cancels the phase terms in (6b), and therefore, the couplingof the oscillating TE0 mode into the driven TE1 mode will

average out to zero. Note also that (6a) and (6b) resembles thecoupled-mode equations of Kogelnik [19], except that the self-coupling terms include the local z-dependent saturable materialgain per unit length g(z), where [20]

g(z) = g0 · ln(N(z)Ntr

). (7)

In (7), N(z) is the injected carrier density, Ntr is the carrierdensity necessary to reach transparency, and g0 is a constant.The numerical values of Ntr and g0, as well as other para-meters, are given in Table I. The carrier density N(z) and itsdependence on the photon density is given by

ηi · Jq · d =

N

τ(N)+ g(N)

(1

�ω· neff

2c0µ

)

× (|A0|2 + |B0|2 + |A1|2 + |B1|2)

(8)

where q is the elementary charge, d is the QW thickness, Jis the current density per unit area, ηi is the internal quantumefficiency, c0 is the speed of light in free space, µ is thepermeability, and τ = (a+ bN + cN2)−1 is the spontaneouscarrier lifetime, which includes radiative- and nonradiative-recombination as well as Auger-recombination terms. Thenumerical values of these parameters are given in Table I.Interference terms between A0 and A1, as well as between B0

and B1, do not appear on the right-hand side of (8), becauseof the orthogonality relation (2). Also, the interference betweenforward- and backward-propagating modes is washed out byaxial carrier diffusion and does not appear in (8). As mentionedabove, the effects of lateral carrier diffusion and current spread-ing are neglected in the present simplified analysis.

Assuming a back mirror at z = −L/2, with power reflectiv-ity, for the TE0 and TE1 modes, of Rb,p, p = 0,1, respectively,and a front mirror (from which power is extracted) at z = L/2,with power reflectivity of Rf,p, the boundary conditions are

E+p (−L/2) =

√Rb,p · E−

p (−L/2), p = 0, 1 (9a)

E−p (L/2) =

√Rf,p · E+

p (L/2), p = 0, 1 (9b)

or, in terms of the slowly varying envelope functions Ap andBp, we obtain

Ap(−L/2) =√Rb,p ·Bp(−L/2) · exp (i·βp ·L) (10a)

Bp(L/2) =√Rf,p ·Ap(L/2) · exp (i·βp ·L). (10b)

M =

12 (Γ0g − α) 0 iκ(z) · e−i·∆β·z 0

0 − 12 (Γ0g − α) 0 −iκ(z) · ei·∆β·z

iκ(z) · ei·∆β·z 0 12 (Γ1g − α) 0

0 −iκ(z) · e−i·∆β·z 0 − 12 (Γ1g − α)

(6b)

2228 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006

TABLE ILIST OF THE MATERIAL AND RWG LASER PARAMETERS

Thus, in addition to the slow phase change of Ap(z) and Bp(z)along the laser, they also accumulate a phase difference ofexp(i2βpL) each complete cavity round trip. Finally, the near-field distribution just outside the front mirror is given by

Eout(y) =√

1 −Rf,0 · E+0 (L/2) ·G0(y)

+√

1 −Rf,1 · E+1 (L/2) ·G1(y). (11)

The far-field distribution of the output field is given by theFourier transform ofEout(y) [21]. The total power output is ob-tained by integrating over the power density (the Poynting vec-tor’s z-component), which, due to the orthogonality relation (2),results in

Pout =(Q·neff

2·c0 ·µ){

(1 −Rf,0)·|A0(L/2)|2

+ (1 −Rf,1)·|A1(L/2)|2}

(12)

where Q0 ≈ Q1 = Q was used. As we shall see in the nextsection, the total power output increases linearly with pumpingcurrent density, whether or not the TE1 mode is excited. How-ever, the power coupled into a single-mode fiber, will show thecoherent-kink nonlinearities, due to the beam steering, and isobtained directly from the far-field distribution.

III. DISCUSSION AND RESULTS

We apply our model to the laser structure shown in Fig. 2,including some simplified thermal considerations (i.e., a tem-perature rise of ∆T only underneath the ridge). From a spectral

Fig. 3. Variation of ∆β = β0 − β1 with the injected current density. Indi-cated are the conditions for the coherent-kink resonances. For current densitiessmaller than 1.8 kA/cm2, the TE1 mode is cut off. The temperature rise ∆T atm = 3, 4, and 5 amounts to 9.5, 15, and 23 ◦C, respectively.

shift measurement [22], we find the approximate temperaturerise, as a function of the current density. Assuming ∂n/∂T =3 × 10−4, one obtains a monotonic increase of ∆β with currentdensity (see Fig. 3). As a matter of convenience, we plot theresonance difference 2L∆β/2π. That is, we keep the TE0 modeat a cavity resonance of 2Lβ0 = 2πq (implicitly assuming agradual wavelength shift with the increase of ∆neff), and when

ACHTENHAGEN et al.: COHERENT KINKS IN HIGH-POWER RIDGE WAVEGUIDE LASER DIODES 2229

Fig. 4. Power output as a function of current density. The total power isnearly linear above threshold. At the location of the coherent kinks, thereis a significant contribution from the TE1 mode. The inset shows a fourfoldmagnification of the m = 5 resonance.

the TE1 cavity resonance of 2Lβ1 = 2πp is reached, we definethe coherent-kink orderm as

m ≡ q − p = 2L∆β/2π. (13)

Note that, for our specific example, them = 3 coherent kink isjust barely above cutoff.

The power output as a function of the injected current densityis depicted in Fig. 4. The solid lines represent the power inthe TE0 and TE1 modes separately. However, when a totallyintegrating sphere is used to measure the power output, thetotal power in both modes is detected, which is described bythe dotted lines. The coherent kinks are actually obtained onlywhen a limiting aperture (e.g., single-mode fiber) is used. Theinset shows a four-times magnification of them = 5 resonanceand its vicinity. Note the missing of them = 4 resonance. Here,and in the examples that follow, the coupling coefficient wasarbitrary selected as

κ(z) ={

2 cm−1, −L2 ≤ z < 0

−2 cm−1, 0 ≤ z ≤ L2

. (14)

Since the even-order Fourier components of κ(z) vanish, them = 4 resonance does not appear. Although the fifth-orderFourier component of κ(z) is smaller than the third-orderFourier component, nevertheless, them = 5 resonance containsmore power due to the higher injected current.

The power density |E(y, z)|2 along the cavity for them = 3 resonance is presented in Fig. 5. There are exactlythree maxima alternatively shifted from the optical axis, which

Fig. 5. Lateral and longitudinal intensity distribution inside the laser cavityfor the m = 3 resonance. (a) Three-dimensional plot of the energy density.(b) Contour diagram of the energy distribution.

originate from the lateral-mode beating, in agreement withpreviously reported experimental measurements [9], [10]. Thepower density at the front mirror is higher than that near theback mirror due to the higher reflectivity of the latter. Similarly,the power density for the m = 5 resonance is drawn in Fig. 6.Here, we have five maxima, which are alternatively shifted fromthe optical axis. Since the injected current density is signifi-cantly higher than at the m = 3 resonance, the power densityis also much higher, resulting in a slightly more pronouncedinternal power asymmetry.

The far-field distribution of the output field at them = 5 resonance is given in Fig. 7 (solid line). For comparison,the far-field pattern of the TE0 mode (dashed line) is alsopresented. Note the significant steering of the combined mode,which amounts to a 3◦ beam shift. Statistically, 50% of thelasers may have index perturbations ∆n2(y, z) located on oneside of the optical axis, whereas the other lasers may have theindex perturbations located on the opposite side. Therefore, the

2230 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006

Fig. 6. Lateral and longitudinal intensity distribution inside the laser cavityfor the m = 5 resonance. (a) Three-dimensional plot of the energy density.(b) Contour diagram of the energy distribution.

sign of the coupling coefficient κ(z) [see (4)] will differ forthe two groups. As a result, half of the lasers will have theiroutput beam shifted to the opposite direction. It is worthwhileto indicate that the amount of beam steering is a monotonicfunction of the coupling-coefficient magnitude.

The far-field pattern determines the amount of light cou-pled into a fiber. This is because the fiber core does not trapangular spectrum components that propagate at angles largerthan the numerical aperture of the fiber. The amount of powercoupled into a fiber is an important parameter that determinesthe power in the coherent kinks. For a typical direct-coupledsingle-mode fiber, only the TE0 mode couples, and thus, withnumerical aperture of 0.11, the power coupled into the fibercore is reduced by nearly 5% (experimentally measured) at them = 5 resonance. Therefore, one obtains an L−I curve similarto Fig. 4.

Fig. 7. Far-field pattern of the combined field (TE0 and TE1) at the coherentkink of order m = 5 (solid line). The far-field distribution of the TE0 mode(dotted line) is given as a reference.

Fig. 8. Relative wavelength shift as a function of current density due to thecoherent coupling between the TE0 and TE1 modes.

We note that at, and near, the coherent kinks, the powercontained in the TE1 mode may be quite significant to influencethe oscillating lowest order TE0 mode. Since the coupling termin (3), which includes the TE1-mode amplitude, is complex, thephase of the fundamental mode will also be affected. Therefore,the wavelength at which the lasing TE0 mode oscillates issignificantly shifted near each of the coherent kinks. In Fig. 8,we present the relative wavelength shift ∆λ/λ, from the oscil-lating wavelength at threshold λth, as a function of the injectedcurrent density, where ∆λ = λ− λth. Note that this shift is

ACHTENHAGEN et al.: COHERENT KINKS IN HIGH-POWER RIDGE WAVEGUIDE LASER DIODES 2231

solely due to the coupling effect. It does not include band-gapchange with temperature and the direct impact of the indexvariation with temperature. Therefore, the wavelength shift,which clearly demonstrates a resonance phenomenon, vanishesat the center of each of the coherent kinks.

IV. CONCLUSION

In this paper, a simple model has been presented in order toexplain beam-steering kinks in theL−I curve of RWG lasers. Itis postulated that the source of these kinks is an elastic couplingbetween the oscillating TE0 mode, which is above threshold,and a driven TE1 mode, which is below threshold due to itsexcess mirror losses and/or smaller power filling factor. As theinjected current density is increased, and with it the junctiontemperature, the TE1 mode is brought in and out of resonancetime and again, drawing power from the TE0 mode at eachcoherent kink. In this model, the physical mechanism for themode coupling could be any asymmetric perturbation, which islumped into a coupling parameter. That is, two different per-turbations (e.g., a scratch or a hot spot), at different locations,may cause the same coherent kinks, as long as the appropriateFourier components of the coupling coefficients are the same. Itis shown that the coupled differential equations, which includesaturable gain, give rise to all the phenomena reported earlierin association with the coherent kinks. In this paper, variouslateral effects, such as current spreading, carrier diffusion, andlateral spatial-hole burning, were neglected. These may affectthe magnitude of the coherent-kink phenomenon and will beconsidered elsewhere.

REFERENCES

[1] A. Oosenbrug and A. Jakubowicz, “Operational stability of 980-nm pumplasers at 200 mW and above,” Proc. SPIE, vol. 3004, pp. 62–70, 1997.

[2] N. Chand, S. N. G. Chu, N. K. Dutta, J. Lopata, M. Geva, A. V. Syrbu,A. Z. Mereutza, and V. P. Yakovlev, “Growth and fabrication of high-performance 980-nm strained InGaAs quantum-well lasers for Erbium-doped fiber amplifiers,” IEEE J. Quantum Electron., vol. 30, no. 2,pp. 424–439, Feb. 1994.

[3] C. Harder, P. Buchmann, and H. Meier, “High-power ridge-waveguideAlGaAs GRIN-SCH laser diode,” Electron. Lett., vol. 22, no. 20,pp. 1081–1082, Sep. 1986.

[4] J. Näppi, A. Ovtchinnikov, H. Asonen, P. Savolainen, and M. Pessa, “Lim-itations of two-dimensional passive waveguide model for λ = 980 nmAl-free ridge waveguide lasers,” Appl. Phys. Lett., vol. 64, no. 17,pp. 2203–2205, Apr. 1994.

[5] J. Temmyo and M. Shimizu, “Strained InGaAs quantum well lasers withsmall-divergence angles for high-power pump modules,” Electron. Lett.,vol. 30, no. 24, pp. 2046–2047, Nov. 1994.

[6] J. Temmyo and M. Sugo, “Design of high-power strained InGaAs/AlGaAsquantum-well lasers with a vertical divergence angle of 18◦,” Electron.Lett., vol. 31, no. 8, pp. 642–644, Apr. 1995.

[7] P. Savolainen, M. Toivonen, H. Asonen, M. Pessa, and R. Murison, “High-performance 980-nm strained-layer GaInAs–GaInAsP–GaInP quantum-well lasers grown by all solid-source molecular-beam epitaxy,” IEEEPhoton. Technol. Lett., vol. 8, no. 8, pp. 986–988, Aug. 1996.

[8] M. F. C. Schemmann, C. J. van der Poel, B. A. H. van Bakel,H. P. M. M. Ambrosius, A. Valster, J. A. M. van den Heijkant, andG. A. Acket, “Kink power in weakly index guided semiconductor lasers,”Appl. Phys. Lett., vol. 66, no. 8, pp. 920–922, Feb. 1995.

[9] J. Guthrie, G. L. Tan, M. Ohkubo, T. Fukushima, Y. Ikegami, T. Ijichi,M. Irikawa, R. S. Mand, and J. M. Xu, “Beam instability in 980-nm powerlasers: Experiment and analysis,” IEEE Photon. Technol. Lett., vol. 6,no. 12, pp. 1409–1411, Dec. 1994.

[10] M. Ohkubo, Y. Ikegami, T. Ijichi, and T. Ninomiya, “Experimental studyof beam steering in 980-nm InGaP cladding lasers,” Jpn. J. Appl. Phys.,vol. 35, no. 1A, pp. L34–L36, Jan. 1996.

[11] W. D. Herzog, B. B. Goldberg, and M. S. Unlü, “Beam steering in narrow-stripe high-power 980-nm laser diodes,” IEEE Photon. Technol. Lett.,vol. 12, no. 12, pp. 1604–1606, Dec. 2000.

[12] G. Hunziker and C. Harder, “Beam quality of InGaAs ridge lasers at highoutput power,” Appl. Opt., vol. 34, no. 27, pp. 6118–6122, Sep. 1995.

[13] J. W. R. ten Cate, L. M. Weegels, A. H. van Bakel, C. J. van der Poel,and H. P. M. Ambrosius, “Kinks induced by free-carrier absorption inweakly index guided semiconductor lasers,” Appl. Phys. Lett., vol. 71,no. 1, pp. 19–21, Jul. 1997.

[14] M. L. Xu, G. L. Tan, R. Clayton, and J. M. Xu, “Increased thresholdfor the first-order lateral mode lasing in low-ridge waveguide high powerQW lasers,” IEEE Photon. Technol. Lett, vol. 8, no. 11, pp. 1444–1446,Nov. 1996.

[15] G. L. Tan, R. S. Mand, and J. M. Xu, “Self-consistent modeling of beaminstabilities in 980-nm fiber pump lasers,” IEEE J. Quantum Electron.,vol. 33, no. 8, pp. 1384–1395, Aug. 1997.

[16] B. L. Frescura, C. J. Hwang, H. Luechinger, and J. E. Ripper, “Sup-pression of output nonlinearities in double-heterostructure lasers by useof misaligned mirrors,” Appl. Phys. Lett., vol. 31, no. 7, pp. 770–773,Dec. 1977.

[17] D. R. Scifres, W. Streifer, and R. D. Burnham, “GaAs/GaAlAsdiode lasers with angled pumping stripes,” IEEE J. Quantum Electron.,vol. QE-14, no. 4, pp. 223–227, Apr. 1978.

[18] A. D. Rakic, V. E. Boros, and M. L. Majewski, “Cooperatively frequency-locked multimode operation in proton implanted VCSELs,” in Proc.Conf. Optoelectron. Microelectron. Mater. Devices, Perth, Australia,Dec. 14–16, 1998, pp. 116–119.

[19] H. Kogelnik, “Theory of optical waveguides,” in Guided-Wave Optoelec-tronics, 2nd ed., T. Tamir, Ed. New York: Springer-Verlag, 1990, ch. 2.

[20] L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic IntegratedCircuits. New York: Wiley, 1995.

[21] J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968.

[22] M. Ito and T. Kimura, “Carrier density dependence of refractive index inAlGaAs semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-16,no. 9, pp. 910–911, Sep. 1980.

Martin Achtenhagen received the Ph.D. degree inphysics from the Swiss Federal Institute of Technol-ogy (EPFL), Lausanne, Switzerland, in 1996, for hiswork on gain-coupled distributed feedback (DFB)laser diodes.

After postdoctoral work at the IBM Zurich Re-search Laboratory, Zurich, Switzerland, he becamea Research Staff Member at IBM Zurich in 1997and was involved in work on quantum-well (QW)semiconductor lasers, with the emphasis on the de-sign and characterization of high-power GaAs-based

lasers. By ownership change, in 1997, he became a Research Staff Memberof JDS Uniphase, Eatontown, NJ. In 1998, he was on leave for one year atSpectracom to develop a new generation of pump lasers for erbium-doped fiberamplifier (EDFA) applications and then returned to JDS Uniphase, where hemanaged the forward-looking group with emphasis on Raman amplifiers andEDFAs. In 2002, he became a Senior Research Associate at EPFL, Lausanne,Switzerland, where he is now working on the simulation of long-wavelengthvertical-cavity surface-emitting laser diodes.

Dr. Achtenhagen serves as an Associate Editor of Optical Fiber Technology.

2232 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006

Amos A. Hardy (SM’84–F’97) received the B.Sc.and M.Sc. degrees in physics from the Hebrew Uni-versity, Jerusalem, Israel, in 1966 and 1969, respec-tively and the Ph.D. degree in applied physics fromthe Weizmann Institute of Science, Rehovot, Israel,in 1975.

From 1975 to 1983, he was with the Departmentof Electronics, Weizmann Institute of Science. Whileat the Weizmann Institute, he held the Ruth E. RecuCareer Development Chair. From 1976 to 1979, hewas on leave at Stanford University, Stanford, CA,

working on various laser resonator problems, optical phase conjugation, andoptical rotation-sensing systems. During the summer of 1982, he was a VisitingScientist at Bell Laboratories, Holmdel, NJ, where he worked on problemsrelated to distributed feedback (DFB) lasers. Since 1983, he has been withthe Faculty of Engineering at Tel Aviv University, Tel Aviv, Israel, wherehe was appointed as Associate Professor and later promoted to Professor in1988. From June 1984 to July 1985, he was a Visiting Scientist at XeroxPalo Alto Research Center (PARC), Palo Alto, CA, where he was engagedin the analysis of phase-coupled laser arrays. During the summers of 1985and 1986, he was a Visiting Associate Professor at the Center for HighTechnology Materials, University of New Mexico, Albuquerque. He was onsabbatical leave as a Senior Research Scientist at Spectra Diode Laboratories(SDL) during the academic year of 1988/1989 and spent several summers thereuntil 2000. During these visits, he was engaged in the design and analysisof grating-coupled surface emitters, flared amplifiers, laser arrays, and fiberlasers and amplifiers. From 1991 to 1995, he served as Chairman of theDepartment of Electrical Engineering—Physical Electronics. In 1994 and 1995,and again in 2003 and 2006, he spent several months as Visiting Professor atEcole Polytechnique Federale de Lausanne (EPFL), Switzerland, where he wasengaged in DFB and vertical cavity lasers’ theory. He is the incumbent Chanaand Heinrich Manderman Chair in Optoelectronics. On several occasions, since1997 until 2001, he was a Visiting Scientist at Uniphase Laser Enterprise(formerly IBM Laboratories), Zurich, Switzerland, where he was engaged inproblems related to ridge lasers. During 2001 and 2002, he spent several monthsat Infinera, Sunnyvalle, CA, as a Research Scientist, developing models foroptical amplifiers. His research interests involve analysis of dye laser systems,DFB lasers, distributed Bragg reflector (DBR) lasers, diode lasers, opticalresonators and waveguides, fiber lasers and amplifiers, propagation of laserbeams, optical phase conjugation, and the study of optical systems for inertialrotation sensing. He has performed research in several areas of lasers, integratedoptics and electrooptics, optical phase conjugation, injection locking, gratinganalysis, resonator modes, beam propagation, coupled-mode theory, and otherrelated fields. His work has been published in more than 180 refereed scientificpapers and reported in many scientific meetings.

Dr. Hardy received, in 1993, the prize of the “Polish Jewish Ex-ServicemenAssociation—London” in the field of Applied Electronics for his contributionsto the analysis and design of high-power coherent diode lasers. He is a Fellowof the Optical Society of America. He serves on the Editorial Board for thejournal of Microwave and Optical Technology Letters.

Christoph S. Harder (M’82) received the Diploma EE degree from SwissFederal Institute of Technology (ETH), Zurich, Switzerland, in 1979, and theMaster EE and Ph.D. degrees from California Institute of Technology (Caltech),Pasadena, in 1980 and 1983, respectively.

He is Cofounder and Leader of the R&D effort of the IBM Zurich LaserDiode Enterprise, which pioneered the 980-nm high-power pump laser fortelecom applications. Over the last few years, he and his research groupexpanded into the field of 14xx-nm telecom pumps, as well as 808- and9xx-nm multimode pumps for industrial applications. He has held a varietyof staff and management positions at Caltech, IBM, Uniphase, JDS Uniphase,Nortel, Bookham, and now ETH Zurich. He is the author or coauthor of morethan 100 papers and is the holder of 20 patents.

Dr. Harder has served as General Chair at the International SemiconductorLaser Conference and at the LEOS Annual Meeting and on numerous technicaland steering committees.