Stable high optical power in quantum well lasers with profiled reflection and tapered structures

Opt Quant Electron (2013) 45:401–410DOI 10.1007/s11082-012-9645-1

Stable high optical power in quantum well laserswith profiled reflection and tapered structures

Amire Seyedfaraji · Vahid Ahmadi ·Mahyar Noshiravani

Received: 15 August 2012 / Accepted: 10 December 2012 / Published online: 20 December 2012© Springer Science+Business Media New York 2012

Abstract A comprehensive model is presented to study quantum well tapered lasers andquantum well stripe lasers with profiled reflectivity output facets and to obtain lateral stabilityin high power semiconductor laser. Simulation of semiconductor lasers is performed bynumerically solving space-dependent coupled partial differential equations for the complexoptical forward and backward waves, carrier density distribution and temperature distribution.The coupled equations are solved by finite difference beam propagation method. The effect ofnonlinear parameters like Kerr and linewidth enhancement factors, and precise dependenceof linewidth enhancement factor and gain factor on the carrier density and temperature areconsidered in this paper. We use modal reflector in stripe lasers to confine the lateral mode tothe stripe centre and provide the stable operation. We also use unpumped window to reducethe facet temperature and improve the catastrophic optical mirror damage level of taperedlasers.

Keywords High optical power · Quantum well laser · Profiled reflection ·Tapered structures

1 Introduction

During the last few years, great progress has been made in the development of high-power andhigh-brightness laser diodes (Bull et al. 2005; Erbert et al. 2001). These devices have foundincreased applications in pumping solid state or fiber laser systems for industrial, medicaland direct material processing applications (Zhang et al. 2010; Li et al. 2010).

For high-power performance, the optical mode volume of semiconductor laser source hasto be large enough to reduce the junction temperature and the optical power density at the laser

A. Seyedfaraji · V. Ahmadi (B)Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Irane-mail: [email protected]

M. NoshiravaniLaser Research Center, Tehran, Iran

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402 A. Seyedfaraji et al.

facets. This requirements lead to the design of broad-area devices with large optical cavity(LOC) structures (Mikulla et al. 1998). For broad-area gain regions, the optical field has nolateral confinement, so any increase in the local refractive index may cause self-focusing orself-defocusing, breaking up the lateral mode profile into multiple filaments known as beamfilamentation (Marciante and Agrawal 1996, 1997). Different approaches have been proposedin the last years to solve this problem. Several efforts have been made to develop broad-areastructures that support only one lateral mode: tapered devices (Mikulla et al. 1998; O’Brienet al. 1998), α-distributed feedback (DFB) lasers, antiresonant reflecting optical waveguideslasers (Smudzinski et al. 1995), integrated master oscillator power amplifier (O’Brien et al.1993) and broad-area lasers with modal reflector (Szymanski et al. 2001).

In this paper, we present numerical modeling of quantum well (QW) tapered lasers andQW stripe lasers with modal reflector. The model considers the simultaneous propagation ofboth forward and backward waves and includes variations of carrier density and temperature.We consider the effect of Kerr coefficient and linewidth enhancement factor and solve theequations by finite difference beam propagation method (FD-BPM). For the first time, we usethe exact dependence of gain factor and linewidth enhancement factor on the carrier densityand temperature.

This paper is organized as follows. Section 2, presents the theoretical model and intro-duces the coupled differential equations and their nonlinear parameters. Section 3 deals withinstability and filament formation in a stripe laser with modal reflector and tapered laser. Wesummarize the results of the paper in Sect. 4.

2 Theoretical model

Figure 1 shows schematically the geometries of stripe and tapered lasers. The laser ispumped at a constant current and is assumed to be operating continuously at frequency ω ina single longitudinal mode. The active layer is very thin compared to the diffusion length.Making the paraxial approximation, the counter propagating waves are found to satisfy a setof two coupled equations given by (Marciante and Agrawal 1996).

∂ E f

∂z= i

2k

∂2 E f

∂x2 +[

1

2�(1−iα(N , T ))g(N , T )− αint

2+in2k0

(∣∣E f∣∣2+2 |Eb|2

)]E f

(1)

Fig. 1 Schematic structure of a stripe laser, b tapered laser

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Stable high optical power in quantum well lasers 403

−∂ Eb

∂z= i

2k

∂2 Eb

∂x2 +[

1

2�(1−iα(N , T ))g(N , T )− αint

2+in2k0

(|Eb|2 + 2

∣∣E f∣∣2

)]Eb

(2)

where E f and Eb represent forward and backward travelling waves, � is the transverseconfinement factor, αint is internal loss, n2 is Kerr coefficient, g(N , T ) is the local gain thatdepends on carrier density and temperature, respectively. To reach exact gain we use Fermi‘sgolden rule and Lorentzian shaped broadening function. k = nef f · k0 is mode propagationconstant, k0 = ω/c is free space propagation constant and nef f is the effective index of

Fig. 2 Algorithm of modelingthe laser using FD_BPM

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refraction which is a function of temperature (Bissessur et al. 1993).

nef f (T (x, z)) = nef f (Ths) + dnef f

dT(T (x, z) − Ths) (3)

where Ths is temperature of the heat sink. In (1) and (2), α is linewidth enhancement factorfor a quantum well given by (Westbrook and Adams 1988)

α = −12 log

[(Eg1−Ec0)2+�2

c(Eg−E)2+(h/τ)2

]+ (Ec0−E)

�c

[π2 − tan−1 (Eg1−Ec0)

�c

]π2 − tan−1 (Eg1−E)

h/τ

(4)

In this equation, Eg1 is energy difference between the first energy levels in the conductionband and valence band, and Γc and Ec0 are

�c = 2kT mc

mr(5)

Ec0 = Eg1 + mc

mrE f c (6)

where mc is electron effective mass, mr is reduced mass, k is Boltzmann’s constant andT is temperature. In Eq. (6), E f c is the quasi-Fermi level for electrons which dependson temperature and carrier density, so the linewidth enhancement factor is a function oftemperature and carrier density.

The carrier density distribution is obtained by solving the diffusion equation (Marcianteand Agrawal 1996).

D∂2 N (x, z)

∂x2 = − J (x, z)

qd+ N (x, z)

τnr+ B N 2(x, z) + Caug(T )N 3(x, z)

+�g(N , T )

hω

(∣∣E f∣∣2 + |Eb|2

)(7)

where D is the diffusion constant, τnr is the nonradiative lifetime, B is the spontaneous-emission coefficient and Caug is the Auger recombination coefficient given by (Menzel1998)

Caug(T ) = 4.2 × 10−42 exp

(TA

300 ◦K− TA

T

) √T

TA(8)

The characteristic temperature TA describes the temperature dependence of Auger recombi-nation phenomenologically. In Eq. (7), J is the injected current density which is zero outsidethe stripe. For a stripe structure, J is constant over the stripe width and in a tapered structure,as the width of metal contact increases, J reduces linearly.

To involve thermal effect, Eqs. (1), (2) and (7) are coupled by the heat conduction equation.

r

(∂2T

∂x2 + ∂2T

∂z2

)+ 1

ρmC p(q(N , T ) − γ (T − Ths)) = 0 (9)

where ρm is the mass density, C p is the specific heat capacity, γ describes the balance betweencooling by the heatsink and heating by other processes not specified in the model, and r is

r = kz

ρmC p(10)

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Table 1 Parameters’ values used in numerical simulation

Physical quantity Symbol Value

Cavity length L 250 μm (Smudzinski et al. 1995)

Active layer thickness d 8.5 nm

Transverse confinement factor Γ 0.017

Facet power reflectivity R0, RL Variable

Laser wavelength λ 820 nm

Effective index nef f 3.5

Internal loss αint 10 cm−1

Diffusion constant D 33 cm2/s

Non-radiative lifetime τnr 5 ns

Spontaneous-emission coefficient B 1.4 × 10−10 cm3/s

Current density on the stripe contact J 900 A/cm2

Deviation of refraction index with temperature dn/dT 3 × 10−4 K−1

Interband relaxation time τ 0.1 ps

Characteristic temperature TA 468.4 K

Mass density ρm 5.26 g/cm3

Specific heat capacity C p 342.5 J/Kg K

kz is thermal conductivity of the material which is a function of temperature and given by(Menzel 1998)

kz(T ) = 0.46 ×(

300

T

)4/3

(11)

The function q(N , T ) in Eq. (9) describes the power density of heat production within theactive region and given by (Menzel 1998)

q(N , T ) = Eq(T ) · Caug(T ) · N 3 (12)

where Eq(T ) models the bandgap shrinkage (Menzel 1998).We solve Eqs. (1), (2), (7) and (9) using FD-BPM considering the longitudinal and lateral

boundary conditions (Marciante and Agrawal 1996; Menzel 1998; Hess et al. 1995). Algo-rithm of modeling which is based on FD_BPM is illustrated in Fig. 2. The parameters andtheir values used in numerical simulation are presented in Table 1.

3 Results and discussion

3.1 Stripe laser with modal reflector

In broad-area gain regions, the light has no lateral confinement, so any increase in the localrefractive index can lead to self-focusing, which breaks up the lateral mode profile into mul-tiple filaments. Using output mirror with lateral reflectivity RL(x) described by the Gaussianfunction can confine the lateral mode to the stripe center through gain-guiding and cause

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Fig. 3 Lateral profiles of a 50-μm stripe-width laser with R0 = 0.95, Rmin = 0.05, Rmax = 0.5,

W = 5, 14 and ∞ μm. a Mirror profiles, b near field intensity, c far field intensity

Fig. 4 Lateral profiles of a 50-μm stripe-width laser with R0 = 0.95, W = 5 μm, Rmin = 0.05 andRmax = 0.50, 0.55 and 0.60. a Mirror profiles, b near field intensity, c far field intensity

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Fig. 5 a Near field and b far field of stripe laser with stripe width of 15 μm (dashed curve) and taperedlaser with filter section width and length of 3 and 10 μm, respectively, and taper angle of 6◦ (solid curve),R0 = 0.95, RL = 0.05

Fig. 6 Temperature distributions in active region of a stripe laser, b tapered laser. Parameters are the same asin Fig. 5. Maximum temperature of facet in stripe structure is 347 K and in tapered structure is 387 K

Fig. 7 Schematic structure of the unpumped window in a semiconductor laser

stable operation. The Gaussian function is given by

RL(x) = Rmin + (Rmax − Rmin) exp

(−

( x

W

)2)

(13)

where Rmin and Rmax are minimum and maximum of reflection coefficient, respectively.Figure 3a, b, c show the output mirror profiles, lateral intensity profiles and corresponding

far-field distributions, respectively at the output facet of a 50-μm stripe width quantum well

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Fig. 8 a Near field and b far field of a tapered laser with (dashed curve) and without (solid curve) UPW.R0 = 0.95, RL = 0.05, filter section width and length are 3 and 10 μm, respectively and taper angle is 6◦

Fig. 9 Temperature distribution in active region of tapered structure a without, b with UPW. Parameters arethe same as in Fig. 8. Maximum temperature of facet without UPW is 387 K and with UPW is 336 K

laser for Rmin = 0.05, Rmax = 0.5 and W = 5, 14 μm and ∞. For W = 5 μm, the laseroperation is stable, but larger W , increases the width of the Gaussian function and destabilizesthe laser operation. For W = 14 μm, the filaments are fully developed, but both the near andfar fields remain symmetric. For W = ∞, both near and far fields become asymmetric andthe lateral profile becomes unstable.

Figure 4a, b, c show mirror profile and the near and far fields for Rmin = 0.05, W = 5 μmand different Rmax. For larger Rmax, the stable output power increases. But as can be seen inFig. 4c there is the evidence of “rabbit ears” effect in the far field, a well-known feature ofsemiconductor laser that is attributed to astigmatism induced by the linewidth enhancementfactor (Marciante and Agrawal 1996). As the Rmax increases, the “rabbit ears” effect in thefar field becomes more pronounced.

3.2 Tapered structures

Figure 5a, b show the near and far fields of a quantum well stripe laser and quantum welltapered laser with equal volume of active region and equal injected current. It is assumedthat the stripe laser has stripe width of 15 μm (dashed curve) and the tapered laser has afilter section with width and length of 3 and 10 μm, respectively, and taper angle of 6◦

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(solid curve), R0 = 0.95, RL = 0.05. Tapered structure has stable operation while in thestripe structure filaments are fully developed.

The tapered structure has a big problem. As can be seen in Fig. 6a, b, temperature of activeregion near the mirror with larger reflectivity in the tapered structure is higher than stripestructure. In our model, maximum temperature in tapered structure is 387 K and in stripestructure is 347 K. The optical power density at the laser facet is high which could lead tocatastrophic optical mirror damage (COMD). The local facet heating mainly consists of twocontributions: surface carrier nonradiative recombination and reabsorption of the emittinglight. The heating leads to a reduction of the semiconductor bandgap and an increase ofthe local absorption loss. This establishes a feedback mechanism for the facet heating. Thefacet temperature of a high-power laser can be reduced by the introduction of an unpumpedwindow (UPW) which is a current blocking region located at the front facet of the laser (Liuet al. 2006) as shown in Fig. 7. The blocking layer effectively prevents current injection nextto the facet and thus reduces the carrier density and the surface nonradiative recombination.

Figure 8a, b show near and far fields of a tapered structure with and without UPW. Themaximum output power of laser with 2.5-μm UPW is almost unchanged but as can be seen inFig. 9a, b, the temperature of waveguide filter section decreases and maximum temperatureof facet is 336 K.

4 Conclusion

One method to achieve higher output power in semiconductor laser is to widen its activeregion. With broad area structure, however, semiconductor lasers face the problem of beamfilamentation. To overcome this problem, we propose using stripe lasers with modal reflectorand tapered structure.

Gaussian modal reflector in stripe lasers can confine the lateral mode to the stripe centrethrough gain-guiding and cause a stable operation. Smaller width of the Gaussian profileimproves the stability of laser operation. Increasing maximum reflectivity in Gaussian func-tion results in higher stable output power but “rabbit ears” effect appears in the far fielddistribution.

Using tapered structure is another method to achieve stable high output power. However,this structure has a big problem. Temperature of active region in filter section is high andthe width of this section is very small. Therefore the optical power density at the laserfacet is high which could lead to COMD. This phenomenon is one of the major failuremechanisms of laser diodes which limits the maximum output power. The facet heating canbe reduced by introduction of UPW which almost does not change the maximum outputpower.

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Stable high optical power in quantum well lasers with profiled reflection and tapered structures