Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes

Wilson, G.C.; Kuchta, Daniel M.; Walker, J.; Smith, J. S.

doi:10.1063/1.111097

Cited by 67 publications

(14 citation statements)

References 8 publications

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“…[3][4][5][6] It is indeed the major effect that induces transitions to higher order modes. Spatial hole burning is referring to the local depletion of the carrier density at points within the laser where the modal intensity is large.…”

Section: Introductionmentioning

confidence: 98%

Modeling spatial hole burning and mode competition in index-guided VCSELs

Schatz

Peeters

2003

SPIE Proceedings

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We have derived and implemented a simplified dynamical multi-mode model for vertical-cavity surface-emitting lasers (VCSELs) requiring minimal computing resources while remaining realistic. A set of spatially independent rate equations with a minimum of parameters is extracted from the general spatially resolved equations and reduced to dimensionless form to expose its essentials. The shape of the carrier density distribution is approximated with a linear sum of the modal shapes which are considered to be bias independent for index-guided devices. Despite this simplification the model, which can be extended to any number of laser modes, includes important effects like spatial hole burning (SHB), carrier diffusion and inhomogeneous injection and shows good agreement with spatially resolved models.We describe the reduction and nondimensionalization of the general spatially resolved equations. The implementation inside a C++ rate-equation framework is discussed and shown to provide a powerful and flexible environment to efficiently study the contribution of different factors.The effect of spatial hole burning (SHB) and mode competition on the small signal modulation response is investigated in three basic cases. The comparison between a single mode VCSEL without SHB, a single mode VCSEL including SHB and two mode VCSEL including SHB enables us to pinpoint which contributions are due to SHB and which are due to the modal competition.Finally,the possibility of using this approach to model polarization switching in VCSELs is discussed. The unavoidable small birefringence (with elasto-optic and electro-optic contributions) present in all VCSELs leads to a doubling of each mode into two orthogonal polarization states which are almost degenerate. Although small, the birefringence causes gain differences: part of which are due to frequency dependent gain and loss of the materials and part of which are due to slightly different transverse modal shapes. As these gain differences depend on the injected current, they can be one of the causes of polarization switching.

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Section: Introductionmentioning

confidence: 98%

Modeling spatial hole burning and mode competition in index-guided VCSELs

Schatz

Peeters

2003

SPIE Proceedings

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“…The well-known spatial hole burning (SHB) effect which is produced by the local interaction between the optical field and carrier distributions in the laser active layer is regard as the primary cause of high-order transverse mode emitting [5][6][7][8] . In order to describe SHB and other effects related to the inhomogeneous lateral distribution of carriers and photons in the cavity, the space-and time-dependent rate equations, which describe the rates of change of the carrier and photon populations in the active layer, are adopted to provide excellent foundation for our VCSEL model in this paper.…”

Section: Introductionmentioning

confidence: 99%

The multi-mode behavior of vertical-cavity surface-emitting lasers under a spatially periodical current injection

Zheng

Ren

et al. 2005

Optoelectronic Materials and Devices for Optical Communications

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A two-dimensional spatially independent rate equation model of vertical-cavity surface-emitting lasers (VCSELs) is derived and then used to analysis the multi-mode behaviour of VCSELs. The transverse mode characteristics of VCSELs, the carrier distribution in both the radial and the azimuthal directions, and the effects of the azimuthal non-uniformity of the injection current on the transverse mode behaviours are investigated in detail. By using both Bessel and Fourier expansion of carrier density, the 2D spatially independent rate equations for transverse mode are formulated, which take into account carrier diffusion both in the radial and in the azimuthal direction as well as gain non-uniformity in the lateral direction. The equations are numerical solved self-consistently using the Runge-Kutta method for different spatial periodic injection current. Results show that a proper current injection profile can separate the sine mode and cosine mode of the same order transverse modes observably. It is found that an injection current with periodic change in the azimuthal direction is favourable for the excitation of the modes whose mode profile match the current profile best. The results are useful to the design and control of transverse mode characteristics of a VCSEL.

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“…A single transverse mode operation can be achieved via the introduction of mode-selective losses or by reducing the size of the cavity in both transverse and longitudinal directions [5,6]. The primary cause of the transverse mode competition is attributed to the well-known spatial hole burning effects (SHB-effects), which are produced by the interaction between the carriers and the multi-transverse modes in the laser active layer [7][8][9][10][11][12]. It signifies that the injection current plays a very important role in the multitransverse mode behavior of VCSELs.…”

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confidence: 99%

Influences of the Current Transverse Profile on the Transverse Mode Competition of VCSELs Diodes

Zhang

2007

Int J Infrared Milli Waves

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A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed. The results are useful to the optimum design of the optical transverse modal structure of VCSELs.

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Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes

Abstract: Articles you may be interested inPhysics of mode selectivity of vertical-cavity surface-emitting diode lasers

Cited by 67 publications

References 8 publications

Modeling spatial hole burning and mode competition in index-guided VCSELs

Modeling spatial hole burning and mode competition in index-guided VCSELs

The multi-mode behavior of vertical-cavity surface-emitting lasers under a spatially periodical current injection

Influences of the Current Transverse Profile on the Transverse Mode Competition of VCSELs Diodes

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