Efficient rigorous calculations of power flow in grating coupled surface-emitting devices

Moharam, M. G.; Greenwell, Andrew

doi:10.1117/12.549477

Cited by 8 publications

(13 citation statements)

References 11 publications

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“…It does, however, prevent the scattering matrices from having the ability to be arbitrarily interchanged. Conceptually, this problem is overcome by the novel approach of separating all of the layers composing the device with gaps composed of free space [33]. As long as these gaps are given zero thickness, they will have no effect on the performance of the device.…”

Section: Reformulation Of Scattering Matricesmentioning

confidence: 99%

“…Today, scattering parameters are so common that the terms "S 11 " and "S 21 " are often used synonymously for "reflection" and "transmission." Despite this strong and longstanding convention, the CEM community is adopting inefficient and unconventional formalisms for scattering matrices for use in semianalytical methods [7,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The majority of the literature on this topic appears in optics journals, where the benefits of semianalytical methods are more pronounced and the use of scattering parameters in experiments is less common.…”

Section: Introductionmentioning

confidence: 99%

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Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

136

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Abstract-The literature describing scattering matrices for semianalytical methods almost exclusively contains inefficient formulations and formulations that deviate from long-standing convention in terms of how the scattering parameters are defined. This paper presents a novel and highly improved formulation of scattering matrices that is consistent with convention, more efficient to implement, and more versatile than what has been otherwise presented in the literature. Semi-analytical methods represent a device as a stack of layers that are uniform in the longitudinal direction. Scattering matrices are calculated for each layer and are combined into a single overall scattering matrix that describes propagation through the entire device. Free space gaps with zero thickness are inserted between the layers and the scattering matrices are made to relate fields which exist outside of the layers, but directly on their boundaries. This framework produces symmetric scattering matrices so only two parameters need to be calculated and stored instead of four. It also enables the scattering matrices to be arbitrarily interchanged and reused to describe longitudinally periodic devices more efficiently. Numerical results are presented that show speed and efficiency can be increased by more than an order of magnitude using the improved formulation.

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Section: Reformulation Of Scattering Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

136

View full text Add to dashboard Cite

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“…It results in a linear relationship between the field coefficients, c p and c n in two neighboring layers. In a multilayer structure, various algorithms can be used to connect the coefficients, such as transfer matrices [51], hybrid matrices [52], admittance matrices [53], and scattering matrices (S-matrices) [25], [41], [54]. Among them, the S-matrices are used widely in the literature, due to various advantages such as elegant physical interpretations, unconditional stability and memory efficiency [41].…”

Section: F Scattering Matricesmentioning

confidence: 99%

“…There are several variants of S-matrix implementations for the FMM [25], [41]. In the variant implemented in this work, all the layers are separated by a gap composed of freespace [41], [54]. As long as the free-space gap thickness is zero, it has no influence on the performance of the structure.…”

Section: F Scattering Matricesmentioning

confidence: 99%

“…As long as the free-space gap thickness is zero, it has no influence on the performance of the structure. The advantage of using the artificial free-space regions, is that the S-matrices of each layer only depends on the layer itself, not on its adjacent layers [41], [54]. It reduces the numerical effort for the cases where only one layer is changing, since only the S-matrices of that layer should be updated instead of all adjacent layers.…”

Section: F Scattering Matricesmentioning

confidence: 99%

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Numerical Investigation of Vertical Cavity Lasers With High-Contrast Gratings Using the Fourier Modal Method

Taghizadeh¹,

Mørk²,

Chung³

2016

J. Lightwave Technol.

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Abstract-We show the strength of the Fourier modal method (FMM) for numerically investigating the optical properties of vertical cavities including subwavelength gratings. Three different techniques for determining the resonance frequency and Q-factor of a cavity mode are compared. Based on that, the Fabry-Perot approach has been chosen due to its numerical efficiency. The computational uncertainty in determining the resonance frequency and Q-factor is investigated, showing that the uncertainty in the Q-factor calculation can be a few orders of magnitude larger than that in the resonance frequency calculation. Moreover, a method for reducing 3D simulations to lower-dimensional simulations is suggested, and is shown to enable approximate and fast simulations of certain device parameters. Numerical calculation of the cavity dispersion, which is an important characteristic of vertical cavities, is illustrated. By employing the implemented FMM, it is shown that adiabatic heterostructures designs are advantageous compared to abrupt heterostructures for minimizing the cavity scattering loss.

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Surface-Emitting QDs Laser with a Monolithically Integrated Grating Outcoupler

Smolski

Yilmaz

et al. 2009

Advances in Optical Sciences Congress

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Efficient rigorous calculations of power flow in grating coupled surface-emitting devices

Cited by 8 publications

References 11 publications

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Numerical Investigation of Vertical Cavity Lasers With High-Contrast Gratings Using the Fourier Modal Method

Surface-Emitting QDs Laser with a Monolithically Integrated Grating Outcoupler

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