Plane Wave Admittance Method Research Articles

Precise Lateral Mode Control in Photonic Crystal Vertical-Cavity Surface-Emitting Lasers

We demonstrate an oscillatory behavior of resonant wavelengths and threshold gains of the fundamental and first-order transverse mode of photonic crystal vertical-cavity surface-emitting laser (PhC VCSEL) with the PhC etching depth. To this aim we use a full vectorial, 3-D optical model (plane wave admittance method) combined with a thermal model and an exemplary 1300 nm quantum-dot VCSEL structure. Such oscillatory behavior poses a strong restriction on the etching depth precision: about 0.1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\mu{\rm m}$</tex></formula> in order to achieve a threshold gain not higher than 10% the threshold gain minimum and twice higher precision for simultaneous strong discrimination of the first-order transverse mode.

Microphotoluminescence investigation of InAs quantum dot active region in 1.3 μm vertical cavity surface emitting laser structure

Microphotoluminescence (μ-PL) investigation has been performed at room temperature on InAs quantum dot (QD) vertical cavity surface emitting laser (VCSEL) structure in order to characterize the QD epitaxial structure which was designed for 1.3 μm wave band emission. Actual and precise QD emission spectra including distinct ground state (GS) and excited state (ES) transition peaks are obtained by an edge-excitation and edge-emission (EEEE) μ-PL configuration. Conventional photoluminescence methods for QD-VCSELs structure analysis are compared and discussed, which indicate the EEEE μ-PL is a useful tool to determine the optical features of the QD active region in an as-grown VCSEL structure. Some experimental results have been compared with simulation results obtained with the aid of the plane-wave admittance method. After adjustment of epitaxial growth according to EEEE μ-PL measurement results, QD-VCSEL structure wafer with QD GS transition wavelength of 1300 nm and lasing wavelength of 1301 nm was obtained.

Semivectorial method based on effective index for VCSEL analysis

A combination of the plane-wave expansion method with the effective-index approximation is presented, which allows vectorial properties of electromagnetic field in three-dimensional structures to be considered. I formulate mathematical equations that are the basis of this combined approach, and then I show the simulation of the optical properties of oxide-confined vertical-cavity surface-emitting lasers (VCSELs). The results are compared with the ones obtained with the classical effective-index method and with the fully vectorial plane-wave admittance method. Next the semivectorial properties of the new model are utilized to analyze a birefringent VCSEL structure.

Modal gain and confinement factors in top- and bottom-emitting photonic-crystal VCSEL

We investigate the modal characteristics of a phosphide photonic-crystal vertical-cavity surface-emitting diode laser (VCSEL) by using the three-dimensional, full vectorial plane wave admittance method. A single-defect, photonic crystal is defined as a regular, hexagonal net of holes with varying depths. The modal gain and confinement factors are compared for two VCSEL structures: with emission either through the DBR with the photonic crystal or through the DBR free of photonic crystal. Significant improvement in the beam quality is demonstrated for the second design.

Exactness of simplified scalar optical approaches in modelling a threshold operation of possible nitride vertical‐cavity surface‐emitting diode lasers

AbstractModern small‐size vertical‐cavity surface‐emitting diode lasers (VCSELs) require principally fully vectorial optical modelling because their cavity sizes are of the order of the wavelength of emitted radiation. However, much simpler scalar approaches are often surprisingly exact even beyond the limits of their confirmed validity. Therefore, in the present paper, reasonable limits of an application of simplified scalar optical approaches (instead of more exact but also much more involved and time‐consuming rigorous vectorial ones) are determined to model threshold operation of possible nitride VCSELs equipped with tunnel junctions with the aid of a comparison of results of the scalar effective frequency method with those obtained using the fully vectorial three‐dimensional plane wave admittance method. Both these optical methods have been found to give usually quite close results for the fundamental transverse mode. Larger discrepancies between the results of both approaches have been found for first‐order transverse modes (and even larger are expected for higher‐order ones) and for larger (or very small) active regions. Some structural modifications of nitride VCSELs, which may enable their low‐threshold single‐fundamental‐mode room‐temperature continuous‐wave operation, are proposed. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Optimal Parameters of Photonic-Crystal Vertical-Cavity Surface-Emitting Diode Lasers

We investigate the modal characteristics of a 1300-nm InP-based photonic-crystal (PC) vertical-cavity surface- emitting diode laser. To this aim, we apply the plane-wave admittance method and analyze a broad range of PC parameters such as hole etching depth, distance between the holes, and their diameters. We determine a range of technologically feasible PC parameters providing an optimal laser performance.

Modeling of single- and multimode photonic-crystal planar waveguides with the plane-wave admittance method

In this paper we present the plane-wave admittance method (PWAM) in application to modeling light propagation in photonic crystal waveguides. We determine out-of-plane losses in single- and multimode waveguides and analyze the coupling of fundamental and higher-order modes in the latter case. Finally we compute the group velocity of light and show the possibilities and costs of achieving a very slow light regime.

Impact of the hole depth on the modal behaviour of long wavelength photonic crystal VCSELs

We investigate the modal characteristics of a telecommunication-oriented, phosphide photonic crystal vertical-cavity surface-emitting laser (VCSEL) as a function of the hole depth by using a three–dimensional, full vectorial plane-wave admittance method. The interplay of diffraction–waveguiding is considered and the optimal depth of the photonic crystal holes is determined, providing single mode operation with the smallest etching depth of the photonic crystal structure.

Numerical analysis of high Q-factor photonic-crystal VCSELs with plane-wave admittance method

The paper presents the application of a novel plane-wave admittance method (PWAM) to the three-dimensional and fully vectorial modeling of vertical-cavity surface-emitting lasers with incorporated photonic crystal. The basic mathematical details of the method are given and its convergence is verified for a sample structure. Then the simulations performed with PWAM are used to determine the optimal photonic crystal parameters for low-loss, high-Q-factor regime.

Modal behavior of photonic-crystal vertical-cavity surface-emitting diode laser analyzed with Plane Wave Admittance Method

A three-dimensional, full vectorial model has been applied for investigation the modal characteristics of a phosphide photonic-crystal vertical-cavity surface-emitting diode laser. The photonic crystal has been defined as a regular, hexagonal net of holes, etched in the upper, p-type Distributed Bragg Reflector of the laser. The electromagnetic field has been confined to the active region by a single defect of the photonic crystal providing overlapping with carriers funneled by a tunnel junction. We have determined the range of design parameters, which provide single mode operation.

Single mode condition and modes discrimination in photonic-crystal 1.3 μm AlInGaAs/InP VCSEL

We determine the single mode condition and analyze the modes discrimination of 1.3 mum InP based photonic-crystal vertical-cavity surfaceemitting diode laser. To this aim we apply the fully vectorial, three dimensional Plane Wave Admittance Method and analyze a broad range of photonic-crystal parameters such as hole etching depth, distance between the holes and their diameters.

Plane Wave Admittance Method - a novel approach for determining the electromagnetic modes in photonic structures

In this article we present a novel approach for determining the electromagnetic modes of photonic multilayer structures. We combine the plane wave expansion method with the method of lines resulting in a fast and accurate computational technique which we named the plane wave admittance method. In addition, we incorporate perfectly matched layers at the boundaries parallel to the multilayer surfaces which allow for easy determination of leaky modes. The convergence of the method is verified for the case of photonic crystal slab showing very good agreement with the results obtained with full three-dimensional plane wave expansion method while the numerical effort is largely reduced. The numerical implementation of the method will be soon available on the web.