Threshold performance of pulse-operating quantum-cascade vertical-cavity surface-emitting lasers.

Quantum-cascade (QC) vertical-cavity surface-emitting lasers (VCSELs) could combine the single longitudinal mode operation, low threshold currents, circular output beam, and on-wafer testing associated with VCSEL configuration and the unprecedented flexibility of QCs in terms of wavelength emission tuning in the infrared spectral range. The key component of QC VCSEL is the monolithic high-contrast grating (MHCG) inducing light polarization, which is required for stimulated emission in unipolar quantum wells. In this paper, we demonstrate a numerical model of the threshold operation of a QC VCSEL under the pulse regime. We discuss the physical phenomena that determine the architecture of QC VCSELs. We also explore mechanisms that influence QC VCSEL operation, with particular emphasis on voltage-driven gain cumulation as the primary mechanism limiting QC VCSEL efficiency. By numerical simulations, we perform a thorough analysis of the threshold operation of QC VCSELs. We consider the influence of optical and electrical aperture dimensions and reveal the range of aperture values that enable single transversal mode operation as well as low threshold currents.

Convergence analysis of various factorization rules in the Fourier-Bessel basis for solving Maxwell equations using modal methods.

The choice of factorization rule can strongly affect the convergence of solutions to Maxwell equations based on the orthogonal expansion of electromagnetic fields. While this issue has already been investigated thoughtfully for the Fourier basis (plane-wave expansion), for other bases it has not yet received much attention. Although there are works showing that, in the case of the Fourier-Bessel basis (cylindrical-wave expansion), the use of an inverse factorization rule can provide faster convergence than Laurent's rule, these works neglect the fact that other rules are also possible. Here, I mathematically demonstrate four different factorization rules for solving Maxwell equations in cylindrical coordinates using the Fourier-Bessel expansion in both infinite and finite domains. I compare their convergence for a step-index fiber (which has a known exact solution and thus enables the absolute numerical error to be determined), as well as for several VCSEL structures. I show that the cylindrical-wave expansion differs from the plane-wave expansion and that the application of an inverse factorization rule for the electric field component perpendicular to the discontinuities can result in deterioration of numerical convergence. Finally, I identify the factorization rule that gives the fastest convergence of the modal method using the Fourier-Bessel basis.

Planar focusing reflectors based on monolithic high contrast gratings: design procedure and comparison with parabolic mirrors.

Here, we describe in detail a procedure for the numerical design of planar focusing mirrors based on monolithic high contrast gratings. We put a special emphasis on the reconstruction of the hyperbolic phase of these mirrors and we conclude that the phase does not have to be perfectly mimicked to obtain a focusing reflector. We consider here the grating mirrors that focus light not in the air but in the GaAs substrate and we compare them with conventional parabolic reflectors of corresponding dimensions. The light intensity at the focal point of the focusing grating mirrors was found to be comparable to that of the parabolic reflector. Moreover, the reflectivity of the focusing grating mirrors is almost as high as that of parabolic mirrors covered with an additional reflecting structure, if the ratio of the reflector width to the focal length is less than 0.6. Planar focusing grating mirrors offer a good alternative to parabolic mirrors, especially considering the complexity of fabricating three-dimensional structures compared to planar structures.

Transparent electrode employing deep-subwavelength monolithic high-contrast grating integrated with metal.

This paper demonstrates designs of transparent electrodes for polarized light based on semiconductor deep-subwavelength monolithic high-contrast gratings integrated with metal (metalMHCG). We provide theoretical background explaining the phenomena of high transmittance in the gratings and investigate their optimal parameters, which enable above 95% transmittance for sheet resistance of 2 ΩSq-1 and over 90% transmittance for extremely small sheet resistance of 0.04 ΩSq-1 in a broad spectral range below the semiconductor band-gap. The analysis is based on our fully vectorial optical model, which has been verified previously via comparison with the experimental characteristics of similar structures. The transparent electrodes can be realized in any high refractive index material used in optoelectronics and designed for light in spectral ranges starting from ultra-violet with no upper limit for the wavelength of the electromagnetic waves. They not only enable lateral transport of electrons but can also be used as an electric contact for injecting current into a semiconductor.

Tuning of reflection spectrum of a monolithic high-contrast grating by variation of its spatial dimensions.

We report the first experimental parametric analysis of subwavelength monolithic high-contrast grating (MHCG) mirrors. To date, subwavelength grating mirrors have been fabricated by suspending a thin grating membrane in the air or placing it on a low refractive index material - a scheme that requires sophisticated processing and makes the gratings sensitive to mechanical stress, impeding current injection, and heat dissipation if used in active devices. Inherently MHCGs are well suited for optoelectronic devices because they can be fabricated in all possible material systems. Here we demonstrate above 90% optical power reflectance, strong polarization discrimination. Based on experimental analysis aided by numerical simulations, we demonstrate the possibility of tuning the spectral characteristics of MHCGs reflectance for more than 200 nm via modification of the duty cycle of the MHCG stripes. We show our MHCG tuning method is convenient to define the properties of MHCG devices during the device processing.

Impact of an Antiresonant Oxide Island on the Lasing of Lateral Modes in VCSELs.

Use of antiresonant structures is a proven, efficient method of improving lateral mode selectivity in VCSELs. In this paper, we analyze the impact of a low-refractive antiresonant oxide island buried in a top VCSEL mirror on the lasing conditions of lateral modes of different orders. By performing comprehensive thermal, electrical, and optical numerical analysis of the VCSEL device, we show the impact of the size and location of the oxide island on the current-crowding effect and compute threshold currents for various lateral modes. If the island is placed close to the cavity, the threshold shows strong oscillations, which for moderate island distances can be tuned to increase the side mode discrimination. We are therefore able to pinpoint the most important factors influencing mode discrimination and to identify oxide island parameters capable of providing single-lateral-mode emission.

Numerical Investigation of the Impact of ITO, AlInN, Plasmonic GaN and Top Gold Metalization on Semipolar Green EELs.

In this paper, we present the results of a computational analysis of continuous-wave (CW) room-temperature (RT) semipolar InGaN/GaN edge-emitting lasers (EELs) operating in the green spectral region. In our calculations, we focused on the most promising materials and design solutions for the cladding layers, in terms of enhancing optical mode confinement. The structural modifications included optimization of top gold metalization, partial replacement of p-type GaN cladding layers with ITO and introducing low refractive index lattice-matched AlInN or plasmonic GaN regions. Based on our numerical findings, we show that by employing new material modifications to green EELs operating at around 540 nm it is possible to decrease their CW RT threshold current densities from over 11 kA/cm2 to less than 7 kA/cm2.

Influence of Various Bottom DBR Designs on the Thermal Properties of Blue Semiconductor-Metal Subwavelength-Grating VCSELs.

In this paper, we consider several designs for nitride-based vertical-cavity surface-emitting lasers (VCSELs) with a top semiconductor-metal subwavelength grating (SMSG) as the facet mirror. The constructions of the bottom distributed Bragg reflectors (DBRs) used in the VCSEL designs were inspired by devices demonstrated recently by several research groups. A multiparameter numerical analysis was performed, based on self-consistent thermal and electrical simulations. The results show that, in the case of small aperture VCSEL designs, dielectric-based DBRs with metallic or GaN channels enable equally efficient heat dissipation to designs with monolithically integrated DBRs. In the case of broad aperture designs enabled by SMSGs, monolithically integrated DBRs provide much more efficient heat dissipation in comparison to all other considered designs.

Subwavelength grating as both emission mirror and electrical contact for VCSELs in any material system.

Semiconductor-metal subwavelength grating (SMSG) can serve a dual purpose in vertical-cavity surface-emitting lasers (VCSELs), as both optical coupler and current injector. SMSGs provide optical as well as lateral current confinement, eliminating the need for ring contacts and lateral build-in optical and current confinement, allowing their implementation on arbitrarily large surfaces. Using an SMSG as the top mirror enables fabrication of monolithic VCSELs from any type of semiconductor crystal. The construction of VCSELs with SMSGs requires significantly less p-type material, in comparison to conventional VCSELs. In this paper, using a three-dimensional, fully vectorial optical model, we analyse the properties of the stand-alone SMSG in a number of semiconductor materials for a broad range of wavelengths. Integrating the optical model with thermal and electrical numerical models, we then simulate the threshold operation of an exemplary SMSG VCSEL.

Optimal parameters of monolithic high-contrast grating mirrors.

In this Letter a fully vectorial numerical model is used to search for the construction parameters of monolithic high-contrast grating (MHCG) mirrors providing maximal power reflectance. We determine the design parameters of highly reflecting MHCG mirrors where the etching depth of the stripes is less than two wavelengths in free space. We analyze MHCGs in a broad range of real refractive index values corresponding to most of the common optoelectronic materials in use today. Our results comprise a complete image of possible highly reflecting MHCG mirror constructions for potential use in optoelectronic devices and systems. We support the numerical analysis by experimental verification of the high reflectance via a GaAs MHCG designed for a wavelength of 980 nm.

Transverse mode control in high-contrast grating VCSELs.

This paper presents an extensive numerical analysis of a high-contrast grating VCSEL emitting at 0.98 µm. Using a three-dimensional, fully vectorial optical model, we investigate the influence of a non-uniform grating with a broad range of geometrical parameters on the modal behavior of the VCSEL. Properly designed and optimized, the high-contrast grating confines the fundamental mode selectively in all three dimensions and discriminates all higher order modes by expelling them from its central region. This mechanism makes single mode operation possible under a broad range of currents and could potentially enhance the single-mode output power of such devices. The high-contrast grating design proposed here is the only design for a VCSEL with three-dimensional, selective, optical confinement that requires relatively simple fabrication.

Numerical methods for modeling photonic-crystal VCSELs.

We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR, a fraction of the top-mirror DBR or just the VCSEL cavity. The different models are evaluated by comparing the predicted resonance wavelengths and threshold gains for different hole diameters and pitches of the PC. The agreement between the models is relatively good, except for one model, which corresponds to the effective index method. The simulation results elucidate the strength and weaknesses of the analyzed methods; and outline the limits of applicability of the different models.

Photonic crystal vertical-cavity surface-emitting lasers with true photonic bandgap.

By calculating the band diagrams for the distributed Bragg mirrors of vertical-cavity surface-emitting lasers (VCSELs) with triangular two-dimensional lattice of etched holes we show that true photonic bandgap (PBG) confinement is possible for TE-like polarized light. We confirm this true PBG confinement for a low-index line defect as well as for a low-index cavity mode. Such PBG-VCSELs are compatible with the VCSEL technology and do not require a complicated assembly of three-dimensional photonic crystals.

Optimal radii of photonic crystal holes within DBR mirrors in long wavelength VCSEL.

The modal characteristics of a Photonic-Crystal Vertical-Cavity Surface-Emitting diode Laser (PC-VCSEL) have been investigated. Photonic crystal structure, realized by a regular net of air holes within the layers, has been etched in the upper DBR mirror. An advanced three-dimensional, vectorial electromagnetic model has been applied to a phosphide - based device design featuring InGaAlAs active region, AlGaAs/GaAs mirrors and a tunnel junction to confine the current flow. For the structure under consideration a single mode operation has been found for the hole diameter over photonic crystal lattice constant ratio between 0.1 - 0.3.

Single mode condition and modes discrimination in photonic-crystal 1.3 mum 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.

PlaneWave 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.