Oxide-confined Vertical-cavity Lasers Research Articles

(Invited) Light Management for Engineering Luminescence in Nanoscale Environments By Numerical Optimization

The spontaneous emission rate of fluorescencent species in general is affected by its environment. Geometrical structure and material composition of the environment can yield strongly increased rates. This effect is known as Purcell effect, and the magnitude of enhancement of the emission rate in a cavity is known as Purcell factor. The Purcell factor is proportional to the cavity mode's quality factor (Q factor) and inversely proportional to the modal volume. This implies that strongly resonant structures with small length scales (of the order of the wavelength of light) can greatly influence fluorescence. However, not only the emission rate can be controlled by a suitably chosen environment, but also the directional properties of the emitted light field can be engineered by placing the emitter in custom-made environments. In the regime of optical wave phenomena on nano-meter length scales (nano optics), Maxwell's equations for the 3D, vectorial electromagnetic field distribution can to be solved numerically in order to quantify the expected emission rate and far field radiation patterns. In order to obtain specific functionalities of optical devices, numerical optimization is performed. I.e., in numerical computations, structural parameters (layer thicknesses, structure dimensions, material composition, etc) are varied until a parameter set is reached which yields best performance for the specific functionality. This numerically optimized structure can then serve as design pattern for experimental realizations. We review our recent developments of finite-element method based and machine-learning inspired optimization algorithms [1]. We have applied these methods in order to optimize light extraction efficiency of quantum dots embedded in deterministically fabricated cavities [2] and in periodic nano-structures [3], as well as extraction efficiency from structured light emitting diodes (LED, OLED) [4]. We have also investigated possibilities to manipulate emission properties in chiral photonic structures [5], and to design vertical cavity lasers [6]. Further, in applications like light trapping in solar cells, for enhanced photovoltaic efficiency, the related problem of maximizing coupling of light of specific spectral properties into nanostructured solar cells can be treated [7]. In this contribution we will further present recent results on optimization of photon extraction efficiency from single photon sources for applications in quantum technology. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 675745 (MSCA-ITN-EID NOLOSS) and from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 14IND13 (PhotInd). We further acknowledge funding by Einstein Foundation Berlin (ECMath-SE6) and by Freie Universität Berlin (Dahlem Research School). [1] P.-I. Schneider, et al. Global optimization of complex optical structures using Bayesian optimization based on Gaussian processes. Proc. SPIE 10335, 103350O (2017).[2] M. Gschrey, et al. Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography. Nat. Commun. 6, 7662 (2015).[3] C. Barth, et al. Increased fluorescence of PbS quantum dots in photonic crystals by excitation enhancement. Appl. Phys. Lett. 111, 031111 (2017).[4] L. Zschiedrich, et al. Numerical analysis of nanostructures for enhanced light extraction from OLEDs. Proc. SPIE 8641, 86410B (2013).[5] P. Gutsche, et al. Locally enhanced and tunable optical chirality in helical metamaterials. Photonics 3, 60 (2016).[6] N.N. Ledentsov, et al. Direct Evidence of the Leaky Emission in Oxide-Confined Vertical Cavity Lasers. IEEE J. Quant. Electron. 52, 2400207 (2016).[7] K. Jäger, et al. Simulations of Sinusoidal Nanotextures for Coupling Light into c-Si Thin-Film Solar Cells. Opt. Express 24, A569 (2016).

Direct Evidence of the Leaky Emission in Oxide-Confined Vertical Cavity Lasers

We report the observation of narrow tilted lobes in the far-field emission pattern of leaky oxide-confined vertical-cavity surface-emitting lasers (VCSELs). The VCSEL cavity is surrounded by two selectively oxidized aperture layers, which are intentionally designed to produce a high lateral leakage of the high-order transverse modes of the vertical cavity. The device operates in the fundamental transverse mode at oxide aperture diameters below $5~\mu \text{m}$ and currents up to 4 and 5 mA. At higher currents or larger aperture diameters, an additional high-order transverse optical mode evolves. This mode is revealed by the appearance of a shorter wavelength emission line in the electroluminescence spectra of the device, resulting in multi-mode lasing and in the related changes in the near- and far-field patterns. In the far-field pattern, the evolution of the high-order mode is revealed by the evolution of the two overlapping emission lobes at moderate (~5°) tilt angles with respect to the normal to the surface and by the appearance of a multi-spot or a ring pattern in the CCD camera images. Most importantly, the appearance of this high-order transverse mode is accompanied by an observation of much narrower lobes in the far-field pattern observed at significantly larger tilt angles (~35°). The tilt angle and the narrow angular width of these emission lobes in the far-field spectrum are in agreement with those calculated in the 3-D cold cavity modeling of the optical modes of the device. These narrow tilted lobes revealed in this paper are the fingerprints of the leakage effect in specially designed oxide-confined VCSELs with their intensity being proportional to the optical power leaving the aperture region in the direction parallel to the surface and propagating into the oxidized region. The effect can be applied for engineering of single-mode VCSELs, coherently-coupled 2-D VCSEL arrays, laterally integrated VCSEL-photodetector chips, and VCSELs integrated to slow light waveguides, for coupled optical gates for optical computers and other types of photonic integrated circuits.

Extended Model of a VCSEL with Non-Uniform Laser Structure

Results of investigation of the oxide-confined vertical-cavity laser (VCSEL) including non-uniformity of diffusion processes, dynamical effects, and transparent cavity modes are presented. The influence of the spatial hole burning effect on laser characteristics is investigated and discussed. It was shown that decreasing of oxide mesa radius leads to increasing of the modulation bandwidth of the VCSEL. Obtained results allow optimizing laser properties by changing of geometrical parameters.

Electro-Thermal Analysis of Oxide-Confined Vertical-Cavity Lasers

The performance of oxide-confined vertical-cavity lasers (VCLs) can be severely limited by current leakage and self-heating. This paper investigates electrical and thermal effects of lateral oxidation on wafer-bonded 1.55 μm VCLs. Measurements are combined with two-dimensional finite-element simulations to analyze internal device physics. Charged defects at the p-side fused interface are found to increase the threshold voltage as well as lateral current spreading. An optimum oxide aperture for minimum device heating is calculated. Loss reductions are predicted to lead to a minimization of self-heating with small apertures.

Transverse-mode structure and pattern formation in oxide-confined vertical-cavity semiconductor lasers

We analyze the transverse profiles of oxide-confined vertical-cavity laser diodes as a function of aperture size. For small apertures we demonstrate that thermal lensing can be the dominant effect in determining the transverse resonator properties. We also analyze pattern formation in lasers with large apertures where we observe the appearance of tilted waves.

Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes

We analyze the transverse mode structure of selectively oxidized vertical-cavity surface-emitting semiconductor lasers as a function of the aperture size and injection current. Measurements of the spectral splittings, the near and far field sizes and the response to pulsed operation demonstrate that a parasitic thermal lens can be a dominant factor in determining the transverse resonator properties of small (<3 μm) lasers.

Low-truncation-error finite difference equations for photonics simulation. II. Vertical-cavity surface-emitting lasers

For part I see, ibid., p. 134, 1998. The basic approach outlined in the previous article is applied to the difficult problem of computing the optical modes of a vertical-cavity surface-emitting laser. The formulation utilizes a finite difference equation based upon the lowest order term of an infinite series solution of the scalar Helmholtz equation in a local region. This difference equation becomes exact in the one-dimensional (1-D) limit, and is thus ideally suited for nearly 1-D devices such as vertical-cavity lasers. The performance of the resulting code is tested on both a simple cylindrical cavity with known solutions and an oxide-confined vertical-cavity laser structure, and the results compared against second-order-accurate code based upon Crank-Nicolson differencing.

Bistable operation of coupled in-plane and oxide-confined vertical-cavity laser 1×N routing switches

We report on the observation of two-mode intensity bistability in intracavity-coupled in-plane lasers and oxide-confined vertical-cavity surface emitting lasers (VCSELs) operating under room-temperature CW conditions.

Spontaneous emission factor in oxide confined vertical-cavity lasers

We report on measurements of the spontaneous emission factor for oxide-confined InGaAs vertical cavity surface emitting lasers. The spontaneous emission factor is determined as a function of the active layer volume from the measurement of small-signal harmonic distortion at threshold. For a 3×3 μm oxide aperture device we obtain spontaneous emission factor of 4.2⋅10−2 at room temperature.

Threshold investigation of oxide-confined vertical-cavity laser diodes

We report an experimental and theoretical analysis of the threshold properties of infrared oxide-confined vertical-cavity surface emitting lasers. We find good agreement between experiment and theory on the wavelength dependencies of the threshold current density and intrinsic voltage. The threshold voltage is shown to equal the sum of the calculated quasi-Fermi energy separation and the ohmic drop arising from a record low 17 to 30 Ω series resistance in these vertical-cavity lasers. Our analysis provides two independent means for determining the material threshold gain. A threshold gain of 500 cm−1 is found for these oxide-confined lasers, which is half that estimated for ion-implanted lasers with inferior electrical and optical confinement.

Index guiding dependent effects in implant and oxide confined vertical-cavity lasers

Implant and oxide confined vertical-cavity surface-emitting lasers are compared in terms of properties dependent upon the nature of index guiding in the two structures including CW threshold current scaling with size, light-current linearity, pulsed operation delay, and beam profiles. The oxide confined lasers, fabricated by wet thermal oxidation, have a built-in index guide and thus exhibit substantially better properties than do lasers from the same wafer fabricated by proton implantation which rely on a thermal lens to reduce diffraction losses.

Oxide-confined vertical-cavity laser with additional etched void confinement

A vertical-cavity surface-emitting laser that incorporates oxide confinement with additional etched void photon confinement is described. A room-temperature continuous-wave threshold of 75 µA for a 3.5 µm-diameter lateral device size is achieved.

Self-pulsing oxide-confined vertical-cavity lasers with ultralow operating current

Selectively oxidised vertical-cavity lasers which exhibit self-pulsating lasing at currents as low as 470 nA are reported. Characteristics including linearly polarised emission, narrow linewidths and coherent near- and far-field diffraction indicate that these devices operate as lasers at DC currents 1 mA.