Threshold Material Gain Research Articles

Optimal waveguide structure for low-threshold InGaN/GaN-based photonic-crystal surface-emitting lasers

We analyzed the optimal waveguide structure of two types of InGaN-based photonic crystal surface-emitting lasers (PCSELs) to suppress the coupling with leaky modes via mode simulations. To minimize the threshold material gain (gth), we calculated the confinement factor and quality factor of PCSELs with varying waveguide layer thicknesses in the separate confinement heterostructure (SCH) layer. The optical mode intensity profile revealed the coupling between the fundamental mode of SCH and parasitic leaky modes in the cladding layer or substrate as the primary root cause of the low-quality factor and high threshold gain of PCSELs. The asymmetric nature of the SCH structure yielded the optimal waveguide structure to be dependent on the position of the air holes. With a proper waveguide thickness and air hole depth, the optimized threshold modal gain of PCSELs with the n-side air holes can be less than 30 cm−1.

Gain measurements on VCSEL material using segmented contact technique

We report direct measurements of the optical gain on vertical-cavity surface-emitting laser (VCSEL) material using a stripe-length method featuring segmented contacts. We utilise the similarity of the in-plane transverse electric (TE) polarised matrix element and that of the VCSEL lasing mode and a simple method to reduce round trip effects. The confinement factor is determined from cold-cavity simulations of the in-plane TE polarised slab waveguide mode and used to convert the measured in-plane modal gain into the vertical-cavity modal gain, as required for the VCSEL structure. This gives a threshold material gain of 1440 ± 140 cm−1 at 30 °C for this structure. A comparison with the threshold material gain values determined from the lasing condition, where internal optical losses due to doping induced absorption is included using parameters taken from the literature, indicates the presence of an additional source of optical loss in the experiment which increases the threshold material gain by ∼450 cm−1. A best fit is obtained by increasing the optical loss in the n-DBR (distributed Bragg reflectors) layers to 40 cm−1, which is consistent with previous work on additional scattering losses due to interface roughening in the n-DBR layers. To further demonstrate the utility of this method for rapid optimisation, the gain-peak wavelength is measured directly, and its temperature dependence is compared to the lasing wavelength.

Electromagnetic analysis of optimal pumping of a microdisk laser with a ring electrode

We study the lasing modes of microdisk lasers with ring-like electrodes or active regions, in two-dimensional (2-D) formulation. The considered eigenvalue problem is adapted to the extraction of both modal spectra and thresholds from the Maxwell equations with exact boundary conditions. We reduce it to a transcendental equation and solve it numerically. The obtained lasing frequencies and the associated values of threshold material gain of the ring-pumped laser are compared with similar quantities of the fully active microdisk. This comparison shows that the optimal position of the active ring is shifted inward from the disk rim. Its location and width can be used as an engineering instrument to manipulate the thresholds. This effect is explained using the optical theorem and overlap coefficients.

Optical Engineering of Modal Gain in a III-Nitride Laser with Nanoporous GaN

By using a novel conductivity-based selective electrochemical etching, we have introduced nanometer-sized pores into GaN to significantly decrease its refractive index while maintaining its crystallinity. Such advantages of nanoporous (NP) GaN can thus overcome the epitaxial (strain) and optical (index) limitations of AlGaN, which has been used as the cladding layers in InGaN laser diodes for two decades. Compared to Al0.1Ga0.9GaN cladding, which has a refractive index contrast (Δn) of 0.04 to GaN, the Δn of NP-GaN to GaN can be engineered to be over 0.4 without inducing any tensile strain. The high Δn not only increases the optical confinement factor (Γ) from lower than 3% in the state-of-the-art (SOTA) InGaN laser diodes to 9% but also offers a broad tunability of the Γ and the modal gain as well. We have observed a clear correlation between the Γ and the modal gain by using the variable stripe length method and have demonstrated an over 100% increase of the modal gain by engineering the Γ of the waveguides. The increase of the Γ also leads to a more than 2-fold reduction of the lasing threshold under optical pumping. A threshold material gain (gth) of 401.1 cm–1, which is more than 50% lower than the threshold of the SOTA LDs (gth > 1000 cm–1), suggests opportunities in lowering the lasing threshold and increasing the efficiencies of future III-nitride laser diodes.

Facilitating Single-Transverse-Mode Lasing in VCSELs via Patterned Dielectric Anti-Phase Filters

A novel method to achieve single-fundamental-mode lasing and higher order mode suppression using a multi-layer, patterned, dielectric anti-phase filter is employed on the top of oxide-confined vertical-cavity surface-emitting lasers (VCSELs). Dielectric layers are deposited and patterned on individual VCSELs in a wafer-scale process to modify (increase/decrease) the mirror reflectivity across the oxide aperture via anti-phase reflections, creating spatially dependent threshold material gain and VCSEL lasing-mode control. A 1-D plane-wave propagation method is used to calculate the dielectric layer thicknesses in each spatial region needed to facilitate or suppress lasing. A single-fundamental-mode, continuous-wave output power of 3.5 mW is achieved at a lasing wavelength of 850 nm. This additive, non-destructive method allows for mode selection at any lasing wavelength and for any VCSEL layer structure without the need for destructive etching techniques or epitaxial regrowth. It also offers the capability of a tailored filter design based on available materials and deposition methods.

Engineering the Lateral Optical Guiding in Gallium Nitride-Based Vertical-Cavity Surface-Emitting Laser Cavities to Reach the Lowest Threshold Gain

In order to improve the current injection in GaN-based blue vertical-cavity surface-emitting lasers (VCSELs) a dielectric aperture is generally used in combination with an indium–tin-oxide (ITO) layer on the top intracavity p-contact layer. The most straightforward way to realize this introduces a depression of the structure near the optical axis and we show, by using a two-dimensional (2D) effective index method and a three-dimensional (3D) coupled-cavity beam propagation method, that this typically results in optically anti-guided structures with associated high optical losses and thus very high threshold gains. Remarkably, the threshold gain reduces with increased negative guiding, which is due to improved lateral confinement and reduction of lateral leakage. Still, moderately positively guided designs should be preferred to avoid the detrimental effect of lateral leakage and high diffraction loss. To ensure positive index guiding, we propose to planarize the structure or introduce an elevation near the optical axis by additional processing, with an associated reduction in threshold material gain from 6000 to 2000 cm-1 for the studied structures.

Design of subwavelength-size, indium tin oxide (ITO)-clad optical disk cavities with quality-factors exceeding 10^4

Indium tin oxide is used as a top cladding electrode of optical disk resonators with subwavelength size in all dimensions. Calculated quality (Q)-factors exceed 10⁴ in visible wavelengths (650-670nm). The disk aspect ratio is an important parameter to optimize the resonator properties. The Q-factor and threshold material gain based on finite-difference time-domain method are optimized for eight different disk resonator optical modes. Proposed cavity designs are promising for building electrically-pumped, low-threshold nano-lasers at room temperature.

Metal-Coated Zinc Oxide Nanocavities

We theoretically demonstrate that metals can be useful for increasing the quality factor and confinement factor of a zinc oxide (ZnO) nanocavity. For small cavities, the advantages of low radiation loss and significant mode confinement due to metal coating outweigh the disadvantage of absorption loss from metal and efficiently lower the threshold material gain. The performances of ZnO cavities without metal coating, with aluminum (Al) coating, and with silver (Ag) coating are investigated. The results indicate that while surface-wave-like plasmonic modes are lossy due to metal loss, the performances of well-confined dielectric modes are indeed improved significantly as a result of metal. Both Al and Ag can significantly reduce the threshold material gain of the uncoated ZnO cavity from 16 613 cm-1 to less than 5000 cm-1. In particular, the threshold material gain of Ag-coated cavity is reduced to only 3206 cm-1.

Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing

The lasing characteristics of a photonic molecule in the form of two optically coupled semiconductor microdisks are investigated. Electromagnetic analysis of the lasing spectra and linear thresholds of the coupled whispering-gallery (WG) modes of four different symmetry classes is presented. Here, Maxwell's equations and accurate boundary and radiation conditions are considered as a specific cold-cavity-with-gain eigenvalue problem. Each eigenvalue is a pair of real-valued parameters -frequency and threshold material gain. In the two-dimensional (2-D) approximation, based on the introduction of an effective refractive index, this problem is reduced to a determinant equation with favorable features. A secant-type method is further used to calculate thresholds and lasing frequencies numerically. Results obtained show that optical coupling may lead to a further reduction of the ultralow thresholds of the WG modes, although the opposite, i.e., threshold spoiling, is more common.

Cold-cavity thresholds of microdisks with uniform and nonuniform gain: quasi-3-D modeling with accurate 2-D analysis

An electromagnetic analysis of thin-disk semiconductor resonators with uniform and nonuniform gain regions is presented. A "cold-cavity-with-gain" Maxwellian formulation, including accurate boundary and radiation conditions, is considered as an eigenvalue problem, for the real-valued parameters of frequency and threshold material gain. Although the well-known approximate effective-index method is used to reduce a three-dimensional (3-D) field problem to a two-dimensional (2-D) one, a rigorous formulation of the latter is retained. A quasi-3-D feature is provided through full account of the multiple-wave nature and dispersion of the effective index. Results obtained quantify the ultralow thresholds of the whispering-gallery modes and show the advantage of a ring-shaped gain region.

Comparison of optical VCSEL models on the simulation of oxide-confined devices

We compare the results of different optical vertical-cavity surface-emitting laser models on the position-dependent effects of thin oxide apertures. Both scalar and vectorial models as well as hybrid models are considered. Physical quantities that are compared are resonance wavelength, threshold material gain, and modal stability. For large device diameters and low-order modes, the agreement between the different models is quite good. Larger differences occur when considering smaller devices and higher order modes. It is also observed that the spread in the resonance wavelengths is smaller than that for the threshold material gain.

Simulation results of transverse-optical confinement in airpost, regrown, and oxidized vertical-cavity surface-emitting laser structures

Based on a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting laser, we investigate the influence of transverse-optical confinement in airpost, regrown, and oxidized structures. In each of these cases, we demonstrate the trade-off that needs to be made between low threshold for the fundamental laser mode and good modal stability.

Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance

We present a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting lasers. It is based on a vectorial solution of Maxwell's equations and therefore gives exact results where other approaches fail, e.g., in the case of oxide-confined devices, which have high lateral index contrasts. Results are given concerning the influence of oxide window thickness and position on threshold gain and modal stability. We also propose an intuitive plane-wave model to enhance the physical understanding of these effects.

Feasibility study on the application of the quantum disk to the gain-coupled distributed feedback laser

This numerical study investigated the possibility of using quantum disks in a gain-coupled distributed feedback (DFB) laser, specifically whether the laser would oscillate when the number of electrons in a disk (N/sub th/) is less than the maximum possible number of electrons in the disk (i.e., oscillate at a threshold material gain (g/sub th/) less than the maximum peak material gain for each quantum disk). The influences of the disk diameter and thickness, the number of disks stacked vertically in a layer (N/sub st/), the device length, the period perpendicular to the light propagation direction, and facet reflectivity on the g/sub th/, the threshold current density (J/sub th/), and the normalized gain-coupling coefficient (K/sub g/L) were also examined. When N/sub st/ is increased, g/sub th/ decreases to less than the value estimated when assuming that the product of g/sub th/ and N/sub st/ is constant. Although closely spaced disks are useful for reducing g/sub th/, there is an optimum disk distribution minimizing J/sub th/, and this distribution depends on the parameters described above. The J/sub th/ also depends on the disk size and is smallest when the diameter is 6 nm. The magnitude of K/sub g/L is about 0.76 and is independent of the height of the gain grating (i.e., N/sub st/), but it can be controlled by adjusting the disk diameter and the facet reflectivity.