We report a theoretical study on laterally-coupled pairs of vertical-cavity surface-emitting lasers (VCSELs) operated under conditions that generate or suppress high-speed optical spiking regimes, and show their potential in exemplar functionalities for use in photonic neuromorphic computing systems. The VCSEL numerical analysis is based on a system of five coupled mode equations, which, for the case of weak coupling, are reduced to a set of three equations that predict the saddle-node stability boundary in terms of device parameters and operating conditions. These results guide numerical simulation to demonstrate multiple neuron-like dynamics, including single- and multiple-spike emission, spiking inhibition, and rebound spiking directly in the optical domain. Importantly, these behaviours are obtained at sub-nanosecond rates, hence multiple orders of magnitude faster than the millisecond timescales of biological neurons. The mechanisms responsible are explained by reference to appropriate phase portraits. The coupled VCSELs model is then used for demonstration of high-speed, all-optical digital-to-spiking encoding and for representation of digital image data using rate-coded spike trains.

Recent increased interest in spin-polarised vertical-cavity surface-emitting lasers (spin-VCSELs) as potential high-speed sources has spurred research into the analysis of their dynamics. This has often been explored by combining the spin-flip model (SFM) with numerical methods. However, numerical simulation does not readily expose key dependencies and to date there is a lack of accessible closed-form analytical results for the steady-state solutions and dynamic stability boundaries. Thus in the present contribution we address this and show that, for zero dichroism, the five rate equations of the SFM can be reduced to a set of three. These can be solved in the steady-state in terms of the intensity and polarisation of the pump (optical or electrical), and the ellipticity of the output. Additionally, a small-signal analysis leads to analytic results for the boundaries between stable and unstable operation in the plane of pump ellipticity versus pump intensity. Comparison of the results from these expressions with those from numerical bifurcation and continuation methods shows very good agreement. The accuracy of the reduced set of equations is confirmed by comparing the results with those from the full set of SFM equations. In the limiting case of very high birefringence, as would be required for a potential THz source, a simple algebraic relation is derived for the spin relaxation rate in terms of other parameters. Hence we find that the range of spin relaxation rates to achieve THz oscillations is very limited. The relative simplicity of the present approach thus offers a rapid, intuitive and convenient route to study the dynamics of spin-VCSELs.

The five coupled rate equations used to describe laterally-coupled pairs of lasers with weak coupling and unequal pumping are reduced to a new system of three equations. This enables approximate closed-form steady-state solutions and explicit expressions for the boundaries between regions of stable and unstable dynamics to be found. The results of applying these approximations to specific cases of coupled laser pairs are shown to be in good agreement with results obtained from numerical solutions of the original set of five equations as well as earlier results from the literature. In addition the approximations based on the reduced set of equations allow a systematic investigation of the effects of material, device and operating conditions on trends and novel features in the dynamics of laterally-coupled laser pairs. The algebraic results give insight into trends with parameters without the need for extensive numerical computation and should therefore be of use in modelling two-element VCSEL arrays for numerous potential applications.

A general model for the dynamics of arrays of coupled spin-polarised lasers is derived. The general model is able to deal with waveguides of any geometry with any number of supported normal modes. A unique feature of the model is that it allows for independent polarisation of the pumping in each laser. The particular geometry is shown to be introduced via ’overlap factors’, which are a generalisation of the optical confinement factor. These factors play an important role in determining the laser dynamics. The model is specialised to the case of a general double-guided structure, which is shown to reduce to both the spin flip model in a single cavity and the coupled mode model for a pair of guides in the appropriate limit. This is applied to the particular case of a circular-guide laser pair, which is analysed and simulated numerically. It is found that increasing the ellipticity of the pumping tends to reduce the region of instability in the plane of pumping strength versus guide separation.

Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) are known to support high-frequency continuous birefringence-induced oscillations whose frequency is not determined by the relaxation oscillation (RO) mechanism usually recognized in conventional laser diodes. However, this depends on the pumping condition as well as some key parameters. For example, the reported hybrid pumping consisting of standard electrical pumping and polarized light pulse excitation only results in damped high-frequency birefringence-induced oscillations. Here we focus on the optically pumped spin-VCSELs which have not been fully understood compared to those under hybrid pumping. We consider both periodic and continuous-wave (CW) regimes for exploiting high-frequency operation. In the periodic regime, the regions of period-one (P1) oscillations are identified via bifurcation diagrams and peak amplitude curves/maps, where the dependence on some key parameters is systematically studied. In the CW regime, we explore the high-frequency polarization modulation. In particular, double peak response curves are found when spin-VCSELs are pumped with a certain polarization degree and the RO frequency related peak in the frequency response curve is extremely sensitive to the variation of the polarization degree, which leads to rich modulation dynamics in spin-VCSELs. Additionally, the effects of the spin relaxation rate on the polarization modulation bandwidth are illustrated by using two-parameter bandwidth maps. These findings help us better understand the underlying high-frequency dynamics of the optically pumped spin-VCSELs.

A newly-developed normal mode model of laser dynamics in a generalised array of waveguides is applied to extend the spin-flip model (SFM) to pairs of evanescently-coupled spin-VCSELS. The effect of high birefringence is explored, revealing new dynamics and regions of bistability. It is shown that optical switching of the polarisation states of the lasers may be controlled through the optical pump and that, under certain conditions, the polarisation of one laser may be switched by controlling the intensity and polarisation in the other.

This chapter traces the development of diode laser resonators from basic double heterostructure to the complicated designs used for optical integration. In order to set the scene, a brief preliminary discussion is given of diode laser fundamentals; a more detailed account will be found in a recent book. The structure makes use of a light–guiding effect which occurs in double heterostructures and which is commonly used in semiconductor lasers. The emission wavelength of a laser is determined primarily by the band–gap of the active semiconductor. The feedback required to give lasing action is provided by some form of resonant cavity, either using mirrors as in the case of the Fabry-Perot laser, or using a grating as in the case of the distributed Bragg reflector (DBR) and distributed feedback lasers. For single–longitudinal–mode operation of a DBR laser, one grating should have low reflectivity for optimal output coupling and the second grating must have narrow bandwidth and high reflectivity for mode selectivity.

It is shown that cavities formed between a multilayer quarter-wave Bragg reflector and a metal mirror which support Tamm plasmons can be modelled by using a hard-mirror approximation including appropriate penetration depths into the mirrors. Results from this model are in excellent agreement with those found by numerical methods. In addition Tamm modes that are laterally confined by the presence of a metallic disc deposited on the Bragg reflector can be described by the effective index model that is commonly used for vertical-cavity surface-emitting lasers (VCSELs). This enables the lateral modes confined by a circular disc to be found from conventional weakly-guiding waveguide theory similar to that used for optical fibres. The resonant wavelengths of these linearly-polarised (LP) guided modes are calculated as functions of disc diameter and other parameters.

We analyse the dynamics and conditions for stability in an array of two laterally-coupled nanowire lasers in terms of their separation, difference in resonant frequencies and pumping rate under conditions of weak coupling. We find that the regions of stability are very small and are found close to zero frequency offset between the lasers. Outside these regions various forms of instability including periodic oscillation, chaos and complex dynamics are predicted. Importantly, the analysis of the frequency of periodic oscillations for realistic laser separations and pumping yields values of order 100 GHz thus underlining the significant potential of nanowire laser arrays for ultra-high frequency on-chip systems with very low foot-print and energy requirements.

The polarisation properties of a quantum well spin & x2013; vertical cavity surface emitting laser (spin & x2013; VCSEL), both without injection and with variable polarisation optical injection, are investigated experimentally and compared with the spin flip model (SFM). Without injection, we demonstrate two distinct types of VCSEL-pump response depending on the signs of the linewidth enhancement factor, birefringence and dichroism: firstly where the pump and VCSEL have the same sign of the ellipticity, and secondly where the VCSEL ellipticity, accompanied by the linear polarisation, switches sign. We show that by controlling the injected power, ellipticity or linear angle, near circular polarisation can be obtained. These responses both give insight into the electro-optical injected spin-VCSEL system, and have practical implications for the use of spin VCSELs in unique applications exploiting the ellipticity degree of freedom.

A general model for the dynamics of arrays of coupled, spin-polarised lasers is derived, which is shown to reduce to both the spin flip model in a single cavity and the coupled mode model for a pair of guides in the appropriate limit. The general model is able to deal with waveguides of any geometry with any number of supported normal modes. A unique feature of the model is that it allows for independent polarisation of the pumping in each laser. The particular geometry is shown to be introduced via `overlap factors', which are a generalisation of the optical confinement factor. These factors play an important role in determining the laser dynamics. The model is specialised to the case of a general double-guided structure, which is then analysed and simulated numerically. For this case it is found that increasing the ellipticity of the pumping tends to enhance the regions where stable solutions are predicted in the plane of pumping strength versus guide separation.

The dynamic behaviour of coupled pairs of semiconductor lasers is studied using normal-mode theory, applied to one-dimensional (slab) and two-dimensional (circular cylindrical) real index confined structures. It is shown that regions of stable behaviour depend not only on pumping rate and laser separation, but also on the degree of guidance in the structures. Comparison of results between normal-mode and coupled-mode theories for these structures leads to the tentative conclusion that the accuracy of the latter is determined by the strength of self-overlap and cross-overlap of the symmetric and antisymmetric normal modes in the two lasers.

We present our recent results on quantum dot-based VCSELs for O-band telecoms applications. The incorporation of Si-rich SiNx/SiO2 distributed Bragg mirrors, which have been studied by spectroscopic ellipsometry, as well as using high-contrast SiNx 1D gratings will lead to a significant size reduction desirable for the fabrication.

By employing Tamm optical states—states localized between a thin metal microdisk and a semiconductor distributed Bragg reflector—we demonstrate near 1300 nm (O-band), narrow wavelength (20 nm FWHM), highly spatially localized photodetection. By varying the size of the microdisk, we show spectral tuning (7 nm) of the peak optical response. Furthermore, by reducing the symmetry of the microstructures, we lift the degeneracy of the polarization, producing a polarization sensitivity in our detector. These confined Tamm states are useful not only for sensing but also for photoconductive switch applications such as optical microwave switches and terahertz generation.

The nonlinear gain properties of GaInNAs vertical-cavity semiconductor optical amplifier operated in reflection mode are reported. A step-like differential gain and the anticlockwise bistability are predicted. The dependence of the optical bistability on the applied current and phase detuning are analyzed.

Regions of stability in two laterally-coupled InP nanowire lasers are analysed in terms of their separation, difference in resonant frequencies and pumping rate. The frequency of periodic oscillations for realistic laser separations and pumping is estimated to be of order 100- 1000 GHz.

We consider a modified version of the spin-flip model (SFM) that describes optically pumped quantum dot (QD) spin-polarized vertical-cavity surface-emitting lasers (VCSELs).Maps showing different dynamical regions and those consisting of various key bifurcations are constructed by direct numerical simulations and a numerical path continuation technique, respectively.A comparison between them clarifies the physical mechanism that governs the underlying dynamics as well as routes to chaos in QD spin-VCSELs.Detailed numerical simulations illustrate the role played by the capture rate from wetting layer (WL) to QD ground state, the gain parameter, and the amplitude-phase coupling.By tuning the aforementioned key parameters in turn we show how the dynamical regions evolve as a function of the intensity and polarization of the optical pump, as well as in the plane of the spin relaxation rate and linear birefringence rate, which is of importance in the design of spin lasers promising potential applications.By increasing the capture rate from WL to QD our simulation accurately describes the transition from the QD spin-VCSEL to the quantum well case, in agreement with a previous mathematical derivation, and thus validates the modified SFM equations.

Closed-form expressions are derived for the relationship between the polarisation of the output and that of the pump for spin-polarised vertical-cavity surface-emitting lasers. These expressions are based on the spin-flip model (SFM) combined with the condition that the carrier recombination time is much greater than both the spin relaxation time and the photon lifetime. Allowance is also included for misalignment between the principal axes of birefringence and dichroism. These expressions yield results that are in excellent agreement both with previously published numerical calculations and with further tests for a wide range of parameters. Trends with key parameters of the SFM are easily deduced from these expressions.

We study modulation properties of two-element phased-array semiconductor lasers that can be described by coupled mode theory. We consider four different waveguide structures and modulate the array either in phase or out of phase within the phase-locked regions, guided by stability diagrams obtained from direct numerical simulations. Specifically, we find that out-of-phase modulation allows for bandwidth enhancement if the waveguide structure is properly chosen; for example, for a combination of index antiguiding and gain-guiding, the achievable modulation bandwidth in the case of out-of-phase modulation could be much higher than the one when they are modulated in phase. Proper array design of the coupling, controllable in terms of the laser separation and the frequency offset between the two lasers, is shown to be beneficial to slightly improve the bandwidth but not the resonance frequency, while the inclusion of the frequency offset leads to the appearance of double peak response curves. For comparison, we explore the case of modulating only one element of the phased array and find that double peak response curves are found. To improve the resonance frequency and the modulation bandwidth, we introduce simultaneous external injection into the phased array and modulate the phased array or its master light within the injection locking region. We observe a significant improvement of the modulation properties, and in some cases, by modulating the amplitude of the master light before injection, the resulting 3 dB bandwidths could be enhanced up to 160 GHz. Such a record bandwidth for phased-array modulation could pave the way for various applications, notably optical communications that require high-speed integrated photonic devices.

Using continuous-wave optical pumping of a spin-VCSEL at room temperature, we find high spin amplification of the pump close to threshold within the communications wavelength window, here at 1300 nm. This facilitates a strong switch from left to right circularly polarised light emission, which has potential applications in polarisation encoding for data communications. We use a simple spin flip model to fit the experimental results and discuss the VCSEL parameters that affect this amplification.