Solitary Vertical-cavity Surface-emitting Laser Research Articles

Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

This paper explores the dynamics, microcontroller validation of a vertical-cavity surface-emitting laser (VCSEL) under current modulation (CM) and employs it to model a process of pseudo-random number generator (PRNG). Solitary VCSEL has three equilibrium points whose stabilities depend on the direct current density. VCSEL under CM (VCSELCM) experiences antimonotonicity, chaotic bubble attractor as well as chaotic attractor. A microcontroller implementation of VCSELCM is used to establish the dynamical behaviors spotted in VCSELCM during the numerical simulations. Lastly, the chaotic characteristics depicted by the VCSELCM are used to design a process of PRNG. The generated random bits are validated successfully by a standard statistical tool set by the National Institute of Standards and Technology (NIST-800–22).

Compact solid-state vertical-cavity-surface-emitting-laser beam scanning module with ultra-large field of view

A solid-state beam scanner is key element for next-generation 3D sensing. To overcome problems of current solid-state beam scanners, such as small field of view, limited resolutions and difficulties in large-scale manufacturing, we previously invented a solitary vertical-cavity surface-emitting laser (VCSEL) beam scanner based on a VCSEL waveguide/amplifier. In this paper, we proposed and demonstrated an electrical beam scanning module by integrating a tunable surface grating VCSEL to the solitary VCSEL scanner and by assisting with a diffractive optical element and prism mirror for an ultra-large field of view. We realized continuous fan beam scanning with a record field of view of >100° and obtained resolution points number of 1400. The module size could be managed within 10 mm × 6 mm × 1 mm.

Time-delay signature suppression of polarization-resolved wideband chaos in VCSELs with dual-path chaotic optical injections.

The combining investigation on the time-delay signature (TDS) and chaos bandwidth have been theoretically investigated in a vertical-cavity surface-emitting laser (VCSEL) system with dual-path chaotic optical injections. In this scheme, the polarized chaos with the TDS from an external-cavity master VCSEL is routed into two different paths and then unidirectionally injected into another solitary slave VCSEL. With the aid of the autocorrelation function and the effective bandwidth calculation, the TDS and bandwidth of polarized chaos from the chaotic system are quantitatively evaluated. The results show that, in such a dual-path chaotic optical-injection system, the high-quality polarized chaos with the successful TDS suppression and chaotic bandwidth enhancement can be achieved in wider parameter regions in contrast with the case for the single-path chaotic optical injection. Further research also finds that the injected time-delay difference between two injection paths is desired to mismatch the feedback time delay, which is conducive to suppressing TDS and expanding bandwidth of polarized chaos. Besides, the better chaotic quality with low TDS and wide bandwidth can be expected by choosing the appropriate injection strengths of two injection paths.

Chaos in Solitary VCSELs: Exploring the Parameter Space With Advanced Sampling

We explore the parameter space of the so-called spin-flip model by advanced sampling techniques to analyze the requirements leading to polarization chaos in solitary vertical-cavity surface-emitting lasers. We first investigate the performances of different sampling techniques for multidimensional parameter space exploration. Purely random sampling and tensor-product grids require a large amount of samples to uniformly cover the whole space, and we show that other schemes are highly superior to this regard, hence allowing a reduced number of samples and computation to be used to reach the same level of insight in the system behavior. Considering the scarcity of the chaotic regions and their sharp boundaries, combined with quite involved computations to identify chaotic dynamics, the proposed approach is shown to be highly beneficial. Here, we are able to highlight two thresholds limiting the range of injection current for which chaos can be observed, and to link them to a fine balance between the spin relaxation rate and the birefringence.

Strain induced polarization chaos in a solitary VCSEL

Physical curiosity at the beginning, optical chaos is now attracting increasing interest in various technological areas such as detection and ranging or secure communications, to name but a few. However, the complexity of optical chaos generators still significantly hinders their development. In this context, the generation of chaotic polarization fluctuations in a single laser diode has proven to be a significant step forward, despite being observed solely for quantum-dot vertical-cavity surface-emitting lasers (VCSELs). Here, we demonstrate experimentally that a similar polarization dynamics can be consistently obtained in quantum-well VCSELs. Indeed, by introducing anisotropic strain in the laser cavity, we successfully triggered the desired chaotic dynamics. The simplicity of the proposed approach, based on low-cost and easily available components including off-the-shelf VCSELs, paves the way to the wide spread use of solitary VCSELs for chaos-based applications.

Injection Locking and Polarization Switching Bistability in a 1550 nm VCSEL Subject to Parallel Optical Injection

We present experimental and theoretical results of bistable polarization switching in a single transverse mode 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. We focus our analysis on the bistability induced by power variation of the master laser found on the recently observed state of simultaneous injection locking of the parallel polarization mode and excitation of the orthogonal polarization mode, IL+PS. Experimental stability maps identifying, in the injected power-frequency detuning plane, where this state is observed, and corresponding bistable regions are reported for several bias currents. We find bistability between the IL+PS state and the single polarization mode injection locked solution. We also find bistability between the IL+PS and different periodic dynamics in the parallel polarization mode. The width of the hysteresis cycle increases when increasing the bias current or when increasing the wavelength of the optical injection beyond the solitary VCSEL wavelength. We theoretically confirm these types of bistability by numerically simulating the spin-flip model and by performing a linear stability analysis for the different stable states. Excellent agreement is found between experimental and theoretical results.

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

Polarization Switching Regions of Optically Injected Long-Wavelength VCSELs

We report on an experimental study of the injected optical power required for polarization switching (PS) in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection. This power is found as a function of the frequency detuning between the injected light and suppressed linear polarization of the solitary VCSEL. Increasing the injected power, we found two types of PS when injecting light with wavelength close to the wavelength of the suppressed linear polarization and to that of the linear polarization of the solitary VCSEL. These two types of PS are, respectively: 1) single and double (with two minima of injected power necessary for PS) and 2) double PS (with two islands of PS and a separate region with a single minimum of injected power). Our experimental results confirm the theoretical predictions of Torre et al. Double PS is observed around the elliptically polarized injection locked states found by Lin et al. Different dynamics are found in the route to PS.

Dynamic Characteristics of an All-Optical Inverter Based on Polarization Switching in Long-Wavelength VCSELs

An all-optical inverter using polarization switching (PS) of a long-wavelength single-mode vertical-cavity surface-emitting laser (VCSEL) is experimentally demonstrated. PS appears when linearly polarized light is injected orthogonally to the linear polarization of the solitary VCSEL. The dynamic behavior of an all-optical inverter under different pulsed optical inputs is analyzed. Time traces, rise and fall times of the linearly polarized output signals are reported. The dependence of these quantities on the bias current and injected optical power is investigated. This analysis permits us to identify proper operation conditions for the all-optical inversion. The PS-based all-optical inverter is demonstrated with a 2.5-Gb/s non-return-to-zero input signal.

Current-dependence of polarisation switching and locking in an optically injected 1550 nm vertical-cavity surface-emitting laser

The authors have studied the effects of polarised optical injection in a 1550 nm vertical-cavity surface-emitting laser (VCSEL) operated at currents up to 4.5 times threshold. Regions of stable injection locking have been measured for cases where the injected signal is polarised to match one of the two polarisations of the fundamental transverse mode of the solitary VCSEL. In addition regions of polarisation switching have been found for the case where the input polarisation is matched to that of the subsidiary mode of the solitary VCSEL. The variation of this behaviour with current has been investigated.

Transverse Mode Selection and Bistability in Vertical-Cavity Surface-Emitting Lasers Induced by Parallel Polarized Optical Injection

Modal selection induced by parallel polarized optical injection in a vertical-cavity surface-emitting laser (VCSEL) emitting in two transverse modes is analyzed from a theoretical point of view. We show that the selection of the fundamental transverse mode can be achieved when the two transverse modes have parallel polarizations. This selection is accompanied by locking of the fundamental mode to the optically injected signal for large enough values of the wavelength detuning between the fundamental mode and the externally injected signal. The injected power needed to induce modal selection grows as the VCSEL bias current is increased for small positive wavelength detunings, while it is independent on the bias current for larger wavelength detunings. That power exhibits a minimum with respect to the injection wavelength at a value λ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</i> that is slightly longer than the wavelength of the fundamental mode of the solitary VCSEL. We also show that the selection process exhibits bistable behavior when the wavelength of the optically injected signal increases beyond λ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</i> . The width of the bistable region increases linearly with the wavelength of the optically injected signal. Our results show that λ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</i> also increases linearly with the VCSEL bias current. Higher order transverse mode selection and bistability, similar to those found for the fundamental mode, are obtained when the optical injection wavelength is close to that of the higher order mode. Our results are in agreement with the experimental results reported earlier.

Experimental Study of Transverse Mode Selection in VCSELs Induced by Parallel Polarized Optical Injection

Modal selection induced by parallel polarized optical injection is studied experimentally in a vertical-cavity surface-emitting laser (VCSEL) with emission in two transverse modes. We report that the selection of the fundamental transverse mode can be achieved when the two transverse modes have parallel polarizations. The selection of the fundamental mode is accompanied by locking of that mode to the optically injected signal for large enough values of the wavelength detuning between the fundamental mode and the externally injected signal. The injected power needed to induce modal selection grows as the VCSEL bias current is increased and exhibits a minimum with respect to the injection wavelength at a value ?min that is slightly longer than the wavelength of the fundamental mode of the solitary VCSEL. We also report that the selection process exhibits a bistable behaviour when the wavelength of optical injection increases beyond ?min. The width of the observed bistable region grows linearly with the wavelength of the optically injected signal. Selection of the higher order transverse mode is achieved when the optical injection wavelength is close to that of the higher order transverse mode. The qualitative behavior associated with the selection of the higher order mode is similar to that of the fundamental mode.

Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings

We propose a novel design for multi-wavelength arrays of vertical cavity surface-emitting lasers (VCSELs) using high-contrast gratings (HCGs) as top mirrors. A range of VCSEL cavity wavelengths in excess of 100 nm is predicted by modifying only the period and duty-cycle of the high-contrast gratings, while leaving the epitaxial layer thickness unchanged. VCSEL arrays fabricated with this novel design can easily accommodate the entire Er-doped fiber amplifier bandwidth with emission wavelengths defined solely by lithography with no restrictions in physical layout. Further, the entire process is identical to that of solitary VCSELs, facilitating cost-effective manufacturing.

Wavelength Polarization Switching and Bistability in a 1550-nm VCSEL Subject to Polarized Optical Injection

Different forms of wavelength polarization switching and bistability are experimentally reported for a 1550-nm vertical-cavity surface-emitting laser (VCSEL) subject to optical injection with different input polarization angles to that of the solitary VCSEL.

Transverse Mode Switching and Locking in Vertical-Cavity Surface-Emitting Lasers Subject to Orthogonal Optical Injection

In this paper, we report on theoretical and experimental investigation on polarization and transverse mode behavior of vertical-cavity surface-emitting lasers (VCSELs) under orthogonal optical injection as a function of the injection strength and of the detuning between the injection frequency and the free-running frequency of the solitary laser. As the injection strength increases the VCSEL switches to the master laser polarization. We find that the injection power necessary to obtain such polarization switching is minimum at two different values of the frequency detuning: the first one corresponds to the frequency splitting between the two linearly polarized fundamental transverse modes, and the second one appears at a larger positive frequency detuning, close to the frequency difference between the first-order and the fundamental transverse modes of the solitary VCSEL. We show theoretically that both the depth and the frequency corresponding to the second minimum increase when the relative losses between the two transverse modes decrease. Bistability of the polarization switching is obtained for the whole frequency detuning range. Such a bistability is found for the fundamental mode only or for both transverse modes, depending on the value of the detuning. The theoretical and experimental optical spectra are in good agreement showing that the first-order transverse mode appears locked to the external injection

Analysis of SFM dynamics in solitary and optically-injected VCSELs

The aim of this paper is to use the spin-flip model (SFM) to investigate how the fundamental parameters of birefringence, spin relaxation and pumping affect the dynamics of solitary and optically-injected vertical-cavity surface-emitting lasers (VCSELs). The SFM predicts that a solitary VCSEL can exhibit diverse polarisation behaviour, including elliptical and linear stability, which can be used in polarisation switching. For given values of pumping, spin relaxation and birefringence, we analyse the electric field components, the carrier densities corresponding to spin-up and spin-down, and the relaxation oscillation frequency for a solitary VCSEL and the stability map for an optically-injected VCSEL.

Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers

The aim of this paper is to investigate the effects of external optical injection taking account of polarization and electron spin properties in vertical-cavity surface-emitting lasers (VCSELs). Using external polarized injection we seek the locked phases and amplitudes of specific polarized fields in terms of injection level and frequency detuning, taking account of two kinds of distinguishable carrier density (spin-up and spin-down). For the conventional form of optical injection without taking account of spin-polarized fields there are three fundamental equations describing the carrier density, field amplitude and phase. However, by using the spin flip model (SFM), the combined effect of polarized fields along two perpendicular crystal axes and electron spin properties results in six equations. We analyse the conditions for stable locking and also the influence of birefringence effects on the stability map of detuning versus optical injection for both cases of injection polarized parallel and perpendicular to the lasing mode of the solitary VCSEL. For given values of pumping and spin relaxation rate there is a minimum birefringence rate for orthogonal injection. Above this value three regions of elliptical polarization are found in the stability map, namely “quasi-stability” (QS), “coupled limit cycle” (CLC) and “coupled chaos” (CC). The three regions of linear polarization, namely chaos, limit cycle and stability, are reduced in area compared to the case of parallel injection. For orthogonal injection it is found that increased birefringence or reduced spin relaxation rate causes the stable locking region to begin at higher injected power and frequency detuning.

Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection

We present an experimental investigation of a vertical-cavity surface-emitting laser (VCSEL) submitted to orthogonal optical injection, i.e., the injected light is linearly polarized and orthogonal to that emitted by the solitary VCSEL. Bifurcation boundaries of qualitatively different dynamics are mapped out in the frequency detuning-injection strength plane. We unveil rich and complex dynamics including injection locking, limit cycle, wave mixing, and period doubling route to chaos.

Mapping of the Dynamics Induced by Orthogonal Optical Injection in Vertical-Cavity Surface-Emitting Lasers

In this paper, the output characteristics of an oxide-confined AlGaAs-As quantum well vertical-cavity surface-emitting laser (VCSEL) under orthogonal optical injection are mapped as a function of the strength of the optical injection and the detuning between the injection frequency and the free-running frequency of the solitary laser, for a very large range of frequency detuning (from -82 to 89 GHz). The injection light is polarized orthogonally with respect to the solitary VCSEL output light. As the injection strength increases the VCSEL switches to the master laser polarization. Polarization switching is accompanied by a rich nonlinear dynamics, including limit cycle, wave mixing, subharmonic resonance and period doubling route to chaos. Polarization switching is found with but also without injection locking. Injection locking occurs with the slave fundamental transverse mode or, for large positive detunings, with the first-order transverse mode.

Polarization-Resolved Relative Intensity Noise Measurements of a Vertical-Cavity Surface-Emitting Laser Subjected to Strong Optical Feedback

We experimentally measure the polarization-resolved relative intensity noise (RIN) in two orthogonal polarization states of a vertical-cavity surface-emitting laser (VCSEL) subjected to strong optical feedback. A comparison is made with the RIN of solitary VCSEL. Optical feedback is shown to enhance the RIN in one polarization direction while suppressing the RIN in the orthogonal polarization. The RIN in the dominant polarization mode exhibits complementary behavior to the RIN in the suppressed polarization mode.