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We propose semiconductor-metal subwavelength grating (SMSG) which can be implemented as VCSEL mirror. Such new type of SMSG plays a double role of the electric contact and mirror simultaneously. It facilitates high optical power reflectance, perfectly vertical current injection. Such construction eliminates the inbuilt current confinement and allows scaling of emitted power by simple variation of SMSG spatial dimensions. To give the credibility to proposed design we perform numerical analysis of VCSEL with SMSG using fully vectorial optical model. We discuss properties of the proposed design realized in arsenide-based material configuration.

High Contrast Gratings (HCGs) become an attractive alternative for Distributed Bragg Reflectors (DBRs) used as high reflecting mirrors for VCSELs. In this paper we propose to implement HCG or monolithic HCG as a top mirror of the 1650nm InP-based VCSEL intended for use as a methane sensing device. Its unique feature is related to the fact that light taking part in the resonance can be accessed without opening the laser cavity due to the slow light phenomenon which occurs in HCG. Particular designs of HCGs allow to concentrate significant part of the mode between the HCG stripes. In such constructions the presence of the substance in the vicinity of the HCG which interacts with light resonating in the laser will change its emission properties. This enables sensing absorption or change to the refractive index in proximity of the laser based on the emission parameters of the laser. We present a numerical analysis of 1650nm MHCG and HCG mirrors based on fully vectorial optical model. We found optimal parameters of HCGs and MHCGs to detect absorption and refractive index variations in the vicinity of the gratings, based on changes in power reflectance of analysed mirrors. Additionally we consider HCG and MHCG constructions which allow for broad wavelength tuning by the change of the refractive index of substance surrounding mirror.

We present experimental results showing alternating lasing and non-lasing regions for the short-wavelength longitudinal mode in a GaAs-based 850 nm coupled-cavity vertical-cavity surface-emitting laser (CC-VCSEL). These regions are situated between the laser threshold and roll-off for this mode. The analyzed structure consists of two identical AlGaAs cavities with GaAs quantum wells, separated with 11.5 pairs of middle DBR. The current apertures are realized by ion-implantation for the top cavity and selective oxidation for the bottom cavity. We then perform fully-vectorial three-dimensional cold-cavity optical simulations to theoretically investigate optical density radial and on-optical-axis profiles of the first order transverse modes corresponding to the two longitudinal modes. We show that the short-wavelength fundamental mode λS-LP01 is subject to periodic changes of its optical field distribution when changing the oxide aperture radius, which can lead to weaker resonance of the short-wavelength LP01 mode within the coupled cavity structure.

We are interested in spatio-temporal dynamics of cavity solitons (CSs) in a transverse section of a broad area vertical cavity surface emitting laser (VCSEL) with saturable absorbtion subjected to time-delayed optical feedback. In the absence of delayed feedback, a single branch of localized solutions appears in the parameter space. However, in the presence of the delayed feedback, multistability of CS solutions emerges; The branches of CSs fill the surface of the "solution tube" in the parameter space, which is filled densely with increasing delay time. Further, our study reveals that the multistability of stationary solutions is caused by a delayed-induced phase bifurcation of CSs. Furthermore, it was shown that stability properties of CSs strongly depend on the delayed feedback parameters. In particular, the thresholds of the drift and phase bifurcations as well as corresponding bifurcation diagrams are obtained by a combination of analytical and numerical continuation methods. It turns out that both thresholds tend to zero in the limit of large delay times. In addition, we demonstrate that the presence of the delayed optical feedback can induce Andronov-Hopf bifurcation and a period doubling route to chaos. Moreover, a coupling between this bifurcation scenario with aforementioned delay-induced multistability leads to a complex spatio-temporal behavior of the system in question. The results of analytical bifurcation analysis are in agreement with those obtained by direct numerical integration of the model equation.

The huge increase of datacom capacities requires lasers sources with more and more bandwidth performances. Vertical-Cavity Surface-Emitting Lasers (VCSEL) in direct modulation is a good candidate, already widely used for short communication links such as in datacenters. Recently several different approaches have been proposed to further extend the direct modulation bandwidth of these devices, by improving the VCSEL structure, or by combining the VCSEL with another high speed element such as lateral slow light modulator or transistor/laser based structure (TVCSEL). We propose to increase the modulation bandwidth by vertically integrating a continuous-wave VCSEL with a high-speed electro-modulator. This vertical structure implies multiple electrodes with sufficiently good electrical separation between the different input electrical signals. This high frequency modulation requires both good electrical insulation between metal electrodes and an optimized design of the coplanar lines. BenzoCyclobutene (BCB) thanks to its low dielectric constant, low losses, low moisture absorption and good thermal stability, is often used as insulating layer. Also, BCB planarization offers the advantages of simpler and more reliable technological process flow in such integrated VCSEL/modulator structures with important reliefs. As described by Burdeaux et al. a degree of planarization (DOP) of about 95% can be achieved by simple spin coating whatever the device thickness. In most of the cases, the BCB planarization process requires an additional photolithography step in order to open an access to the mesa surface, thus involving a tight mask alignment and resulting in a degraded planarization. In this paper, we propose a self-aligned process with improved BCB planarization by combining a hot isostatic pressing derived from nanoimprint techniques with a dry plasma etching step.

The complexity of chaos generated in two systems has been studied experimentally. The complexity of the chaos is quantified by calculating average normalized permutation entropy (HS(P)). In the first system, a chaotic output from a master laser (ML) is injected into a CW slave laser (SL). The results show that the complexity of chaos generated in the SL decreases with absolute value of the frequency detuning Δf1, which means the complexity of the chaos is compromised with enhancing the bandwidth, as Δf1 is increased. The second system comprises three vertical-cavity surface-emitting lasers (VCSELs); the first VCSEL (used as ML) was rendered chaotic by optical feedback, the second VCSEL is used as intermediate laser (IL), which is rendered chaotic when it is subject to optical injection from the chaotic ML and the third VCSEL is used as a SL and is a subject of optical injection from the chaotic IL, thus entering chaotic dynamics. In this three-VCSEL system, small, intermediate and wide bandwidths of the injecting chaos signals, have been used to study the effect of the bandwidth of the injecting chaos on the complexity of chaos generated in the SL. The results show that the bandwidth of the chaotic injection beam does not impact the complexity of the chaos generated in the SL for positive frequency detuning; however, for large negative frequency detuning, the complexity of the chaos in the SL has been reduced significantly for the intermediate and lower bandwidth of the chaotic injection beam.

We study the formation of three-dimensional structures in type-I intracavity second harmonic generation model where polarization degrees of freedom due to the birefringence of the x(2) crystal is not considered. The device consists of an optical cavity filled with a quadratic nonlinear material and driven by an external beam at the fundamental frequency. The transmitted part of this field is coupled into the cavity where it undergoes second harmonic conversion. These dissipative structures consist of regular or localized 3D lattices of bright spots travelling at the group velocity of light in the material. We show evidence of stable three dimensional structures such as stripes and cylinders.

We study theoretically and experimentally spectral and polarization characteristics of hybrid systems of VCSELs integrated within liquid crystal (LC) cells. Three cases are considered: Nematic or cholesteric LC on top of VCSEL, coupled-cavity system with the second cavity next to the VCSEL’s one filled in with nematic LC and a system with a nematic LC inside the VCSEL cavity. For the case of nematic liquid crystal - VCSEL coupled cavity system we demonstrate selection between two orthogonal directions of linear polarization of the fundamental mode by changing the LC length or by electro-optical tuning of the LC director. For the case of cholesteric liquid crystal-VCSEL system we demonstrate lasing on circularly polarized (CP) modes due to the LC band gap for CP light. The transition from nematic to isotropic phase of the LC when increasing temperature leads to a drastic change of the polarization of the generated light from left-handed circular to linear polarization. Finally, we investigate the possibility of efficient wavelength tuning by utilizing electrooptical effect in nematic LC layer integrated next to the active region in a VCSEL cavity.

We investigate a control technique, known as rocking, for the formation of phase bistable patterns of light by means of spatially periodic injection in a broad area nonlinear optical system. More precisely, we consider a vertical-cavity surface-emitting laser (VCSEL). The spatial periodic injection or spatial rocking is found to convert the initially phase-invariant oscillatory system into a phase-bistable pattern forming one. We investigate the role of carrier lifetime on the efficiency of rocking in a broad-area VCSEL structure. This simple and robust device received a special attention owing to advances in semiconductor technology. We show that the regime where rocking works depends strongly on the ratio between the time scales associated with the electric field and the carrier density. The size of the rocking region depends on the ratio between the time scales.

We consider a broad area vertical-cavity surface-emitting laser(VCSEL) subject to injection and to time-delayed feedback. We present analytical and numerical analysis of the dependence of the drift instability threshold and on the feedback strength, feedback phase, and carrier relaxation time. we demonstrate that due to finite carrier relaxation rate the delay induced drift instability can be suppressed to a certain extent. We give analytical estimation of the soliton velocity near the drift instability point which is in a good agreement with numerical results obtained using the full model equations.

A self-consistent model of a GaAs-based 850 nm coupled-cavity vertical-cavity surface-emitting diode laser is presented. The analyzed laser consists of two identical AlGaAs cavities with GaAs quantum wells, separated with 10 pairs of middle DBR. The current apertures are realized by ion-implantation for the top cavity and selective oxidation for the bottom. To accurately simulate the physical phenomena present in the CW regime of the analyzed device, we use a multi-physical model, which comprises self-consistent Finite Element Method (FEM) thermo-electrical model. The numerical parameters have been found by the calibration based on experimental results. We have analyzed and shown the influence of the driving voltages on the temperature distribution within the analyzed structure and current densities in both cavities.

We consider a broad area vertical-cavity surface-emitting laser (VCSEL) subject to optical injection. We experimentally investigate the spontaneous formation of a Cavity Soliton (CS) in a medium size (80mum diameter) VSCEL. CSs are generated and erased when sweeping optical injection power and proper frequency detuning between the master laser and the VCSEL is set.

We present the optimization of the carrier injection, heat flow and optical confinement aimed at single mode operation in anti-guiding long-wavelength VCSELs and VCSEL arrays. The analyzed structure incorporates InP/AlGaInAs quantum wells within an InP cavity. The cavity is bounded by GaAs/AlGaAs DBRs. The tunnel junction is responsible for carrier funneling into the active region. The air-gap etched at the interface between cavity and top DBR provides the confinement of the lateral modes. To rigorously simulate the physical phenomena taking place in the device we use a multi-physical model, which comprises three-dimensional models of optical (Plane Wave Admittance Method), thermal and electrical (Finite Element Method) phenomena. In the analysis we investigate the influence of the size of single and multiple emitters and the distance between the emitters in the case of the VCSEL arrays. As a result, we illustrate the complex competition of the modes and determine the geometrical parameters favoring specific array modes in the considered designs and compare the designs with respect to mode discrimination.

A technological platform for a vertical cavity surface emitting laser (VCSEL) with tunable polarization is presented. It is realized by integrating an 850nm VCSEL chip in a liquid crystal (LC) cell that uses photo-alignment (PA) to orient the LC. Two kinds of LC are filled in and form a thin layer over the emitter of the VCSEL: nematic LC or chiral nematic LC (cLC). The VCSEL and the nematic LC layer can be electrically driven with separate electrodes. The polarization state of the laser emission can be controlled by applying an appropriate voltage over the nematic LC layer. The chiral nematic LC has a reflection band that contains the VCSEL emission wavelength, so that one circular polarized mode of the laser emission is reflected as a feedback into the VCSEL. We found that the emission from the VCSEL with cLC overlay is circularly polarized.

We study theoretically the spectral and polarization threshold characteristics of Vertical-Cavity Surface-Emitting Lasers with nematic and cholesteric liquid crystal overlay: LC-VCSELs. In the first case, we demonstrate the possibility of selecting between two orthogonal directions of linear polarization (LP) of the fundamental mode (x or y LP) by choosing appropriate NLC length and to achieve strong polarization discrimination: threshold gain difference as large as several times the threshold gain. We also demonstrate an active control of light polarization by electro-optically tuning the LC director and show that either polarization switching between x and y LP modes or continuous change of the LP direction is possible. For cholesteric LC-VCSEL we show that it becomes a coupled system with different spectral, threshold and polarization characteristics than the ones of the stand-alone VCSEL. Due to the existence of a band gap for circularly polarized light in the liquid crystal, lasing occurs in almost circularly polarized modes at the LC side.

We present a design of a high speed electro-optically modulated coupled-cavity vertical-cavity surface emitting laser monolithically integrated in a traveling wave electrode structure (TW EOM CC-VCSEL). Such electrical configuration allows to overcome RC time constant limitations of a traditional lumped electrodes design. We use segmented transmission line to match the impedance of the whole structure to the 50 Ω electrical network. We use transmission matrix method to model the response of the device and reflections at the voltage source interface. The CC-VCSEL optical design is based on longitudinal mode switching induced by the electro-optic effect, which has been recently experimentally demonstrated. In the paper we present analysis of electrical equivalent circuits of passive and modulator sections. We optimize our structure with respect to the device physical dimensions, frequency response, microwave reflections and modulation efficiency. We propose two different designs that are theoretically able to reach modulation speeds limited only by carrier extraction time from the quantum wells of the modulator and at the same time having lower than -20 dB reflections to the voltage source. For 1.5 λ long modulator cavity, carrier saturation velocity limits the bandwidth of proposed structures to ≈ 390 GHz.

Vertical-Cavity Surface-Emitting Lasers, due to their properties, are one of the best choices for optical communication purposes. Although direct modulated VCSELs have reached error free operation at speed of 40 Gbit/s, however, their cut-off frequency is limited by the relaxation oscillation phenomenon and is not likely to be further increased. Recently, it has been suggested that properly designed Coupled Cavity VCSEL with one cavity used as a reverse-biased Electro-Optic Modulator, can be only limited by the 3 dB electrical bandwidth cut-off frequency. Therefore, it is important to develop a high-speed electrical design for such VCSELs. In this paper we first present an analysis of an electrical equivalent circuit of EOM CC-VCSEL with lumped electrodes. We base our design on record high-speed structures reported in the literature. We optimize our structure with respect to modulator cavity length, number of top and middle distributed Bragg reflectors, doping levels of layers, radii of both mesas and non-ion implantation region in the DBR as well as the contact pad area. We show that the most influencing parameters are the mesa capacitance, series resistance and polyimide capacitance. The 3 dB bandwidth is enhanced by reducing the contact pad area and modulator cavity diameter, together with increasing the modulator cavity length. Faster operation is provided by pnp structure, instead of npn - one. A realistic structure design that is theoretically able to work with a 90 GHz modulation speed is suggested. Finally we also discuss the possibility of using a design concept of a EOM CC-VCSEL based on traveling wave electrode configuration.

In this work we show the analysis of high contrast vertical-cavity surface-emitting lasers (VCSEL) mirror with etched photonic crystal, which provide the true photonic band-gap (PBG) for TE-like polarized light. We confirm that PBG is the main light confinement mechanism by analyzing a low-index line-defect as well as a low-index cavity mode. In the latter case we are able to obtain very high cavity Q-factor. Such PBG-VCSELs are compatible with the VCSEL technology and do not require a complicated assembly of three-dimensional photonic crystals.­

We consider a broad area vertical-cavity surface-emitting laser (VCSEL) subject to injection and to time-delayed feedback. We show that near the nascent optical bistability regime, the space-time dynamics of this device is described by a generalized Swift-Hohenberg equation with delay. We classify different regime of stability of the homogeneous steady states in terms of dynamical parameters. We show that the delay modifies strongly the stability domain of both periodic and localized structures solutions. Finally, we show that the delay feedback induces a spontaneous motion of bright peaks in one and in two-dimenional transverse plane. Bifurcation diagram associated with these localized structures is constructed.

We developed an in- house technology to overlay liquid crystal (LC) on top of a 850nm Vertical Cavity Surface Emitting Laser (VCSEL) creating a so-called LC-VCSEL. Prior to this, the effect of the cell thickness on the planar alignment of the E7 LC is investigated. It is observed that the LC orientation is planar, uniformly aligned over the whole cell with an average pre-tilt of 22.5 0 in a thin a cell of 13μm thickness; such alignment uniformity is not observed in a thick cell of 125μm. Nevertheless, several domains of good uniformity are still present. Further, the polarization resolved LI characteristics of LC-VCSEL are investigated with and without the insertion of LC in a cell glued directly onto VCSEL package. Before filling in the LC, the VCSEL emits linearly polarized light and this linear polarization is lost after LC filling. The output intensity as a function of polarizer angle shows partial planar alignment of the E7 LC, which is very important for the further advancement of the LC-VCSEL integrated system.

We experimentally and numerically report on polarization switching (PS) mechanism which involves a two-mode limit cycle dynamics in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection from a master laser (ML). The VCSEL (slave laser, SL) emits a horizontal linearly polarized (LP) fundamental mode, without optical injection. The VCSEL is injected by a vertically polarized light from ML. Dynamical characteristics of the VCSEL are investigated as a function of optical injection parameters, i.e., injection strength and frequency detuning between master and slave lasers. We experimentally resolve an injection parameter region for which, as the injection strength is increased for fixed detunings, a limit cycle dynamics in both non-injected and injected modes is abruptly excited. For larger injection strengths, the VCSEL switches from the two-mode to a single-mode limit cycle dynamics which involves only the injected mode. Using continuation methods, we numerically identify two torus bifurcation mechanisms, namely TR 1 and TR 2 , which support such a switching scenario. We show that both TR 1 and TR 2 originate from a particular Hopf bifurcation which plays a key role in the polarization dynamics of the injected VCSEL. Furthermore, our results reveal that the newly observed switching dynamics are generic features of VCSEL two-mode systems.

A Semiconductor Saturable Absorber Mirror utilising the electroabsorption effect in a self-biased stack of extremely shallow quantum wells or in a bulk semiconductor is proposed and analysed theoretically and numerically. The saturation flux and recovery time of the proposed device when operated with picosecond incident pulses are shown to compare very favourably with existing all-optical constructions.

In this paper we summarize our recent theoretical and experimental results concerning optical injection in VCSELs. First, we develop phenomenological rate equation model for the normalized photon densities of the two fundamental VCSEL modes with orthogonal linear polarization when injecting external light polarized along the direction of polarization of the nonlazing mode. We then perform a simple analytical analysis of optically induced polarization switching in VCSELs, which takes into account both the current-dependent linear dichroism and the nonlinear dichroism. We also present detailed investigation of polarization dynamics induced by optical injection using an alternative rate equation model for VCSELs which takes into account the microscopic spin-flip processes in the active medium. In particular we predict that two injection locked solutions may coexist: the first one exhibits the polarization of the master laser, while the second one corresponds to an elliptically polarized injection locking. Continuation techniques allow us to find the bifurcation scenario leading to such an elliptically locked state. We also report on our first experimental results on polarization switching and injection locking for the case of an orthogonal optical injection in VCSELs and demonstrate rich dynamical behavior. The polarization switching is accompanied by a cascade of bifurcations to timeperiodic and possibly chaotic dynamics. Our experimental results show evidence of a period doubling route to chaos.

In this paper we present the application of a novel fully vectorial and three-dimensional computational method for planar devices to simulation of electromagnetic modes in classical and photonic-crystal-based VCSELs. We show the mathematical basis of the method and present results of computations of a resonant wavelength, optical losses, and a threshold gain of a classical arsenide VCSEL with oxide confinement and also of a purely photonic-crystal confined one. Furthermore we analyze the analytical reduction of computational domain to two dimensions in axisymmetric geometries with cylindrical-wave expansion, discuss the mathematical problems which occurs in such coordinates and suggest a method to overcome them.

We present a new three dimensional, fully vectorial optical modeling of oxide confined as well as shallow relief vertical-cavity surface-emitting laser. Our model is based on the combination of the plane wave expansion method with the method of lines resulting in a fast and accurate computational technique. We carry out hereby a comparison between the Plane Wave Admittance Method (PWAM) and other numerical approaches for VCSEL optical modeling and show very good agreement. Furthermore, this procedure makes it possible to find optimal basic computational parameters for the PWAM in the case of VCSELs.

We study the out-of-plane photonic band structure of a two dimensional (2D) lattice with pillars made of left-handed material (LHM) or metal embedded in host dielectric. The band structures of 2D photonic crystals made of impedance-matched or impedance-unmatched LHM-RHM elements show resemblance to dielectric-dielectric and metal-dielectric structures, respectively. In particular, lossless LHM-RHM impedance-unmatched lattice supports lossless slow surface modes analogous to lossy modes at a metal-dielectric boundary.

Bandgap guidance in photonic crystal fibers (PCF) is strongly selective spectrally and in this sense resembles guidance in fibers with Bragg gratings. The photonic band-edge shifts when the optical properties of the material in the fiber are affected by external factors such as strain, temperature, pressure, static fields, chemical vapour penetration etc. This analogy allows for the development of optical sensors with similar principle of operation as fibers with Bragg gratings, however with novel sensing characteristics. Here we study theoretically PCF filled with LC when material anisotropy plays a strong role in the creation of the bandgap.

We investigate polarization and intensity all-optical bi- and tri-stability in interference structures that include both a birefringent LiNbO3 layer of different crystallographic orientations and an absorbing layer. The origin of this multistability is the thermo-optical nonlinearity present in the structures. Regenerative pulsations are demonstrated using the electro-optical and the photorefractive properties of the LiNbO3 crystal. The unstable dynamical behavior is explained heuristically as being due to competing nonlinearities.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We present a comprehensive study of coupled-cavity VCSEL structure (or CC-VCSEL), i.e. two optical cavities that share a coupling mirror and that can be independently biased using three electrical contacts. Each cavity contains multi-quantum-wells (MQW) serving as a gain or absorbing medium. We perform a thorough theoretical modeling of the CC-VCSELs taking into account the modification of the MQW optical absorption in a perpendicular external electric field, i.e. the Quantum Confined Stark Effect. Our model considers the situation of single and double wavelength lasing in forward biased cavities. We also consider the case when the light generated in one cavity optically pumps the second one with a strength that depends on the applied reverse bias to the second cavity. On this basis we develop a rate equation model that properly considers the optical field distribution of the two longitudinal modes of the coupled-cavity VCSEL. The number of modes drastically increases when one takes into account the polarization of light and the transverse mode properties. We compare our results with recently obtained experimental results on CC-VCSELs. Finally, we exploit the possibilities to realize high-speed optical switching devices such as optical modulators and field-effect QW lasers based on the QCSE in CC-VCSELs for applications in large capacity optical communications systems.

Vertical-cavity surface-emitting lasers (VCSELs) have now entered the stage of implementation in optical devices and networks. Besides the number of properties superior to EEL, VCSELs have the drawback of less stabilized polarization. As any semiconductor laser, VCSELs are sensitive to Optical Feedback (OF) due to parasitic reflections inevitable in practical applications. Here we experimentally and numerically investigate the spectral and polarization properties of VCSELs subject to polarization insensitive optical feedback from an extremely short external cavity -ESEC (few microns). We observe that the total output power and the wavelength of laser emission are sinusoidally, in-phase modulated with the external cavity (EC) length and with a period equal to half the wavelength of the VCSEL. Moreover the currents at which the switches between the two linearly polarized (LP) modes happen and the hysteresis width are also sinusoidally modulated with the same period. When biasing the VCSEL at the switching current polarization switching between two orthogonal linearly polarized states happens at different EC lengths. This polarization switching happens through a hysteresis when decreasing and increasing the EC length. We have also develop a two modes rate equation model that proves and explains the changes of all VCSEL characteristics observed in the experimental part, showing very good agreement with the experimental results.

We study the influence of delayed optical feedback from a short external cavity on the emission dynamics of semiconductor lasers using the Lang and Kobayashi rate equation model. We present the bifurcation scenario leading to regular pulse packages (RPP) and give examples of bistability between RPP and time-periodic or steady state solutions. We investigate the change of the shape of the envelope of RPP in the transition to LFF. We analyze regions of feedback parameters for which RPP occurs. Detailed mapping shows that with increasing the delay time the windows of RPP broaden, merge and finally shrink when approaching the relaxation oscillation (RO) period. In such a way the largest region of RPP occurs for delays around half of the RO period of the solitary laser. Moreover, the period of RPP also possesses a minimum as a function of the delay time corresponding to approximately the half of the RO period. For smaller delays the RPP period shows an oscillatory behavior with the delay which we identify as being due to the destabilization of the RPP in the vicinity of newly born external cavity modes. Furthermore, we reveal continuous increase of the period of the RPP with the feedback rate. Finally, we study the scaling of the frequency of the pulse package envelope with the injection current. Our results contribute to better understanding of the origin and the peculiarities of the RPP dynamics.

We have recently unveiled a new dynamics in Vertical-Cavity Surface-Emitting Lasers (VCSELs), induced by a time-delayed optical feedback [M. Sciamanna et al., Opt. Lett. 28, 1543-1545 (2003)]. The optical feedback is responsible for multiple polarization switchings as we increase the injection current. If the current is fixed close to a switching point, the VCSEL exhibits a bistable regime: the laser randomly hops between the two VCSEL linearly polarized (LP) modes, this mode hopping being driven by the laser spontaneous emission noise. Each hop is accompanied by delayed feedback induced instabilities such as rapid anticorrelated oscillations in the intensities of the two LP modes at the frequency of the external cavity (EC). These rapid delay-periodic oscillations therefore complement the slow polarization bistable mode-hopping. Here we summarize our previous theoretical and experimental conclusions and we report on further statistical studies of this optical feedback induced polarization mode-hopping in VCSELs. Interestingly, we show that the addition of an optimal amount of noise on the VCSEL injection current may give rise to coherence resonance. When the noise intensity is optimal, the delay-periodic oscillations in the VCSEL mode-hopping regime exhibit a maximal regularity, i.e. the VCSEL exhibits a sequence of regular pulses at the EC frequency. This almost periodic signal is generated by the interaction between the time-delay and the noise driven mode-hopping dynamics, without the need for an external periodic signal. Our results contribute to recent investigations of coherence resonance in non excitable systems and give evidence of coherence resonance in a realistic, optical bistable system with time-delay, that is, a mode-hopping VCSEL subject to optical feedback.

We investigate the polarization dynamics of vertical-cavity surface-emitting lasers (VCSELs) when they are subject to a large current modulation, but still operate within the fundamental transverse regime. New, interesting, nonlinear dynamics are unveiled in the two fundamental transverse, orthogonal, linearly polarized (LP) modes of the VCSEL. The intensities of the two LP modes may exhibit in phase time-periodic pulsating dynamics at one of the multiples of the modulation period (subharmonic cascade), but chaotic regimes are also obtained, in whic the LP mode intensities exhibit a combination of inphase pulsing at the modulation time-scale and antiphase dynamics on a slower time-scale. Our results suggest furthermore that, in contrast to conventional edge-emitting lasers, chaotic dynamics in directly modulated VCSELs would appear even for small modulation amplitudes (a few tens of percents of DC current) and small modulation frequencies (hundreds of MHz).

We report on new dynamics in vertical-cavity surface-emitting lasers (VCSELs), which is induced by a polarization preserving optical feedback. Our solitary VCSEL, i.e. without feedback, emits in a single linearly polarized (LP) and fundamental transverse mode. Optical feedback induces multiple polarization switchings in the L-I curve. When the injection current is set close to one of the multiple polarization switching points, the laser system exhibits a random anticorrelated hopping of the two orthogonal LP fundamental modes. Of particular interest is the observation of antiphase oscillations in the two LP modes that occur with a period corresponding to the delay time, and which complement the slow mode-hopping. Moreover, the LP-resolved optical spectra show random frequency hops between ECMs. The laser system is therefore not only bistable between the LP modes, but also multistable between ECMs. A theoretical rate equation approach yields a good qualitative agreement with our experiment. We report similar delay-periodic oscillations complementing a mode hopping in a scalar delay differential equation modeling the motion of a particle in a double well potential. Such a model was recently investigated by Tsimring and Pikovsky, in a very general context. Our results in VCSELs yield the first experimental evidence of delay-periodic oscillations in a bistable physical system with noise, and are therefore thought to be of general interest for many other processes in biology, medicine, etc. that exhibit interaction of noise, delay and bistability.

We present an experimental and rate-equation based theoretical study of the current-driven polarization modulation properties of VCSELs. In such lasers a high-contrast polarization flip is often observed at a particular value of the pump current. When modulating the current around the polarization switching value, we measure the critical modulation amplitude necessary to force synchronized back-and-forward polarization flips, as a function of the modulation frequency. This yields the polarization modulation frequency response. For a proton-implanted VCSEL the shape of the measured response curve is characterized by time constants that are very long compared with the usual time scales of laser dynamics (such as photon and carrier lifetimes), and compatible with the measured thermal relaxation time. Indeed, both the polarization modulation and the thermal frequency response curves show a cut-off frequency of about 90kHz, independent of the particular value of the switching current. In the frequency response curve of an air-post VCSEL one clearly sees remnants of the thermal influence on the switching. However, one cannot say that a thermal cut-off inhibits polarization switching above a certain modulation frequency. Notwithstanding the difference in impact of thermal effects depending on the type of device under study, our results indicate that it is necessary to incorporate a temperature-dependent variable in realistic models describing the dynamical polarization properties of VCSELs.

Current driven switching between two orthogonal linear polarizations in the fundamental mode of VCSELs is the object of intensive experimental and theoretical work. We developed a model based on the experimental evidence that the gain/loss difference between the two modes is an important factor in polarization switching. We analytically and numerically study a nearly-degenerate two-mode intensity rate equation model. The gain coefficients we use are current dependent and gain saturation with increasing optical power is also taken into account. Two types of stationary solutions emerge: pure-mode solutions (one mode lases) and mixed mode solutions (both modes lase). Stability analysis shows that when the gains equalize, switching between the two pure-mode solutions occurs. The nonlinear gain induces a region of bistability around the switching point. Taking into account the different time scales present in the model and using asymptotic techniques, we can further reduce the model to a single dynamical equation, which can be solved analytically. Stochastic effects (e.g. due to spontaneous emission) can be incorporated in this 1D Langevin-type equation. This allows us to explain the mode hopping in terms of a First Passage Time over the potential barrier in a double potential well.

In this contribution, we bring forward and compare the polarization switching (PS) dynamics and the polarization modulation characteristics of gain- and index-guided VCSELs. We then discuss the steady-state and dynamic characteristics of both types of VCSELs. Finally we focus on the polarization modulation limit and the average mode hopping frequency, which both scale over 8 orders of magnitude when the switching current is varied from just above threshold up to 2 times the threshold current.

The intriguing polarization properties of Vertical-Cavity Surface-Emitting Lasers (VCSELs) are discussed and different physical mechanisms to explain this behavior are proposed. Experimental results obtained on different types of VCSELs will be confronted with the predictions from different theoretical models.

The reconfigurability of optical interconnects is often translated in polarization-selectivity. To this aim, polarizing highspatial frequency gratings in GaAs [1], polarizing holographic optical elements in DCG [21, polarization-selective computer-generated holograms in LiNbO3 [3] and polarization-selective diffractive optical elements in calcite [41 have been developed. Polarization-selective, or anisotropic, diffractive optical elements (ADOEs) implementing calcite in combination with an index-matching polymer have proven to have several advantages over LiNbO3 [41. Recently we implemented ADOEs in a free-space reconfigurable optical interconnect using liquid crystal retarders (LCR) to control polarization of light [5]. The reconfiguration rate in this case was limited by the switching speed of the LCR, which is 20Hz in the case of a nematic LCR, and 20kHz in the case of a ferroelectric LCR. Very recently electrically controlled polarization switching in VCSEL's has been demonstrated up to 50MHz [6,7] with a polarization contrast ratio of 20:1 [7]. Here we report on the implementation of these polarization-switching VCSEL's in a reconfigurable interconnect demonstrator based on ADOEs. We present reconfigurable interconnects at 30MHz, and we demonstrate the proof-ofprinciple of a data transparent reconfigurable interconnection scheme with a bit rate of 1MHz and a reconfiguration rate of 40kHz. Both the bit rate and the reconfiguration rate are limited by the available electronic source of modulation.

Experimental results concerning the light coupling between a curved single-mode fiber and a planar waveguide with different thicknesses are presented. Different theoretical approaches (an equivalent planar waveguide geometry and a real waveguide geometry couple mode theory, as well as the beam propagation method) are applied to describe the light propagation.

Experimental and theoretical results concerning the characteristics of polished single-mode fiber-optic couplers with an intermediate waveguiding optical layer between the two fiber half- blocks are presented. Different theoretical approaches are compared and a suitable equivalent planar geometry is chosen and treated in the limits of coupled-mode theory. Mechanism of light transfer from first to the second coupler channel is investigated. Both the experimental and theoretical results are presented concerning the properties of the glued optical fiber coupler for three different thicknesses of the glue layer. These couplers are compared in respect to their spectral characteristics.

The multilayer metal-dielectric coatings allowing the realization of electrooptical interference modulator of laser light are investigated. That type of modulators operates with driving voltage of about 100 volts. Some possibilities for application are discussed.