Search

We measure the maximal distance at which two absorbed photons can jointly trigger a detection event in NbN nanowire superconducting single photon detector microbridges by comparing the one-photon and two-photon efficiencies of bridges of different overall lengths, from 0 to 400 nm. We find a length of 23 ± 2 nm. This value is in good agreement with the size of the quasiparticle cloud at the time of the detection event.Nanowire superconducting single photon detectors (SSPDs)1 are a crucial technology for a variety of applications.2 These devices consist of a thin superconducting film which detects photons when biased to a significant fraction of its critical current. Although details of the microscopic mechanism are still in dispute,3 the present understanding of this process in Niobium Nitride (NbN) SSPDs is as follows:4–13 after the absorption of a photon, a cloud of quasiparticles is created, which is known as a hotspot. This cloud diffuses, spreading out over some area of the wire. This causes the redistribution of bias current, which unbinds a vortex from the edge of the wire, if the applied bias current is such that the current for vortex entry is exceeded. The transition of a vortex across the wire creates a normal-state region, which grows under the influence of Joule heating from the bias current, leading to a voltage pulse and a detection event.14

We examine the polarization differential Goos-Hänchen beam shift upon total internal reflection, for a graded-index dielectric interface. We find a generic scaling law where the magnitude of this shift depends solely on the product of wavelength and gradient steepness. The analytic results are extended using transmission matrix calculations in cases where the assumptions made to allow analytical treatment might become questionable. Two important cases in this category are: (i) incident angle close to the critical angle and (ii) gradients with an overall thickness of the order of a wavelength. We demonstrate this effect experimentally using a polymer-blend sample with a gradual refractive-index transition induced by diffusion.

The Law of Reflection of a light ray incident upon a mirror (θin = θout) was first formulated by Euclid around 300 bc in his book Catoptrics1; it has been a tenet of geometrical optics ever since. However, more recently, a small angular deviation of the Law of Reflection has been predicted for a physical light beam when this is regarded as the implementation of a ray2,3,4,5. The deviation is a diffractive consequence of the angular dependence of the reflectivity and should occur for any mirror with less than 100% reflectivity. We report here experimental proof of this angular deviation by determining the direction of an optical beam after reflection from an air–glass interface, using a position detector with nanometre resolution. Our results are relevant for angular metrology in general and cantilever-based surface microscopies in particular. Analogous angular deviations are expected for reflection of acoustic waves and quantum matter waves. A small angular deviation of the law of reflection has been previously predicted for a light beam, and is a consequence of the angular dependence of the reflectivity. Experimental proof of such a deviation at near-infrared wavelengths is now reported.

Diamond-machining of mirrors produces a different type of irregularities than traditional grinding and polishing does. The mirrors studied in this article have been made by dielectric multi-layer coating of a diamond-machining produced substrate. We analyze first a single mirror and subsequently a two-mirror Fabry–Perot resonator.

We demonstrate and discuss the formation of an intriguing interference fringe pattern that is visible in stable resonators at resonator lengths corresponding to a higher-order frequency-degeneracy. The optical trajectories that form these fringes are described for arbitrary degeneracy; the fringes can be used to visualize and quantify imaging aberrations of the cavity relative to a cavity consisting of ideal mirrors.

We present a unifying point of view which allows to understand spectral features reported in recent experiments with two-dimensional arrays of subwavelength holes in metal films. We develop a Fano analysis of the related scattering problem by distinguishing two interfering contributions to the transmission process, namely a non-resonant contribution (direct scattering) and a resonant contribution (surface plasmon excitation). The introduction of a coupling strength between these two contributions naturally induces resonance shifts and asymmetry of profiles which satisfy simple scaling relations. We also report an experiment to confirm this analysis., Comment: 5 pages

External feedback applied to a high-power semiconductor laser is found to be responsible for a drop in output power and an increased noise-level when the optical external cavity length is an integral multiple of the optical internal cavity length. The power drops and extra noise originates from a scan of the quasi-single-mode laser over its internal cavity modes, caused by a lack of interferometric stability. In the case of interferometric stability, the wavelength of the laser exhibits a staircase-like dependence on the external cavity length. All experimental results can be described by a simple rate equation model.

We discuss how the polarization dependence of the saturation in vertical-cavity surface emitting lasers (VCSELs) can be influenced by the design of the quantum-well (QW) gain medium. As an important concept in our discussion, we use carrier reservoirs, i.e., we separate the carrier population into a number of subpopulations. Specifically, we treat VCSELs in which the carriers are separated on the basis of their spin, their momentum, or on the basis of their spatial position. By numerically analyzing the rate equations for one specific case, we show how a properly chosen polarization dependence of the saturation leads to polarization self-modulation.

We describe a new technique to study and control the polarization properties of planar vertical-cavity semiconductor lasers. The technique consists of the application of a controllable amount of strain by means of the thermal expansion that results from local heating in the vicinity of the device. Analytical expressions are derived for the strain and birefringence induced with this hot-spot technique. Experimentally, the relation between strain and birefringence is found to be highly anisotropic; this allows a natural interpretation of the distribution of the native polarization angles.

We report that the polarization of the emission of an optically pumped vertical-cavity surface-emitting laser (VCSEL) is sensitive to the polarization state of the pump light. By measuring this memory effect for circularly polarized pump light, we determine the normalized relaxation rate of the carrier spin, /spl Gamma//sub s/, which is a vital parameter in current theoretical models of VCSEL polarization. We find /spl Gamma//sub s/=300/spl plusmn/150, a value which is significantly larger than previously estimated. We also observe a memory effect for the orientation of linearly polarized pump light. This signals that, apart from the carrier spin, the VCSEL polarization is also determined by the carrier momentum.

We have measured the quantum-limited linewidths of small HeNe 3.39 /spl mu/m and HeXe 3.51 /spl mu/m lasers. In contrast to the expected Schawlow-Townes behaviour strong deviations from the inverse power dependence are observed, leading to a double-valued relation between the linewidth and the output power. This phenomenon is analyzed in terms of the increase of spontaneous emission, by a factor N/sub sp/, due to incompleteness of the inversion. Our analysis shows that typically N/sub sp/ has a value ranging from 1-10. Combining existing models for the pump power dependence of the level populations with measurements of the small signal gain, we are able to explain the observed double-valued linewidth behaviour in a quantitative way.

The quantum-limited linewidth of a short HeNe 3.39-/spl mu/m laser was measured and seen to increase with increasing nonuniformity of the intracavity intensity distribution. Experiments were done inside as well as outside the bad-cavity regime; in this regime the polarization of the gain medium cannot be adiabatically eliminated but acts as a memory. Good quantitative agreement with theory is obtained inside as well as outside the bad-cavity regime. The effect of nonuniformity is well described by the longitudinal Petermann K-factor. The bad-cavity and nonuniformity effects can be separated from each other as predicted by theory. >

We have measured the optical spectrum of a vertical cavity surface-emitting laser (VCSEL) operating below threshold. The spectrum consists of a strongly asymmetric central peak with weak structures in the wings that denote the edges of the DBR stopband. We show that the striking asymmetry of the central resonant part is caused by rays emitted at an angle with respect to the surface normal. The asymmetry can be removed by spatial filtering in the far-field. Analysis of the so obtained Lorentzian spectrum yields the current-dependent cavity loss rate and resonance frequency and thus, provides a new tool to analyze VCSEL's. >

The effect of a mild form of optical injection on the bias voltage and optical spectrum of a Fabry-Perot-type AlGaAs laser has been studied. At small frequency detuning between the injection and the injected laser, injection locking is observed. The change in bias voltage, as a function of detuning, is dispersive-like and asymmetric, From the asymmetry, the alpha -parameter of the laser is determined. When the detuning is increased beyond the locking range, the effect of optical injection on bias voltage remains noticeable. Additional dispersive-like structures appear around the relaxation oscillation frequency. In the optical spectrum, four-wave mixing and reduced damping of the relaxation oscillations are observed. >

The polarization stability of the fundamental lasing super-mode obtained from coherently coupled arrays of vertical-cavity surface-emitting lasers has been investigated. Various devices have been analyzed and none showed the abrupt change of the polarization direction (flip) often observed in solitary devices. This polarization stability is due to a current independent dichroism of 0.5 GHz.

In a homogeneously-broadened ring laser strong coupling between the counter-propagating travelling waves leads to stable oscillation in one direction at a time. Such behaviour has never been reported for semiconductor ring lasers in spite of the fact that their gain saturation has a homogeneous character. To explain this different nature of the mode competition, we have calculated the strength of the nonlinear coupling between the counter-propagating travelling waves in a semiconductor ring laser. Crucial elements of the calculation are the carrier diffusion in the amplifying medium and the large mismatch losses at the amplifier facets; the latter lead to a spatially non-uniform amplitude of the eigenmodes of the ring cavity. Additionally, we show how reflection from one of the facets leads to a linear coupling of the counter-propagating waves with a mixed conservative-dissipative nature. The final result of the mode competition depends on the interplay of linear and nonlinear coupling. Experimental resul...

A novel and relatively simple expression is given for the optical spectrum of a single-mode semiconductor laser which, due to the presence of relaxation oscillations, consists of a strong central line with a broad weak sideband at each side. The coupling between phase and amplitude fluctuations is included in this derivation and is shown to result in an asymmetry between the relaxation oscillation sidebands. This asymmetry can be used to determine the linewidth enhancement factor. Using optical heterodyne detection, the spectrum of a Fabry-Perot-type AlGaAs laser has been measured as a function of output power. Information on the dynamics of the relaxation oscillations was thus obtained. The power dependence of the frequency and damping of the relaxation oscillations allowed the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (gain saturation) to be separately determined. >

The visibility, i.e. the absolute value of the field-autocorrelation function, of a semiconductor laser subject to optical feedback has been measured. The feedback was provided by a mirror that was placed at a distance exceeding the coherence length of the emitted light. The amount of feedback varied between zero and the maximum feedback, for which the laser still operated in a single longitudinal mode of the semiconductor chip. The results are compared with numerical solutions of the Lang and Kobayashi equations. Over the whole range of feedback excellent agreement between experiment and theory was found. However. this agreement requires an unusually high value of the linewidth enhancement factor, i.e. a=10; the reason for this remains unclear. The self-sustained noise model, which is based on a statistical-analytical solution of the Lang and Kobayashi equations and which has been used in the past for analyzing feedback effects, is found to yield an inaccurate description of the experiments. Suggestions are given to explain this inadequacy. >

The interpretation of self-heterodyne spectra is difficult if, apart from spontaneous emission, additional noise sources are presented. Measurements on an external-cavity semiconductor laser show how, for a relatively long delay, the high-frequency (Lorentzian) wings of the self-heterodyne spectrum are a sensitive measure for the quantum-limited (Schawlow-Townes) laser linewidth. The quantum-limited laser linewidth is shown to be inversely proportional to the output power. Values below 5 kHz are routinely measured. The full width at half maximum (FWHM) laser linewidth is larger than this due to excess low-frequency fluctuations, which are shown to result from the presence of side modes. >

We show quantitatively how the limited polarization stability of vertical-cavity semiconductor lasers is related to the small dichroism and large quantum noise in these lasers. We introduce several techniques to measure this dichroism and noise. Suitable polarization projections are shown to yield either the heterodyne beat or the partition noise of the two polarization modes.

Birefringence induced by the electro-optic effect is demonstrated in vertical-cavity surface-emitting lasers (VCSEL). This is done by comparing two types of optically pumped VCSELs: VCSELs with standard pin-doping and VCSELs with symmetrical pip-doping. The observed birefringence in these VCSELs differs by an order of magnitude, a difference that we ascribe to the presence and absence, respectively, of electro-optic birefringence.

We demonstrate a technique to modify the strain in a planar vertical‐cavity semiconductor laser. The technique consists of locally melting a hole in the wafer next to the device by means of a focused laser beam. This allows manipulating both the magnitude and the orientation of the native birefringence in a permanent way.

We report a new technique to apply strain to a vertical‐cavity surface‐emitting semiconductor laser. This has allowed us to study the relation between strain and birefringence. We have found that the corresponding tensor is anisotropic, with a measured anisotropy 2p44/(p11−p12)=4.7±0.6. This anisotropy explains the natural preference of the polarization for the [110]/[110] axes.

We have studied the interaction between two optically pumped vertical‐cavity surface‐emitting lasers (VCSELs) on a wafer as a function of their separation d. The VCSELs are strongly coupled for d⩽13 μm, leading to the appearance of higher‐order lateral modes. For d⩾13 μm the VCSELs are weakly coupled, leading to phase locking of the individual emitters.

By performing interferometric measurements on the fundamental transverse mode of a planar VCSEL, we have determined the wave front curvature inside the VCSEL cavity. The results show that the (apparent) position of the beam waist is 0–8 μm below the surface of the top DBR, i.e., up to 25% of the Rayleigh range. From these results we estimate the amount of index and gain guiding in the VCSEL.

High resolution spectral measurements on a commercial VCSEL array are reported. The authors observe frequency splittings that result from birefringence, typically 3-22 GHz, and from transverse anisotropy between differently oriented first-order modes, typically 3-17 GHz. The spectral splittings between the various transverse modes are found to be independent of polarisation.

The voltage of a current-driven optically injected semiconductor laser has been measured. The experiments not only show the well known phenomenon of injection locking but also reveal unprecedented dispersive-like structures around the relaxation oscillation frequencies. Based on the single-mode rate equations a theoretical explanation of both phenomena is given. The dispersive-like structures are shown to be caused by four wave mixing.

Studying the bias voltage of an injection-locked semiconductor laser allows determination of the linewidth-enhancement factor α solely from the asymmetry in the locking range. This method was recently demonstrated for DFB lasers, but was thought to be unsuitable for FP lasers. The Letter shows that it can also be applied to FP lasers.