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This paper describes optical propagation beyond the paraxial limit in rotational symmetric short Fabry-Perot cavities and long fibers with parabolic-index profiles. Frequency shifts due to paraxial and nonparaxial effects, the so-called spectral fine structure and vector corrections, are calculated with perturbation theory and expressed in a single dimensionless expansion parameter. The results obtained for short cavities and fibers have similar functional forms but are surprisingly different. These similarities and differences are pointed out and discussed, including their consequences for mode multiplexing in fibers.

In 1995, Hadley formulated an elegant effective-index model to describe the formation of transverse modes in optical cavities (Hadley 1995 Opt. Lett. 20 1483–5). We apply this model to Fabry–Perot cavities and discuss its limitations, using the well-known paraxial solutions of these cavities as reference. We also introduce a new model, which we call the phase-plate model, that has less limitations and yields the correct first-order correction to the resonance frequencies for longer cavities. The analysis uses scalar optical fields in the paraxial limit.

The penetration depth in a Distributed Bragg Reflector (DBR) co-determines the resonance condition, quality factor, and mode volume of DBR-based microcavities. Recent studies have used an incomplete description of the penetration depth and incorrect equations. We present a complete analysis that involves three different penetration depths. We also present a series of experiments on microcavities to accurately determine the frequency and modal penetration depth of our DBRs and compare these results with theoretical predictions. The obtained results are relevant for anyone who models a DBR as an effective hard mirror if lengths of the order of the wavelength are relevant, as is the case for microcavities., 16 pages, 7 figures

We present a simple extension of the semi-classical model for a two-level system in a cavity, in order to incorporate multiple polarized transitions, such as those appearing in neutral and charged quantum dots (QDs), and two nondegenerate linearly polarized cavity modes. We verify the model by exact quantum master equation calculations, and experimentally using a neutral QD in a polarization non-degenerate micro-cavity, in both cases we observe excellent agreement. Finally, the usefulness of this approach is demonstrated by optimizing a single-photon source based on polarization postselection, where we find an increase in the brightness for optimal polarization conditions as predicted by the model., Comment: 8 pages, for simple code see https://doi.org/10.5281/zenodo.3476660

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

Surface plasmon propagation and scattering on structured metal–dielectric interfaces are important tools for field confinement and enhanced atom–field interaction. In this paper, we demonstrate a new type of surface plasmon (SP) lasing that more closely resembles the usual mirror-based laser, in a geometry that comprises a central 50-μm-long flat region between two metal hole arrays that serve as reflecting mirrors. The lasing mode shows features of double-slit interference modulated by the radiation pattern of, and selection rules set by, the scattering of SPs on the 2D hole arrays. Our results also provide information on the group velocity of surface plasmons and their scattering and penetration in hole arrays.

We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to the conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is observed. We find a minimum second-order correlation g((2))(0) approximate to 0.37, which corresponds to g((2))(0) approximate to 0.005 when corrected for detector jitter, and observe the expected polarization dependency and photon bunching and antibunching; close by in parameter space, which indicates the abrupt change from phase to amplitude squeezing.

A new experimental approach is demonstrated to probe the scattering properties of complex media. Using phase-only modulation of the light illuminating a random scattering sample, we induce and record fluctuations in the reflected speckle patterns. Using predictions from diffusion theory, we obtain the scattering and absorption coefficients of the sample from the average change in the speckle amplitude. Our approach, which is based on interference, is in principle able to give better signal to noise ratio as compared to an intensity modulation approach. We compare our results with those obtained from a knife-edge illumination method and enhanced back-scattering cone. Our work can find application in the non-invasive study of biological specimens as well as the study of light propagation in random scattering devices like solar cells or LEDs.

We demonstrate surface-plasmon lasing in hexagonal metal hole arrays with a semiconductor gain medium. The device can be tuned between two laser modes, with distinct wavelengths, spatial distributions, and polarization patterns, by changing the size of the optically pumped area. One of the modes exhibits a six-fold polarization pattern, while the mode observed for larger pump spots has a rotationally symmetric polarization pattern. We explain the mode tuning by the differences of in-plane and radiative out-of-plane losses of the modes. The spatial and polarization properties of the modes are conveniently described by a sum of vectorial orbital angular momentum beams with orbital, spin, and total angular momentum j=l+s.

We study surface plasmons on hexagonal hole arrays in gold on actively-pumped semiconductor. The observed dispersion yields the angle-dependent scattering. Lasing occurs in a radially-polarized donut beam and a hexagonal mode with mixed radial/azimuthal polarization.

High quality sources of single and identical (indistinguishable) photons are essential for photonic quantum information processing including boson sampling, cluster-state quantum computing, and optical quantum repeaters. To enable the use of several single photon sources in parallel and to allow the implementation of complex photonic networks, it is essential that the single photon source can be integrated easily and efficiently with optical fiber technology. Here we show a first all-solid-state InGaAs quantum dot based, integrated cavity-QED enhanced, single photon source. The source is operated by resonant optical pumping through an excitation fiber, and the single photons are collected in the fiber attached to the transmission channel of the cavity.

A high-fidelity source of identical single photons is essential for numerous quantum technologies such as quantum repeaters and optical quantum information processing. Hallmarks thereof are a near-unity single-photon purity, near-unity indistinguishability of consecutively emitted photons, and high brightness through a near-unity number of photons per time bin. In order to embed such sources in quantum networks, optical fiber integration is essential but complicated by cryogenic compatability and noise. Here we demonstrate a resonantly pumped, quantum dot (QD) based, transmission operated, single-mode fiber coupled single photon source with a purity of 97%, indistinguishability of 90%, and a brightness of 17%. This is achieved by deploying a unique micropillar cavity design in a closed-cycle cryostat, which is operated using a through-fiber cross-polarization technique to remove the pump laser light from the resonantly scattered single photons. These results pave the way for fully fiber integrated photonic quantum networks, as our technology is equally applicable for cavity-QED based photonic quantum gates., Comment: 10 pages, 10 figures

We present the first angle resolved measurements of extraordinary optical transmission (EOT) through hole array gratings in a gold film. Varying the lattice spacing of the arrays and looking at higher diffraction orders, we retrieve the angular emission pattern of the constituent holes with better signal to noise ratio than with single-hole experiments. We present a method to determine separately the angular dependence of the direct and resonant contribution to EOT by using the spectral features of the diffraction orders together with an established model. The comparison of our results with the known angular transmission of a single hole in a metal film yields a good agreement for s-polarized light. Deviations are found for illumination with p-polarized light and we address the discrepancy with Coupled Mode Model calculations and Finite Difference Time Domain simulations. These measured deviations are currently not fully understood., Stichting voor Fundamenteel Onderzoek der Materie (FOM) (program ”Stirring of Light!”); Ministerio de Economía y Competitividad (MINECO) (project MAT2014-53432-C5-1-R).

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.

We present a systematic experimental study on the optical properties of plasmonic crystals (PlC) with hexagonal symmetry. We compare the dispersion and avoided crossings of surface plasmon modes around the Γ-point of Au-metal hole arrays with a hexagonal, honeycomb and kagome lattice. Symmetry arguments and group theory are used to label the six modes and understand their radiative and dispersive properties. Plasmon-plasmon interaction are accurately described by a coupled mode model, that contains effective scattering amplitudes of surface plasmons on a lattice of air holes under 60°, 120°, and 180°. We determine these rates in the experiment and find that they are dominated by the hole-density and not on the complexity of the unit-cell. Our analysis shows that the observed angle-dependent scattering can be explained by a single-hole model based on electric and magnetic dipoles.

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 probe the local detection efficiency in a nanowire superconducting single-photon detector along the cross-section of the wire with a far subwavelength resolution. We experimentally find a strong variation in the local detection efficiency of the device. We demonstrate that this effect explains previously observed variations in NbN detector efficiency as a function of device geometry.

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

We determine the full photon number response of a NbN superconducting nanowire single photon detector via quantum detector tomography, and the results show the separation of linear, effective absorption efficiency from the internal detection efficiencies. In addition, we demonstrate an error budget for the complete quantum characterization of the detector. We find that for short times, the dominant noise source is shot noise, while laser power fluctuations limit the accuracy for longer timescales. The combined standard uncertainty of the internal detection efficiency derived from our measurements is about 2%. (C) 2015 AIP Publishing LLC.

We use quantum detector tomography to identify photon assisted vortex entry as the photon detection mechanism in superconducting NbN nanowires. We exploit the polarization dependence to resolve the response of the nanowire with subwavelength resolution.

International audience; We experimentally investigate the effect of a magnetic field on photon detection in superconducting single-photon detectors (SSPDs). At low fields, the effect of a magnetic field is through the direct modification of the quasiparticle density of states of the superconductor, and magnetic field and bias current are interchangeable, as is expected for homogeneous dirty-limit superconductors. At the field where a first vortex enters the detector, the effect of the magnetic field is reduced, up until the point where the critical current of the detector starts to be determined by flux flow. From this field on, increasing the magnetic field does not alter the detection of photons anymore, whereas it does still change the rate of dark counts. This result points at an intrinsic difference in dark and photon counts, and also shows that no enhancement of the intrinsic detection efficiency of a straight SSPD wire is achievable in a magnetic field. (C) 2015 AIP Publishing LLC.

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 study the scattering of surface plasmons from sub-wavelength holes and find that it exhibits a stronger wavelength dependence than the traditional λ(-4) scaling found for Rayleigh scattering of light from small particles. This experimental observation is consistent with recent theoretical work and linked to the two-dimensional nature of the surface plasmon and the wavelength dependence of its spatial extent in the third dimension. The scattering cross sections are obtained with a frequency-correlation technique, which compares intensity speckle patterns observed behind various random structures of holes and recorded at different wavelengths. This powerful technique even allows us to distinguish between scattering of surface plasmons into photons and scattering into other surface plasmons.

We explore spatial correlations created by stimulated pair emission in frequency degenerate parametric down-conversion from a periodically poled KTP crystal pumped by ∼2 ps duration laser pulses. The ratio of stimulated pairs over spontaneous pairs reaches as high 0.8 in the experiment. This ratio is a direct measure of the total number of modes relevant to the down-conversion process. We identify a universal curve for this ratio that accounts for the effect of the focused pump, introducing a coherence diameter r(0) related to the diffraction limited size of the pump beam in the far-field. Measurements of the spatial correlations of the PDC light for longer crystals and tight focusing conditions show that the description given in terms of a universal curve is surprisingly robust and breaks down only for a laser beam focussed to a waist smaller than 40 μm in a 2 mm long PPKTP crystal.

We present a theoretical analysis of the polarization dynamics of a vertical-cavity surface-emitting laser with either linear anisotropies or nonlinear anisotropies. In both cases, we demonstrate that the polarization excursions follow a loxodrome spiral curve on the Poincare sphere of the polarization.

We have measured the photon number probability distribution of a laser in which the inversion is not slaved to the field. For the experiments, we have used a Nd(3+):YVO(4) laser which has a sufficiently slow inversion to allow measurement of the photon fluctuations at a time scale much shorter than that of the relaxation oscillations. The photon distribution function becomes highly nonstandard (i.e., non-Poissonian) in such a laser; this is consistent with available theoretical work. We point out the relevance of our results for the case of the semiconductor microlaser.

We report single-frequency operation of a Nd 3+ :YVO 4 laser in geometric modes when its cavity is strongly frequency degenerate. These geometric modes closely resemble closed ray paths, and are the result of gain-guiding induced phase and frequency locking of Hermite–Gaussian modes. The finite locking range observed around frequency degenerate cavity configurations is in good agreement with theory.

The transverse-mode profiles for a plano‐concave Nd:YVO4 microchip laser near threshold are examined, both experimentally and theoretically, and in both the near and the far field. We study in particular the transition from dominant quadratic index guiding to dominant gain guiding. The modal profiles change dramatically in this transition, and the agreement between experiment and the theoretical model is excellent. © 2001 Optical Society of America OCIS codes: 140.0140, 140.3530, 140.3410, 140.5680, 140.4780, 230.7370.

We have observed stable single-mode oscillation in a family of high-order daisy modes for a vertical-cavity surface-emitting laser that is optically-pumped with a doughnut-shaped beam. Measurements of the frequency separations and the radial profiles of the various modes show that the waveguiding has a near-quadratic nature.

For a general class of two-mode lasers, simple analytic expressions are derived for the magnitude of, and the correlation between, the intensity fluctuations in the two modes. The mode-partition fluctuations and overall intensity dynamics are demonstrated to be almost decoupled, so that the former can be treated as a small perturbation to the standard description of intensity squeezing in a single-mode laser. An example is formed by polarization partition noise in vertical-cavity surface-emitting lasers (VCSELs). Mode-partition noise in general, and polarization fluctuations in VCSELs in particular, are thus predicted to have only a limited deteriorating effect on the attainable intensity squeezing.

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 report, theoretically and experimentally, how polarization fluctuations in vertical-cavity semiconductor lasers are affected by optical anisotropies. We develop a spin-eliminated (class A) description of laser polarization and show how the various model parameters can be extracted from the experimental data. In practice, the linear anisotropies are often much stronger than the nonlinear anisotropies, so that the polarization modes defined by the linear anisotropies form a useful basis. For this case we derive a one-dimensional model for polarization noise, with simple expressions for the relative strength of the polarization fluctuations and the rate of polarization switches. For the other, more extreme, case where the nonlinear anisotropies are as strong (or even stronger) than the linear anisotropies, the spin-eliminated description remains valid. However, in this case the concept of polarization modes is shown to lose its meaning, as a strong four-wave-mixing peak appears in the optical spectrum and polarization fluctuations become highly nonuniform.

We study the spontaneous emission spectra of optically pumped vertical-cavity surface-emitting lasers (VCSELs) operating below threshold. By spatial and angular filtering of the spontaneous emission spectra we can relate the observed asymmetrical shape of these spectra to the subthreshold guiding properties of the VCSELs. We find a substantial difference between VCSELs with a thin gain medium, consisting of quantum wells, and VCSELs with a thick gain medium, consisting of bulk GaAs; this difference is explained by analyzing the relative weights of thermal index guiding and carrier-induced index anti-guiding.

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.

For symmetry reasons, vertical-cavity semiconductor lasers might be expected to show polarization isotropy. Practical devices, however, operate in a well-defined polarization state, which indicates the presence of residual anisotropies. We have performed a systematic experimental study of these residual anisotropies by applying additional anisotropies in a controlled and continuous way. The results are compared with a coupled-mode model that describes the effect of linear anisotropies on the polarization eigenmodes. We conclude that the polarization state of a practical device is dominantly determined by these linear anisotropies; nonlinear anisotropies are found to play at most a minor role.

We show experimentally that the emission of a surface-emitting semiconductor laser becomes elliptically polarized in the presence of an axial magnetic field. This ellipticity is accompanied by a change of the mode spectrum. The overall results are consistent with a linear model describing the combined effect of birefringence and Faraday rotation. A weak onset of non-linear polarization behavior is observed; this is ascribed to the polarization dependence of the gain saturation.

The effect of spectral inhomogeneity of the gain medium on the Schawlow-Townes linewidth of a laser is demonstrated. This is done by measuring the linewidth of a HeXe 3.51 μm laser as a function of the ratio of the homogeneous linewidth and the Doppler linewidth. Effects of inhomogeneity are observed when the cavity loss rate becomes of the order of the gain bandwidth. Both theory and experiment indicate that the quantum-limited laser linewidth is not solely determined by the homogeneous component of the gain bandwidth but by the total gain bandwidth.

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.

If a laser is made sufficiently small, its (unavoidable) technical noise can be overwhelmed by the quantum noise, i.e. the spontaneous emission. We discuss the conditions which are required for this situation to occur, specializing to the case of a small gas laser. Experimental examples taken from recent work are used to illustrate the quantum regime of phase noise and polarization noise. Using scaling arguments we compare these quantum-noise effects in small gas lasers with those in semiconductor lasers.

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. >

Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.

Higher-order optical vortices are inherently unstable in the sense that they tend to split up in a series of vortices with unity charge. We demonstrate this vortex-splitting phenomenon in beams produced with holograms and spatial light modulators and discuss its generic and practically unavoidable nature. To analyze the splitting phenomena in detail, we use a multi-pinhole interferometer to map the combined amplitude and phase profile of the optical field. This technique, which is based on the analysis of the far-field interference pattern observed behind an opaque screen perforated with multiple pinholes, turns out to be very robust and can among others be used to study very ’dark’ regions of electromagnetic fields. Furthermore, the vortex splitting provides an ultra-sensitive measurement method of unwanted scattering from holograms and other phase-changing optical elements.

We give a quantitative explanation for the intriguing double-peaked structure in the intensity noise spectrum of an external-cavity semiconductor laser. We find strong suppression of the intensity noise due to coupling between the subthreshold modes (FM-locking). The measured power dependence of the shift and broadening of the double-peaked structure allows detailed diagnostic of the laser.