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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

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.

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.

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.

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.

Single photon nonlinearities based on a semiconductor quantum dot in an optical microcavity are a promising candidate for integrated optical quantum information processing nodes. In practice, however, the finite quantum dot lifetime and cavity-quantum dot coupling lead to reduced fidelity. Here we show that, with a nearly polarization degenerate microcavity in the weak coupling regime, polarization pre- and postselection can be used to restore high fidelity. The two orthogonally polarized transmission amplitudes interfere at the output polarizer; for special polarization angles, which depend only on the device cooperativity, this enables cancellation of light that did not interact with the quantum dot. With this, we can transform incident coherent light into a stream of strongly correlated photons with a second-order correlation value up to 40, larger than previous experimental results, even in the strong-coupling regime. This purification technique might also be useful to improve the fidelity of quantum dot based logic gates., Single-photon optical nonlinearity is possible using an optical cavity to create strong coupling between a cavity mode and a two-level quantum system. Here, the authors demonstrate it is also possible in the weak-coupling regime by using quantum interference in a polarization-degenerate cavity.

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

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.

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 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 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.

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. >

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.

The spontaneous emission factor N sp = N 2 (N 2 − N 1 ) of a 3.39 μm HeNe laser is determined from spontaneous emission light radiated from the side of the gain tube. Nsp is shown to depend linearly on the intra-cavity optical intensity. This linear power dependence of Nsp will give rise to a power-independent contribution to the quantum-limited spectral linewidth of the laser. We predict that at an output power of 190 μW this contribution will already make up half of the fundamental laser linewidth.

In theory, there are analogous transformations of light's spin and orbital angular momentum [Allen and Padgett, J. Mod. Opt. 54, 487 (2007)]; however, none have been observed experimentally yet. In particular, it is unknown if there exists for the orbital angular momentum of light an effect analogous to the spin angular momentum-based optical rotation; this would manifest itself as a rotation of the corresponding Hermite-Gauss mode. Here we report an experimental search for this effect in a cholesteric liquid crystal polymer, using strongly focussed, spin-orbit coupled light. We find that the relative phase velocities of the orbital modes constituting the Hermite-Gauss mode agree to within 10 -5.

We experimentally study the spatial properties of the field generated by spontaneous parametric down-conversion (SPDC) when the pump laser beam is strongly focused in the nonlinear crystal. Special attention is paid to classical intensity measurements with a CCD camera. We introduce the concept of a classical equivalent source that replicates all the coherence properties of SPDC light and explains all our experimental results. We show that, in contrast with experiments with a well-collimated pump, here both the phase-matching conditions and the position of the focusing plane determine the measured intensity profiles in the image plane of the crystal. The transition from the near-field regime to the far field is investigated. Measurements of two-photon correlations under strong focusing are also presented and the special features thereof are discussed.

We report on spectral filtering within the fundamental or Schawlow-Townes linewidth of a laser. Intensity correlation functions of the filtered laser light have been calculated assuming the phase-diffusion model (PDM), the phase-jump model (PJM) and the phase-increment model (PIM) as the model underlying the statistics of the laser phase noise. Experiments have been performed on semiconductor lasers; either a one-line or a two-line filter has been positioned underneath the Schawlow-Townes linewidth of the semiconductor laser. We observe that a one-line filter converts (amplitude-stable) laser light into chaotically fluctuating light in the limit that the filter linewidth is much smaller than the Schawlow-Townes linewidth. Two such narrow filters, when sufficiently separated spectrally, lead to two independent chaotic sources. Distribution functions and correlation functions of the filtered light have also been measured as a function of the filter bandwidth. In this case the various models for laser-phase noise lead to different theoretical predictions. We find that the experimental results agree with the phase-diffusion model and not with the other models.

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.

We have studied the linewidth around threshold of the lasing and nonlasing polarization mode (x and y) in a TEM00 oxide-confined vertical-cavity semiconductor laser (VCSEL). We experimentally demonstrate: (i) that the nonlasing mode shows surprising behavior when the lasing mode passes through threshold, and (ii) that the polarization fluctuations in a VCSEL are limited by the same quantum noise that sets its finite Schawlow–Townes linewidth.

We demonstrate that the transverse eigenmodes in a waveguide that combines a parabolic index guide with a Gaussian gain guide can be highly nonorthogonal. The excess-noise factor K that arises from this nonorthogonality exhibits resonant features with maximum values that can easily reach K approximately 400 . This simple model applies directly to stable-cavity microchip lasers with focused gain.

We study the spatial coherence of a partially coherent beam before and after being transmitted through a spiral phase plate that changes the overall orbital angular momentum of the field. The two-point coherence function is measured and directly visualized on a CCD through interference in a Mach–Zehnder interferometer equipped with an image rotator. We show, in particular, how the coherence singularities associated with Airy rings are strongly affected by the spiral phase plate.

We implement an interferometric method to measure the orbital angular momentum (OAM) spectrum of photon pairs generated by spontaneous parametric down-conversion. In contrast with previous experiments, which were all limited by the modal capacity of the detection system, our method operates on the entire down-conversion cone and reveals the complete distribution of the generated OAM. In this geometry, new features can be studied. We show that the phase-matching conditions can be used as a tool to enhance the azimuthal Schmidt number and to flatten the spectral profile, allowing the efficient production of high-quality multidimensional entangled states.

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...

We show experimentally that the output light of a single-mode semiconductor laser is changed into chaotic light after passage through a narrow spectral filter. Simple linear filtering allows us to distinguish between different statistical models of laser phase noise. The experimental results agree with the phase-diffusion model.

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. >

We have accurately measured the visibility of a Fabry-Perot type AlGaAs laser as a function of its output power. A damped oscillation in the visibility indicates the presence of relaxation oscillations in the laser. From the data we obtained the output-power dependence of both the relaxation oscillation frequency and damping rate. This allowed us to separately determine the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (nonlinear gain).