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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 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.

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 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.

We calculate the statistical distribution P_2(I_2) of the speckle pattern produced by a photon pair current I_2 transmitted through a random medium, and compare with the single-photon speckle distribution P_1(I_1). We show that the purity Tr rho^2 of a two-photon density matrix rho can be directly extracted from the first two moments of P_1 and P_2. A one-to-one relationship is derived between P_1 and P_2 if the photon pair is in an M-dimensional entangled pure state. For M>>1 the single-photon speckle disappears, while the two-photon speckle acquires an exponential distribution. The exponential distribution transforms into a Gaussian if the quantum entanglement is degraded to a classical correlation of M>>1 two-photon states. Two-photon speckle can therefore discriminate between multi-dimensional quantum and classical correlations., 5 pages, 2 figures

We measure the direction of a TEM 00 Gaussian beam reflected from an air-glass interface. We report experimental evidence of an angular deviation of the beam axis from the Reflection Law for a light ray.

We report the first observation of the Goos-H$\rm \ddot{\textbf{a}}$nchen shift of a light beam incident on a metal surface. This phenomenon is particularly interesting because the Goos-H$\rm \ddot{\textbf{a}}$nchen shift for $p$ polarized light in metals is negative and much bigger than the positive shift for $s$ polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a $p$ polarized beam of light., Comment: The parer was published on Optics Express. The new version is modified according to the reviewers suggestions

Using microscopic imaging, we study the generation and propagation of beams of surface plasmons (SPs) on a hexagonal metal nanohole array. We discuss the wavelength-dependent propagation, a Fano-type interference and the possibility to generate focused SP beams. Prominent forking of these beams is attributed to resonant (Bragg) scattering from consecutive lattice planes. This claim is supported by a coupled-mode model.

We study the spatial coherence of entangled photon pairs that are generated via type-I spontaneous parametric down-conversion SPDC . By manipulating the spatial overlap between the two down-converted beams in a Hong-Ou-Mandel interferometer we observe the spatial interference of multiple transverse modes for an even and an odd number of mirrors in the interferometer. We demonstrate that the two-photon spatial coherence, which is quantified in terms of a transverse coherence length, differs completely for the two mirror geometries and support this result by a theoretical and experimental explanation in terms of photon labeling.

Spontaneous parametric down-conversion SPDC has become the common method to generate entangled photon pairs for experimental studies on fundamental features of quantum mechanics 1–3 . Though these photon pairs can be simultaneously entangled in energy, momentum, and polarization for type-II SPDC , the use of polarization entanglement is most popular due to its simplicity. The general theoretical aspects of two-photon entanglement in type-II SPDC are well known and thoroughly studied in 4,5 . More specifically, also the effect of the spectral properties of the pump on the down-converted light has been the topic of investigation in several papers, including the effect of the spectral pump width on the spatial coherence of the downconverted beams 6 and the spectral consequences of broadband pulsed 7,8 pumping in type-II SPDC. The role of the spatial properties of the pump in type-II SPDC, and particularly that of focused pumping 9,10 , is a less explored regime, though. Proper focusing of the pump laser is certainly necessary when the entangled photon pairs are detected with fiber-coupled photon counters 11,12 . In order to optimize the collection of entangled photon pairs, both the size of the backward-propagated fiber mode and the transverse beam walk-off in the crystal have to match the size of the pump spot 11 . A potentially beneficial effect of focused pumping may also arise when using “bucket” detectors behind apertures for pair detection. A simple argument that suggests such effect is that the large wave-vector spread associated with focused pumping will generally broaden the two rings that comprise the usual SPDC pattern. The increased area of the ring crossings might thus allow us to work with larger apertures and enhance the yield of polarization-entangled photon pairs. To investigate the feasibility of this scheme and check for any side effects in both the bucket and fiber-coupled detection scheme, a better understanding of the role of focused pumping in SPDC is needed. In this paper, we study the effect of focused pumping on the single-photon image generated via type-II SPDC, contrary to papers that specifically treat the effect on coincidence imaging 9,10 . In particular, we theoretically and experimentally demonstrate that the transition from plane-wave to focused pumping leads to the same asymmetric broadening of both down-converted rings. Our theoretical description follows the approach that Grice and Walmsley 8 use to analyze the difference between the ordinary and extraordinary spectrum in the transition from cw pumping to broadband pulsed pumping, which could be loosely called “the effects of focusing in time” instead of space . We also study the consequences of focused pumping for the measured photon yield and entanglement quality of the polarizationentangled photon pairs. We present the experimental data that support these consequences for bucket detection only and include the case of fiber-coupled detection in an outlook discussion.

We show experimentally that the combination of soft-edged gain and index guiding can lead to resonant excess quantum noise. Resonances with excess noise factors close to 100 are observed in end-pumped Nd 3+ YVO 4 lasers for cavity lengths in which two modes experience similar gain. An associated increase in the relaxation oscillation damping rate demonstrates that the fluctuation enhancement is indeed caused by excess quantum noise and not by dynamic instabilities.

We investigate the role of excess quantum noise in type-II degenerate parametric down conversion in a cavity with non-orthogonal polarization eigenmodes. Since only two modes are involved we are able to derive an analytical expression for the twin-photon generation rate measured outside the cavity as a function of the degree of mode nonorthogonality. Contrary to recent claims we conclude that there is no evidence of excess quantum noise for a parametric amplifier working so far below threshold that spontaneous processes dominate., 7 pages, 3 figure in the text. Submitted to Optics Communications

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, macroscopic approach offers complete and easy control and allows unprecedented study of optical wave chaos.

It is shown that the transverse modes of a Raman amplifier with Gaussian pump are equivalent to those of a microchip laser with combined quadratic index guiding and Gaussian gain guiding. This equivalence allows for considerable cross-fertilization between these two hitherto separate fields.

We report stochastic polarization switching in vertical-cavity semiconductor lasers, with residence times that vary by 8 orders of magnitude for a single such laser by changing its switch current with a hot-spot technique. In spite of the potentially complicated polarization dynamics of these lasers, the experimental results agree with Kramers hopping in a 1D double-well potential initiated by quantum fluctuations. We confirm the validity of this surprisingly simple theoretical model by independent measurements of the potential barrier between the wells and the spontaneous emission noise strength.

To meet recent experimental advances, we generalize the intuitively appealing nonorthogonal-mode theory of excess quantum noise by introducing a Maxwell-Bloch description of the gain medium. The resulting equations extend the nonorthogonal-mode approach beyond the class A linear-gain regime providing a general starting point for theoretical descriptions of excess quantum noise. As an illustration of our theory, we derive rate equations describing excess quantum noise in class B lasers and obtain the non-Lorentzian spectrum due to the coloring of excess noise in class A lasers accounting for gain saturation.

By taking carrier momentum into account, we present an extension of the commonly used model that describes the polarization properties of vertical-cavity surface-emitting lasers (VCSEL's). We study how this modifies the polarization dependence of the gain saturation, and introduce the role of the crystalline symmetry of the semiconductor material. On a macroscopic level we show that a limited number of parameters is sufficient to describe fully the polarization properties of the VCSEL. On a microscopic level we show how the magnitudes of these parameters are determined by the dependence of the interband-transition dipole matrix element on the relative orientation of the carrier momentum and optical polarization. It turns out to be essential that the component of the carrier momentum in the plane of the quantum well is non-negligible. Furthermore, the relaxation rates of the carrier momentum and carrier spin are crucial in determining the magnitude of the polarization effects. Inclusion of the carrier momentum changes the interpretation of experimental results on the polarization of VCSEL's, and makes it possible to understand experimental results that were until now unexplained.

Whereas quantum noise in a laser is essentially white, we show that excess quantum noise is colored. The coloring is determined by both the geometry (nonorthogonality) and the dynamics (eigenvalues) of the eigenmodes of the laser resonator. Experimentally, we demonstrate these concepts by using nonorthogonal polarization modes. We also show that the induced correlations between the modes can be used to greatly reduce the excess quantum noise.