Resonant electro-optic frequency comb.

High-speed optical telecommunication is enabled by wavelength-division multiplexing, whereby hundreds of individually stabilized lasers encode information within a single-mode optical fibre. Higher bandwidths require higher total optical power, but the power sent into the fibre is limited by optical nonlinearities within the fibre, and energy consumption by the light sources starts to become a substantial cost factor1. Optical frequency combs have been suggested to remedy this problem by generating numerous discrete, equidistant laser lines within a monolithic device; however, at present their stability and coherence allow them to operate only within small parameter ranges2-4. Here we show that a broadband frequency comb realized through the electro-optic effect within a high-quality whispering-gallery-mode resonator can operate at low microwave and optical powers. Unlike the usual third-order Kerr nonlinear optical frequency combs, our combs rely on the second-order nonlinear effect, which is much more efficient. Our result uses a fixed microwave signal that is mixed with an optical-pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant enhancement enables us to work with microwave powers that are three orders of magnitude lower than those in commercially available devices. We emphasize the practical relevance of our results to high rates of data communication. To circumvent the limitations imposed by nonlinear effects in optical communication fibres, one has to solve two problems: to provide a compact and fully integrated, yet high-quality and coherent, frequency comb generator; and to calculate nonlinear signal propagation in real time5. We report a solution to the first problem.

Publisher Correction: Resonant electro-optic frequency comb.

Change history: In the Methods section of this Letter, there were formatting errors to the equations of motion using the Heisenberg picture; see accompanying Amendment for further details. This has been corrected online.

Lenslet array-free efficient coherent combining of broadband pulses at the output of a multicore fiber with a square core grid.

An efficient optical scheme for coherent combining of radiation from the output of a multicore fiber (MCF) with a square array of cores in the out-of-phase supermode is proposed. The scheme uses only simple optical elements and is suitable for an arbitrary number of MCF cores. In a proof-of-concept experiment broadband pulses transmitted through a 25-core fiber were combined with 81% efficiency and good beam quality. In numerical modeling a close to unity efficiency is obtained for a large number of cores. The proposed scheme can be used in a reverse direction for efficient beam splitting and launching the out-of-phase supermode into the MCF.

From polarization multipoles to higher-order coherences.

We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments are measured after the light has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific values of the angles of the wave plates. For more general two-mode problems, equivalent measurements can be performed.

Anticaustics in a Fabry-Perot interferometer.

We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anticaustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn out to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot interferometer from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit.

Microsphere kinematics from the polarization of tightly focused nonseparable light.

Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica2, 864 (2015)10.1364/OPTICA.2.000864]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.

Towards polarization-based excitation tailoring for extended Raman spectroscopy.

Undoubtedly, Raman spectroscopy is one of the most elaborate spectroscopy tools in materials science, chemistry, medicine and optics. However, when it comes to the analysis of nanostructured specimens or individual sub-wavelength-sized systems, the access to Raman spectra resulting from different excitation schemes is usually very limited. For instance, the excitation with an electric field component oriented perpendicularly to the substrate plane is a difficult task. Conventionally, this can only be achieved by mechanically tilting the sample or by sophisticated sample preparation. Here, we propose a novel experimental method based on the utilization of polarization tailored light for Raman spectroscopy of individual nanostructures. As a proof of principle, we create three-dimensional electromagnetic field distributions at the nanoscale using tightly focused cylindrical vector beams impinging normally onto the specimen, hence keeping the traditional beam-path of commercial Raman systems. In order to demonstrate the convenience of this excitation scheme, we use a sub-wavelength diameter gallium-nitride nanostructure as a test platform and show experimentally that its Raman spectra depend sensitively on its location relative to the focal vector field. The observed Raman spectra can be attributed to the interaction with transverse and pure longitudinal electric field components. This novel technique may pave the way towards a characterization of Raman active nanosystems, granting direct access to growth-related parameters such as strain or defects in the material by using the full information of all Raman modes.

Distillation of squeezing using an engineered pulsed parametric down-conversion source.

Hybrid quantum information processing combines the advantages of discrete and continues variable protocols by realizing protocols consisting of photon counting and homodyne measurements. However, the mode structure of pulsed sources and the properties of the detection schemes often require the use of optical filters in order to combine both detection methods in a common experiment. This limits the efficiency and the overall achievable squeezing of the experiment. In our work, we use photon subtraction to implement the distillation of pulsed squeezed states originating from a genuinely spatially and temporally single-mode parametric down-conversion source in non-linear waveguides. Due to the distillation, we witness an improvement of 0.17 dB from an initial squeezing value of -1.648 ± 0.002 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher-order cumulants. With this, we demonstrate the source's suitability for scalable hybrid quantum network applications with pulsed quantum light.

Highly efficient coherent beam combining of tiled aperture arrays using out-of-phase pattern.

We propose a simple, highly scalable, and very efficient scheme for coherent combining of tiled aperture arrays. The scheme relies on changing the beam phasing paradigm from the commonly used in-phase pattern to the out-of-phase pattern (interleaved 0/π phases in the neighboring channels) and using an additional simple combining stage (a beamsplitter). In a proof-of-concept experiment with a one-dimensional fiber array, we achieved 89% of the power in the main combined beam. In numerical modeling, we found optimal conditions leading to 98% efficiency for an unlimited number of channels and arbitrary small initial aperture fill factors. The scheme is highly resistant to the effect of sub-aperture clipping and suitable for combining ultrashort pulses.

Chalcogenide fibers for Kerr squeezing.

We propose and investigate theoretically the Kerr squeezing of light at a wavelength of 2 µm in chalcogenide fibers with large nonlinearity and-this is the advance-with much reduced attenuation. We present suitably realistic but straightforward designs of low-loss step-index single-mode fibers with the nonlinear Kerr coefficient 3 to 4 orders of magnitude higher than for standard telecommunication fibers, and we give estimations of optimal squeezing for continuous wave laser signal in the considered fibers based on As2S3 or As2Se3 glasses.

Single Photons Emitted by Nanocrystals Optically Trapped in a Deep Parabolic Mirror.

We investigate the emission of single photons from CdSe/CdS dots-in-rod which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4π emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap, we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble of linear dipoles with the electromagnetic field in free space.

Universal Compressive Characterization of Quantum Dynamics.

Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum processes using much fewer measurements compared to conventional methods. This technique utilizes compressive projective measurements that are generalizable to an arbitrary number of subsystems. Both numerical analysis and experimental results with unitary gates demonstrate low measurement costs, of order O(d^{2}) for d-dimensional systems, and robustness against statistical noise. Our work potentially paves the way for a reliable and highly compressive characterization of general quantum devices.

Weak Measurement Enhanced Spin Hall Effect of Light for Particle Displacement Sensing.

A spherical nanoparticle can scatter tightly focused optical beams in a spin-segmented manner, meaning that the far field of the scattered light exhibits laterally separated left- and right-handed circularly polarized components. This effect, commonly referred to as giant spin Hall effect of light, strongly depends on the position of the scatterer in the focal volume. Here, a scheme that utilizes an optical weak measurement in a cylindrical polarization basis is put forward to drastically enhance the spin-segmentation and, therefore, the sensitivity to small displacements of a scatterer. In particular, we experimentally achieve a change of the spin-splitting signal of 5% per nanometer displacement.

Investigating the Optical Properties of a Laser Induced 3D Self-Assembled Carbon-Metal Hybrid Structure.

Carbon-based and carbon-metal hybrid materials hold great potential for applications in optics and electronics. Here, a novel material made of carbon and gold-silver nanoparticles is discussed, fabricated using a laser-induced self-assembly process. This self-assembled metamaterial manifests itself in the form of cuboids with lateral dimensions on the order of several micrometers and a height of tens to hundreds of nanometers. The carbon atoms are arranged following an orthorhombic unit cell, with alloy nanoparticles intercalated in the crystalline carbon matrix. The optical properties of this metamaterial are analyzed experimentally using a microscopic Müller matrix measurement approach and reveal a high linear birefringence across the visible spectral range. Theoretical modeling based on local-field theory applied to the carbon matrix links the birefringence to the orthorhombic unit cell, while finite-difference time-domain simulations of the metamaterial relates the observed optical response to the distribution of the alloy nanoparticles and the optical density of the carbon matrix.

Compressed sensing of twisted photons.

The ability to completely characterize the state of a system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing-inspired method to ascertain any rank-deficient qudit state, which we experimentally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it only requires a small number of intensity measurements, our technique provides an easy and accurate way to identify quantum sources, channels, and systems.

Characterization of an underwater channel for quantum communications in the Ottawa River.

We examine the propagation of optical beams possessing different polarization states and spatial modes through the Ottawa River in Canada. A Shack-Hartmann wavefront sensor is used to record the distorted beam's wavefront. The turbulence in the underwater channel is analysed, and associated Zernike coefficients are obtained in real-time. Finally, we explore the feasibility of transmitting polarization states as well as spatial modes through the underwater channel for applications in quantum cryptography.

Indefinite-Mean Pareto Photon Distribution from Amplified Quantum Noise.

Extreme events appear in many physics phenomena, whenever the probability distribution has a "heavy tail" differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among their many manifestations in physics, from "rogue waves" in the ocean to Lévy flights in random walks, Pareto dependences can follow very different power laws. For some outstanding cases, the power exponents are less than 2, leading to indefinite values not only for higher moments but also for the mean. Here we present the first evidence of indefinite-mean Pareto distribution of photon numbers at the output of nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.31 when BSV is used as a pump for supercontinuum generation, and other heavy-tailed distributions (however, with definite moments) when it pumps optical harmonics generation. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. This extremely fluctuating light is interesting for ghost imaging and for quantum thermodynamics as a resource to produce more efficiently nonequilibrium states by single-photon subtraction, the latter of which we demonstrate experimentally.

Chiroptical response of a single plasmonic nanohelix.

We investigate the chiroptical response of a single plasmonic nanohelix interacting with a weakly focused circularly polarized Gaussian beam. The optical scattering at the fundamental resonance is characterized experimentally and numerically. The angularly resolved scattering of the excited nanohelix is verified experimentally and it validates the numerical results. We employ a multipole decomposition analysis to study the fundamental and first higher-order resonance of the nanohelix, explaining their chiral properties in terms of the formation of chiral dipoles.

Stabilization of transmittance fluctuations caused by beam wandering in continuous-variable quantum communication over free-space atmospheric channels.

Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.

Quantum cryptography with twisted photons through an outdoor underwater channel.

Quantum communication has been successfully implemented in optical fibres and through free-space. Fibre systems, though capable of fast key and low error rates, are impractical in communicating with destinations without an established fibre link. Free-space quantum channels can overcome such limitations and reach long distances with the advent of satellite-to-ground links. However, turbulence, resulting from local fluctuations in refractive index, becomes a major challenge by adding errors and losses. Recently, an interest in investigating the possibility of underwater quantum channels has arisen. Here, we investigate the effect of turbulence on an underwater quantum channel using twisted photons in outdoor conditions. We study the effect of turbulence on transmitted error rates, and compare different quantum cryptographic protocols in an underwater quantum channel, showing the feasibility of high-dimensional encoding schemes. Our work may open the way for secure high-dimensional quantum communication between submersibles, and provides important input for potential submersibles-to-satellite quantum communication.