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Space-time duality in paraxial optical wave propagation implies the existence of intriguing effects when light interacts with a material exhibiting two refractive indexes separated by a boundary in time. The direct consequence of such time-refraction effect is a change in the frequency of light while leaving the wavevector unchanged. Here, we experimentally show that the effect of time refraction is significantly enhanced in an epsilon-near-zero (ENZ) medium as a consequence of the optically induced unity-order refractive index change in a sub-picosecond time scale. Specifically, we demonstrate broadband and controllable shift (up to 14.9 THz) in the frequency of a light beam using a time-varying subwavelength-thick indium tin oxide (ITO) film in its ENZ spectral range. Our findings hint at the possibility of designing (3 + 1)D metamaterials by incorporating time-varying bulk ENZ materials, and they present a unique playground to investigate various novel effects in the time domain.

The exact compensation for the bias in the classical polar-to-Cartesian conversion is shown to be multiplicative and to depend on the statistics of the cosine of the angle measurement errors. An unbiased conversion is presented. A comparison between this unbiased conversion and the previously presented debiased conversion is made. The unbiased spherical-to-Cartesian conversion is also presented and evaluated. CORRESPONDENCE

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field. DOI: 10.1103/PhysRevLett.119.263602 In recent years, the transverse structure of optical photons has been established as a resource for storing and communicating quantum information [1]. In contrast to the twodimensional Hilbert space of polarization, it takes an unbounded Hilbert space to provide a mathematical representation for the transverse structure of the optical field. The large information capacity of structured photons has been recently utilized to enhance quantum key distribution [2][3][4][5] and a multitude of other applications [6][7][8][9][10]. The orbital angular momentum (OAM) modes have become increasingly popular for implementing multidimensional quantum states due to the relative ease in generation [11], manipulation [12], and characterization of these modes [13,14].Although the OAM modes provide a basis set for representing the azimuthal structure of photons, they cannot completely span the entire transverse state space, which encompasses an extra (radial) degree of freedom. The Laguerre-Gaussian (LG) mode functions provide a basis to fully represent the spatial structure of the transverse field [15][16][17]. These modes are characterized by two numbers, the radial mode index p ∈ f0; 1; 2; …g and the azimuthal mode index l ∈ f0; AE1; AE2; …g. While the azimuthal number l is well studied due to its association with the OAM of light [16]; the radial index p has so far remained relatively unexplored. The quantum coherence of photons in a superposition of orthogonal radial modes has been recently demonstrated in the context of quantum communication and high-dimensional entanglement [17][18][19]. The radial LG modes also hold a number of promising features, and have been studied in the contexts of self-healing [20], super-resolution [21], and hyperbolic momentum charge [22]. Despite the growing theoretical interest in utilizing the radial structure of photons, the experimental realizations have thus far been impeded because of the difficulty of measuring these modes.The initial step in characterization of the radial degree of freedom of light is to find a radial ...

Self-calibration methods play an important role in reducing the negative effects of array imperfections during direction-of-arrival (DOA) estimation. However, the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios, such as low signal-to-noise ratio (SNR) and limited snapshots. This paper aims at formulating a unified framework and sparse Bayesian perspective for array calibration and DOA estimation. A comprehensive model of the array output is presented first when a single type of array imperfection is considered, with mutual coupling, gain/phase uncertainty, and sensor location error treated as typical examples. The spatial sparsity of the incident signals is then exploited, and a Bayesian method is proposed to realize array calibration and source DOA estimation. The array perturbation magnitudes are assumed to be small according to most application scenarios, and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear. Cramer-Rao lower bounds (CRLBs) for the array calibration and DOA estimation precisions are also obtained. The sparse Bayesian method is finally extended to deal with the DOA estimation problem when more than one type of array perturbation coexists.Index Terms-Direction-of-arrival (DOA) estimation, array calibration, perturbed array output formulation, Cramer-Rao lower bound (CRLB), sparse Bayesian reconstruction.

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We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each projector of a measurement. The saturation of all these bounds results in the saturation of the multi-parameter quantum Cramér-Rao bound. Necessary and sufficient conditions are obtained for the optimal measurements that give rise to the multiparameter quantum Cramér-Rao bound associated with a general quantum state. We find that nonlocal measurements on replicas of a pure or full ranked state do not help saturate the multiparameter quantum Cramér-Rao bound if no optimal measurement exists for a single copy of such a state. As an important application of our results, we construct several local optimal measurements for the problem of estimating the three-dimensional separation of two incoherent optical point sources.

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