Interactions of Fundamental Mie Modes with Thin Epsilon-near-Zero Substrates.

Extensive research has focused on Mie modes in dielectric nanoresonators, enabling the creation of thin optical devices surpassing their bulk counterparts. This study investigates the interactions between two fundamental Mie modes, electric and magnetic dipoles, and the epsilon-near-zero (ENZ) mode. Analytical, simulation, and experimental analyses reveal that the presence of the ENZ substrate significantly modifies these modes despite a large size mismatch. Electric and magnetic dipole modes, both with ∼12 THz line widths, exhibit 21 and 26 THz anticrossings, respectively, when coupled to the ENZ mode, indicating strong coupling. We also demonstrate that this strongly coupled system yields notably large subpicosecond nonlinear responses. Our results establish a solid foundation for designing functional, nonlinear, dynamic dielectric metasurfaces with ENZ materials.

Using an acousto-optic modulator as a fast spatial light modulator.

High-speed spatial light modulators (SLM) are crucial components for free-space communication and structured illumination imaging. Current approaches for dynamical spatial mode generation, such as liquid crystal SLMs or digital micromirror devices, are limited to a maximum pattern refresh rate of 10 kHz and have a low damage threshold. We demonstrate that arbitrary spatial profiles in a laser pulse can be generated by mapping the temporal radio-frequency (RF) waveform sent to an acousto-optic modulator (AOM) onto the optical field. We find that the fidelity of the SLM performance can be improved through numerical optimization of the RF waveform to overcome the nonlinear effect of AOM. An AOM can thus be used as a 1-dimensional SLM, a technique we call acousto-optic spatial light modulator (AO-SLM), which has 50 µm pixel pitch, over 1 MHz update rate, and high damage threshold. We simulate the application of AO-SLM to single-pixel imaging, which can reconstruct a 32×32 pixel complex object at a rate of 11.6 kHz with 98% fidelity.

Orthogonal spatial coding with stimulated parametric down-conversion.

Orthogonal optical coding is widely used in classical multi-user communication networks. Using the phase conjugation property of stimulated parametric down-conversion, we extend the current time-domain orthogonal optical coding scheme to the spatial domain to encode and decode image information. In this process, the idler beam inherits the complex conjugate of the field information encoded in the seed beam. An encoding phase mask introduced onto the input seed beam blurs the image transferred to the idler. The original image is restored by passing the coded transferred image through a corrective phase mask placed in the momentum space of the idler beam. We expect that this scheme can also inspire new techniques in secure image transmission, aberration cancellation, and frequency conversion imaging.

Optically tunable bianisotropy in a sphere made from an epsilon-near-zero material.

Bianisotropic media can be used to engineer absorbance, scattering, polarization, and dispersion of electromagnetic waves. However, the demonstration of a tunable light-induced bianisotropy at optical frequencies is still lacking. Here, we propose an experimentally feasible concept for a light-induced tunable bianisotropic response in a homogeneous sphere made of an epsilon-near-zero (ENZ) material. By exploiting the large linear absorption and the large possible intensity-dependent changes in the permittivity of ENZ materials, the direction-dependent scattering and absorption cross sections could be obtained. Our findings pave the way for further studies and applications in the optical regime requiring full dynamic control of the bianisotropic behavior.

Automatic turbulence mitigation for coherent free-space optical links using crystal-based phase conjugation and fiber-coupled data modulation.

There are various performance advantages when using temporal phase-based data encoding and coherent detection with a local oscillator (LO) in free-space optical (FSO) links. However, atmospheric turbulence can cause power coupling from the Gaussian mode of the data beam to higher-order modes, resulting in significantly degraded mixing efficiency between the data beam and a Gaussian LO. Photorefractive crystal-based self-pumped phase conjugation has been previously demonstrated to "automatically" mitigate turbulence with limited-rate free-space-coupled data modulation (e.g., <1 Mbit/s). Here, we demonstrate automatic turbulence mitigation in a 2-Gbit/s quadrature-phase-shift-keying (QPSK) coherent FSO link using degenerate four-wave-mixing (DFWM)-based phase conjugation and fiber-coupled data modulation. Specifically, we counter-propagate a Gaussian probe from the receiver (Rx) to the transmitter (Tx) through turbulence. At the Tx, we generate a Gaussian beam carrying QPSK data by a fiber-coupled phase modulator. Subsequently, we create a phase conjugate data beam through a photorefractive crystal-based DFWM involving the Gaussian data beam, the turbulence-distorted probe, and a spatially filtered Gaussian copy of the probe beam. Finally, the phase conjugate beam is transmitted back to the Rx for turbulence mitigation. Compared to a coherent FSO link without mitigation, our approach shows up to ∼14-dB higher LO-data mixing efficiency and achieves error vector magnitude (EVM) performance of <16% under various turbulence realizations.

Designing high-performance propagation-compressing spaceplates using thin-film multilayer stacks.

The development of metasurfaces has enabled unprecedented portability and functionality in flat optical devices. Spaceplates have recently been introduced as a complementary element to reduce the space between individual metalenses, which will further miniaturize entire imaging devices. However, spaceplates necessitate an optical response which depends on the transverse spatial frequency component of a light field - therefore making it challenging both to design them and to assess their ultimate performance and potential. Here, we employ inverse-design techniques to explore the behaviour of general thin-film-based spaceplates. We observe a tradeoff between the compression factor R and the numerical aperture NA of such devices; we obtained a compression factor of R=5.5 for devices with an NA = 0.42, and up to a record R=340 with NA of 0.017. Our work illustrates that even simple designs consisting of realistic materials (i.e., silicon and glass) permit capable spaceplates for monochromatic applications.

Cross-polarized surface lattice resonances in a rectangular lattice plasmonic metasurface.

Multiresonant metasurfaces could enable many applications in filtering, sensing, and nonlinear optics. However, developing a metasurface with more than one high-quality-factor or high-Q resonance at designated resonant wavelengths is challenging. Here, we experimentally demonstrate a plasmonic metasurface exhibiting different, narrow surface lattice resonances by exploiting the polarization degree of freedom where different lattice modes propagate along different dimensions of the lattice. The surface consists of aluminum nanostructures in a rectangular periodic lattice. The resulting surface lattice resonances were measured around 640 nm and 1160 nm with Q factors of ∼50 and ∼800, respectively. The latter is a record-high plasmonic Q factor within the near-infrared type-II window. Such metasurfaces could benefit such applications as frequency conversion and all-optical switching.

Suppression of Nonlinear Optical Rogue Wave Formation Using Polarization-Structured Beams.

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

Relaxed Phase-Matching Constraints in Zero-Index Waveguides.

The utility of all parametric nonlinear optical processes is hampered by phase-matching requirements. Quasi-phase-matching, birefringent phase matching, and higher-order-mode phase matching have all been developed to address this constraint, but the methods demonstrated to date suffer from the inconvenience of only being phase matched for a single, specific arrangement of beams, typically copropagating, resulting in cumbersome experimental configurations and large footprints for integrated devices. Here, we experimentally demonstrate that these phase-matching requirements may be satisfied in a parametric nonlinear optical process for multiple, if not all, configurations of input and output beams when using low-index media. Our measurement constitutes the first experimental observation of direction-independent phase matching for a medium sufficiently long for phase matching to be relevant. We demonstrate four-wave mixing from spectrally distinct co- and counterpropagating pump and probe beams, the backward generation of a nonlinear signal, and excitation by an out-of-plane probe beam. These results explicitly show that the unique properties of low-index media relax traditional phase-matching constraints, which can be exploited to facilitate nonlinear interactions and miniaturize nonlinear devices, thus adding to the established exceptional properties of low-index materials.

Generation of volumetrically full Poincaré beams.

Optical communications, remote sensing, particle trapping, and high-resolution imaging are a few research areas that benefit from new techniques to generate structured light. We present a method of generating polarization-structured laser beams that contain both full and partial polarization states. We demonstrate this method by generating an optical beam that contains every state of partial and full polarization. We refer to this beam as a volumetrically full Poincaré beam to distinguish it from full Poincaré beams, which contain all states of full polarization only. In contrast to methods relying upon spatial coherence to generate polarization-structured beams with partial polarization, our method creates well-collimated beams by relying upon temporal coherence.

Adiabatic Frequency Conversion Using a Time-Varying Epsilon-Near-Zero Metasurface.

A time-dependent change in the refractive index of a material leads to a change in the frequency of an optical beam passing through that medium. Here, we experimentally demonstrate that this effect-known as adiabatic frequency conversion (AFC)-can be significantly enhanced by a nonlinear epsilon-near-zero-based (ENZ-based) plasmonic metasurface. Specifically, by using a 63-nm-thick metasurface, we demonstrate a large, tunable, and broadband frequency shift of up to ∼11.2 THz with a pump intensity of 4 GW/cm2. Our results represent a decrease of ∼10 times in device thickness and 120 times in pump peak intensity compared with the cases of bare, thicker ENZ materials for the similar amount of frequency shift. Our findings might potentially provide insights for designing efficient time-varying metasurfaces for the manipulation of ultrafast pulses.

Experimental demonstration of superresolution of partially coherent light sources using parity sorting.

Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced over direct imaging through the use of mode sorting. Here we theoretically and experimentally investigate the effect of partial coherence on the sub-diffraction limit localization of two sources based on parity sorting. With the prior information of a negative and real-valued degree of coherence, higher Fisher information is obtained than that for the incoherent case. Our results pave the way to clarifying the role of coherence in quantum-limited metrology.

Experimental demonstration of superresolution of partially coherent light sources using parity sorting: erratum.

The authors include references that appeared on arXiv during the preparation of their paper [Opt. Express29, 22034 (2021)10.1364/OE.427734].

Confocal super-resolution microscopy based on a spatial mode sorter.

Spatial resolution is one of the most important specifications of an imaging system. Recent results in the quantum parameter estimation theory reveal that an arbitrarily small distance between two incoherent point sources can always be efficiently determined through the use of a spatial mode sorter. However, extending this procedure to a general object consisting of many incoherent point sources remains challenging, due to the intrinsic complexity of multi-parameter estimation problems. Here, we generalize the Richardson-Lucy (RL) deconvolution algorithm to address this challenge. We simulate its application to an incoherent confocal microscope, with a Zernike spatial mode sorter replacing the pinhole used in a conventional confocal microscope. We test different spatially incoherent objects of arbitrary geometry, and we find that the resolution enhancement of sorter-based microscopy is on average over 30% higher than that of a conventional confocal microscope using the standard RL deconvolution algorithm. Our method could potentially be used in diverse applications such as fluorescence microscopy and astronomical imaging.

Tunable Doppler shift using a time-varying epsilon-near-zero thin film near 1550 nm.

We experimentally investigate the tunable Doppler shift in an 80 nm thick indium-tin-oxide (ITO) film at its epsilon-near-zero (ENZ) region. Under strong and pulsed excitation, ITO exhibits a time-varying change in the refractive index. A maximum frequency redshift of 1.8 THz is observed in the reflected light when the pump light has a peak intensity of ∼140GW/cm2 and a pulse duration of ∼580fs, at an incident angle of 40°. The frequency shift increases with the increase in pump intensity and saturates at the intensity of ∼140GW/cm2. When the pump pulse duration increases from ∼580fs to ∼1380fs, the maximum attainable frequency shift decreases from 1.8 THz to 0.7 THz. In addition, the pump energy required to saturate the frequency shift decreases with the increase in pump pulse duration for ∼x<1ps and remains unchanged for ∼x>1ps durations. Tunability exists among the pump pulse energy, duration, and incident angle for the Doppler shift of the ITO-ENZ material, which can be employed to design efficient frequency shifters for telecom applications.

Direct Tomography of High-Dimensional Density Matrices for General Quantum States of Photons.

Quantum-state tomography is the conventional method used to characterize density matrices for general quantum states. However, the data acquisition time generally scales linearly with the dimension of the Hilbert space, hindering the possibility of dynamic monitoring of a high-dimensional quantum system. Here, we demonstrate a direct tomography protocol to measure density matrices of photons in the position basis through the use of a polarization-resolving camera, where the dimension of density matrices can be as large as 580×580 in our experiment. The use of the polarization-resolving camera enables parallel measurements in the position and polarization basis and as a result, the data acquisition time of our protocol does not increase with the dimension of the Hilbert space and is solely determined by the camera exposure time (on the order of 10 ms). Our method is potentially useful for the real-time monitoring of the dynamics of quantum states and paves the way for the development of high-dimensional, time-efficient quantum metrology techniques.

Entanglement: quantum or classical?

From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.

Fast generation and detection of spatial modes of light using an acousto-optic modulator.

Spatial modes of light provide a high-dimensional space that can be used to encode both classical and quantum information. Current approaches for dynamically generating and measuring these modes are slow, due to the need to reconfigure a high-resolution phase mask such as a spatial light modulator or digital micromirror device. The process of updating the spatial mode of light can be greatly accelerated by multiplexing a set of static phase masks with a fast, image-preserving optical switch, such as an acousto-optic modulator (AOM). We experimentally realize this approach, using a double-pass AOM to generate one of five orbital angular momentum states with a switching rate of up to 500 kHz. We then apply this system to perform fast quantum state tomography of spatial modes of light in a 2-dimensional Hilbert space by projecting the unknown state onto six spatial modes comprising three mutually unbiased bases. We are able to reconstruct arbitrary states in under 1 ms with an average fidelity of 96.9%.

Minimalist Mie coefficient model.

When considering light scattering from a sphere, the ratios between the expansion coefficients of the scattered and the incident field in a spherical basis are known as the Mie coefficients. Generally, Mie coefficients depend on many degrees of freedom, including the dimensions and electromagnetic properties of the spherical object. However, for fundamental research, it is important to have easy expressions for all possible values of Mie coefficients within the existing physical constraints and which depend on the least number of degrees of freedom. While such expressions are known for spheres made from non-absorbing materials, we present here, for the first time to our knowledge, corresponding expressions for spheres made from absorbing materials. To illustrate the usefulness of these expressions, we investigate the upper bound for the absorption cross section of a trimer made from electric dipolar spheres. Given the results, we have designed a dipolar ITO trimer that offers a maximal absorption cross section. Our approach is not limited to dipolar terms, but indeed, as demonstrated in the manuscript, can be applied to higher order terms as well. Using our model, one can scan the entire accessible parameter space of spheres for specific functionalities in systems made from spherical scatterers.

Ultrafast modulation of the spectral filtering properties of a THz metasurface.

We demonstrate ultrafast tuning of a plasmonic spectral filter at terahertz (THz) frequencies. The device is made of periodically spaced gold crosses deposited on the surface of an undoped silicon wafer in which transient free carriers can be optically injected with a femtosecond resonant pulse. We demonstrate the concept by measuring the transmission spectrum of a notch filter using time-domain THz spectroscopy. Proper synchronization of the THz probe and visible excitation pulses leads to an enhanced transmission at the resonance by more than two orders of magnitude. Finite-difference time-domain simulations, which are in agreement with the experimental results, show that the underlying mechanisms responsible for the resonance blueshift and linewidth broadening can be attributed to the photoinduced change in dielectric properties of the substrate. This is supported by the numerically simulated field distribution and reflection/transmission coefficients. The device can be used in future pulse shaping and ultrafast switching experiments.