Photonic Phase Research Articles

Divergence of the Variance of the Optical Phase in Gain-Switched Semiconductor Lasers Described by Stochastic Rate Equations

We report a theoretical study of the phase diffusion in a gain-switched single-mode semiconductor laser. We use stochastic rate equations for the electric field to analyze the phase statistics of the gain-switched laser. Their use avoids the instabilities obtained with rate equations for the photon number and optical phase when the photon number is small. However, we show that a new problem appears when the field equations are integrated: the variance of the optical phase becomes divergent. This divergence cannot be observed with the numerical integration of the commonly used equations for the photon number and optical phase because of the previous instabilities. The divergence of the phase variance means that this quantity does not reach a fixed value as the integration time step is decreased. We find that the phase variance increases as the integration time step decreases, with no sign of saturation behavior even for tiny steps. We explain the divergence by making the analogy of our problem with two-dimensional Brownian motion. The fact that the divergence appears is not surprising because in 1940 Paul L\`evy demonstrated that the variance of the polar angle in two-dimensional Brownian motion is a divergent quantity. Our results show that stochastic rate equations for the photon number and phase are not appropriate for describing the phase statistics when the photon number is small. Simulation of the stochastic rate equations for the electric field are consistent with L\`evy's results but gives unphysical results since an infinite value is obtained for a quantity that can be measured.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces.

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Topological phoxonic crystals for simultaneously controlling electromagnetic and elastic waves

We propose two-dimensional silicon valley phoxonic crystals (VPxCs) to simultaneously exhibit the topological states for electromagnetic and elastic waves. By rotating the trilobal air holes, the coexistence of topological photon and phonon valley Hall phase transitions is achieved due to the breakdown of mirror symmetry. Utilizing this kind of VPxCs, we construct the topological edge states and simultaneously realize topologically valley transmission for both electromagnetic and elastic waves. The simulated results using finite element method show that the proposed VPxCs have robustness against disturbances for both electromagnetic and elastic waves. The acousto-optic (AO) interaction in a topological waveguide-cavity coupled system based on VPxCs is further studied. Results show that obvious shifts of transmission valley of electromagnetic waves during one period of elastic wave. The proposed VPxCs allow for constructing high-performance platforms to realize highly controllable topological photon-phonon interactions with an ultra-small footprint size.

Optical pulse interharmonic extraction and repetition rate division based on a microwave photonic phase detector.

Microwave photonic phase detectors (MPPDs) can extract ultrastable microwaves from a mode-locked laser (MLL), but their frequencies are often limited by the pulse repetition rate. Few works studied methods to break the frequency limitation. Here, a setup based on an MPPD and an optical switch is proposed to synchronize an RF signal from a voltage-controlled oscillator (VCO) to an interharmonic of an MLL and to realize the pulse repetition rate division. The optical switch is employed to realize pulse repetition rate division, and the MPPD is followed to detect the phase difference between the frequency-divided optical pulse and the microwave signal from the VCO, which is then fed back to the VCO via a proportional-integral (PI) controller. Both the optical switch and the MPPD are driven by the signal from the VCO. When the system reaches its steady state, the synchronization and repetition rate division are achieved simultaneously. An experiment is conducted to verify the feasibility. The 80½th, 80⅓rd, and 80⅔rd interharmonics are extracted, and pulse repetition rate division factors of two and three are realized. The phase noises at offset frequency of 10 kHz are improved by more than 20 dB.

Probing virtual ALPs by precision phase measurements: time-varying magnetic field background

We propose an experimental scheme for detecting the effects of off-shell axion-like particles (ALPs) through optical cavities. In this proposed experiment, linearly polarized photons are pumped into an optical cavity where an external time-dependent magnetic field is present. The magnetic field mediates an interaction between the cavity photons and ALPs giving rise to a modification in the phase of the cavity photons. The time-dependent nature of the external magnetic field prompts a novel amplification effect which significantly enhances this phase modification. A detection scheme is then proposed to identify such axion-induced phase shifts. We find that the phase modification is considerably sensitive to the photon-ALPs coupling constants gaγγ for the range of ALPs mass 3.1 μeV ⩽ ma ⩽ 44.4 μeV.

Photonic Radio Frequency Orbital Angular Momentum Generation and Beam Steering

Orbital angular momentum (OAM) is a fundamental property of electromagnetic waves and is inherently carried by all frequencies of waves. In particular, OAM applications at radio frequencies (RFs) have attracted much attention due to their unique functionalities in communications. Enabled by the present wireless communication system, employing a circular antenna array (CAA) is a highly compatible and cost-effective approach for generating RF-OAM beams. In this paper, recent progress on RF-OAM communication systems with CAAs from the transceiver to the controller is summarized. A new scheme for RF-OAM generation and beam steering systems is proposed based on dual-wavelength control using CAA with the energy-conserved feature, where an integrated chip incorporating an arrayed waveguide grating (AWG) structure is introduced. Either microwave photonic phase shift or optical true time delay (OTTD) can be operated by this chip, benefiting from the phase amplification concept and the design of delay channels. Utilizing their combination, RF-OAM beams with arbitrary OAM states can be achieved for multiplexing and steered simultaneously. Furthermore, RF-OAM beam steering can be achieved without distortion in the desired transmission direction. This photonics-assisted method with an integrated chip is a potential strategy for improving the signal quality and reducing the system complexity of RF-OAM transmission systems.

All-Polarization-Maintained Microwave Photonic Phase Detector Based on a DP-DMZM

An all-polarization-maintained microwave photonic phase detector (MPPD) based on a dual-polarization dual-drive Mach-Zehnder modulator (DP-DMZM) is demonstrated to detect the phase difference between a microwave signal and an optical pulse train. The robustness of the MPPD can be significantly improved with the all-polarization-maintained structure. A proof-of-concept experiment is carried out. An 8.032-GHz dielectric resonator oscillator (DRO) is locked to an optical pulse train through this MPPD with its phase noise reducing from −109.68 dBc/Hz to −135.41 dBc/Hz at 10-kHz offset frequency. The DP-DMZM-based MPPD shows that the minimum value of the noise floor is around −154 dBc/Hz, and the integrated residual timing jitters from 100 Hz to 100 kHz, 1 MHz, and 3 MHz are 276 as, 696 as, and 2.50 fs, respectively. The MPPD has good stability against external vibrations and stresses.

Computing Liquid‐Crystal Photonics Platform Enabled Wavefront Sensing

AbstractDetecting the wavefront of photons in an efficient and accurate way is crucial to retrieve the information of an optical field. Liquid crystal (LC) possesses strong ability to manipulate the phase and polarization of photons with high diffraction efficiency and therefore offers a promising avenue toward this aim. In this paper, LC performing analog optical processing is explored and a computing LC platform is proposed to implement the wavefront sensing via tuned bias retardation. It is demonstrated that precisely introducing a tiny Pancharatnam–Berry phase by LC can achieve flexible separation of two spin components with high resolution. Modulating the retardation by rotation of an analyzer, the computing LC platform is used to reconstruct wavefronts with phase‐contrast patterns. In particular, combining this scheme with microscopy can precisely retrieve a micro‐scale phase distribution. The result suggests that the computing LC platform can perform as a wavefront sensor with high efficiency and may open up new opportunities in the applications of precision metrology, real‐time analog optical processing, and high‐contrast microscopy.

An integrated photonic-assisted phased array transmitter for direct fiber to mm-wave links

Millimeter-wave (mm-wave) phased arrays can realize multi-Gb/s communication links but face challenges such as signal distribution and higher power consumption hindering their widespread deployment. Hybrid photonic mm-wave solutions combined with fiber-optics can address some of these bottlenecks. Here, we report an integrated photonic-assisted phased array transmitter applicable for low-power, compact radio heads in fiber to mm-wave fronthaul links. The transmitter utilizes optical heterodyning within an electronically controlled photonic network for mm-wave generation, beamforming, and steering. A photonic matrix phase adjustment architecture reduces the number of phase-shift elements from M × N to M + N lowering area and power requirements. A proof-of-concept 2 × 8 phased array transmitter is implemented that can operate from 24–29 GHz, has a steering range of 40°, and achieves 5 dBm EIRP at an optical power of 55 mW without using active mm-wave electronics. Data streams at 2.5 Gb/s are transmitted over 3.6 km of optical fiber and wirelessly transmitted attaining bit-error rates better than 10−11.

Excitation wavelength dependent photon emission and phase change probing in CsPbBr3 quantum dots

Inorganic lead halide perovskites such as CsPbBr3 exhibit tremendous potential for use in optoelectronic and radiation detection devices. This experimental work on CsPbBr3 Quantum Dots (QD) seeks to explore and report on the physics behind their response to photoexcitation using two different laser wavelengths. One of the excitation wavelengths photoexcites the electron deeper into the conduction band while the other slightly above the reported bandgap. Photoluminescence spectra from the sample show a contrasting behavior, both in terms of emission wavelengths and probing of the widely known phase change behavior in these material systems. While the former is tentatively attributed to what the dominant structural phase is, we speculate that the latter is due to a change in the energy band structure (with a corresponding change in optical transitions) of the system as it transitions from an orthorhombic phase to a tetragonal one.

3D printing of responsive chiral photonic nanostructures

Finely controlled flow forces in extrusion-based additive manufacturing can be exploited to program the self-assembly of malleable nanostructures in soft materials by integrating bottom-up design into a top-down processing approach. Here, we leverage the processing parameters offered by direct ink-writing (DIW) to reconfigure the photonic chiral nematic liquid crystalline phase in hydroxypropyl cellulose (HPC) solutions prior to deposition on the writing substrate to direct structural evolution from a particular initial condition. Moreover, we incorporate polyethylene glycol (PEG) into iridescent HPC inks to form a physically cross-linked network capable of inducing kinetic arrest of the cholesteric/chiral pitch at length scales that selectively reflect light throughout the visible spectrum. Based on thorough rheological measurements, we have found that printing the chiral inks at a shear rate where HPC molecules adopt pseudonematic state results in uniform chiral recovery following flow cessation and enhanced optical properties in the solid state. Printing chiral inks at high shear rates, on the other hand, shifts the monochromatic appearance of the extruded filaments to a highly angle-dependent state, suggesting a preferred orientation of the chiral domains. The optical response of these filaments when exposed to mechanical deformation can be used in the development of optical sensors.

Geometric phase for twisted light.

Polarization vectors of light traveling in a coiled optical fiber rotate around its propagating axis even in the absence of birefringence. This rotation was usually explained due to the Pancharatnam-Berry phase of spin-1 photons. Here, we use a purely geometric method to understand this rotation. We show that similar geometric rotations also exist for twisted light carrying orbital angular momentum (OAM). The corresponding geometric phase can be applied in photonic OAM-state-based quantum computation and quantum sensing.

Floquet engineering of non-equilibrium superradiance

We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to sustain a coherent light-field. In particular, our model applies to solids within a two-band approximation, in which the electrons act as Schwinger fermions. We propose to use this Floquet-assisted superradiant phase to obtain controllable optical gain for a laser-like operation.

Photon orbits and phase transition for non-linear charged anti-de Sitter black holes

In this work, we investigate the relation between the photon sphere radius and the first-order phase transition for the charged Einstein-power-Yang-Mills AdS black hole. Through the analysis, we find with a certain condition there exist the non-monotonic behaviors between the photon sphere radius, the impact parameter, the non-linear Yang-Mills charge parameter, temperature, and pressure. And both the changes of photon sphere radius and impact parameter before and after phase transition can be regarded as the order parameter, their critical exponents near the critical point are equal to the same value 1/2, just like the ordinary thermal systems. These indicate that there maybe exists a universal relation of gravity nearby the critical point for a black hole thermodynamical system. Furthermore, the effect of impact parameter on the deflect angle is also investigated.

Synchronization of Two Microwave Sources With Femtosecond-level Residual Timing Jitters Using a Microwave Photonic Phase Detector

A microwave photonic phase detector (MPPD) for simultaneous synchronization of two independent microwave sources to a single mode-locked laser (MLL) with femtosecond-level residual timing jitters is firstly proposed and experimentally demonstrated. A Sagnac loop is built based on a dual-polarization dual-drive Mach-Zehnder modulator (DP-DMZM). Each path consisting a branch of the modulator forms an MPPD due to its feature of polarization multiplexing. Thus, two dielectric resonator oscillators (DROs) can be synchronized simultanesously. A proof-of-concept experiment is carried out. Two independent DROs with frequencies of 8.0320 and 8.3332 GHz are synchronized to an MLL. The phase noises of the synchronized 8.0320-GHz signal are −109.79 and −135.14 dBc/Hz at the 1-kHz and 10-kHz offset frequencies, respectively, and those of the 8.3332-GHz signal are −106.87 and −133.86 dBc/Hz. The residual timing jitters of the two synchronized signals (integrated from 100 Hz to 1 MHz) are around 2.12 fs and 5.93 fs, respectively. The impact of the amplitude and phase imbalances of the driven signals to the DP-DMZM on the performance of the MPPD is investigated.

Statistical analysis of intensity fluctuations in the second harmonic of a multimode Nd:YAG laser through a modified Pearson correlation coefficient

We apply a recently proposed modified Pearson correlation coefficient to investigate the statistical properties of intensity fluctuations in the second harmonic as well as fundamental mode of a multimode $Q$-switched Nd:yttrium aluminum garnet laser. Above threshold the system displays a photonic ferromagneticlike spontaneous mode-locking phase with replica symmetry breaking (RSB). Differently from the photonic glassy phase in random lasers in which modes do not oscillate synchronously, in the present case a relevant fraction of modes oscillate coherently, but the synchronous oscillation of some modes is frustrated with the RSB arising from the fact that a given subset of modes is randomly activated at each excitation pulse with dominating coherent oscillation, frustrating the emergence of other modes. From a single set of measurements, the modified Pearson coefficient allows to identify that the onset of the RSB phenomenon between distinct spectra as the lasing threshold is crossed coincides with the emergence of correlations between different wavelengths in the same spectrum. As different subsets of longitudinal modes are nondeterministically activated after each shot, the RSB property indicates that distinct spectra can be either correlated or anticorrelated around both the fundamental mode and the second harmonic.

Photonic topological phases in Tellegen metamaterials.

We investigate the photonic topological phases in Tellegen metamaterials characterized by the antisymmetric magnetoelectric tensors with real-valued quantities. The underlying medium is considered a photonic analogue of the topological semimetal featured with a displaced Weyl cone in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two Tellegen metamaterials with opposite sign of the magnetoelectric parameter exist at their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a pair of bended and a pair of twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the Tellegen metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Proof-of-Principle Direct Measurement of Particle Statistical Phase

The symmetrization postulate in quantum mechanics is formally reflected in the appearance of an exchange phase governing the symmetry of identical-particle global states under particle swapping. Many indirect measurements of this fundamental phase have been reported thus far, but a direct observation has been achieved only recently for photons. Here, we propose a general scheme capable of directly measuring the exchange phase of any type of particle (bosons, fermions, or anyons), exploiting the operational framework of spatially localized operations and classical communication. We experimentally implement it on an all-optical platform, providing a proof of principle for different simulated exchange phases. As a by-product, we supply a direct measurement of the real bosonic exchange phase of photons. Additionally, we analyze the performance of the proposed scheme when mixtures of particles of different nature are injected. Our results confirm the symmetrization tenet and provide a tool to explore it in various scenarios. Finally, we show that the proposed setup is suited to generating indistinguishability-driven $\mathrm{NOON}$ states useful for quantum-enhanced phase estimation.

Photonic Weyl semimetals in pseudochiral metamaterials

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones in the frequency-wave vector space. As the ’spin’-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Phase customization in photonic integrated circuits with trimmed waveguides.

Accurate photon phase control on a chip is essential to improve the expandability and stability of photonic integrated circuits (PICs). Here, we propose a novel, to the best of our knowledge, on-chip static phase control method in which a modified line is added close to the normal waveguide with a lower-energy laser. By controlling the laser energy and the position and length of the modified line, the optical phase can be precisely controlled with low loss and a three-dimensional (3D) path. Customizable phase modulation ranging from 0 to 2π is performed with a precision of λ/70 in a Mach-Zehnder interferometer. The proposed method can customize high-precision control phases without changing the waveguide's original spatial path, which is expected to control the phase and solve the phase error correction problem during processing of large-scale 3D-path PICs.