Optical Phase Difference Research Articles

Common-mode phase noise suppression with an open-loop differential phasemeter.

We present direct differential phase recovery-an open-loop phasemeter topology for differential optical interferometric measurements. The technique aims to remove common mode signal dynamics prior to phase-tracking, which reduces the dynamic range requirements of the phasemeter tracking optical phase differences. A phase difference measurement is experimentally demonstrated with this technique, achieving a phase sensitivity of 1 × 10-6rad/Hz with a common-mode noise rejection of 141 dB. We demonstrate this performance whilst individual channels are subject to numerous cycle slips and unable to track phase.

The influence of timescales and data injection schemes for reservoir computing using spin-VCSELs

Reservoir computing with photonic systems promises fast and energy efficient computations. Vertical emitting semiconductor lasers with two spin-polarized charge-carrier populations (spin-VCSEL), are good candidates for high-speed reservoir computing. With our work, we highlight the role of the internal dynamic coupling on the prediction performance. We present numerical evidence for the critical impact of different data injection schemes and internal timescales. A central finding is that the internal dynamics of all dynamical degrees of freedom can only be utilized if an appropriate perturbation via the input is chosen as data injection scheme. If the data is encoded via an optical phase difference, the internal spin-polarized carrier dynamics is not addressed but instead a faster data injection rate is possible. We find strong correlations of the prediction performance with the system response time and the underlying delay-induced bifurcation structure, which allows to transfer the results to other physical reservoir computing systems.

Spherical shock waveform reconstruction by heterodyne interferometry.

The indirect measurement of shock waveforms by acousto-optic sensing requires a method to reconstruct the field from the projected data. Under the assumption of spherical symmetry, one approach is to reconstruct the field by the Abel inversion integral transform. When the acousto-optic sensing modality measures the change in optical phase difference time derivative, as for a heterodyne Mach-Zehnder interferometer, e.g., a laser Doppler vibrometer, the reconstructed field is the fluctuating refractive index time derivative. A technique is derived that reconstructs the fluctuating index directly by assuming plane wave propagation local to a probe beam. With synthetic data, this approach is compared to the Abel inversion integral transform and then applied to experimental data of laser-induced shockwaves. Time waveforms are reconstructed with greater accuracy except for the tail of the waveform that maps spatially to positions near a virtual origin. Furthermore, direct reconstruction of the fluctuating index field eliminates the required time integration and results in more accurate shock waveform peak values, rise times, and positive phase duration.

In-Situ Observation of the Formation and Relaxation Processes of Concentration Gradients in a Lithium Bis(fluorosulfonyl) Amide–Tetraglyme Solvate Ionic Liquid Using Digital Holographic Interference Microscopy

Introduction Next-generation Lithium-ion batteries (LIBs) require fast charge–discharge operations, during which a steep concentration gradient (CG) is formed between the two electrodes. The formation of a concentration profile between the electrodes in an LIB with a solvate ionic liquid (SIL) is observed at a distance of less than 1 mm using holographic interferometry. This in situ technique enables the visualization of concentration profile formation near both electrodes during electrolysis, which relaxes after the electrolysis is stopped. The diffusion coefficients near both the electrodes are calculated from the concentrations of transient species near the electrode surfaces. The diffusion coefficient is smaller on the anode side of the cell than that on the cathode side owing to the viscosity of the electrolyte in the diffusion layer. This viscosity effect may have caused the concentration profile to become asymmetrical during the relaxation of the CG. Experimental Li metal was used for the anode and cathode. The distance between the electrodes was 600 μm. The electrolyte was a SIL mixture of LiFSA (lithium bisfluorosulfonylamide) and G4 (tetraglyme) at a molar ratio of 1:1. After 100 seconds of Li electrodeposition and dissolution at a constant current density (3 mA cm-2), the current was stopped, and the relaxation process of the concentration gradient generated by electrolysis was observed with a laser interference microscope (Lyncee Tec) for 1700 seconds. The Li+ concentration near the electrode was calculated from the optical phase difference based on the bulk electrolyte outside the diffusion layer. The electrode surface concentration and transference number of Li+ were used to obtain the diffusion coefficients of Li+ near both electrodes. The time variation of the diffusion layer thickness during and after electrolysis was measured to study the mass transfer phenomenon during the formation-relaxation process of the concentration gradient.

On-chip interference of scattering from two individual molecules

Integrated photonic circuits offer a promising route for studying coherent cooperative effects of a controlled collection of quantum emitters. However, spectral inhomogeneities, decoherence, and material incompatibilities in the solid state make this a nontrivial task. Here, we demonstrate efficient coupling of a pair of Fourier-limited organic molecules embedded in a polyethylene film to a TiO2 microdisc resonator on a glass chip. Moreover, we tune the resonance frequencies of the emitters with respect to that of the microresonator by employing nanofabricated electrodes. For two molecules separated by a distance of about 8 µm and an optical phase difference of about π/2, we report on a large collective extinction of the incident light in the forward direction and the destructive interference of its scattering in the backward direction. Our work sets the ground for coherent coupling of several quantum emitters via a common mode and realization of polymer-based hybrid quantum photonic circuits.

Single-shot digital holography of multiple-beam Fizeau holograms for optical phase reconstruction through the focal depth of optical fibers

Multiple-beam Fizeau interference (MBFI) is characterized by its ability to represent the fine features of phase objects. Single-shot digital holographic interferometry (SSDHI) is used for numerical focusing of the recorded holograms. In this work, the two methods are gathered and employed for solving the problem of studying the thick phase objects. The problem of thick phase objects, such as optical fibers, in MBFI is the full focusing of the fiber's optical phase in one-time single shot phase map. The proposed method is designed to collect the optical phase map due to the optical fiber through the focal depth. The main idea is based on the analysis of the MBFI to several two-beam interference sets. Each two-beam interference is treated by SSDHI method to get the optical phase at different planes of focus inside the object. Then, the resultant optical phase due to the optical fiber is collected from these planes of focus. Retrieving the optical phase maps of the multiple-beam holograms through the focal depth, for the first time, is possible using the angular spectrum method. In this case, a laser source with quite long coherence length is used as a light source.The proposed method is applied on two thick samples of, single mode and graded index, optical fibers to reconstruct the resultant optical phase maps through the focal depth. The reconstructed optical phase maps are determined for the harmonics of MBFI holograms’ angular spectra. The method proves its ability to provide more accurate, numerical focusing and phase maps reconstruction. Where, MBFI analyses indicate the magnification of optical phase differences.

Electrically tunable gradient-index lenses via liquid crystals: beyond the power law.

In this study we present an investigation of electrically tunable progressive lenses utilizing liquid crystals (LC). We introduce a polarized progressive LC lens capable of dynamically adjusting its focal length, functioning as either a positive or negative lens. Our findings reveal that the spatial distribution of lens power within the progressive LC lens, ranging from +4D to -3D, far surpassing the range of -0.87D to +0.87D which one may expect within the parabolic wavefront approximation. For a lens with a 30 mm aperture a total tunable range is 7.6 D (from +5.6D to -2D) which is 4.75 times larger than the traditional parabolic prediction∼1.6D (from +0.8D to -0.8D). This study not only challenges conventional limitations set by optical phase differences in gradient-index LC lenses (the power law) but also ushers in a new possibility for ophthalmic applications. The profound insights and outcomes presented in this paper redefine the landscape of LC lenses, paving the way for transformative advancements in optics and beyond.

Optical differential phase shift keying transceiver systems performance efficiency at high data rate optical systems in the presence of Pr doped amplifiers

Abstract This work has been clarified the optical differential phase shift keying transceiver systems performance efficiency at high data rate optical systems in the presence of pr doped amplifiers. The Max optical signal power variations after fiber link versus wavelength variations at various system data rates are demonstrated. The total optical power within optical fiber at data rates from 10 to 100 Gbps are indicated. The Max electrical signal power variations against frequency after receiver variations at various system data rates are clarified. The total electrical power after receiver at various system data rates are demonstrated. The light/electrical power received, OSNR and SNR variations in relation to data rate variations are also studied.

A study on angular distribution of THz radiation driven by two-colour laser-induced microplasma

We present an analytical method to study the angular distribution of THz radiation driven by two-colour laser-induced microplasma in nitrogen gas. Directionally dependent temporal waveforms of the radiated THz pulse is calculated. To do so, we have extended the photo-current model to calculate three-dimensional distribution of the photo-induced current from which the far-field THz radiation is computed. We have also studied the effect of optical polarization state and phase difference on the angular distribution of radiation. Our study shows that for two orthogonally-polarized colours, not only THz polarization state, but also the angular distribution of THz radiation is mostly influenced by the second optical harmonic. The possibility of rotating the angular radiation pattern around the axis of the laser propagation is illustrated for circularly-polarized laser drivers by changing the optical phase difference.

Interferometric measurements of laser-induced shockwaves in air: Variable laser energy

When focused to a small spot size in air, a sufficiently energetic laser pulse initiates a rapidly expanding plasma. After a delay, a shockwave detaches from the plasma boundary and propagates. General features of the shockwaves can be deduced from condenser microphone measurements. However, the minimum range is limited by damage thresholds, and the presence of the microphone introduces a number of measurement artifacts. Distortion of the signal is caused by diffraction around the sensor, and the limited bandwidth does not allow rise times to be correctly quantified. In contrast, optical interferometry is a nonintrusive diagnostic for quantifying shockwave characteristics. In this study, a Nd:YAG laser is focused through a converging lens in order to generate laser-induced shockwaves. By using a variable attenuator, four laser energy outputs are examined: 25, 50, 75, and 100% of the maximum energy transmission. Heterodyne Mach–Zehnder interferometer measurements are made from 10 mm to 200 mm from the focal point of the lens. Virtual velocity signals, proportional to the time derivative of optical phase differences, are used to estimate density and pressure time histories, along with peak pressure as a function of distance.

Entangling remote qubits using the single-photon protocol: an in-depth theoretical and experimental study

The generation of entanglement between remote matter qubits has developed into a key capability for fundamental investigations as well as for emerging quantum technologies. In the single-photon, protocol entanglement is heralded by generation of qubit-photon entangled states and subsequent detection of a single photon behind a beam splitter. In this work we perform a detailed theoretical and experimental investigation of this protocol and its various sources of infidelity. We develop an extensive theoretical model and subsequently tailor it to our experimental setting, based on nitrogen-vacancy centers in diamond. Experimentally, we verify the model by generating remote states for varying phase and amplitudes of the initial qubit superposition states and varying optical phase difference of the photons arriving at the beam splitter. We show that a static frequency offset between the optical transitions of the qubits leads to an entangled state phase that depends on the photon detection time. We find that the implementation of a Charge-Resonance check on the nitrogen-vacancy center yields transform-limited linewidths. Moreover, we measure the probability of double optical excitation, a significant source of infidelity, as a function of the power of the excitation pulse. Finally, we find that imperfect optical excitation can lead to a detection-arm-dependent entangled state fidelity and rate. The conclusion presented here are not specific to the nitrogen-vacancy centers used to carry out the experiments, and are therefore readily applicable to other qubit platforms.

A novel needle probe for deeper photoacoustic viscoelasticity measurement

We present for the first time, to the best of our knowledge, a needle probe for photoacoustic viscoelasticity (PAVE) measurements at a depth of 1 cm below the sample surface. The probe uses a gradient index rod lens, encased within a side-facing needle (0.7 mm outer diameter), to direct excitation light (532 nm) and detection light (1325 nm) focused on the sample, collecting and directing the returned detection light in a spectral domain low coherence interferometry system, which allows for obtaining optical phase differences due to photoacoustic oscillations. The feasibility of needle probe for PAVE depth characterization was investigated on gelatin phantoms and in vitro biological tissues. The experimental results in an in vivo animal model predict the great potential of this technique for in vivo tumor boundary detection.

Amplified sensing of optical phase difference through the phase of the resultant field

A generalized scheme to enhance the sensitivity in the measurement of phase difference in an optical interference by measuring the phase of the resultant field is presented. In the proposed scheme, the weak measurement in scalar optical interferometry is achieved by directly accessing the phase of the output state, rather than looking at the centroid shift in the intensity. The spatial confinement or beam-like characteristics for the optical field, an essential criterion for centroid calculation, is not a requirement for the scheme. The ability to uniquely sense and distinguish contributions to the phase difference from individual optical fields; an aspect with potential to improve the measurement accuracy in optical gyroscopes and gravitational wave sensing, is also presented.

Analytic model of a laser-controlled thermally deformable mirror.

We report on an analytic model of a laser-controlled thermally deformable mirror. The model shows the spatial low pass behavior of such a mirror system regarding the intensity distribution that controls the temperature distribution and the optical phase difference distribution of the deformable mirror. The model is validated using the data of measurements described by Schmid and Mahnke [J. Opt. Soc. Am. B35, 2661 (2018)JOBPDE0740-322410.1364/JOSAB.35.002661].

Magneto-optical effects of MgFe2O4 nanoparticles in solutions and thin films of polystyrene using digital Mach-Zehnder interferometer: An optical based sensor for energy storage controller

In this work, the effects of magnetic fields on the refractive index profiles and induced birefringence of polystyrene/MgFe2O4 nanoparticles (15 nm) solutions and thin films were investigated. Both the refractive index and the induced birefringence profiles of the solutions and thin films were investigated as a function of the applied magnetic field strength using the digital two-beam Mach-Zehnder interferometric method. Image processing algorithm, based on the fast Fourier transform (FFT) analysis, was applied to extract the optical phase differences of the recorded micro-interferograms for all samples under investigation. Then the refractive index and birefringence profiles are calculated. A good correlation between the applied magnetic field and the change of refractive index (Δn) was obtained (R2~0.94). This could be useful for electric energy storage sensors based on the magneto-optical properties of polystyrene/MgFe2O4 solutions and thin films.

Efficient vortex beam generation using gradient refractive-index microphase plates.

Vortex beams were theoretically demonstrated by patterning a fiber facet with $N$-segment microphase plates. By changing the aluminum oxynitride material composition of each segment, gradient refractive-index phase plates (GRPs) were designed and introduced a ${{2}}\pi l$ azimuthal optical phase difference. The gradient index profile was able to convert a fiber Gaussian mode to a Laguerre-Gaussian mode with varieties of topological charge $l$. A three-dimensional finite-difference time-domain method was applied to calculate the near-field optical phase maps and the far-field beam profiles projected from the micro-GRPs. A uniform vortex beam with a symmetrical doughnut shape was obtained by optimizing the GRPs' radii and the number of segments. The micro-GRPs enabled flat optical components for efficient vortex beam generation.

A Miniature Fiber Tip Polystyrene Microsphere Temperature Sensor With High Sensitivity

A fiber-optic temperature sensor based on fiber tip polystyrene microsphere is proposed. The sensor structure can be formed simply by placing and fixing a polystyrene microsphere on the center of an optical fiber tip. Since polystyrene has a much larger thermal expansivity, the structure can be used for high-sensitive temperature measurement. By the illuminating of the sensor with a broadband light source and through the optical Fabry-Perot interference between the front and back surfaces of the polystyrene microsphere, the optical phase difference (OPD) or wavelength shift can be used for the extraction of temperature. Temperature measurement experiment shows that, using a fiber probe polystyrene microsphere temperature sensor with a spherical diameter of about 91.7 µm, a high OPD-temperature sensitivity of about −0.617 96 nm/°C and a good linearity of 0.991 6 were achieved in a temperature range of 20°C–70°C.

Dissipative Josephson effect in coupled nanolasers

Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker–Planck equation and show that it exhibits an interesting non-equilibrium phase diagram as a function of the coherent coupling between nanolasers. As we increase that coupling, we find a non-equilibrium phase transition between a phase-locked (PL) and a non-phase-locked (NPL) steady-state, in which phase coherence is destroyed by the photon tunneling process. In the coherent, PL regime, an imbalanced photon number population appears if there is a phase difference between the nanolasers, which appears in the steady-state as a result of the competition between competing local dissipative dynamics and the Josephson photo-current. The latter is amplified for large incoherent pumping rates and it is also enchanced close to the lasing phase transition. We show that the Josephson photocurrent can be used to measure optical phase differences. In the quantum limit, the accuracy of the two nanolaser interferometer grows with the square of the photon number and, thus, it can be enhanced by increasing the rate of incoherent pumping of photons into the nanolasers.

Compact all-fiber thermo-optic modulator based on a Michelson interferometer coated with NaNdF4 nanoparticles.

We propose and investigate an all-fiber thermo-optic modulator based on a side-polished twin-core fiber (TCF) Michelson interferometer (MI) coated with NaNdF4 nanoparticles. The MI was fabricated by tapering the splicing point between the TCF and a single mode fiber (SMF). A short suspended core fiber (SCF) is spliced to one core of the TCF to introduce a fixed optical phase difference (OPD). The side-polished core is coated with photo-thermal material NaNdF4. Owing to the ohmic heating of NaNdF4 nanoparticles under 808 nm pump laser, the effective refractive index of the polished core is changed, resulting in a phase shift of the MI. The MI has a significant modulation phase shift with 2.9 π near the wavelength of 1260 nm and can obtain an optical switching with a rise (fall) time of 152 (50) ms. The proposed device will have a great application potential in optical modulators due to compact structure and strong robustness.

History of Development of the Methods and Interference Devices for Measuring a Small Optical Phase Difference (Review)

Interferometry methods, which are applied for measuring quite small phase differences in fundamental and applied problems, are considered. It is shown that first improvements of the interferometric methods for measuring small phase differences to detect various physical phenomena in the second half of the 19th century and in the early 20th century were made by H. Fizeau, A.A. Michelson, E.W. Morley, Lord Rayleigh, D.C. Miller, and G. Sagnac. It is also shown that the most sensitive method of modulation interferometry was developed in 1949–1952 by Soviet radiophysicists A.A. Andronov, I.L. Bershtein, and G.S. Gorelik. Note that the method of modulation interferometry could be implemented even in 1914 using a photocell with external photoelectric effect or in 1923 using a photocell with internal photoelectric effect (photodiode). However, professional opticians used conventional methods of measuring a small phase difference at that time, and radiophysics only began to develop as science. It is shown that the methods of electric and photoelectric harmonic analysis developed in the late 19th century and in the beginning of the 20th century could be successfully applied in interferometry; however, they have been almost completely forgotten by the time of their possible practical application.