Amplitude Of Optical Field Research Articles

All-optical complex field imaging using diffractive processors.

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Polarization-Dependent Fiber Metasurface with Beam Collimating and Deflecting

Metasurfaces can arbitrarily manipulate the amplitude, phase, and polarization of optical fields on subwavelength scales. Due to their arbitrary manipulation and compact size, the metasurface can be well integrated with optical fibers. Herein, we demonstrate a polarization-dependent metasurface using birefringent meta-atoms, which can independently control X- and Y-polarization incident light. Each meta-atom allows for the division of phase into 16 steps ranging from 0 to 2π for both X- and Y-polarization, resulting in 256 nanopillars selected from the meta-atom library to satisfy the required phase. With the different effective refractive indices of the cuboid meta-atoms along the X- and Y-axis, we can achieve collimation of the X-polarization emitted beam from an optical fiber while deflecting orthogonally polarized light. As a result, the proposed metasurface collimates an X-polarized beam with a beam radius of 20 μm at z = 1 mm and 43.9 μm at z = 2 mm. Additionally, the metasurface can effectively deflect the Y-polarized beam to 36.01°, consistent with the results of the theoretical computation. The proposed metasurface exhibits a deflection efficiency of 55.6% for Y-polarized beams with a relative polarization efficiency of 82.2%, while the efficiency for the X-polarization is 71.4%. Our work is considered a promising application for optical communication, sensing, and quantum measurement.

Influence of Raman gain on dynamics of spatiotemporal chaos in optical ring microresonators

We theoretically investigate on the evolution of spatiotemporal chaos under the influence of Raman gain, in an optical ring microresonator. The dynamics of the system is shown to be governed by the Lugiator–Lefever equation, with an additional real and imaginary Raman gain term. In the absence of pump field intensity and Raman gain, we observe an increase in the amplitude and frequency of the traveling optical field as the pump detuning frequency increases. However this field gradually vanishes as time increases, owing to the intra-cavity loss. By exploring an appropriate ansatz which incorporate a chirping parameter, the modified Lugiator–Lefever equation is transformed to a set of four coupled first-order nonlinear ordinary differential equations. Fixed point stability analysis strongly suggest that variation in Raman gain has the propensity of inducing the co-existence of bright and dark solitons in the anomalous dispersion regime. Results of numerical simulations underscore that the structural profiles of the optical field amplitude are greatly modified by the Raman effects. Variation in Raman gain equally leads to a bifurcation analysis of the system, in which the Lyapunov exponent diagrams reveal regions of period doubling and chaos. We finally observe that for a fixed value of the real part of Raman gain coefficient, an increase in the effects of soliton self-frequency shift generally drives the system to chaotic regime.

Generation of structured light beams by dual phase modulation with a single spatial light modulator

Precise control of amplitude and wavefront of optical fields are prerequisites for many applications, especially in singular optics. This has led to the increasing efforts for developing efficient techniques to control the shape of the light in different dimensions. A spatial light modulator (SLM) can be efficiently used for phase-only or amplitude-only modulation; but offers limitation in complex light field modulation. Hence, shaping the complex amplitude of optical beams is challenging mainly because there are no complex modulators. While there is ongoing research to develop complex amplitude modulating SLMs, a solution is still non-existent. In this study, to achieve complex light modulations, a simple experimental set-up employing single phase-only SLM has been proposed. The SLM has been used as operating in a split-screen-mode. The non-iterative approach of dual-pass modulation has been applied where two cascaded phase value distributions (PVD) are encoded side-by-side onto the SLM. The first PVD is designed to enable amplitude modulation in the second PVD plane which finally helps achieve wavefront shaping. Hence, both amplitude and phase modulation of light beam are possible in this configuration. Commonly known singular beams such as Laguerre–Gaussian and Bessel-Gaussian modes have been generated theoretically as well as experimentally to verify the feasibility of the proposed technique. The method used helps to achieve arbitrary shaped beams as well.

Sinusoidal-amplitude binary phase mask and its application in achieving an ultra-long optical needle.

Optical needle has become a hot research topic in recent years, due to the excellent properties and potential applications. To achieve a sub-diffraction optical needle, there are three common methods including planar diffractive lenses, reflective mirrors or axicons, and high-NA objective lenses with the designed phase or amplitude elements. Here, we propose a new kind of designed phase and amplitude element called the sinusoidal-amplitude binary phase mask (SA-BPM), which modulates the amplitude and phase distributions of the incident vector optical fields (VOFs) simultaneously. Based on Richards-Wolf vector diffraction integral, the corresponding parameters of SA-BPM and the optimal optical needle length are calculated by exhaustive method and genetic algorithm. We further upgrade the SA-BPM by adding a Gaussian function in the amplitude modulation, and design the Gaussian SA-BPM (GSA-BPM). We find that the ultra-long optical needles are achieved with the SA-BPM and GSA-BPM, and the depth of focus of the optical needles are improved by 30%-70% compared with the case of binary phase mask. Such SA-BPM and GSA-BPM we proposed have great potential for manipulation and utilization of the ultra-long optical needles.

Nonlinear magnetoelectric effect in atomic vapor and its application to precision radio-frequency magnetometry

We demonstrate the nonlinear magnetoelectric (ME) effect in atomic vapor achieved through the parametric interaction of optical electric and radio-frequency (rf) magnetic fields leading to the generation of new optical electric fields. Density matrix calculations are performed to validate the experimental results. Moreover, the predicted dependence of the generated optical electric field amplitudes on the rf magnetic field strength is experimentally verified to confirm the ME effect. The system provides a technique for precision rf magnetometry based on this phenomenon. We could experimentally achieve an rf magnetic field sensitivity of 70 $\mathrm{fT}/\sqrt{\text{Hz}}$ at 1 kHz to 7.5 $\mathrm{pT}/\sqrt{\text{Hz}}$ at 3 MHz for zero bias field in an unshielded environment. The appealing features of the proposed rf magnetometer using our system include a high dynamic range up to ${10}^{12}$, 6 dB bandwidth of 450 kHz, and arbitrary frequency resolution, which are intrinsic to the nonlinear ME effect in the medium.

Freeform wavelength division multiplexing metagrating based on topology optimization

Metasurfaces consist of arrays of artificial atoms arranged on a subwavelength scale, and have significant advantages in modulating the phase, amplitude, and polarization of optical field. Limited by the discrete sampling principle and the assumption of periodicity, the conventional forward design method suffers unavoidable design errors, which easily leads the device performance to degrade. In this paper, a freeform wavelength division multiplexing (WDM) metagrating with a large deflection angle and polarization-insensitive characteristics is inversely designed by using an adjoint multi-objective topology optimization method. The simulation results show that the topology-optimized WDM metagrating has superior polarization in sensitivity compared with the discrete regular structure, with a deflection angle of 70.8° at 510 nm, an absolute deflection efficiency of 48%, and a transmission efficiency of 98% for 852 nm incident light. On this basis, the absolute deflection efficiency can be optimized to more than 70% by using a random initial structure. The freeform WDM metagrating designed in this paper has the advantages of large deflection angle, high efficiency, and low spatial crosstalk, and has potential applications in optical communication, micro and nano-optical field modulation, and Rydberg atom-based microwave measurements.

Virtual source for the fractional-order Bessel–Gauss beams

First, the nonparaxial integral expression of fractional-order Bessel–Gauss (FBG) beams during propagation is rigorously derived by using the virtual source technique and the principle of independent transmission and superposition of light, together with Weber integral formula and Fourier–Bessel transform pair. Then, the analytic expression of the important axial optical field amplitude of FBG beams is obtained. Finally, the on-axis intensity and phase of FBG beams are calculated on the basis of the analytic expression. Calculated results quantitatively revealed some important intensity information regarding the near-field propagation characteristic of FBG beams.

Lossless Complex-Valued Optical-Field Control with Compound Metaoptics

Forming a desired optical field distribution from a given source requires precise spatial control of a field's amplitude and phase. Low-loss metasurfaces that allow extreme phase and polarization control of optical fields have been demonstrated over the past few years. However, metasurfaces that provide amplitude control have remained lossy, utilizing mechanisms such as reflection, absorption, or polarization loss to control amplitude. Here, we describe the amplitude and phase manipulation of optical fields without loss, by using two lossless phase-only metasurfaces separated by a distance. We first demonstrate a combined beam-former and splitter optical component using this approach. Next, we show a high-quality computer-generated three-dimensional hologram. The proposed metaoptic platform combines the advantage of lossless, complex-valued field control with a physically small thickness. This approach could lead to low-profile, three-dimensional holographic displays, compact optical components, and high precision optical tweezers for micro-particle manipulation.

Designing Optical Fields in Three Dimensions Using Source-Boundary Transformations

Recent advances in optical beam shaping have enabled a wide class of structured lights that follow exotic trajectories, opening many routes for numerous applications. Although the Helmholtz equation sets stringent conditions on the fields that can be physically realized, these constraints can be removed if sources can be introduced inside the medium. However, introducing sources is not always possible or practical. Here, we propose an analytical approach that transforms the effects of the required sources from the inside of the medium to its boundaries. The derived boundary conditions can then be used to generate any desired optical field (amplitude and phase). We demonstrate the feasibility of the approach by experimentally generating two optical fields inside a source-free simple medium, demonstrating control over the trajectories, phases, and intensities of the fields.

Computational estimation of point-spread-function field in axially symmetric optical systems

The Point-Spread-Function (PSF) field characterizes the geometric and diffractive properties of most optical system designs for imaging applications. The conventional method of computing the PSF field is carried out in two steps: first, geometrical computation of the wave aberration function, and then, diffraction evaluation. That method usually applies two approximations: (1) the exit and entrance pupil ray intersection coordinates are equal; and (2) the optical field amplitude distribution does not change between exit and entrance pupil planes. We propose here a variation of the conventional method that allows overcoming these two approximations in axially symmetric optical systems. To show the potentials of the method we applied it to a Cooke triplet. We analyse the influence of the number of traced rays on the measured accuracy of the method. We also evaluate the differences in the PSF estimation accuracy with respect to a method where the two aforementioned approximations were applied.

Designing the phase and amplitude of scalar optical fields in three dimensions.

The ability to generate any arbitrarily chosen optical field in a three-dimensional (3D) space, in the absence of any sources, without modifying the index of refraction, remains an elusive but much-desired capability with applications in various fields such as optical micromanipulation, imaging, and data communications, to name a few. In this work, we show analytically that it is possible to generate any desired scalar optical field with predefined amplitude and phase in 3D space, where the generated field is an exact duplicate of the desired field in case it is a solution of Helmholtz wave equation, or if the existence of such field is strictly forbidden, the generated field is the closest possible rendition of the desired field in amplitude and phase. The developed analytical approach is further supported via experimental demonstration of optical beams with exotic trajectories and can have a significant impact on the aforementioned application areas.

Interference effects in the high-order harmonic amplification process in the active medium of a plasma-based X-ray laser modulated by an optical field

We study the process of propagation of high harmonics of optical radiation in an active medium of a plasma-based X-ray laser, simultaneously irradiated by an intense optical field of fundamental frequency. It is shown that for moderate plasma dispersion of the active medium at the frequency of the modulating optical field, the energy and relative amplitudes of the harmonics at the output of the medium are determined by their phases at the entrance to the medium, as well as by the time-delay of the harmonics with respect to the modulating field. These dependences are due to interference of high-order harmonics with a set of multi-frequency fields generated by each of the harmonics in the process of coherent scattering in a modulated active medium. The possibilities of using these effects to increase the efficiency of harmonic amplification, to control the harmonic spectrum, and determine the relative phases at the entrance to the medium are discussed on the example of the active medium of hydrogen-like Li2+ ions (with a 13.5 nm wavelength of an inverted transition).

Multi-dimensional manipulation of optical field withmetasurfaces and its optimization based on machine learning

Metasurfaces, as two-dimensional artificial subwavelength nanostructures, have shown novel optical phenomena and abilities of flexible and multi-dimensional optical field manipulation with a more integrated platform. Relative to the metasurfaces with single-dimensional manipulation, the metasurfaces with multi-dimensional manipulation of optical fields show significant advantages in various practical application areas, such as optical holograms, sub-diffraction imaging, generating vector optical fields, and so on. However, the design of metasurfaces with multi-dimensional manipulation of optical fields is more complex in most cases. Optimization based on machine learning can effectively lower the difficulty of the design and achieve more accurate multi-dimensional manipulation, which has attracted great interest in recent years. In this review, we firstly classified and discussed the recent advances of two-dimensional manipulation of optical fields with metasurfaces. Then, we further introduced the multi-dimensional manipulation method of optical fields based on machine learning. We first provide a following classification and review recent works related to two-dimensional manipulation of optical fields with metasurfaces. (1) Manipulating amplitude and phase of optical fields simultaneously. In scalar optics, the transmission of complete optical field information requires both amplitude and phase modulations, as the wave equation implies. Thus, the metasurfaces with both amplitude and phase manipulation can provide full optical field information and better performance in various areas, such as optical holograms, energy-tailorable metasurfaces, generating Airy beams and bidirectional perfect absorbers. (2) Manipulating phase and polarization of optical fields simultaneously. In vectorial optics, many intriguing phenomena occur which seem impossible in scalar optics. However, in conventional optics, complex optical systems including polarizers and curved mirrors are often required to achieve simultaneous manipulation of phase and polarization. Metasurfaces with both phase and polarization manipulation can be utilized to achieve various novel functionalities, such as generating vector beams, giant optical activity without chiral structures, chiral holograms, arbitrary spin-to-orbital angular momentum conversion of light and anisotropic coding metasurfaces, with an integrated optical system. (3) Manipulating amplitude and polarization of optical fields simultaneously. Utilizing the abundant interlayer effects provided by metasurfaces, one can tailor their reflection, transmission, and absorption properties of electromagnetic waves in different polarization states. Metasurfaces with both amplitude and polarization manipulation can be utilized to achieve various novel phenomena which are difficult to be realized in conventional optics, such as asymmetric transmission and giant circular dichroism. (4) Manipulating frequency and amplitude of optical fields simultaneously. In linear optical region, the unique frequency-dependent absorption and scattering properties of metasurfaces in the visible frequencies are utilized to print color at the nanoscale, which is known as structural colors. In nonlinear optical region, the exponential relationship between the intensities of the nonlinear optical signal and the fundamental frequency signal, many optical phenomena can be further amplified, such as circular dichroism. (5) Manipulating frequency and phase of optical fields simultaneously. In linear optical region, achromatic meta-lenses can be realized by utilizing the dispersion characteristics of different nano antennas to compensate for phase dispersion at different frequencies. In nonlinear optical region, metasurfaces with efficient phase modulation of nonlinear waves have received great attention in recent years for their great value in the realization of many novel nonlinear functionalities, such as multiplexed holograms, multiplexed coding meta-devices, and terahertz generators. (6) Multi-dimensional manipulation of on-chip optical field. With the integration with the waveguides, metasurfaces can also realize multi-dimensional manipulation of on-chip optical field. Metasurfaces consisting of phased nanoantennas can be used to control guided waves via strong optical scattering at subwavelength intervals. Different on-chip meta-devices have been demonstrated based on this design principle, such mode converters, spin-selective and wavelength-selective demultiplexing devices, polarization emitters, waveguide devices supporting asymmetric optical power transmission and phase-matching-free second harmonic generator. Then, we introduce the new multi-dimensional manipulation method of optical fields based on machine learning. The manipulation method based on machine learning can quickly obtain the optimal structural parameter solution in a huge parameter space, which improves the efficiency of parameter optimization exponentially. At the same time, machine learning can be used to design complex discrete structures, which breaks the period limitation of conventional devices. The optical field manipulation with metasurfaces based on machine learning has great application value in metalens, holographic imaging, coding metasurface and so on.

Study of the nonparaxial propagation of asymmetric Bessel–Gauss beams by using virtual source method

Abstract The virtual source method, which is also known as the complex source point method was used to study the nonparaxial propagation of asymmetric Bessel–Gauss (aBG) beams. According to optical independence transmission and superposition principles of beam propagation, an aBG beam was expanded into superposition of the infinite Bessel–Gauss beams. Superposition of infinite virtual source points of the expanded aBG beams was used to correspond to electric rings generating an aBG beam. Then Fourier–Bessel transform theory was used to derive the nonparaxial integral expression of aBG beams. Finally, the analytic expression of axial optical field amplitude of an aBG beams was derived when they are kept to third-order nonparaxial correction term.

Optical field amplitude distribution on the pattern plate of optoelectronic system for measuring of dither system parameters in ring laser gyro

Optical field amplitude distribution on the pattern plate of optoelectronic system for measuring of dither system parameters in ring laser gyro

Digital coherent receiver based transmitter penalty characterization.

For optical communications links where receivers are signal-power-starved, such as through free-space, it is important to design transmitters and receivers that can operate as close as practically possible to theoretical limits. A total system penalty is typically assessed in terms of how far the end-to-end bit-error rate (BER) is from these limits. It is desirable, but usually difficult, to determine the division of this penalty between the transmitter and receiver. This paper describes a new rigorous and computationally based method that isolates which portion of the penalty can be assessed against the transmitter. There are two basic parts to this approach: (1) use of a coherent optical receiver to perform frequency down-conversion of a transmitter's optical signal waveform to the electrical domain, preserving both optical field amplitude and phase information, and (2): software-based analysis of the digitized electrical waveform. The result is a single numerical metric that quantifies how close a transmitter's signal waveform is to the ideal, based on its BER performance with a perfect software-defined matched-filter receiver demodulator. A detailed description of applying the proposed methodology to the waveform characterization of an optical burst-mode differential phase-shifted keying (DPSK) transmitter is experimentally demonstrated.

Fast numerical autofocus of multispectral complex fields in digital holographic microscopy with a criterion based on the phase in the Fourier domain.

The knowledge of the complex amplitude of optical fields, that is, both quantitative phase and intensity, enables numeric reconstruction along the optical axis. Nonetheless, a criterion is required for autofocusing. This Letter presents a robust and rapid refocusing criterion suitable for color interferometric digital holographic microscopy, and, more generally, for applications where complex amplitude is known for at least two different wavelengths. This criterion uses the phase in the Fourier domain, which is compared among wavelengths. It is applicable whatever the nature of the observed object: opaque, refractive, or both mixed. The method is validated with simulated and experimental holograms.

On conformity of solutions for one-dimensional photorefractive screening solitons with the Kukhtarev–Vinetskii model

In the present paper, the problem of one-dimensional screening photorefractive solitons is reconsidered in the context of the accordance of soliton solutions with the Kukhtarev–Vinetskii model. In all theoretical and experimental works dealing with the analysis of such type solitons, one assumes that under the slowly varying approximation for the optical field amplitude the reduced form of photorefractive rate equations can be employed. In this work, we point out that the crucial and commonly accepted approximation within this scheme has a limited range of applicability as regards dark solitons. This author proposes a relatively simple modification of the standard saturable photorefractive response formula to obtain the plausible self-consistent solutions. The improved solutions for screening black solitons have been derived and discussed by comparison with standard solutions.

Resolving near-field from high order signals of scattering near-field scanning optical microscopy.

The ability of using scattering-type near-field scanning optical microscopy (s-NSOM) to characterize amplitude and phase of optical near fields was investigated. We employ numerical simulations to compute signals scattered by the tip, using a bowtie nano-aperture as the example, and compare with the data obtained from s-NSOM measurements. Through demodulation of higher order harmonic signals, we show that, with the increasing order of harmonic signals, both the simulated and measured near fields are in closer agreement with the anticipated near field results. The polarization-resolved detection also helps to establish a tip-dependent transfer matrix that relates the local field components with the s-NSOM signals, which characterizes the scattering of the tip with respect to different field components. This work illustrates the importance of using higher order signals in obtaining near field in an s-NSOM measurement.