We present a numerical method for the reconstruction and optimization of complex field synthesis using coherent pulse combination systems. A genetic algorithm utilizing a Fourier optics based propagation method is developed for accurate convergence and modeling of near and far field distributions, achieving better than $π/10$ phase accuracy in reconstructed input parameters.
We investigate the mechanism of the nonparaxial propagation of the tightly focused beams in the view of Fourier optics. It shows that it is the phase of the angular spectrum which induces the interesting evolution of the tightly focused beams. Based on the theory of Fourier optics, we propose an approach on controlling and detecting the focusing spot of the tightly focused beams.
Genetic algorithms (GAs) have a long history of over four decades. GAs are adaptive heuristic search algorithms that provide solutions for optimization and search problems. The GA derives expression from the biological terminology of natural selection, crossover, and mutation. In fact, GAs simulate the processes of natural evolution. Due to their unique simplicity, GAs are applied to the search space to find optimal solutions to various problems in science and engineering. Using GAs for lens design was investigated mostly in the 1990s, but were not fully exploited. But in the past few years th…
Using numerical simulations, here we demonstrate that a single sheet of graphene with properly designed inhomogeneous, nonuniform conductivity distributions can act as a convex lens for focusing and collimating the transverse-magnetic (TM) surface Plasmon polariton (SPP) surface wave propagating along the graphene. Consequently, we show that the graphene can act as a platform capable of obtaining spatial Fourier transform of infra-red (IR) SPP signals. This may lead to rebirth of the field of Fourier Optics on a one-atom-thick structure.
The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghos…
Light microscopy enables multifunctional imaging of biological specimens at unprecedented depths and resolutions. However, the performance of all optical methods degrades with the imaging depth due to sample-induced aberrations. Methods of adaptive optics (AO) are aimed at pre-compensation of these distortions but state-of-the-art adaptive optics still provides a limited field of view and imaging depth. Here I propose a new approach to overcome these limitations: Fourier image plane conjugate AO. Two possible experimental designs of the new approach are investigated and an accurate comparison …
A recent advance in optical coherence tomography (OCT), termed swept-source OCT, is generalized into a new technique, Fourier-domain OCT. It represents a realization of a full-field OCT system in place of the conventional serial image acquisition in transverse directions typically implemented in "flying-spot" mode. To realize the full-field image acquisition, a Fourier holography system illuminated with a swept-source is employed instead of a Michelson interferometer commonly used in OCT. Fourier-domain OCT offers a new leap in signal-to-noise ratio improvement, as compared to flying-spot OCT …
A cascaded iterative Fourier transform (CIFT) algorithm is presented for optical security applications. Two phase-masks are designed and located in the input and the Fourier domains of a 4-f correlator respectively, in order to implement the optical encryption or authenticity verification. Compared with previous methods, the proposed algorithm employs an improved searching strategy: modifying the phase-distributions of both masks synchronously as well as enlarging the searching space. Computer simulations show that the algorithm results in much faster convergence and better image quality for t…
Fourier optics, the principle of using Fourier Transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and has been widely applied to optical information processing, imaging, holography etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e. the paraxial approximation, which put a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution inform…
We present theoretical formulation and experimental demonstration of a novel technique for the fast compression-less terahertz imaging based on the broadband Fourier optics. The technique exploits k-vector/frequency duality in Fourier optics which allows using a single-pixel detector to perform angular scan along a circular path, while the broadband spectrum is used to scan along the radial dimension in Fourier domain. The proposed compression-less image reconstruction technique (hybrid inverse transform) requires only a small number of measurements that scales linearly with the image linear s…
We present a thorough analysis of the signal line shapes of Fourier transform-based noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS). We discuss the signal dependence on the ratio of the modulation frequency, f${_m}$, to the molecular line width, Γ. We compare a full model of the signals and a simplified absorption-like analytical model that has high accuracy for low f${_m}$/Γ ratios and is much faster to compute. We verify the theory experimentally by measuring and fitting NICE-OFCS spectra of CO${_2}$ at 1575 nm using a system based on an Er:fiber femtosecond lase…
We demonstrate control over attosecond pulse generation and shaping by numerically optimizing the synthesis of few-cycle to sub-cycle driver waveforms. The optical waveform synthesis takes place in an ultrabroad spectral band covering the ultraviolet-infrared domain. These optimized driver waves are used for ultrashort single and double attosecond pulse production (with tunable separation) revealing the potentials of the light wave synthesizer device demonstrated by Wirth et al. [Science 334, 195 (2011)]. The results are also analyzed with respect to attosecond pulse propagation phenomena.
Short-pulse fibre lasers are a complex dynamical system possessing a broad space of operating states that can be accessed through control of cavity parameters. Determination of target regimes is a multi-parameter global optimisation problem. Here, we report the implementation of a genetic algorithm to intelligently locate optimum parameters for stable single-pulse mode-locking in a Figure-8 fibre laser, and fully automate the system turn-on procedure. Stable ultrashort pulses are repeatably achieved by employing a compound fitness function that monitors both temporal and spectral output proper…
Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems - a concept popular in Fourier Optics and in scalar diffraction theory. In this context, a layered flat lens is a one-dimensional spatial filter characterised by the point spread function. However, depending on the model of the source, the definition of the point spread function for multilayers with sub-wavelength resolution may be formulated in several ways. Here, a distinction is made between a soft source and hard electric or magnetic sources. Each of these definitions leads…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging systems can thus be performed and the the performance retrieved. For a better understanding of the optical study, we present a short introduction of the Fourier optics and we review the mathematical treatment depending on the illumination conditions of the imaging system. Furthermore, resolution criteria based on Fourier optics are detailed. Also, the impac…
Square-wave pulse generation with a variable duty ratio can be realized with the help of ideas of Talbot array illuminators formulated for binary phase gratings. A binary temporal phase modulation of CW laser field propagating through a group-delay-dispersion circuit of the fractional Talbot length $P/Q$ results in a well defined sequence of square-wave-form pulses. When $P=1$ a duty ratio of the pulses $D$ is $1/2$ for $Q=4$ and $1/3$ for $Q=3$ and 6. Maximum intensity of the pulses doubles and triples compared to the CW intensity for $D=1/2$ and $1/3$, respectively. These pulses can be used …
Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies regularly arise as the results depend on the choice of a complex wavevector or a complex frequency. In particular, the shape of the dispersion curves depends on this choice. When discussing diffraction of surface plasmon a scalar approximation is often used. In this work, we derive two equivalent vectorial representations of a surface plasmon field using an expansio…
We perform micromagnetic simulations to investigate the propagation of spin-wave beams through spin-wave optical elements. Despite spin-wave propagation in magnetic media being strongly anisotropic, we use axicons to excite spinwave Bessel-Gaussian beams and gradient-index lenses to focus spin waves in analogy to conventional optics with light in isotropic media. Moreover, we demonstrate spin-wave Fourier optics using gradient-index lenses. These results contribute to the growing field of spin-wave optics.
An optimal control approach based on multiple parameter genetic algorithms is applied to the design of plasmonic nanoconstructs with pre-determined optical properties and functionalities. We first develop nanoscale metallic lenses that focus an incident plane wave onto a pre-specified, spatially confined spot. Our results illustrate the role of symmetry breaking and unravel the principles that favor dimeric constructs for optimal light localization. Next we design a periodic array of silver particles to modify the polarization of an incident, linearly-polarized plane wave in a desired fashion …
We demonstrate a simple scheme for high-resolution imaging of nanoplasmonic structures that basically removes most of the resolution limiting allowed light usually transmitted to the far field. This is achieved by implementing a Fourier lens in a near-field scanning optical microscope (NSOM) operating in the leakage-radiation microscopy (LRM) mode. The method consists of reconstructing optical images solely from the plasmonic `forbidden' light collected in the Fourier space. It is demonstrated by using a point-like nanodiamond-based tip that illuminates a thin gold film patterned with a sub-wa…
This paper contains a transcript of my presentation at the Wyant Tribute Symposium on August 2, 2021 at SPIE's Optics & Photonics conference in San Diego, California. The technical part of the paper has no overlap with a previous article of mine that was published in Applied Optics last year, bearing the same title as this one.1 The applications of Fourier transformation described in the present paper include the central limit theorem of probability and statistics, the Shannon-Nyquist sampling theorem, and computing the electromagnetic field radiated by an oscillating magnetic dipole.
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as filtering, convolution, and correlation. Digital FFTs are limited in speed by the necessity of moving charge within logic gates. An analog temporal FFT in fiber optics has been demonstrated with highest data bandwidth. However, the implementation with discrete fiber optic FFT components is bulky. Here, we present and analyze a design of an optical FFT in Silic…
College of Information Science and Technology, Jinan University（暨南大学信息科学技术学院）
The light scattering of multilayer nanoparticles can be solved by Maxwell equations. However, it is difficult to solve the inverse design of multilayer nanoparticles by using the traditional trial-and-error method. Here, we present a method for forward simulation and inverse design of multilayer nanoparticles. We combine the global search ability of genetic algorithm with the local search ability of neural network. First, the genetic algorithm is used to find a suitable solution, and then the neural network is used to fine-tune it. Due to the non-unique relationship between physical structures…
Fourier light-field microscopy (FLFM) uses a micro-lens array (MLA) to segment the Fourier Plane of the microscopic objective lens to generate multiple two-dimensional perspective views, thereby reconstructing the three-dimensional(3D) structure of the sample using 3D deconvolution calculation without scanning. However, the resolution of FLFM is still limited by diffraction, and furthermore, dependent on the aperture division. In order to improve its resolution, a Super-resolution optical fluctuation Fourier light field microscopy (SOFFLFM) was proposed here, in which the Sofi method with abil…
In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing to derive their basic theoretical relationships as convolution or cross correlation products suitable for fast and accurate computation. Several unusual designs, such as a super-resolving telescope utilizing a mosaicking observation procedure or a free-flying, axially recombined interfe…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand all the richness that can be derived from joint analysis in the temporal and spectral domains, particularly in the field of optics. As part of the second year of the Master's degree in Physics Lasers and Materials at the University of Burgundy, we have set up a set of experiments to highlight these concepts and to show, on a non-trivial example of periodic …
Fourier optics is a powerful and efficient tool for solving many diffraction problems, but relies on the assumption of scalar diffraction theory and ignores the three-dimensional structure and material properties of the diffracting element. Recent experiments of sub-scale starshade external occulters revealed that the inclusion of these physical properties is necessary to explain the observed diffraction at 1e-10 of the incident light intensity. Here, we present a methodology for implementing non-scalar diffraction while maintaining the efficiency and ease of standard Fourier optics techniques…
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical situati…
Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires an applied field (>10 G) to separate the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we decompose the NV ensemble magnetic resonance spectrum…
Corneal evaluation in ophthalmology necessitates cellular-resolution and fast imaging techniques allowing accurate diagnoses. Currently, the fastest volumetric imaging technique is Fourier-domain full-field optical coherence tomography (FD-FF-OCT) that uses a fast camera and a rapidly tunable laser source. Here, we demonstrate high-resolution, high-speed, non-contact corneal volumetric imaging in vivo with FD-FF-OCT that can acquire a single 3D volume with a voxel rate of 7.8 GHz. The spatial coherence of the laser source was suppressed to prevent it from focusing to a spot on the retina, and …
Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered. Further advances could exploit Fourier optics, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well-defined amplitude, spatial frequency, and phase. However, because fabrication techniques typically yield profiles with at most a few…
Nonlinear optical microscopy allows rapid high-resolution microscopy with image contrast generated from intrinsic properties of the sample. Established modalities such as multiphoton excited fluorescence and second/third-harmonic generation can be combined with other nonlinear techniques, such as coherent Raman spectroscopy which typically allow chemical imaging of a single resonant vibrational mode of a sample. Here, we utilize a single ultrafast laser source to obtain broadband coherent Raman spectra on a microscope, together with other nonlinear microscopy approaches on the same instrument.…
Optical coherence tomography (OCT) is a volumetric imaging modality that empowers clinicians and scientists to noninvasively visualize the cross-sections of biological samples. As the latest generation of its kind, Fourier-domain OCT (FD-OCT) offers a micrometer-scale axial resolution by taking advantage of coherence gating. Based on the current theory, it is believed the only way to obtain a higher-axial-resolution OCT image is to physically extend the system's spectral bandwidth given a certain central wavelength. Here, we showed the belief is wrong. We proposed a novel reconstruction framew…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\mathcal{O}(D\log^{2}D)$ floating point operations to compute $D…
The design of broad-band polarimeters with high performance is challenging due to the wavelength dependence of optical components. An efficient Genetic Algorithm (GA) computer code was recently developed in order to design and re-optimize complete broadband Stokes polarimeters and Mueller matrix ellipsometers (MME). Our results are improvements of previous patented designs based on two and three ferroelectric liquid crystals (FLC), and are suited for broad-band hyperspectral imaging, or multichannel spectroscopy applications. We have realized and implemented one design using two FLCs and compa…
The integration of miniaturized optical spectrometers into mobile platforms will have an unprecedented impact on applications ranging from unmanned aerial vehicles (UAVs) to mobile phones. To address this demand, silicon photonics stands out as a platform capable of delivering compact and cost-effective devices. The Fourier transform spectrometer (FTS) is largely used in free-space spectroscopy, and its implementation in silicon photonics will contribute to bringing broadband operation and fine resolution to the chip scale. The implementation of an integrated silicon photonics FTS (Si-FTS) mus…
Wave-optical formulation of the image-rotation property in Dove prisms: A Fourier-optics approach
Semnan University（塞姆南大学）；University of Trieste（的里雅斯特大学）；National Institute of Optics (CNR-INO)（国家光学研究所（CNR-INO））；Amirkabir University of Technology（阿米尔卡比尔理工大学）
Diffractive zone plate optics uses a thin micro-structure pattern to alter the propagation direction of the incoming light wave. It has found important applications in extreme-wavelength imaging where conventional refractive lenses do not exist. The resolution limit of zone plate optics is determined by the smallest width of the outermost zone. In order to improve the achievable resolution, significant efforts have been devoted to the fabrication of very small zone width with ultrahigh placement accuracy. Here, we report the use of a diffractometer setup for bypassing the resolution limit of z…
Quantum Optical Coherence Tomography (Q-OCT) is a non-classical equivalent of Optical Coherence Tomography and is able to provide a twofold axial resolution increase and immunity to resolution-degrading dispersion. The main drawback of Q-OCT are artefacts which are additional elements that clutter an A-scan and lead to a complete loss of structural information for multilayered objects. Whereas there are successful methods for artefact removal in Time-domain Q-OCT, no such scheme has been devised for Fourier-domain Q-OCT (Fd-Q-OCT), although the latter modality - through joint spectrum detectio…
The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic based QCs (LOQCs) as an unconventional design, targets to obtain scalability and practical problem solving. It samples the intensity from the interference of exponentially increasing number of propagation paths obtained in multi-plane diffraction (MPD) of classical particle sources. QPC exploits MPD based quantum temporal correlations of the paths and freel…
The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra $so(4)$. Two distinct subalgebra chains are used to model arrays of $N^2$ points placed a…
