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 situations (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual "waist" where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature.
We experimentally realize a Fabry-Perot-type optical microresonator near the cesium D2 line wavelength based on a tapered optical fiber, equipped with two fiber Bragg gratings which enclose a sub-wavelength diameter waist. Owing to the very low taper losses, the finesse of the resonator reaches F = 86 while the on-resonance transmission is T = 11 %. The characteristics of our resonator fulfill the requirements of non-linear optics and cavity quantum electrodynamics in the strong coupling regime. In combination with its demonstrated ease of use and its advantageous mode geometry, it thus opens …
We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media, and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $ρ$ and the wavenumber of resonant light $k$ satisfy $ρk^{-3}\gtrsim 1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes correlated. The deviations from mean-field theory app…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the angular momentum of an EM field will be shown to have an intimate relationship; a source radiating EM angular momentum will, of necessity, pick up an equal but opposite amount of mechanical angular momentum; and the spin and orbital angular momenta of the EM field, when absorbed by a small particle, will be seen to elicit different responses from the particle…
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.
The Planck constant ($\hbar$) plays a pivotal role in quantum physics. Historically, it has been proposed as postulate, part of a genius empirical relationship $E=\hbar ω$ in order to explain the intensity spectrum of the blackbody radiation for which classical electrodynamic theory led to an unacceptable prediction: The ultraviolet catastrophe. While the usefulness of the Planck constant in various fields of physics is undisputed, its derivation (or lack of) remains unsatisfactory from a fundamental point of view. In this paper, the analysis of the blackbody problem is performed with a series…
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.
Spontaneously generated coherence and enhanced dispersion in a V-type, three-level atomic system interacting with a single mode field can considerably reduce the radiative and cavity decay rates. This may eliminate the use of high finesse, miniaturized cavities in optical cavity quantum electrodynamics experiments under strong atom-field coupling conditions.
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.
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…
We show the planned upgrade of a cavity QED experimental apparatus. The system consists of an optical cavity and an ensemble of ultracold $^{85}$Rb atoms coupled to its mode. We propose enhancements to both. First, we document the building process for a new cavity, with a planned finesse of $\sim$20000. We address problems of maintaining mirror integrity during mounting and improving vibration isolation. Second, we propose improvements to the cold atom source in order to achieve better optical pumping and control over the flux of atoms. We consider a 2-D optical molasses for atomic beam deflec…
We experimentally realize an optical fiber ring resonator that includes a tapered section with subwavelength-diameter waist. In this section, the guided light exhibits a significant evanescent field which allows for efficient interfacing with optical emitters. A commercial tunable fiber beam splitter provides simple and robust coupling to the resonator. Key parameters of the resonator such as its out-coupling rate, free spectral range, and birefringence can be adjusted. Thanks to the low taper- and coupling-losses, the resonator exhibits an unloaded finesse of F=75+/-1, sufficient for reaching…
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…
Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access in the quantum optical nature of the interaction as they treat the driving-field classically and unaffected by the interaction. Here, using a full quantum-optical approach, we demonstrate that the sub-cycle electronic response in a strongly driven se…
In vacuum high-intensity lasers can cause photon-photon interaction via the process of virtual vacuum polarization which may be measured by the phase velocity shift of photons across intense fields. In the optical frequency domain, the photon-photon interaction is polarization-mediated described by the Euler-Heisenberg effective action. This theory predicts the vacuum birefringence or polarization dependence of the phase velocity shift arising from nonlinear properties in quantum electrodynamics (QED). We suggest a method to measure the vacuum birefringence under intense optical laser fields b…
The equations of electromagnetic fields in a medium is usually written in the rest frame of the medium. We outline a method of generalizing the discussion to arbitrary inertial frames. In the discussion, we also include the possibility that the medium is optically active, a possibility that is often overlooked in discussions of electromagnetic fields in a medium.
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.
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 …
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…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac f…
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.
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
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…
A canonical quantization scheme for localized surface plasmons (LSPs) in a metal nanosphere is presented based on a microscopic model composed of electromagnetic fields, oscillators that describe plasmons, and a reservoir that describes excitations other than plasmons. The eigenmodes of this fully quantum electrodynamic theory show a spectrum that includes radiative depolarization and broadening, including redshifting from the quasi-static LSP modes, with increasing particle size. These spectral profiles correctly match those obtained with exact classical electrodynamics (Mie theory). The pres…
