We present a new formalism for light beam optics starting with an exact eight-dimensional matrix representation of the Maxwell equations. The Foldy-Wouthuysen iterative diagonalization technique is employed to obtain a Hamiltonian description for a system with varying refractive index. Besides, reproducing all the traditional quasiparaxial terms, this method leads to additional contributions, which are dependent on the wavelength, in the optical Hamiltonian. This alternate prescription to obtain the aberration expansion is applied to the axially symmetric graded index fiber. This results in the wavelength-dependent modifications of the paraxial behaviour and the aberration coefficients. Furthermore it predicts a wavelength-dependent image rotation. In the low wavelength limit our formalism reproduces the Lie algebraic formalism of optics. The Foldy-Wouthuysen technique employed by us is ideally suited for the Lie algebraic approach to optics. The present study further strengthens the close analogy between the various prescription of light and charged-particle optics. All the associated machinery used in this formalism is described in the text and the accompanying appendices.
We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including \emph{reconfigurable} lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and {\emph{widely separated}} multi-wavelength lenses ($λ= 1\,μ$m and $10\,μ$m). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths…
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's equation. Maxwell's action can be obtained from quantum electrodynamics using the framework of effective field theory, and so the leading order short distance corrections to Maxwell's action can also be obtained from the derivative expansion of the same effective field theory. Such short distance corrections will be universal for all quantum optical systems, a…
We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model, where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of …
We present the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli-Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit for the effective nuclei the for…
Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell's fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of …
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrical approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics constructio…
Light carries energy, and therefore, it is the source of a gravitational field. The gravitational field of a beam of light in the short wavelength approximation has been studied by several authors. In this article, we consider light of finite wavelengths by describing a laser beam as a solution of Maxwell's equations and taking diffraction into account. Then, novel features of the gravitational field of a laser beam become apparent, such as frame-dragging due to its spin angular momentum and the deflection of parallel co-propagating test beams that overlap with the source beam. Even though the…
Slow waves and tunneling waves can meet at the cutoff wavelengths and/or transmission band edges of optical and quantum mechanical waveguides. The experimental investigation of this phenomenon, previously performed using various optical microstructures, is challenged by fabrication imperfections and material losses. Here, we demonstrate this phenomenon in situ for whispering gallery modes slowly propagating along a standard optical fiber, which possesses the record uniformity and exceptionally small transmission losses. Slow axial propagation dramatically increases the longitudinal wavelength …
We demonstrate a collinear acousto-optic modulator in a suspended film of lithium niobate employing a high-confinement, wavelength-scale waveguide. By strongly confining the optical and mechanical waves, this modulator improves by orders of magnitude a figure-of-merit that accounts for both acousto-optic and electro-mechanical efficiency. Our device demonstration marks a significant technological advance in acousto-optics that promises a novel class of compact and low-power frequency shifters, tunable filters, non-magnetic isolators, and beam deflectors.
Lasers designed to emit at multiple and controllable modes, or multi-wavelength lasers, have the potential to become key building blocks for future microwave photonic technologies. While many interesting schemes relying on optical injection have been proposed, the nonlinear mode coupling between different modes of a multi-wavelength laser and their dynamical behavior under optical injection remains vastly unexplored. Here, we experimentally and numerically study the effect of optical injection around the suppressed mode of a dual12 wavelength laser and the resulting interactions with the domin…
We present the first system penalty measurements for all-optical wavelength conversion in an integrated ring resonator. We achieve wavelength conversion over a range of 27.7nm in the C-band at 2.5 Gb/s by exploiting four wave mixing in a CMOS compatible, high index glass ring resonator at ~22 dBm average pump power, obtaining < 0.3 dB system penalty.
We demonstrate sub-picosecond wavelength conversion in the C-band via four wave mixing in a 45cm long high index doped silica spiral waveguide. We achieve an on/off conversion efficiency (signal to idler) of +16.5dB as well as a parametric gain of +15dB for a peak pump power of 38W over a wavelength range of 100nm. Furthermore, we demonstrated a minimum gain of +5dB over a wavelength range as large as 200nm.
We design sub-wavelength high-performing non-reciprocal optical devices using recently discovered magnetic Weyl semimetals. These passive bulk topological materials exhibit anomalous Hall effect which results in magnetooptical effects that are orders of magnitude higher than those in conventional materials, without the need of any external magnetic bias. We design two optical isolators of both Faraday and Voigt geometries. These isolators have dimensions that are reduced by three orders of magnitude compared to conventional magneto-optical configurations. Our results indicate that the magnetic…
