Necessary Condition for Temporal Self Imaging in a Linear Dispersive Medium

Abstract

It was recently shown that a periodic pulse train will reproduce itself at periodic distances upon propagation in a linear dispersive medium. By drawing an analogy between this temporal self-imaging problem and the well known spatial self-imaging phenomenon, we derive the necessary condition for temporal self-imaging and show that the class of temporally self-reproducing signals is much broader than the subset of periodic signals.     

Kronig-Penney model for periodically segmented waveguides

Physical insight into the propagation characteristics of periodically segmented waveguides can be obtained by viewing the guiding layer as a thin slab of an idealized infinite medium with periodic layers along the direction of propagation. One can analyze the properties of this infinite medium using a formal analogy with the Kronig-Penney model used to describe the propagation of electron wave functions in a periodic crystal potential. The model correctly gives the effective refractive index of the layer, gives insight into the electric field profiles at different points on the dispersion curve, and leads to a qualitative explanation of why the optical loss diminishes at both large and small duty cycles.     

Optical trapping with modified exponential decay in optical waveguides via dressed continuum

Simultaneous interaction of two side-coupled waveguides with the dressed continuum represented by a linear waveguide array causes cross-coupling between the two evanescent decay-channels and results in the phenomenon of trapping of the light field in the spatial domain during propagation through the waveguide system. For specific parameter values, it has been shown that the trapping effect is possible for all relative positions of the waveguides side-coupled to the dressed continuum. The model also demonstrates non-exponential decay characteristics of the optical field amplitudes in the waveguides. Depending on the values of the propagation mismatch, the nonlinearity arising in the decay-rate characteristics exhibits features like optical Zeno and anti-Zeno effects.     

Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field.     

Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach

A surface integral formulation for light scattering on periodic structures is presented. Electric and magnetic field equations are derived on the scatterers' surfaces in the unit cell with periodic boundary conditions. The solution is calculated with the method of moments and relies on the evaluation of the periodic Green's function performed with Ewald's method. The accuracy of this approach is assessed in detail. With this versatile boundary element formulation, a very large variety of geometries can be simulated, including doubly periodic structures on substrates and in multilayered media. The surface discretization shows a high flexibility, allowing the investigation of irregular shapes including fabrication accuracy. Deep insights into the extreme near-field of the scatterers as well as in the corresponding far-field are revealed. This method will find numerous applications for the design of realistic photonic nanostructures, in which light propagation is tailored to produce novel optical effects.     

Surface plasmon polariton analogue to Young's double-slit experiment

When a light wave strikes a metal film it can, under appropriate conditions, excite a surface plasmon polariton (SPP)--a surface electromagnetic wave that is coupled to the free electrons in the metal. Such SPPs are involved in a wide range of phenomena, including nanoscale optical waveguiding, perfect lensing, extraordinary optical transmission, subwavelength lithography and ultrahigh-sensitivity biosensing. However, before the full potential of technology based on SPPs (termed 'plasmonics') can be realized, many fundamental questions regarding the interaction between light and matter at the nanoscale need to be answered. For over 200 years, Young's double-slit experiment has been a valuable pedagogical tool for demonstrating the wave nature of light. Here, we perform a double-slit experiment with SPPs to reveal the strong analogy between SPP propagation along the surface of metallic structures and light propagation in conventional dielectric components (such as glass waveguides). This allows us to construct a general framework to describe the propagation, diffraction and interference of SPPs. It also suggests that there is an effective diffraction limit for the lateral confinement of SPPs on metal stripe waveguides, and justifies the use of well-developed concepts from conventional optics and photonics in the design of new plasmonic devices.     

Polarization changing and beam profile deformation of light during the isotropic Raman-nath acousto-optic interaction

A spatial Fourier transform approach is used to study the phenomena of polarization changing and beam profile deformation of light during the Raman-Nath, acousto-optic interaction in isotropic media. Starting from the vector version of the well-known Raman-Nath interaction equation and using a spatial Fourier transform allows analytic solutions that encompass the effects of polarization changing and beam-profile deformation for the multiple scattered light to be found in the spatial-frequency domain. Two kinds of sound wave, longitudinal and shear, are assumed to be interacted with the light, whose transverse spatial profile and state of polarization are arbitrary. It is shown that, for light with an arbitrary spatial profile after interaction with the sound wave in the Raman-Nath regime, the spatial profiles of the scattered light are almost the same shape as those of the input light. For the polarization changing part, it is found that the state of polarization and the direction of rotation can alter, depending not only on the sound amplitude but also on the propagation mode of the sound wave. Simulation results are provided to confirm the validity of this approach.     

Numerical simulation of a dual frequency all-optical flip-flop based on a nonlinear semiconductor distributed feedback laser structure

A new all-optical flip-flop generating light at two different wavelengths λ1 (state "a"), or λ2 (state "b") was suggested. It consists of an active layer and a nonlinear wave-guiding layer. Two parallel nonlinear gratings having different periods and periodic negative nonlinearities exist along the propagation direction in the wave-guiding layer. In state "a," the first grating provides the optical feedback for lasing, and the second grating is weak. In state "b," due to optical nonlinearity, the first grating weakens, and the second one provides the optical feedback for lasing. The refractive index nonlinearity is due to the direct absorption of photons at the Urbach tail. The device is triggered from state "a" to state "b" and vise versa by input optical pulses of wavelengths λ2 and λ1, respectively. The time domain simulations show switching dynamics in nanosecond time scale.     

Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications

Giving a new physical interpretation to the principle of longitudinal coherence control, we propose an improved method for synthesizing a spatial coherence function along the longitudinal axis of light propagation. By controlling the irradiance of an extended quasi-monochromatic spatially incoherent source with a spatial light modulator, we generated a special optical field that exhibits high coherence selectively for a specific pair of points at specified locations along the axis of beam propagation. This function of longitudinal coherence control provides new possibilities for dispersion-free measurements in optical tomography and profilometry. A quantitative experimental proof of principle is presented.     

Propagation of a random electromagnetic beam through a misaligned optical system in turbulent atmosphere

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system in turbulent atmosphere is derived. Some analyses are illustrated by numerical examples relating to changes in the state of polarization of an electromagnetic Gaussian Schell-model beam propagating through such an optical system. It is shown that the misalignment has a significant influence on the intensity profile and the state of polarization of the beam, but the influence becomes smaller for the beam propagating in strong turbulent atmosphere. The method in this paper can be applied for sources that are either isotropic or anisotropic. It is shown that the isotropic sources and the anisotropic sources have different polarization properties on beam propagation.     

Diffraction engineering Anderson localization of light in nonlinear waveguide array with Kerr and two photon absorption effects

Role of two-photon absorption (TPA) effect on light propagation in one-dimensional nonlinear waveguide array (NWA) is studied numerically with solving nonlinear Schrodinger equation. Our investigation includes unperturbed, diagonally and off-diagonally disordered NWA with inclusion of Kerr and TPA and the results are compared with each other. The simulations show that the increase of incident wave amplitude to NWA intensifies TPA and Kerr effects and these nonlinear optical effects, dramatically affect the output intensity profile and loss. Variations of intensity distribution in periodic NWA is about two and three times higher than in off-diagonal and diagonal disordered NWA, respectively. It means that localization of light in periodic NWA is more tunable than disordered lattices. These variations of intensity distribution under nonlinear optical effects enable us to propose and design a reconfigurable localization and diffraction-engineered discrete soliton.     

Spatial shift of spatially modulated light projected on turbid media

This work extends modulated imaging, a recently developed technique based on the projection of structured light on a turbid medium that is able to measure optical properties of the high-scattering medium and perform tomography. We observe that structured light obliquely projected on a turbid medium undergoes a spatial shift during propagation. We propose a method to measure the spatial phase shift of a sinusoidal fringe pattern projected in a turbid medium, and we present a model derived from the diffusion approximation to describe the light propagation. Experimental validation by measurements performed on liquid phantoms is presented.     

Finite element model for the coupled radiative transfer equation and diffusion approximation

In this paper a coupled radiative transfer equation and diffusion approximation model for light propagation in tissues is proposed. The light propagation is modelled with the radiative transfer equation in sub‐domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The method is tested with simulations. The results of the proposed approach are compared with finite element solutions of the radiative transfer equation, the diffusion approximation and a previously proposed hybrid model. The results show that the method improves the accuracy of the forward solution for diffuse optical tomography compared to the conventional diffusion model. Copyright © 2005 John Wiley & Sons, Ltd.     

Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation.     

Electro-optical logic application of multimode interference coupler by multivalued controlling

Electro-optical hybrid logic is a potential solution to implement both electrical and optical signal processing, which receives analog or digital, electrical or optical signals and produces logic signals in a desired manner. In light of the transfer matrix theory, we found that one can steer light into different output ports of a multimode interference coupler by controlling the phases in a multivalued manner on the image-extended arms. This implementation acts as an analog-to-digital convertor from electric domain to optical domain. Also, an electrical-to-optical 2-to-2(2) binary-coded decoder is described and examined by the 3D beam propagation method.     

Efficient numerical representation of the optical field for the propagation of partially coherent radiation with a specified spatial and temporal coherence function

We propose a method to narrow the gap between the rigorous methods for the propagation of partially coherent light, which require excessive computational capacity, and the numerical methods used in practical engineering applications, where it is not clear how to handle spatial and temporal coherence in a statistically correct manner. As is the case for the latter methods, the numerical method described can deal with fields with a large spatial and temporal extent, which is necessary in practical applications such as laser fusion or optical lithography. However, the method also takes a few steps toward a more rigorous, yet efficient, representation of the optical field, which depends on detailed specified coherence properties of the radiation. The described method uses a set of independent monochromatic fields at different oscillation frequencies. The frequencies are chosen such that the statistical properties of the integrated intensity closely resemble those from a full-time trace treatment. Finally, we demonstrate the capabilities and limitations of the method with a few numerical examples of the propagation of a large field with a specified spatial and temporal coherence.     

Light transmission through a triangular air gap

Abstract

Due to the recent interest in studying propagation of light through triangular air gaps, we calculate, by using the analogy between optics and quantum mechanics and the multiple step technique, the transmissivity through a triangular air gap surrounded by an homogeneous dielectric medium. The new formula is then compared with the formula used in the literature. Starting from the qualitative and quantitative differences between these formulas, we propose optical experiments to test our theoretical results.     

Diffraction of femtosecond pulses; nonparaxial regime

We present a systematic study of linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media, and vacuum. The applied method of amplitude envelopes makes it possible to estimate the limits of the slowly varying amplitude approximation and to describe an amplitude integrodifferential equation governing propagation of optical pulses in the single-cycle regime in solids. The well-known slowly varying amplitude equation and the amplitude equation for the vacuum case are written in dimensionless form. Three parameters are obtained defining different linear regimes of optical pulse evolution. In contrast to previous studies we demonstrate that in the femtosecond region the nonparaxial terms are not small and can dominate over the transverse Laplacian. The normalized amplitude nonparaxial equations are solved using the method of Fourier transforms. Fundamental solutions with spectral kernels different from those according to Fresnel are found. Exact unidirectional analytical solution of the nonparaxial amplitude equations and the 3D wave equations with initial conditions compatible with Gaussian light bullets are obtained also. One unexpected new result is the relative stability of light bullets (pulses with spherical and spheroidal spatial form) when we compare their transverse enlargement with paraxial diffraction of light beams in air. It is important to emphasize here the case of light disks, i.e., pulses whose longitudinal size is small with respect to the transverse one, which in some partial cases are practically diffractionless over distances of a thousand kilometers. A new formula that calculates the diffraction length of optical pulses is suggested. Finally, propagation of single-cycle pulses in air and vacuum was investigated, and a coronal (semispherical) form of diffraction at short distances was observed.     

Simple Mathematical Models for Temporal,Spatial, Angular,and Attenuation Characteristics of Light Propagating Through the Atmosphere for Space Optical Communication:

Abstract

Mathematical models are developed to characterize propagation through a turbid medium at three different wavelengths in the visible and near infrared spectral range. These models are based upon relations between the temporal, angular, and spatial spread of electromagnetic unpolarized radiation, geometrical path length, particle size distribution, and the medium's propagation parameters such as Mie scattering, and absorption coefficients, Mie phase-function, and optical thickness. Calculations of the radiation characteristics were carried out using Monte Carlo simulations. Here, atmospheric particulates are used to model turbid media for optical thickness between 1 and 6, emphasizing optical communication applications, The advantage of this work is the ability to predict simply and in real time important radiation parameters relevant to any optical communication system. Results indicate very high correlation between optical thickness and propagation characteristics. For transmission, comparison is made to Bucher's model. Results are similar except for absorption effects which are not included in Bucher's model. Some important conclusions are derived such as the prediction that it is advantageous to use longer wavelength radiation through the atmosphere. In addition, there is a very dominant back scattering effect, involving up to 50% of transmitted power for optical densities as low as 6. On the other hand, power density of received scattered light is very low for conventional distances relevant to satellite optical communication, and can be neglected. On the basis of simulation results, the received radiation is of unscattered light only for any optical communication application. The dominant mechanism relating to radiation attenuation is scattering rather than absorption.     

Metasurfaces Atop Metamaterials: Surface Morphology Induces Linear Dichroism in Gyroid Optical Metamaterials

Optical metamaterials offer the tantalizing possibility of creating extraordinary optical properties through the careful design and arrangement of subwavelength structural units. Gyroid‐structured optical metamaterials possess a chiral, cubic, and triply periodic bulk morphology that exhibits a redshifted effective plasma frequency. They also exhibit a strong linear dichroism, the origin of which is not yet understood. Here, the interaction of light with gold gyroid optical metamaterials is studied and a strong correlation between the surface morphology and its linear dichroism is found. The termination of the gyroid surface breaks the cubic symmetry of the bulk lattice and gives rise to the observed wavelength‐ and polarization‐dependent reflection. The results show that light couples into both localized and propagating plasmon modes associated with anisotropic surface protrusions and the gaps between such protrusions. The localized surface modes give rise to the anisotropic optical response, creating the linear dichroism. Simulated reflection spectra are highly sensitive to minute details of these surface terminations, down to the nanometer level, and can be understood with analogy to the optical properties of a 2D anisotropic metasurface atop a 3D isotropic metamaterial. This pronounced sensitivity to the subwavelength surface morphology has significant consequences for both the design and application of optical metamaterials.