Optical Wave Field Research Articles

Quantitative measurement of domain inversion in RuO2:LiNbO3 crystal by digital holographic interferometry

We quantitatively study the domain inversion in a RuO2:LiNbO3 crystal wafer by the digital holographic interferometry. The crystal wafer is placed into one arm of a Mach-Zehnder-type interferometer to record a series of holograms. Making use of the angular spectrum backward propagation algorithm, we reconstruct the optical wave field in the crystal plane. The extracted phase difference from the reconstructed optical wave field is a well linear function of the applied external voltage. We deduce that the linear electro-optic coefficient of the detected RuO2:LiNbO3 crystal sample is 9.1×10−12m∕V. An unexpected phase contrast at the antiparallel domain wall is observed and the influence of the applied external voltage on it is studied in detail. Also the built-in internal field is quantitatively measured as 0.72kV∕mm.

Three-dimensional surface contouring of macroscopic objects by means of phase-difference images

We report a technique to determine the 3D contour of objects with dimensions of at least 4 orders of magnitude larger than the illumination optical wavelength. Our proposal is based on the numerical reconstruction of the optical wave field of digitally recorded holograms. The required modulo 2pi phase map in any contouring process is obtained by means of the direct subtraction of two phase-contrast images under different illumination angles to create a phase-difference image of a still object. Obtaining the phase-difference images is only possible by using the capability of numerical reconstruction of the complex optical field provided by digital holography. This unique characteristic leads us to a robust, reliable, and fast procedure that requires only two images. A theoretical analysis of the contouring system is shown, with verification by means of numerical and experimental results.

Boundaryless finite-difference method for three-dimensional beam propagation

A two-dimensional optical field paraxial propagation scheme, in Cartesian and cylindrical coordinate systems, is proposed. This is achieved by extending the method originally proposed by Ladouceur [Opt. Lett. 21, 4 (1996)] for boundaryless beam propagation to two-dimensional optical wave fields. With this formulation the arbitrary choice of physical window size is avoided by mapping the infinite transverse dimensions into a finite-size domain with an appropriate change of variables, thus avoiding the energy loss through the artificial physical boundary that is usually required for the absorbing or the transparent boundary approach.

Remote metrology by comparative digital holography

A method for the remote comparison of objects with regard to their shape or response to a load is presented. The method allows interferometric sensitivity for comparing objects with different microstructure. In contrast to the well-known incoherent techniques based on inverse fringe projection this new approach uses the coherent optical wave field of the master object as a mask for the illumination of the sample object. The coherent mask is created by digital holography to allow instant access to the complete optical information of the master object at any place desired. The mask is reconstructed by a spatial light modulator (SLM). The optical reconstruction of digital holograms with SLM technology allows modification of reconstructed wavefronts with respect to improvement of image quality, the skilled introduction of additional information about the object (augmented reality), and the alignment of the master and test object.

Off-axis holographic tomography for diffracting scalar wavefields

Inverse scattering theories are available that permit tomographic reconstruction of the complex-valued refractive index distribution of weakly scattering objects from knowledge of intensity measurements. These imaging methods are valuable in applications that involve high-frequency optical wavefields, in which direct wavefield phase measurements can be difficult experimentally. The so-called in-line holographic imaging geometry has been well-studied, in which two measurements of the forward scattered wavefield intensity are acquired on distinct parallel detector planes that are perpendicular to the direction of the illuminating wavefields. In this work, based on the principles of intensity diffraction tomography, a reconstruction theory for off-axis holographic tomography with diffracting scalar wavefields is developed and investigated. A distinct feature of the method is that, at each tomographic view angle, the object is illuminated by use of two plane waves that propagate in different directions. The intensities of the forward scattered wavefields are measured on a single detector behind the object. This permits the direction of the probing wavefield to be varied for acquisition of the necessary measurement data, rather than the detector placement as required by conventional in-line holographic methods. The developed image reconstruction method is validated and investigated by use of computer-simulation studies.

Fast numerical algorithm for the linear canonical transform

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders

Illumination of nano- and micro-particles with a highly focused laser beam will exert a force on them that depends on different parameters, such as the particle size, refractive index and beam waist. In this paper rigorous diffraction theories are used to calculate the force on elliptically shaped dielectric cylinders in three different size regimes. We analyse the conditions for which the particles are attracted or repelled from the optical axis as a function of the geometry. Such a shape dependent response to optical wave-fields could be used to sort particles.

Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves

In this paper it is shown how one can use Bessel beams to obtain a stationary localized wave field with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 </= z </= L of the propagation axis. This intensity envelope remains static, i.e., with velocity v =0; and because of this we call "Frozen Waves" the new solutions to the wave equations (and, in particular, to the Maxwell equations). These solutions can be used in many different and interesting applications, such as optical tweezers, atom guides, optical or acoustic bistouries, various important medical purposes, etc.

Parabolic nondiffracting optical wave fields.

We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields.

The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized method is given. The advantages and the disadvantages of the method with respect to other typical methods are discussed.

Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm

The phase retrieval algorithm has been used in this paper for whole reconstruction of the optical wave fields. The quantitative information of the phase distribution as well as the intensity distribution of the reconstruction field at different locations along the propagation direction has been achieved from double or multi in-line holograms. Numerical reconstructions of the wave fields from experimentally recorded in-line holograms are presented. This technique can be potentially applied for aberrated wave front analyzing and 3D imaging.

Spot-size conversion of guided optical wave with gaussian approximation

We propose an approach to optical wave field spot-size conversion that uses a waveguide structure. An optical wave field is decomposed with a Hermite-Gaussian basis, and we describe its motion with partial differential equations for the field radius and center parameters derived from the propagation of the lower order components. We use the equations to design a spot-size conversion waveguide structure for expanding and reducing a field spot as an example in a quasi-single-mode optical waveguide.

Influence of higher-order dispersion on modulational instability and pulse broadening of partially incoherent light.

The Wigner-Moyal equation for the Wigner distribution of a partially incoherent optical wave field propagating in dispersive and nonlinear media has been generalized to include the effects of both arbitrary order of dispersion and arbitrary nonlinearity. The theory predicts partial incoherence to enhance the pulse broadening during linear wave pulse propagation. Furthermore, an application of the theory to the modulational instability of constant amplitude waves shows how higher-order dispersion affects the instability growth rate.

Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light

We investigate the inverse scattering problem for statistically homogeneous, isotropic random media under conditions of strong fluctuations of optical wavefields. We present a method for determining the spectral density of the dielectric constant fluctuations in such media from scattering of partially coherent light. The method may find applications to a wide class of turbulent media such as the turbulent atmosphere and certain turbulent plasmas where backscattering and depolarization effects are negligible.

Self-imaging of three-dimensional images by pulsed wave fields

Recently, the classical Talbot effect (self-imaging of optical wave fields) has attracted a renewed interest, as the concept has been generalized to the domain of pulsed wave fields by several authors. In this paper we discuss the self-imaging of three-dimensional images. We construct pulsed wave fields that can be used as self-imaging "pixels" of a three-dimensional image and show that their superpositions reproduce the spatial separated copies of its initial three-dimensional intensity distribution at specific time intervals. The derived wave fields will be shown to be directly related to the fundamental localized wave solutions of the homogeneous scalar wave equation - focus wave modes. Our discussion is illustrated by some spectacular numerical simulations. We also propose a general idea for the optical generation of the derived wave fields. The results will be compared to the work, published so far on the subject.

Nonlinear Dynamics of Partially Incoherent Optical Waves Based on the Wigner Transform Method

A novel statistical approach based on the Wigner transform method is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. The Wigner–Moyal equation is derived for the Wigner distribution of the optical wave field governed by the nonlinear Schrödinger equation with an arbitrary nonlinearity. An application to incoherent light propagation in dispersive Kerr media shows that random phase fluctuations of a plane wave solution lead to a linear Landau-like damping effect, which can stabilize the nonlinear modulational instability. A similar effect is shown to occur in the case of the two-stream instability of two partially incoherent optical waves interacting with each other through cross-phase modulation initiated by the nonlinearity. In the limit of the geometrical optics approximation, it is shown that 1D and 2D self-trapped, stationary and incoherent wave pulse structures may exist for a wide class of nonlinear media. Furthermore, time-dependent self-similar 1D and 2D structures have been found in the case of the Kerr nonlinearity.

Whole optical wavefields reconstruction by Digital Holography

In this paper, we have investigated on the potentialities of digital holography for whole reconstruction of wavefields. We show that this technique can be efficiently used for obtaining quantitative information from the intensity and the phase distributions of the reconstructed field at different locations along the propagation direction. The basic concept and procedure of wavefield reconstruction for digital in-line holography is discussed. Numerical reconstructions of the wavefield from digitally recorded in-line hologram patterns and from simulated test patterns are presented. The potential of the method for analysing aberrated wave front has been exploited by applying the reconstruction procedure to astigmatic hologram patterns.

Using rays better. III. Error estimates and illustrative applications in smooth media.

A new method for computing ray-based approximations to optical wave fields is demonstrated through simple examples involving wave propagation in free space and in a gradient-index waveguide. The analytic solutions that exist for these cases make it easy to compare the new estimates with exact results. A particularly simple RMS error estimate is developed here, and corrections to the basic field estimate are also discussed and tested. A key step for any ray-based method is the choice of a family of rays to be associated with the initial wave field. We show that, for maximal accuracy, not only must the initial field be considered in choosing the rays, but so too must the medium that is to carry the wave.

Real-time holograms generated by second-harmonic cross correlation of object and reference optical wave fields

Three-dimensional holographic images of extended diffusing objects are simultaneously recorded and reconstructed by optical cross correlation in a second-order nonlinear crystal. An interaction geometry in which the phase-matched object and reference fields propagate slightly noncollinearly is particularly convenient for producing these second-harmonic-generated holograms.

Holographic properties of the second-harmonic cross correlation of object and reference optical wave fields

We show that second-harmonic cross correlation of the optical field that propagates from an illuminated object with the illuminating field is a process that shares many features with holography. The wave fronts of the double-frequency field are able to reconstruct holographic images of the object whose dimensions and position can be calculated by use of the holographic formalism. Our theory fits the experimental results obtained by use of a Q-switched Nd:YAG laser as the illuminating source and a thin β-barium borate crystal in a noncollinear type I phase-matching geometry for cross correlation.