Nonlinear propagation of optical pulses in fiber Bragg gratings is studied experimentally and with numerical simulations of the coupled mode equations. After a review of enhanced nonlinear interactions for pulse wavelengths near the short wavelength edge of the photonic bandgap associated with the grating, this study explores polarization evolution during nonlinear pulse propagation. Initial results for polarization instabilities and expectations for vector Bragg solitons are described.

We present an overview of several novel types of multi- component envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons in Fibonacci optical superlattices.

Solitons in dispersion-managed (DM) fibers are promising candidates for a modulation format to be used in long distance high-speed optical fiber data transmission. In this paper we perform a bit-error-rate analysis of a wavelength- division multiplexed (WDM) DM soliton system operated at 40 Gbit/s per channel. We consider the intra-channel pulse-to- pulse interaction, the noise-induced timing jitter, the collision-induced time shifts, and the signal-ASE (amplified spontaneous emission) and ASE-ASE beat noise as the factors limiting the system performance. Effects of filters in reducing the collision-induced timing jitter in WDM transmission are also examined. It is shown that the minimum channel spacing required for long-distance transmission can be reduced by the use of in-line filters especially when the noise amplification due to the filter excess gain is suppressed.

Dispersion management with fiber Bragg gratings is studied in a system with zero net dispersion at distances of megameters. The formation of multisoliton states of two and more solitons is observed at long enough distances. These multisoliton solutions present fixed values for the peak powers, phase difference and distance between adjacent pulses, and can propagate for long distances without deformation, being the noise amplification the ultimate limitation to propagation. The formation of these bound states is related to the combined action of nonlinear effects on the fiber link and higher order dispersion terms both on the fiber and the transfer function of the gratings. Higher order effects on the gratings, which are usually neglected, can acquire great relevance in schemes in which a very high number of gratings is used. The distance between peaks in the multisoliton state is lower than the typical interaction distance between adjacent solitons, so they could be used to increase the capacity of the channel.

We examine the influence of the third-order filter contribution on soliton propagation in a system with sliding-frequency guiding filters. The soliton loss in a system with up-sliding than it is in a system with down- sliding. We derive also an analytical expression for the variance of the timing jitter of a soliton transmission system using sliding-frequency guiding filters, taking into account the third-order filter term. The variance of timing jitter is significantly increased by the sliding action. As a consequence of the third-order filter contribution, the timing jitter is lower in a system with down-sliding than it is in a system with up-sliding at the same sliding rate.

Microwave Fiber Optic (MFO) links have attracted much attention recently with their application in wireless access. When a wireless link is in series with the optical link, nonlinear distortion (NLD) of the MFO link becomes the biggest concern. The linearity requirement is high due to the large variations in the RF power through the link. Laser intrinsic nonlinearity is usually the major concern in a directly modulated link. However, in wireless applications significant amplification is required at the antenna site, which introduces additional NLD. In this paper a higher order adaptive fiber is proposed to model the entire MFO link considering all cascaded nonlinearities. The FIR filter runs at the baseband symbol rate and trains itself from the input/output amplitude and phase relationships of the microwave modulated symbols. Thus no accurate knowledge of the link physical parameters is required. The powerful recursive least square algorithm converges quickly, tracking any modification or drift in the link parameters. Simulation results show that, third order Volterra adaptive filters are adequate to model measured AM-AM and AM-PM characteristics of a MFL link under steady state conditions. The link consists of a directly modulated InGaAsP DFB laser and PIN diode receiver with a high gain amplifier.

We analyzed the self-transparency effect of a laser beam traveling in a sample of an unsaturated polyester. Polymer Dispersed Liquid Crystal. This effect is of thermal nature and occurs when a change of the refractive index of the considered composite material is induced by variations of the local temperature due to the incident light power. We studied the mechanism governing this phenomenon and report a detailed 3D map showing how the transmitted beam profile changes as a function of both incident power and time. It is discussed how light intensity and temperature can be used as control parameters for the nonlinear part of the refractive index. Our experimental results indicates the possibility of employing this material to design thermal sensors as devices working as optical switch.

Nonlinear optical organic materials will be the key elements for future telecommunication and photonic technologies. In this report the new ultrafast nonlinear switching and logic based on nonlinear tunneling of optical solitons through organic thin films are proposed and investigated. Numerical simulations of nonlinear soliton tunneling through thin films of polydiacetylene para-toluene sulfonate predict a `reaction-like' phenomenon in which a new colored solitons are formed. It seems very attractive to use the nonlinear soliton tunneling effects predicted in developing a whole class of basically novel soliton logical devices.

The nonlinear pulse propagation in an optical fibers with varying parameters is investigated. The capture of moving in the frequency domain femtosecond colored soliton by a dispersive trap formed in an amplifying fiber makes it possible to accumulate an additional energy and to reduce significantly the soliton pulse duration. Nonlinear dynamics of the chirped soliton pulses in the dispersion managed systems is also investigated. The methodology developed does provide a systematic way to generate of infinite `ocean' of the chirped soliton solutions of NSE model with varying coefficients.

Dynamics of optical soliton attractor described by the generalized NSE model including the cubic and fifth-order nonlinearly and two-photon absorption is investigated. In the spectral range of positive GVD high-order nonlinear terms and two-photon absorption change dramatically the physical picture of high intensity pulse self-action. Instead of well known self-spreading and wave-breaking effects, the intense and short peak is formed on the broad pedestal. The most important results obtained in the numerical experiments are connected with soliton attractor forming in the negative GVD region. One can see that the strong nucleation of multi-soliton pulses creates the possibility to generate a new soliton-like high-energy pulse. An optical soliton attractor can be produced in a thin organic film waveguides by injecting a train of mode- locked laser pulses with the appropriate amplitudes and phases. The dynamics of soliton attractors forming in this case is strongly depends on the relative phases of interacting solitons. As follows from our computational modeling there exists the possibility to discover spatial and temporal soliton attractors in strongly nonlinear optical waveguides.

The modified computer code of direct numerical integration of a system of nonlinear Maxwell's equations were used to investigate the dynamics of generation and interaction of Maxwell's wave solitons of a few femtosecond duration. Computer experiments predict the possibility of generation of the one period and the `stopping' video soliton pulses. The problem of the second harmonic Maxwell's solitons generation is also investigated. If the second-order nonlinearity is so great that the nonlinear length and phase mismatch caused by natural dispersion of the nonlinear medium are the same orders, than a special choice of the phase matching conditions becomes redundant. In this case generation of the higher harmonics does not depend on the phase matching conditions. Our computer experiments predict the new soliton surfing effect, the second harmonic wave Maxwell's solitary pulses are generated at the fronts of the pumping femtosecond pulse. Dynamics of high harmonics generation induced by one period soliton pulse is also calculated.

A mathematical approach for modeling the subpicosecond pulse transmission in inhomogeneous optical fibers is suggested. Propagation of subpicosecond pulses is described under the assumption that they are affected by third-order dispersion and self-steepening. The pulse envelope is shown to obey a generalized nonlinear Schrodinger equation with additional terms characterizing the third-order dispersion and self- steepening of the pulse, and the Cauchy's problem for this equation with the initial values of the soliton type is investigated. Asymptotic solutions to this equation are constructed for the cases of (1) small third-order dispersion and self-steepening, and (2) short distances in the fiber for finite third-order dispersion and self- steepening. Phase distortions are considered for both cases as well.

Modern technology allows for manufacturing of multicore fibers composed of a number of microcores placed on a circle and doped with Nd³⁺ ions. The construction is attractive because of effective absorption of diode laser pump radiation. High-power conditions are easily achievable, and phase coupling between microcore lasers looks very promising for receiving high-brightness radiation from compact fiber lasers. To understand in detail coupling between microcores and evaluate an opportunity to achieve phase-locked operation of the array, a mathematical code describing light propagation in this composed fiber was developed. A numerical code performs direct integration of scalar wave equation in paraxial approximation. Refractive index profile corresponds to N index-guiding microcores. The composite fiber was embedded into square region imitating fiber cladding with lower index. The wave equation was solved using a splitting technique for diffraction/refraction processes on every propagation step. Calculations on the diffraction step were made with help of 2D FFT technique on Cartesian mesh. Numerical accuracy was checked by special tests. Results on simulations of microcore array excitation by injection of a beam into one of microcores will be reported. For realizable in experiments conditions coupling lengths are found. Evolution of far-field patterns for different fiber lengths was studied.

Hollow fibers are developed for transmitting high-power lasers emitting ultraviolet, visible, and infrared light. For Nd:YAG lasers, a glass hollow fiber with silver and polymer inner coating enables low-loss transmission of high- peak power, pulsed laser light. For ArF-excimer lasers, a hollow fiber with inner aluminum coating transmits the ultraviolet laser light with low attenuation.

We analyze the properties of vortex solitons generated in Kerr and non-Kerr nonlinear optical media, including the vortex drift and rotation in a diffracting Gaussian beam. We also present our recent analytical and experimentally results on the vortex-induced break-up of a dark-soliton stripe, and discuss a connection of this phenomenon with the well-known Aharonov-Bohm effect in solids.

Large-scale computer simulations of wide-beam, high-power femtosecond laser pulse propagation in air are presented. Our model, based on the nonlinear Schrodinger equation for the vector field, incorporates the main effects present in air, including diffraction, group-velocity dispersion, absorption and defocusing due to plasma, multiphoton absorption, nonlinear self-focusing and rotational stimulated Raman scattering. The field equation is coupled to a model that describes the plasma density evolution. Intense femtosecond pulses with powers significantly exceeding the critical power for self-focusing in air are simulated to study turbulence-induced filament formation, their mutual interaction via a low-intensity background, dynamics of the field polarization, and evolution of the polarization patterns along the propagation direction.

The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.

We simulate pulse compression mechanism based on a near-two- photon-resonance transition contribution to the nonlinear refractive index of atomic Noble gas filled hollow wave- guides. The negative refractive index contribution in the normal dispersive gas wave-guide, plays a similar role as in the case of soliton compression with positive Kerr non- linearity and anomalous dispersion in optical fibers. The self pulse compression to approximately 15 fsec can be achieved at moderate peak powers (approximately MW) for 100 fsec pulses in the spectral range 100 - 245 nm. We present simulated data concerning pulse and spectral shapes for xenon as a case study. The total throughput of the propagated pulse energy is > 90%, mostly determined by the linear attenuation of the hollow wave-guide propagation mode while two photon absorption and the corresponding enhanced three photon photo-ionization does not significantly reduce the pulse energy.

We present a brief overview of the physics of vector optical spatial solitons formed by an incoherent interaction of two optical beams in a medium with saturable (e.g. photorefractive) nonlinearity and describe the families of two-mode vector spatial solitons, which appear via bifurcations of one-component solitons, and their bound states. We report the results of the experimental observation of bound states formed by two vector spatial solitons due to a force balance between the soliton components, and also demonstrate a link between such bound states and earlier reported multihump multi-mode optical solitons.

There is considered formation and propagation of shock electromagnetic waves (SEW) of visible spectral range as possible nonlinear optical phenomenon taking place at laser intensities characteristic of femtosecond laser interaction with transparent solids. Main regularities of SHEW formation are studied on the basis of 1D model of plane-wave propagation in isotropic dielectric with nonlinear optical response. Special attention is paid to influence of color dispersion and absorption on SEW formation and propagation. Necessary conditions for appearing of SHEW are obtained, in particular, threshold amplitude is estimated. There is presented a model for numerical simulation of SHEW formation and propagation influenced by dispersion of linear and nonlinear parts of refractive index. Using the simulation, we studied dynamics of SHEW formation on several first optical cycles of femtosecond laser pulse in transparent medium. Important observed features of SHEW of optical frequency are discussed. Obtained results are considered from the viewpoint of experiments on femtosecond laser interaction, in particular, laser-induced damage.

Absorption of laser radiation in the optical element leads to depolarization resulting in limitation of isolation ratio. In order to suppress this self-induced depolarization two new optical designs were recently suggested. They utilize two 22.5 degree Faraday rotators and a half wave plate or reciprocal rotator between them. Both schemes allow an increase in isolation ratio at the same beam power. However all other parameters of the isolators were not investigated. All three designs are compared from the viewpoint of the first pass through the isolator. We derive equations for power losses, amplitude and phase distortions as a function of the laser beam power. Both crystal and glass magneto-optical media are investigated. It is shown that the scheme with reciprocal rotator is the best from the viewpoint of the first pass parameters as well as from the viewpoint of the isolation ratio. The results obtained for a Gaussian beam in the present and previous studies are generalized for the case of super Gaussian and flat intensity distribution as well. It is shown that the flat- shaped beam induces the weakest distortions and the Gaussian one induces the strongest ones.

The spatial and temporal dynamics of two short laser pulses propagating in absorbing three-level medium under conditions of induced transparency is investigated in adiabatic approximation. We analyze two cases of electro-magnetically induced transparency creating--coherent population trapping and adiabatic population transfer. It is shown that in both cases the probe pulse can penetrate into a medium at a distance considerably exceeding the length of linear absorption of a single weak probe pulse in absence of a coupling pulse at adjacent transition. The difference of spatial and temporal evolution of level population in processes of coherent population trapping and adiabatic population transfer is although demonstrated.

Results of using the self-focusing effect in Kerr liquids for measurements of small wavefront distortions of laser radiation transmitted through a transparent optical sample are presented. An experimental prototype of a new device, a Scanning Nonlinear Hartmann Sensor, is described.

In wave-based remote sensing of distant objects embedded in a random medium a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field, leading to an anomalous intensity distribution. Here, we present a possible realization for the resolving properties of an object using the double-passage effects and construct the intensity response at the image plane of an optical system, resulting from backward reflection from a target having discontinuities. The object plane-image plane relations are formulated and manageable algorithms are obtained by using the random propagators of the Stochastic Geometrical Theory of Diffraction. The resolving properties of periodic spatial objects ar investigated.

Imaging techniques involving transillumination require detailed knowledge of radiation path(s) between source and detector. When imaging with near infra-red in tissue this is particularly problematic due to the high scattering cross section. The population of `direct path' photons is so small that information must be gathered from the much larger (but still small) population of `snaked path' photons. Path Integral (PI) models set out to find the most likely of these paths, not by random sampling as in Monte Carlo based techniques, but directly: a cost function (Lagrangian) is constructed based on the physics of the scattering processes/absorption and integrated along the photon path to generate a total cost (Action). This is minimized using variational calculus to extract the most likely path. Whilst the PI approach is not new, the work presented here is novel in constructing the Lagrangian using local path descriptors. This allows explicit inclusion of an absorption term and also lends itself to arbitrary numbers of constraints on intermediate `visit' points, path directions, and overall path length. Scaling symmetries are used to further reduce the computational expense of the method.

In this paper we present a theoretical study of focused beam wave pulse propagation and diffusion in highly scattering discrete random media. By using Wigner distributions, we calculate an explicit closed-form expression for the reduced intensity of focused beam waves. From this analysis, we find that the extent to which the reduced intensity focuses depends upon the attenuation it experiences from scattering and absorption. We then solve the diffusion equation for continuous wave sources and delta function input pulses to examine the spatial and temporal spreading of beam wave pulses. Through numerical approximations to the obtained solutions, we find that focusing effects of the diffuse intensity are negligible. Finally, we compare these results to those of collimated beam waves and pulsed plane waves. Through these comparisons, we determine that the spatial spreading of focused beams is similar to that of collimated beams, and the temporal spreading of the focused beam wave pulse is similar to that of plane wave pulses.

The aerosol found in the lowest kilometer over the world's ocean is quite different than that found over land. It includes several unique components of marine origin in addition to a background component, which can be similar to that found over land. Large marine aerosol can have significant interaction with infrared propagation in this region and are thus very important for naval applications. This paper will discuss some of the author's research in this area with special emphasis on the aerosol of interest to the Navy. The topics will include the aerosol found from shipboard level to altitudes above the marine inversion, aerosol found in the boundary layers between the wave tops and shipboard level and the effect of surf produced in the coastal regions. This paper will also describe some aspects of recent series of experiments sponsored by the Office of Naval Research called EOPACE (Electro Optical Propagation in A Coastal Environment). This program has concentrated on looking at the history of the sea salt aerosol produced by the breaking of waves in a surf zone as it interacts with the micrometeorology in the ocean atmospheric surface layer.

On a basis of a multiple-forward-scatter propagation model the atmospheric aerosol contributions to laser beam widening for a horizontal propagation path is estimated and compared with beam widening caused by turbulence. It is shown that the beam widening caused by atmospheric aerosols is significant, often even more significant than that caused by turbulence.

Interest in the use of optical communications over terrestrial links has greatly increased during the last several years. In many applications, the path is horizontal so the index of refraction structure parameter can be taken as constant. In addition, optical communication channels offer a number of advantages over conventional RF channels. However, due to the short wavelength, the reliability of an optical link can be seriously degraded over that of an RF system by atmospheric scintillation. In particular, scintillation can cause severe fading of the channel. In our analysis here we assume that the refractive index structure parameter C²_n is constant and use our recently developed gamma-gamma model and the well known lognormal model to consider the fading statistics associated with a spherical wave model for simplicity. The results are similar to a Gaussian-beam wave with perfect pointing. Our analysis show that compared to the gamma-gamma model, the lognormal model predicts optimistic values of probability of fade, underestimate the number of fades per second and consequently does not measure the mean fade time correctly.

One and ten `micron' wavelength radiation was used to study laser beam propagation through a turbojet aircraft engine's exhaust. Pulse lengths were 0.1 and 2 microsecond(s) respectively, i.e. instantaneous realizations of intensity distribution (up to several thousand frames) were registered.

Density matrix approach has been employed to analyze the pump-probe spectroscopic absorption spectra of small semiconductor quantum dots (QDs) under strong confinement regime with sizes smaller than the bulk exciton Bohr radius such that the Coulombic interaction energy becomes negligible in comparison to the confinement energy. The average time rate of absorption has been obtained by incorporating the radiative and nonradiative decay processes as well as the inhomogeneous broadening arising due to nonuniform QD sizes. The analytical results are obtained for QDs duly irradiated by a strong near resonant pump and broadband weak probe. Numerical estimations have been made for (1) isolated QDs and (2) QD-arrays of GaAs and CdS. The results agree very well with the available experimental observations in CdS QDs. The results in case of GaAs QDs can lead one to experimentally estimate absorption/gain spectra in the important III-V semiconducting mesoscopic structures.

Nonlinear changes in the spectra of 100-picosecond optical pulses at 1061 nm transmitted through Nd³⁺ and Er³⁺ doped optical silica fibers were investigated both experimentally and theoretically. Generation of the Stokes and anti-Stokes frequency satellites was measured in Er³⁺ fibers and identified with the modulation instability due to four-wave mixing and stimulated Raman scattering. The generation of the Stokes Raman component was measured for single-core-mode double-clad Nd³⁺ fibers.

We demonstrate the measurement of path-length-resolved optical phase space distributions as a new framework for exploring the evolution of optical coherence in a turbid medium. This method measures joint transverse position and momentum (i.e., angle) distributions of the optical field, resolved by optical path length in the medium. The measured distributions are related to the Wigner phase space distribution function of the optical field, and can provide complete characteristics of the optical coherence in multiple scattering media. Optical phase space distributions are obtained as contour plots which enable a visual as well as quantitative method of characterizing the spatial coherence properties and wavefront curvature of the input and scattered fields. By using a broad-band source in a heterodyne detection scheme, we observe transmission and backscatter resolved by path length in the random medium, effectively providing timing resolution. New two-window heterodyne detection methods permit independent control of position and momentum resolution with a variance product that surpasses the uncertainty limit associated with Fourier transform pairs. Hence, high position and angular resolution can be simultaneously achieved. These techniques may provide new venues for using optical coherence in medical imaging.

The transverse spatial coherence of light evolves as the light transverses a random, multiple-scattering medium. For near-forward scattering, the wave-transport process can be described by a wave-transport equation for the spatial- angular Wigner function of the light, which is related to the spatial coherence function. Using a novel variable-shear Sagnac interferometer, we measured the Wigner function of initially coherent light after propagation through a multiple-scattering medium. We find good agreement between the wave-transport theory and the experimental results.

We have developed a new theoretical description of the optical coherence tomography (OCT) geometry for imaging in highly scattering tissue. The new model is based on the extended Huygens-Fresnel principle, and it is valid in the single and multiple scattering regimes. The so-called shower curtain effect, which manifests itself in standard OCT systems, is an inherent property of the extended Huygens- Fresnel model. We compare the theoretical analysis with experiments carried out on samples consisting of aqueous suspensions of microspheres and solid phantoms. We calculate the signal-to-noise ratio, and provide an estimation of the maximum attainable probing depth for shot-noise limited detection. Furthermore, we investigate the focusing of the Gaussian probe beam in the tissue using Monte Carlo simulations, and compare it to the extended Huygens-Fresnel model. Finally, we simulate the operation of the OCT system using a specially adapted Monte Carlo simulation code.

Different techniques for diagnostics and visualization of the inhomogeneous scattering media by means of the statistical analysis of spatial-temporal fluctuations of scattered light are considered: (1) polarization diagnostics and imaging based on the application of the polarization degree as visualization parameter; (2) imaging techniques on the basis of measurements of the contrast of multiply scattered speckles induced by partially coherent light scattering in the probed object; (3) modification of the speckle imaging technique based on the statistical analysis of time-integrated electronic images of the speckle patterns under coherent light illumination. Comparison of these methods with traditional approaches to the diagnostics and imaging of macroscopically inhomogeneous multiply scattering objects is made. Experimental results obtained with phantom scattering media and illustrating the potentialities of the discussed approaches are presented.

A confocal microscopy imaging system was devised to selectively detect second harmonic signals generated by biological tissues. Several types of biological tissues were examined using this imaging system, including human teeth, bovine blood vessels, and chicken skin. All these tissues generated strong second harmonic signals. There is considerable evidence that the source of these signals in tissue is collagen. Collagen, the predominant component of most tissues, is known to have second order nonlinear susceptibility. This technique may have diagnostic usefulness in pathophysiological conditions characterized by changes in collagen structure including malignant transformation of nevi, progression of diabetic complications, and abnormalities in wound healing.

Optical radar (LIDAR) is being used to remotely probe the atmosphere. Quantities that can be sensed on a path resolved basis include temperature, pressure, number density for specific molecules and atmospheric winds. We believe that the techniques used can be scaled down and used to analyze tissues in medical optics applications. As our first project using atmospheric optics technique, we are building a Heterodyne, Optical, Coherent tomography system for imaging tissue. This system will be described.

We will present a brief introduction to Mueller matrix imaging from cradle to adolescence and then show how it can be effectively used for detection of objects embedded in a highly scattering medium when ordinary radiance imaging might fail. We will show which elements and combination of elements are important for gaining the highest contrast against the background continuum. The mapping of certain combinations of Mueller matrix elements into an equivalent human visual system will also be discussed.

We present a theoretical analysis on the use of polarized light in the detection of a model target in a scattering and absorbing turbid medium. Monte Carlo numerical simulations are used in the calculation of the effective Mueller matrix which describes the scattering process. Contrasts between various parts of the target and background are analyzed in the images created by ordinary radiance, by elements of the Mueller matrix and by the depolarization index. It is shown that the application of polarized light has distinct advantages in target detection and characterization when compared to the use of unpolarized light.