Recent progress on soliton transmission is described, in which dispersion management plays an important role in increasing the power margin and the dispersion tolerance in TDM and WDM systems. The quality of the dispersion-managed soliton is compared with RZ and NRZ pulses.
Chromatic dispersion is one of the most important transmission limitations in systems operating at 1550 nm, and much effort has been invested in obtaining dispersion compensation schemes for standard fibers already installed. Various different fiber Bragg grating dispersion compensation schemes are studied or a system composed of a directly modulated 1550 nm single-mode semiconductor laser signal propagating through a standard nonlinear fiber link. The laser diode is simulated by its stochastic rate equations, while the apodized chirped fiber Bragg gratings are obtained by numerical resolution of their coupled-mode equations. The optimal grating length for dispersion compensation after transmission through 100 km standard single-mode fiber is obtained by means of minimizing the eye opening penalty of the signal. Pre and post-compensation cases are analyzed separately, and differences between both cases are discussed in detail. Different optimal grating lengths arise for each case, and better results are obtained in general with post-compensation. Pulses with a FWHM of the order of 65 ps with various laser chirp parameters are reconstructed using a 5.75 cm chirped grating with a 16th- order Gaussian apodization function.
Large core high NA glass fibers are often used to distribute the energy in high-power laser material processing systems. It is important to understand mode propagation in these fibers so that laser material processing systems can be designed with the minimal size optics and still have acceptable working distance and delivery efficiencies. The fundamental challenge in this respect is to understand mode propagation in these specialty fibers. The experiments summarized here confirmed that optics much smaller than optics designed through worst-case analysis are effective in practical delivery configurations.
Since they have been predicted and observed six years ago, photorefractive spatial solitons have attracted substantial research interest. Photorefractive solitons bring about several new fundamental aspects related to solitons in general. Perhaps the single most important aspect is being the first system in which solitons were demonstrated. This has enabled the study of interactions between 2D solitons in a full 3D medium, which has revealed a fundamentally new property of interacting solitons: conversation of angular momentum when the solitons are bound to each other in a spiraling configuration. Another key property of the photorefractive nonlinearity that has had a major impact on soliton research, is its non-instantaneous nature. This has allowed us to generate a new type of 'self-trapped' light beams: incoherent solitons, which are made of partially spatially incoherent light or of temporally and spatially incoherent white light. In this review, we start from the formation mechanism of photorefractive spatial solitons, and especially focus on the bright screening solitons. We then describe the waveguides induced by these solitons, and use this understanding to explain and demonstrate soliton interactions, which are probably the most fascinating features of all solitons in nature, because they shows how a soliton is related to areal particle. Then, we describe Incoherent Solitons and end by discussing several ideas on how to utilize the photorefractive solitons for useful applications.
As data rates in individual channels increase in optical communication systems, the nonlinear effects in optical fibers become increasingly important. Initially soliton in optical fibers were suggested as a pulse format to achieve a natural balance between the optical nonlinearity and fiber dispersion, however, at the cost of system complexity. Dramatic progress in NRZ-type formats using dispersion- management have led to impressive increases in channel bit- rates over very long distances. Recently a new data propagation format, called dispersion-managed solitons, has emerged that combines the best of both worlds. This new pulse format eliminates the need for in-line controls that are required for standard solitons thus making them more attractive for use in terrestrial and undersea optical communication systems. Currently, for single channel data rates at 10 Gbits/sec to 40 Gbit/sec the dispersion-managed soliton can reach much longer distances than NRZ-style formats. Dispersion maps, pulse dynamics, amplified spontaneous emission, timing jitter, and bit-error rate measurements are all key elements in understanding and characterizing dispersion-managed soliton communication systems.
The diffraction limited spot size in optical imaging, recording and lithography can be decreased by use of the Solid Immersion Lens (SIL). The simplest form of the SIL utilizes a hemispherical lens with the rays of a focused beam entering along its radii to from a spot a the flat surface of the hemisphere. The spot size is decreased from that in free space by a factor 1/n, where n is the refractive index. If an object to be imaged in spaced close enough to the SIL, this reduced spot size is obtained at the disk. In this case the effective numerical aperture of the lens can be greater than one. Applications of the SIL to microscopy, lithography, and optical storage are discussed. They typical SIL is of the order of 2-3 mm diameter. However, we also raise the possibility of using lenses a few micrometers diameter made by micromachining techniques. The problem of tolerances of such lenses is discussed.
Near-field scanning optical microscopy (NSOM) is begin studied to achieve optical resolution much better than the diffraction limit. Improved resolution is realized when the sample is in the near field of the probe. Strong near-field coupling between sample and probe complicates image analysis. Experiments with well characterized tips and simple samples are needed to produce basic NSOM images. Detailed modeling able to reproduce imags and identify essential features in image formation is required. We analyze experimental NSOM transmission images of nanochannel glass arrays and of Au nanoparticles obtained in illumination mode. We use several approaches, including the discrete dipole method and the transfer matrix method, to simulate these images. Experimental and simulated images are compared to identify the contributions of tip-field structure, sample scattering, and the collection process to the images and to provide a clear interpretation of these NSOM images.
Atmospheric blur is usually attributed in the remote sensing community to forward scatter of light by aerosols, called the adjacency effect, and in the propagation community to optical turbulence. It is our view that both phenomena contribute to atmospheric blur. In some situations such as lines-of-sites close to the ground turbulence is significant, while in others, such as lines of sight with optical depths on the order of unit or more, aerosol blur is significant. However, in general both types of blur should be considered. Examples are cited in which ignoring aerosol scatter leads to incorrect conclusions or in which ignoring turbulence leads to only partial image correction. Both vertical nd horizontal imagin are considered. The purpose of the paper is to emphasize the need for both the remote sensing and propagation communities to consider both aerosol blur and turbulence blue in analyses of experimental results.
A model of irradiance fluctuations for a propagating optic wave through a random medium is developed here under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The upper bound for small turbulent cells is defined by the smallest cell size the Fresnel Zone or transverse spatial coherence radius of the optical wave. The largest cell size between scintillation index, we also develop expressions for the irradiance covariance function and temporal spectrum of irradiance. Quantitative values predicted by these models agree well with experimental and simulation data previously published. An application of the method is also presented for uplink/downlink optical communication channels to/from a satellite.
In this paper, we examine numerical solutions of the two- frequency radiative transfer equation to study pulse propagation through discrete random media. Specifically, we examine the plane-parallel problem using the Henyey- Greenstein phase function for scalar problems and Mie scattering for polarimetric problems. Since standard methods such as the discrete ordinate method and the finite element method are not numerically stable for polarimetric problems at large optical depths, we introduce a Chebyshev spectral method to solve these problems. Then, we examine a few examples of optical pulses in fog layers and millimeter wave pluses in rain layers, and compare our results to first- order scattering and diffusion approximations.
Ray trajectories, as has been shown in the recently formulated Stochastic Geometrical Theory of Diffraction (SGTD), play an important role in determining the propagation properties of high-frequency wave fields and their paired measures. As in the case of deterministic GTD, the main concern is the construction of high frequency asymptotic propagators relating the values of the random field and its statistical measured at some observation plane to their source distributions at the initial plane. We start with the parabolic approximation performed in local coordinates around the curved ray path connecting a source with an arbitrarily located observer in the deterministic background medium. The solution strategy involves the ray- centered coordinates for a typical ray with extraction of the average phase accumulation along that ray. We present a reference wave method to obtain an approximate solution of the parabolic wave equation in a homogeneous background random medium. These solutions are further applied for modeling propagation of a directional beam in a waveguide with randomly varying interior. We show that statistical propagation characteristics can be modeled in terms of stochastic rays and guided modes.
The OMEGA laser at the University of Rochester's Laboratory for Laser Energetics is used for direct-drive inertial confinement fusion (ICF) experiments. To achieve highly symmetric implosions, it is necessary that all of the beams be power balanced. The definition of power balance must be tied to the physics of the ICF targets: in a given time interval what level of nonuniformity can be tolerated before the laser drive disrupts the implosion. We monitor the pulse shape on several of the OMEGA beamlines using multiplexed streak cameras. From a database of over 15,000 individual streaks we have determined that if all the OMEGA beams are energy balanced to the 1 percent level, the present system would have an overall power balance of better than 10-15 percent. This was determined by grouping individual traces by pulse shape and energy. A further improvement in power balance can be obtained by matching the electrical energy stored in Nd:glass amplifiers. This information is important because the first step in achieving power balance will be to energy balance the OMEGA laser. This research tells us what strategies for achieving energy balance will enhance power balance.
We analyze propagation of ultra-short light pulses in transparent, dispersive, nonlinear media. A general formula for a femtosecond wavepacket evolution in birefringent materials is presented and applied to specific problems. Theoretical and experimental results for wavepacket distortion by lenses, wavepacket rotation in birefringent media, group velocity matching in sum frequency generation, and ultra-short pulse propagation in birefringent crystals are presented. Splitting of femtosecond wavepackets in dispersive Kerr media is also discussed.
We have developed a method to precisely propagate short optical pulses through dispersive media with a self-focusing (chi) (3) Kerr-type nonlinear polarization. Above the critical cw self-focusing power, onset of pulse splitting into pulselets separated in time occurs, and for a certain regime of parameters a cyclic series of pulse splitting and pulse recombination occurs for diffraction length smaller than dispersion length. At higher power, another threshold for non-cyclic temporal and spatial pulse splitting is manifest. Self-steepening and self-frequency shifting affect pulse propagation too. We use our formulation to calculate the dynamics of collisions of two pulses in nonlinear optical media, and show how the collision can give rise to pulse splitting. We also investigate the effects of saturation of the nonlinearity on the phenomenon of pulse splitting and pulse collision dynamics.
Propagation of intense femtosecond pulses in solids and liquids is investigated experimentally and numerically. A brief review of experiments in fused silica that reveal complicated spatio-temporal dynamics including temporal pulse splitting is presented. Experiments in methanol show the expected effects of linear dispersion and an instantaneous Kerr nonlinearity as well as a contribution from a noninstantaneous nonlinearity with a response time on the order of 10 femtoseconds. Propagation in these two systems is modeled using a modified (3 + 1)-dimensional nonlinear Schroedinger equation (NLSE) that includes nonlinear shock and space-time coupling terms and a (1 + 1)-dimensional NLSE that includes a response time of the nonlinear part of the refractive index.
The reductive perturbation method was applied to the propagation of two orthogonal polarized sub-100 fs soliton pulses, in a singlemode fiber, to give an analytical propagation model. The analytical propagation model was transformed into a numerical propagation model via the symmetrized split-step Fourier method. The numerical propagation model was then used to analyze the switching efficiency of an inverter soliton-trapping gate (STG) and an inverter soliton-dragging gate (SDG), with a clock time window of about four pulse widths. For the STG and the SDG, with the control on the slow axis, the switching maximum clock time windows are reduced by 32 percent and 62 percent respectively, due to the self and cross Raman effects. However, for the STG and SDG, operated with the control on the fast axis, it was found that the switching maximum clock time windows are increased by 30 percent and 28 percent respectively, due to the self and cross Raman effects.
An experimental demonstration of a set of optical logic gates (OR, XOR, AND) is shown using non-linear mixing in a BBO crystal. Pulses generated by a femtosecond Ti:Sapphire laser at 800 nm are split in 4 beams evenly separated in space and propagating collinearly. The 4 beams are focused by a singlet lens in the non-linear crystal and frequency doubled using a type I non-collinear phase matching. Due to spherical aberrations of the lens, the 2 beams that are far from the optical axis are brought into a focus that is slightly further away from the focus formed by the 2 beams closer to the optical axis. The frequency-doubled light generated by the two foci propagates in the same direction. An OR gate is produced by constructive interference of the frequency doubled pulses. A XOR gate is produced using destructive interference. OR and XOR can be programmed form a single gate by adjusting time delays of the inputs. We raise the possibility of creating a cascaded set of gates for a femtosecond time scale computing system using photoinduced absorption in polyacetylene substitutes.
A lot of laser applications require propagation of extremely high average power radiation through Faraday isolators. Although many investigations are devoted to the thermal lens effect, polarization contamination has not been discussed in detail. However, the depolarization can significantly limit the isolation ratio. The physical reason for the self- induced depolarization is absorption of laser radiation. It results in spatial nonuniform distribution of temperature giving rise to two effects which reduce the isolation ratio: the temperature dependence of Verdet constant and birefringence ratio is sum of two terms which represent these two effects and the last phenomena is more efficient. In order to suppress the self-induced depolarization tow novel optical schemes was suggested and realized in experiment. The idea of compensating depolarization is to replace one 45 degree Faraday rotator by two 22.5 degrees rotators and a reciprocal optical element between them. The polarization distortions which a beam undertakes while passing the first rotator will be partially compensated in the second rotator. Both schemes allow to increase isolation ratio up to 100 times in comparison to the traditional scheme. Different ways of design of Faraday isolator for 1kW average power with isolation ratio about 30 dB are discussed.
The precision focusing and diagnosis experimental system for laser beams in ICF target chamber is introduced in the paper. The experimental system consists of laser source, precision focusing facility with harmonic-step driver aspherical focusing lens, simulated optical fiber planar target, CCD cameras and image acquisition and processing unit. The system is controlled by computer. The experimental results shows that, the error of this focusing and diagnosis system is less than 15 micrometers , the system meets to the technical needs of precision focusing laser beam sin ICF target chamber.
Effects of the single and multispatial filter (SF) on the light field in the ICF laser drive have been studied in detail. It has been found that the low spatial frequency rings and ripples in the intensity distribution of the output light field depend only on the ratio of filtering pinhole size to the diffraction-limit of the input beam. The modulation-depth, focal-depth and filling-factor of the laser beam passing through a SF have also been investigated. For the multi-spatial filter, there exists, in the frequency-domain, a simple and analytical relationship between the input and output frequency spectrum under a special case, and among the filtering pinholes there is a most effective one that performs as if the other filtering apertures can be disregarded.
Dye cell in Shank Type Geometry was excited by multiple sets of 2nd harmonic of a laboratory built cavity dumped Nd:YAG laser to induce multiple dynamic gratings at the same spatial location in dye cell. The result of their concurrent operation are presented in this paper. It will be shown that when the delay between the three sets of excitation beams is varied within coherence length of the pump laser, the number of dynamic volume gratings and hence and colors of multiple oscillating lines become tunable. Five lines were observed from two pairs of excitation beams and maximum nine lines for three pairs of beams. The colors of these 9 spectral lines varied from green to pink and were equally spaced in their spectrum. This experimental study was conduced precisely as a function of optical path differences between three sets of excitation beams varying from 1 to 9 mm among three sets of pump beams. The effect of coherence length and state of polarization of excitation laser on emission of multiple lines were investigated. No external gratings were used to excite the gain medium. The objective of this experimental study was to produce multiple laser sources of different colors to interface it to optical integrated circuits for use in image processing, optical interconnections and photonic switching.
A theoretical model was developed and simulated to confirm the result of our experimental study showing gain accumulation and peak pulse shifting phenomenon during repetitive excitation of distributed feedback dye laser. The dye cell was excited by 10 to 20 pulses of a frequency doubled, passively Q-switched and Mode-locked Nd:YAG laser. The output pulses of DFDL and Nd:YAG laser were investigated by Imacon 675-streak camera. At zero mutual delay of DFDL and Nd:YAG the peak of DFDL output envelope of pulses was delayed from the peak of the excitation Nd:YAG envelope of pulses by more than one inter-pulse period of excitation laser. Various types of cases such as different excitation energies and inter-pulse time periods were studied and a DFDL intensity based model was developed. The delay between the peaks of pulse envelopes of Nd:YAG and DFDL depends upon the inter-pulse period of the excitation laser. A computer program was used to simulate the experimentally measured delay to estimate thermal decay constants and energy retained by the medium. It was found that for smaller inter- pulse periods the effect of gradual gain build-up becomes very significant to effect some of the more sensitive applications such as energy per pulse in laser eye treatment, photonic switching and bit error rate in fiber optic communication.
Solution of R6G was excited by three pairs of 2nd harmonic of Nd:YAG laser in Shank type geometry to produce multiple dynamic gratings at the same spatial location in dye cell. The result of their concurrent operation are presented in this paper. It will be shown that when the delay between the three sets of excitation beams is varied within coherence length of the pump laser, the number of dynamic volume gratings and hence the colors of multiple oscillating lines become tunable. Five lines were observed for two pairs of excitation beams and maximum nine lines for three pairs of beams. The colors of these 9 spectral lines varied from green to pink and were equally spaced in their spectrum. This experimental study was conducted precisely as a function of optical path differences between three sets of excitation beams varying from 1 to 9 mm among three sets of pump beams. The effect of coherence length and state of polarization of excitation laser on emission of multiple lines were investigated. No external gratings were used to excite the gain medium. The results shown promising applications in photonic switching, optical computing and LANs.
We simulate a pulse compression process in hollow wave- guides filled with atomic xenon based on the near blue side two photon resonance contribution to the nonlinear refractive index. The negative nonlinear refractive index contribution in the normal dispersion xenon gas wave-guide play s a similar role as in the case of soliton compression in optical fibers with positive nonlinear refractive index and anomalous dispersion.
A new integro-differential equation with the only first order derivative describing diffraction of arbitrary transversely nonuniform light beam in the homogeneous transparent medium is obtained. At fist, it is introduced for the case of linear media. The ones approximation of the forward propagation is used. It is shown that derived equation in the case of light beams with the great diameter transforms to the well-known parabolic equation, thus our equation is a generalization of the parabolic equation for a case of nonparaxial light beams. The new approach is generalized also for the case of media with the cubical nonlinearity. It is applied for an analysis of the self- focusing phenomenon.
We consider a pencil-shaped active medium consisting of two- level initially excited atoms and described by 1D Maxwell- Bloch equations. With the help of these equations solution without slowly varying envelope approximation we shown, that internal field reflections from the ends of the sample transform the so-called 'lethargic' regime of super-radiance (SR) pulse amplification to the amplification regime similar to usual exponential law. iT can lead to the pulse development acceleration and counter-propagating waves synchronization. A simple formula for SR pulse delay time evaluation is presented. The criterion of the counter- propagating waves synchronization is discussed.
Hollow fibers for variety of IR lasers are introduced. FOr delivery of IR lasers represented by CO2, Er:YAG, and Nd:YAG lasers, hollow fibers having a dielectric and a silver film on the inside of glass tubing have been developed. It is shown that the fibers transmit high-powered laser light with low attenuation due to the interference effect of the internal dielectric layer. Hollow fibers enable many applications in industrial and medical fields that need effective delivery medium of laser light.
Propagation of optical pulses in graded-index light guides is described under the assumption of the combined influence of large power, short duration and inhomogeneity which is supposed to be strong in the transverse and weak in the longitudinal direction. The propagation is treated as a weak nonlinear process modeled with a nonlinear wave equation. This equation is solved by means of a consistent asymptotic procedure with respect to a small parameter related to the pulse amplitude, with the second power of the parameter characterizing the weak longitudinal inhomogeneity of the graded-index light guide. A Sturm-Lionville problem, is obtained for the principal approximation to the asymptotic solution. The transverse distribution of the wave field and the phase of the high-frequency carrier are expressed through eigenfunctions and eigenvalues of this problem. For the pulse envelope the Nonlinear Schroedinger equation is derived, its coefficients depending on the longitudinal coordinate. The Cauchy's problem for this equation with the initial values of the soliton type is investigated. The conditions of persistence of the pulse shape are ascertained and for a large class of weak longitudinal inhomogeneities a distance is estimated where the pulse remains to be a solitary wave. A series of additional pulses with diminishing amplitudes where the pulse remains to be a solitary wave. A series of additional pulses with diminishing amplitudes arises as an effect of the weak longitudinal inhomogeneity. Formulae for these distortions are derived and it is shown that this effect may be eliminated for the case of a special relationship between the characteristics of inhomogeneity.
Using semiclassical time dependent perturbation treatment, the coherence radiation-semiconductor interaction under ultrashort pulsed near band-gap resonant excitation regime has been analytically investigated in a narrow direct-gap semiconductor waveguide structure. The role of excitonic effect is incorporated to study transient pulse propagation effects in GAs/AlGaAs waveguide duly irradiated by a 100 fs Ti:Sapphire laser. Nonlinear Schroedinger equation is employed to examine the role of group velocity dispersion and nonlinear optical effect on the transmission characteristics of the pulse at various excitation intensities and waveguide lengths. The results suggest the occurrence of pulse break-up and pulse narrowing during propagation of the pulse through the GaAs/AlGaAs waveguide.
The equations describing the propagation dynamics of optical pulses consisting of several electrical field cycles and pulses with spectrum bandwidth comparable with the central frequency are presented. The numerical simulation of nonlinear optical phenomena observed in isotropic media with pumping by the pulses with the spectrum in area of the normal group dispersion is carried out. The spectrum ultrabroadening of a short pulse with the temporal broadening, the self-induced changes of the pulse polarization, the simultaneous generation of several Stokes, anti-Stokes components, the third harmonic and sum and difference frequencies generation with self-phase and cross- phase modulation are considered.
The transverse size of a beam is defined as the cross- section size containing the certain part (sigma) of the full energy of the whole beam. It has been proved that under such definition the form of a beam with a given size and maximum length of waist is not Gaussian. The beam with radial symmetry and the maximal length of the waist synthesized as superposition of orthogonal Gaussian modes with the use of Chebyshev polynomials. The intensity transverse distributions are found first for all certain parts of energy 0 < (sigma) < 1. It is shown that intensity distributions are smooth enough while four-five lowest Gaussian modes are used and depends considerably upon value of fixed energy share.