Selection of the design parameters for an adaptive optics system is normally based on consideration of a set of three basic errors referred to by the terms "measurement noise error" , "servo lag error" , and "fitting errorS" In this paper I introduce another basic error, which I refer to by the term "reconstructor formulation error!' This fourth basic error has previous'y been overlooked in analysis of adaptive optics system performance. In this paper the concept of reconstructor formulation error is presented and then the magnitude of the error is developed. It is found that for the forms of wave front sensor and reconstructor formulation considered the mean square value of the reconstructor formulation error is proportional to (?/ro)5/3, with the constant of proportionality having values ranging from about 0.2 to 1.0, times the reconstructor noise gain factor—the relevant value depending on the form of the sensor and the nature of the reconstructor formulation. It is noted that although the (?/ro)5/3-dependence is the same as for the fitting error, reconstructor formulation error is distinct from and in addition to fitting error.

High data rate communication systems at millimeter and optical frequencies used for both mobile and satellite links may be influenced by pulse spreading due to scattering by turbulent inhomogeneities and hydrometeors in the troposphere and by the electron concentration in the ionosphere. Theoretical analysis of pulsed signal propagation is usually based on the analysis of the two-frequency mutual coherence function. In this work we propose a new reference wave method which enables us to present an analytic solution for the equation of the two-frequency mutual coherence function. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Propagation of plane and spherical waves in the more general types ofmedia is considered.

A statistical approach of the propagation of solitons in media with spatially random perturbations is developed. Applying the inverse scattering transform several regimes are put into evidence which are determined by the mass and the velocity of the incoming soliton and also by the correlation length of the perturbation. The mass of the transmitted soliton may tend to zero exponentially (as a function of the size of the slab) or following a power law; or else the soliton may keep its mass if it is initially large enough, while its velocity decreases at a logarithmic rate or even slower. Numerical simulations are in good agreement with the theoretical results.

A new lidar system for measuring simultaneously aerosol extinction, size distribution and turbulence profiles up to 20 km altitude has been developed. On the basis of measurements and a Monte Carlo beam propagation model, the atmospheric aerosol contributions to laser beam widening for a horizontal propagation path at various elevations is estimated and compared with beam widening caused by turbulence.

We theoretically investigate three approaches to trapping atoms above linear integrated optical waveguides. A two- color scheme balances the decaying evanescent elds of red- and blue-detuned light to produce a potential minimum above the guide. A one-color surface trap proposal uses blue-detuned light and the attractive surface interaction to provide a potential minimum. A third proposal uses blue-detuned light in two guides positioned above and below one another. The atoms are con ned to the \dark" spot in the vacuum gap between the guides. We nd that all three approaches can be used in principle to trap atoms in two- or three-dimensions with a few 10's of mW of laser power. Of these three methods, we show that the dark spot guide is the most robust to power fluctuations and provides the most viable design approach to constructing integrated optical circuits that could transport and manipulate atoms in a controlled manner.

Diode laser arrays have become indispensable components as pumps for solid state lasers. Always of compelling interest is their spatial-temporal dynamics. Wavelet signal processing will be applied to elucidate the fine structure of spatial instabilities of a ten stripe phased array of a diode array laser. Noise reduction and multiscale feature detection are expected to be particularly useful in defining peaks of oscillation.

We present a new class of invariant optical fields that we named Mathieu beams because they are described by radial and angular Mathieu functions. The angular spectrum of these beams when mapped on the McCutchen sphere gives the clue to create them in the laboratory. The corresponding experimental setup is described and the results obtained corroborated our theoretical predictions. The experimental parameters can be easily adjusted to obtain a variety of transverse intensity patterns that range from cosine to Bessel. There are two main families of higher order Mathieu beams, one of them are confocal elliptically ringed and can present phase rotating characteristics that are interesting for creating elliptical rotating waves. The other family of these high order beams have bowtie shapes. Mathieu beams are a variant of superposition of uniform conical waves, i.e. Bessel beams, and for these reason they have also the capability of self-reconstruction after finite obstructions.

We present experimental results on induced (driven) modulation instability and associated pattern formation of partially spatially incoherent light. Incoherent modulation instability (MI) is driven by seeding noise through cross-phase-modulation rather than intrinsic noise in a noninstantaneous nonlinear medium. We show that a threshold exists for such driven incoherent MI to occur, which depends on the degree of spatial coherence as well as the strength of the nonlinearity. Above the threshold, the MI leads to formation of ordered and disordered patterns of incoherent light. New class of solitons of incoherent light observed by suppressing incoherent MI will also be reported.

We discuss properties of multicomponent spatial formed by simultaneous co-propagation of few mutually incoherent beams in a slow nonlinear medium. W present experimental results on formation and interaction of these solitons in photorefractive nonlinear crystal.

We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D squarelattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.

The response of atoms and molecules to intense 1013 — 1015 W/cm2 lasers was investigated using two-dimensional (time-frequency) four-wave mixing. The data reveal a transition from a molecular response to a purely electronic (plasma) response.

We analyse parametric processes and harmonic generation in two-dimensional (2D) ? (2) photonic crystals and demonstrate the possibility of multiple phase matching and multicolour parametric frequency conversion in such structures. We suggest a new type of a 2D photonic structure to achieve simultaneous generation of several harmonics; and present both general analytical results and design parameters for 2D periodically poled LiNbO3 photonic crystals. We also discuss tuning properties and the acceptance bandwidth for the second-harmonic generation in 2D ? (2) photonic crystals.

A new equation for self-focusing of extremely focused intense pulses is derived. This method can be generalized to derive propagation equations for intense focused pulses to all orders of diffraction and dispersion with nonlinearity present, including the self-consistent derivation of nonlinear derivative coupling terms. This generalizes both the previously formulation of linear optical pulse propagation to the nonlinear propagation regime, and the cw nonlinear regime to the pulsed regime by including temporal characteristics of the pulse. Here we present the results for isotropic Kerr-type nonlinear media.

We report on the observation of dissipative localized structures in an optical pattern–forming system. After an experimental and theoretical analysis of the mechanism which stabilizes these structures we focus on the demonstration of possible applications of localized structures for information processing.

We analyze the propagation of pulses in noncentrosymmetric crystals by applying high-frequency expansions techniques for Maxwell equations. As a rst application we give a closed-form expression for the anisotropic di raction operator. Given this expression we identify a critical con guration in biaxial crystals where the di raction reduces to a one-dimensional second-order operator for the ordinary wave instead of the standard transverse Laplacian. The beam propagation in such a con guration involves the generation of spatial solitons because of this anomalous onedimensional di raction. As a second application we present closed-form formulas for the interference patterns from biaxial crystal plates between two polarizers. These formulas agree with experimental patterns.

We demonstrate a new technique for femtosecond microfabrication in transparent dielectrics, which employs non-diffracting Bessel-Gauss beams instead of commonly used Gaussian beams. The main advantage achieved this way is the ability to record linear photomodified tracks, extending along the line of non-diffracting beam propagation without sample translation, as would be required for Gaussian beams. The initial near infrared Gaussian laser beam was transformed into the non-diffracting Bessel-Gauss beam by a glass axicon (apex angle 160 deg). The beam was imaged into the bulk of the sample by a telescope consisting oftwo positive lenses, which allowed to vary the focusing cone angle from 5°to 19°, and maximum non-diffracting propagation distance up to 1 cm. We have recorded pre-programmed patterns of multi-shot damage tracks (diameter about 3 µm), extended uniformly along the z-axis by varying the damage spot coordinates in the x - y plane. The experiments were carried out in various transparent dielectrics: silica glass, sapphire, and plexyglass. Physical processes underlying the Gauss-Bessel microfabrication, and its potential applications for stereolithography, 3D microstructuring, and photonic crystal fabrication will be discussed.

We report experimental and theoretical investigation of supercontinuum generation in broad spectral range from 500 nm to 2500 nm induced in water and bulk fused silica by 1mJ 150-fs pulses at 780 nm excitation wavelength. We find that experiments may be modeled theoretically by considering Raman- and Kerr-type nonlinearities such as transient stimulated Raman scattering, parametric four-photon mixing, self-phase modulation and cross-phase modulation.

Transient SRS in mixture of two Raman active media (doubled gas mixtures) with pumping by ultrashort (2 ps) pulses was theoretically analysed. The numerical simulations show that there is strong energy exchange between direct Stokes waves and combination Stokes line during ultrashort pulse propagation in gas mixture. It is necessary to achieve the same phase and temporal dependencies of direct Stokes pulses for effective energy conversion in combination Stokes line. One-peak pulse generation in combination Stokes line with temporal compression is possible at pump intensity from threshold value up to doubled level. The decrease of duration of pulse by 12 times at conversion efficiency of 6% was shown. Increase of input pump energy causes destruction of Stokes pulses form and formation of multipeak Stokes pulses. The results show that the optimum ratio of gas pressure for transient SRS generation of sum and difference combination Stokes lines is proportional to the relation of the g/T2 of mixture components or to the relation of their Raman cross-sections. Our calculation is in good agreement with experimental results1.

Ultrabroadening of spatial spectrum of a self-focusing monochromatic optical wave in a medium with cubic nonlinearity is considered. The formation of optical beams with cross section on the order of a wavelength is considered. Backward self-reflection phenomenon is found to be the fundamental cause for the limitation of nonparaxial self-focusing.

Influence of space-time focusing on spatiotemporal instability in dispersive self-focusing media is investigated on the basis of a modified nonlinear Schrodinger equation (NLSE) beyond the slowly varying envelope approximation. It is found that, for both normal and anomalous dispersions, space-time focusing may lead to the appearance of new instability regions. Space-time focusing influences the original spectra obtained using the standard NLSE mainly by shrinking the instability regions, especially in the case of normal dispersion.

Stimulated Brillouin scattering (SBS) in an optical fiber cavity resonantly couples an optical cw-pump and a backscattered Stokes wave with electrostrictively excited longitudinal GHz hypersound waves. Below a critical feedback the Stokes wave self-structurates into ns pulses, called Brillonin dissipative three-wave solitons; they are able in turn to electrostrictively excite lower frequency acoustic waves (fn = 5 MHz to 1 GHz), due to cladding Brillouin scattering (CBS), transversally propagating with respect to the fiber axis in the fiber's cladding. We derive a four-wave model which couples the transverse CBS dynamics to the nonlinear dissipative three-wave SBS dynamics. Above a critical coupling, the resonant CBS oscillations (f/FSR = integer) are strong enough to break the pulses, while stable compressed or decompressed pulses are still obtained in finite frequency ranges between resonant frequencies: the small damped low frequency CBS vibrations contribute to lock further longitudinal cavity modes which compose the compressed SBS soliton. A stability map is computed. Compression up to a factor 0.4 with respect to the bare Brillouin soliton is numerically obtained, yielding ns pulses of peak intensity up to 14 times the cw launched pump, in fair quantitative agreement with experiments done in long fiber ring cavities.

Pulses of arbitrary temporal shape can be generated by spectrally filtering a short pulse. Frequency selective reflectors, such as fiber Bragg gratings, can be designed to obtain the desired pulse shape. The required distribution of the refractive index modulation, amplitude and phase, can be calculated using inverse scattering techniques. For weak gratings, under the Born approximation, the impulse response of the grating is directly related to the refractive index distribution. The specified refractive index can be photo-written in an optical fiber using standard phase-mask scanning techniques. Two Bragg gratings were specially designed to shape a train of gaussian pulses into antisymmetric Hermite-Gauss pulses. The first grating had a length of 40 mm producing a spectral response over 0.05 nm (peak-to-peak). This grating was interrogated by 100 ps pulses produced by a CW tunable laser with an external modulator. The second grating (L = 10 mm and ?? = 0.18 nm) was interrogated with a mode-locked fiber laser (7 ps). The pulses were characterized in the frequency and time domain. The antisymmetric pulses were propagated in standard fiber to verify the presence of the phase shift between the two lobes. These Hermite-Gauss pulses could be used to study antisymmetric dispersion-managed soliton pulses.

A new type of the double layers polycrystal dielectric film in the quartz capillary has been fabricated. The first film is composed of nanoscale germanium dioxide obtained from controlling reaction temperature, gas flow rate and the proportion of reactants, and the second film is metal layer that has high refractive index at infrared region. So the dual-layer thin film has very high reflectivity at the wavelength range of 8-11 .6 µ m. The hollow-core optical fiber with this film on inner wall can transmit over 400 watts of cw carbon dioxide laser power or the pulse carbon dioxide laser with pulse width of 0.1 second and peak-power of 1000 watts, and transmission loss is less than O.6dB/m at 10.6 µ m in transmitting high power. The transmitting laser power fibers can be applied in medical treatment, mechanical process or the relevant scientific research etc.

The formation of fibre Bragg grating dispersion?managed multisolitons depends on the presence of asymmetric terms in the transfer function of the chirped fibre gratings employed. Given this dependence on higher order terms, it seems clear that the influence of third order dispersion in the fibre link must be important. We study the tolerance of fiber Bragg grating dispersion managed multisolitons to the presence of third order dispersion in the fibre link. On the other hand, the transfer function of a fibre Bragg grating is sensible to its operating conditions, such as pressure and temperature, as well as being subject to experimental indetermination in their manufacture. We study the robustness of multisoliton solutions to the effect of pseudo?random variations in the gratings’ parameters.

In this paper we examine the dynamics of a pulse in fibers with periodic dispersion on the basis of the variational approach. Using this approach a set of two coupled differential equations for the evolution ofthe pulse width and chirp is obtained and numerically solved. We consider two different symmetric dispersion maps. The main difference is found to be on the dependence ofthe pulse energy on the map strength. It is shown that a dispersion —managed (DM) soliton can be supported in an optical fiber even when the average dispersion is in the normal regime. Our results show that the variational approach can be a useful and effective analytical method for optimization of soliton transmission systems with variable dispersion.

We consider a long fiber-optic link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM). Passage of a soliton through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the system's stepsize (cell's size) L comparable to the pulse's dispersion length ZD, SSM supports stable propagation of pulses which almost exactly coincide with fundamental solitons of the corresponding averaged NLS equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly relaxes to it, emitting some radiation. If the initial amplitude of the pulse is too small, it turns into a breather, and, below a certain threshold, it quickly decays into radiation. If L is essentially larger than ZD, the pulse rapidly rearranges itself into another one, with nearly the same area but essentially smaller energy. At L still larger, the pulse becomes unstable, with a complex system of stability windows found inside the unstable region. Moving solitons are generated by "pushing" them with a frequency shift, which makes it possible to consider collisions between solitons in a two-channel model emulating the WDM regime of data transmission in a communication line. We conclude that the collisions are strongly inelastic if they take place inside the nonlinear section of the system, and the solitons pass through each other without interaction if they collide inside the linear section.

In order to realize high data rates over long distances with already installed standard single mode fiber, techniques must be found to overcome the pulse spreading due to the positive chromatic dispersion of the transmission fiber. A dispersion compensation technique for compensating group velocity dispersion in single mode fiber over a wide span (100 nm) of wavelength is presented here by using the large negative waveguide dispersion that occurs for the LP01 mode, thereby ending up with negligible net pulse spreading. Dispersion compensation using higher order modes has been proposed earlier ,but with the limitation of periodic conversion of signal to higher order modes. Here the signal always remain in LP01 mode. Quadratic Finite Element Method (FEM) is used to analyze the propagation characteristics of light within an optical waveguide having chirp type refractive index profile. The maximum compensated dispersion Dcompmax over the wavelength range of 1 500 nm to 1600 nm is then minimized as a function of profile parameters and length ratio. This technique has the potential to eliminate chromatic dispersion over a wide bandwidth which encompasses the gain bandwidth(1530 - 1570 nm) of an erbium - doped fiber amplifier. Computer simulations show that an optimally designed dispersion compensating fiber can reduce the dispersion from 18.62 ps/ km -nm to 1 .40 ps/ km - nm when it is concatenated with the existing step index single mode fiber in a ratio of 15.3 8 : 1.

The soliton propagation and interaction characteristics in the presence of spectral filtering, linear and nonlinear gain are investigated. Using a perturbation approach, it is shown that the nonlinear gain has a significant impact on the soliton interaction when the adjacent solitons have different phases or amplitudes. In a system with purely nonlinear gain, for which arbitrary amplitude solitons can propagate, we find that the phase difference varies continuously and the solitons oscillate only slightly around their initial time separation. Concerning the quintic Ginzburg-Laudau equation and taking into account the soliton chirping, we find the existence of two types of bound states. One of them is unstable, while the other corresponds to practically stable stationary points of the dynamical system governing the interaction. These findings are in accordance with the numerical results obtained by ourselves as well as by other authors.

Numerical simulations of femtosecond soliton pulse amplification in the dispersion managed active optical fiber predict a new phenomenon in which anti Stokes "blue" soliton self-frequency shift is produced. We interpret the numerical results by the parametric interactions of positive (or negative) third-order dispersion with Raman resonances induced in dispersion managed optical fiber.

The methodology based on the quasi-soliton concept provides for a systematic way to discover an infinite number of the novel stable bright and dark soliton management regimes for the nonlinear cubic-quintic Schrödinger equation model with varying dispersion, nonlinearity and gain or absorption. Q uasi-soliton solutions for this model must be of rather general character than canonical solitons of standard nonlinear Schrödinger equation model, because the generalized model takes into account the saturation nonlinear effect and arbitrary variations of group velocity dispersion, nonlinearity and gain or absorption. Novel topological and nontopological quasi-soliton solutions for the nonlinear cubicquintic Schrödinger equation model have been discovered. It is shown that, today, the most attractive media to discover novel topological quasi-solitons are organic thin films and polymeric waveguides.

The nonlinear Bloch's theorem for the fundamental and high-order Schrödinger solitons in periodic dispersive and nonlinear structures has been proven. It is shown that bright and dark solitary nonlinear Bloch's waves exist only under certain conditions and that the parameter functions describing dispersion and nonlinearity periodic inhomogeneities cannot be chosen independently. The formation, interaction and stability of the fundamental and high-order solitary nonlinear Bloch waves have been investigated.

The third-order nonlinear optical properties of a material can be observed through optical bleaching and reverse saturation in absorption aspect, and self-focusing and self-defocusing in refraction side. Among these phenomena, optical bleaching and self-focusing phenomena have an effect of reducing the transmitted optical beam spot and might have an application to enhance the recording density of the optical storage media. In this work, third-order nonlinear optical properties of amorphous silicon (A-Si) film are investigated through open-aperture Z-scan method and near-field scanning optical microscopy (NSOM) technique. The A-Si film is deposited on the coring fusion glass and its thickness was 500nm. First, an open aperture Z-scan with He-Ne laser was used to find the imaginary characteristics of the third-order nonlinear optical susceptibility of a A-Si film. It showed a reverse saturation. Then NSOM technique is used to measure the intensity profile of the focused He-Ne laser beam. We observed a definite decrease in the beam size from 1 .45micro-m to 1 .2 micro-m as the intensity is increased from 5 kW/cm2 to 140 kW/cm2 even though A-Si has a behavior of reverse saturation. The similar self-focusing from 1.45 micro-m to 1.2 micro-m can be also observed with a film ofA-Si as thin as 100nm. Keywords: amorphous silicon film, self-focusing, z-scan, near-field scanning optical microscopy

The Lax pair for the nonlinear Schrödinger equation with varying dispersion and nonlinearity has been constructed. It is shown that Lax's pair, and consequently, the exact integrability of the system, exists only under certain conditions and that the parameter functions describing dispersion and nonlinearity inhomogeneities cannot be chosen independently. The formation, interaction and stability of dispersion managed solitons have been investigated.

For the in-situ measurement of impurities using DIAL, a high repetition rate laser system consisting of a tunable laser and a LD-pumped Nd:YAG laser is developed. With this laser, measurements of concentration of iodine and transient behavior of aerosol are studied.

A new design ofthe Faraday rotator is suggested, which can compensate partly for the depolarization that occurs in magneto-optical element because of heating associated with the absorption of laser radiation. The novel design is analytically and numerically compared with the traditional design for both a glass and crystal magneto-optical medium. It is shown that in the novel design the polarization distortions are considerably lower, enabling effective compensation of birefringence in active elements of lasers even when heat release in the Faraday rotator is great. The results obtained in our study indicate that it should be possible to construct a rotator that can provide compensation of birefringence in active elements with an accuracy 1 % at a 1 kW laser power in the rotator.

A solution of reflection parameter at splice of two regular optical waveguides with arbitrary refractive index profile based on variational method is proposed. Example of calculations for circular waveguide is represented. Applications of approximate solution been obtained by Gaussian approximation for funthmental mode of weakly guiding lightguide are mvestigated.

An analysis of typical irregularities of fiber optic transmission lines is represented. Parameters of irregularities are exammed. A model of piecewise-regular single-mode fiber optic transmission line is proposed. Algorithm of calculation of pulse distortions along line, counter and incidental fluxes and mode noise parameters is offered. Examples of calculations are represented.

We analyze the influence of the interchannel frequency separation on the transmission capacity of a soliton-based wavelength-division multiplexing (WDM) system. The input into the optical fiber is represented by a superposition of N single solitons with equal amplitudes and different frequencies. Two different cases are taken into account. In the first case, all solitons completely overlap but have different frequencies. It is found that there exists a critical frequency separation above which WDM is feasible. Furthermore, it is shown that this critical frequency increases with the number of transmission channels. In the second case, there is a time shift between the overlapping solitons in adjacent channels. It is demonstrated that this combination of time- and wavelength-division multiplexing yields the largest transmission capacity. In addition, it is discussed the case in which the interchannel frequency separation is smaller than the critical frequency. It is found that in this regime the soliton spectrum of the emerging optical field has a rich structure.

We have observed, for the first to the best of our knowledge, time 2+1 dimensional spatial solitons with an Argon-ion beam in planar cells containing an undoped nematic liquid crystal. The cells provided planar anchoring for the liquid crystal molecules, with transparent electrodes for applying an external voltage across the 75µm-thick crystal. The voltage allowed to pre-orientate the director field m the prmcipal plane contammg the lmearly polarized optical field vector thereby elimmatmg the Fréedericks threshold In this regime, powers low enough to prevent thermal effects could be employed to obtam transverse localization through a local light induced mdex mcrease, trappmg the beam into a spatial soliton Self trapping as-well-as guidance of a copolarized probe at 633nm, were demonstrated at biases of 1v with 3.9 mW powers m the green at 514nm. A beam orthogonally polarized with respect to the director tilt-plane failed to produce self localization thereby confirming the reorientational nature of the phenomenon.

Transmission and reflection of ultrashort (100 fs - 100 ps) transform-limited Gaussian light pulses through/from biharmonic Bragg grating with sinusoidally - modulated amplitude and periodically located phase shifts ? is considered theoretically using numerical simulations. The method of investigation comprises coupled-wave theory and spectral approach. The effect of input pulse duration upon the shape of transmitted and reflected pulses is examined. It is shown that 100 Ps input pulses are transmitted through biharmonic grating without distortions if centered at Bragg wavelength (inside grating passband) and are reflected from the grating without distortions if centered at wavelengths inside the stopband. The results of this study indicate that biharmonic gratings can find application for demultiplexing and multiplexing optical signals in multichannel high-bit-rate fiber communication networks with bit rates up to 10 Gbits/s per channel.