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We report on lenses that operate over the visible wavelength band from 450 nm to beyond 700 nm, and other lenses that operate over a wide region in the near-infrared from 650 nm to beyond 1000 nm. Lenses were recorded in liquid crystal polymer layers only a few micrometers thick, using laser-based photoalignment and UV photopolymerization. Waveplate lenses allowed focusing and defocusing laser beams depending on the sign of the circularity of laser beam polarization. Diffraction efficiency of recorded waveplate lenses was up to 90% and contrast ratio was up to 500:1.

Volume Bragg grating (VBG) with refractive index modulation (RIM) apodized with sinusoidal semiperiod profile is studied theoretically and experimentally. An apodized VBG of this type was fabricated with a sequential recording of two VBGs with slightly different resonant Bragg wavelengths in the same glass wafer. As a result, a moire pattern was produced with a constant average refractive index and a slow sinusoidal envelope of RIM. Modeling showed that an apodized VBG with a sinusoidal semiperiod has provided a suppression of the sidelobes in the reflection spectrum. The experimental measurements are in good agreement with the theoretical predictions. This type of VBG is suitable for high-resolution spectroscopy applications due to a significant reduction of sidelobes.

The notion of reflection strength S of a plane wave by an arbitrary non-absorbing layer is introduced, so that the intensity of reflection is R =tanh 2 S . We have shown that the total strength of reflection by a sequence of elements is expressed through particular element strengths and mutual phases between them by a simple addition rule; in particular, its possible maximum is the sum of the absolute strengths of constituents. We show that the standard Fresnel reflection may be understood in terms of variable S as a sum or difference of two separate contributions, due to an impedance step and a speed step. Strength of reflection for propagating acoustic and quantum mechanical waves is also discussed.

International audience; Recording of volume Bragg gratings (VBGs) in photo-thermo-refractive glass is limited to a maximum refractive index change about 0.002. We discuss various saturation curves and their influence on the amplitudes of recorded gratings. Special attention is given to multiplexed VBGs aimed at recording several gratings in the same volume. The best shape of the saturation curve for production of the strongest gratings is the threshold-type curve. Twophotonabsorption as a mechanism of recording also allows increasing the strength of multiplexed VBGs.

Phase masks are important optical elements that have been utilized for several decades in a large variety of applications. Recently, we demonstrated a new type of phase masks fabricated by encoding phase profiles into volume Bragg gratings, allowing these holographic elements to be used as phase masks at any wavelength capable of satisfying the Bragg condition of the hologram. Here, we present a new method of true achromatization of this type of phase masks that removes the need for angle tuning and is implemented by combining this holographic phase masks approach with a pair of surface diffraction gratings.

The teaching of optical phenomena can be enhanced through the use of analogies to the motion of a bi-freguency pendulum. In this text we target demonstrations to four groups of students and scientists: younger schoolchildren to high school seniors; 7th graders to college juniors; college juniors to final-year graduate students in physics, optics and engineering; and college seniors to research scientists. The main defference between the groups is in the level of mathematics required to make the analogy to optical phenomena. Most of the physical ideas may be understood and appreciated even in junior high school and serve as a motivation for deeper study of mathematics and science.

Dependence of phase velocity on propagation direction is shown to be decoupled from birefringence. The latter is propagation difference for two polarizations; it depends on anisotropy of impedance tensor: square root of mu / epsilon.

Chirped Bragg Grating (CBG) at tilted incidence is shown producing wavelength-dependent transverse beam stretching allowing for spectroscopy and spectral beam combining. Moire patterned CBG at normal incidence is shown producing spectral comb filter.

This study shows that a uniform reflecting volume Bragg grating (VBG) can be used as a compact monolithic stretcher of high-power picosecond laser pulses, which is important for cases in which chirped Bragg gratings with the required chirp rate are difficult to fabricate. When an incident short pulse propagates along a grating and experiences local Bragg diffraction, a chirp-free reflected stretched pulse with an almost rectangular shape is generated. The increase in the duration of the reflected pulse is approximately equal to twice the propagation time along the grating. We derive an analytic expression for the diffraction efficiency, which incorporates the incident pulse duration, grating thickness, and amplitude of the refractive index modulation, enabling selection of the optimum grating for pulse stretching. Theoretical models of the extended pulse profiles are found to be in good agreement with experimental autocorrelation measurements. We also propose a simple and reliable method to control the temporal parameters of high-power picosecond pulses using the same laser source and a VBG of variable thickness, which can simplify experiments requiring different pulse durations significantly.

We propose a monolithic large-aperture narrowband optical filter based on a moire volume Bragg grating formed by two sequentially recorded gratings with slightly different resonant wavelengths. Such recording creates a spatial modulation of refractive index with a slowly varying sinusoidal envelope. By cutting a specimen at a small angle, to a thickness of one-period of this envelope, the longitudinal envelope profile will shift from a sine profile to a cosine profile across the face of the device. The transmission peak of the filter has a tunable bandwidth while remaining at a fixed resonant wavelength by a transversal shift of incidence position. Analytical expressions for the tunable bandwidth of such a filter are calculated and experimental data from a filter operating at 1064 nm with bandwidth range 30-90 pm is demonstrated.

We present the results of photon correlation spectroscopy investigations of the influence of the confinement and interfaces on the behavior of nematic liquid crystals (NLC) filled with aerosil particles as well as dispersed in porous matrices of different pore geometry and size. The experiments show significant changes in physical properties of LC in such confinements and suggest that there is some evidence for glass-like dynamical behavior, although bulk LC do not have glassy properties. In NLC with nanoparticle network, at least two well identified decays were observed. We attribute the first decay to the director fluctuations of the bulk NLC. The second, glass-like decay, could be related to director dynamics in surface layers at aerosil - LC interface. The mode corresponding to motions of individual aerosil nanoparticles was not detected. This confirms that the aerosil particles form a network in the LC.

The process of propagation of a polarized light beam through the optical system consisting of nematic liquid crystal layer with irregular thickness and circularly oriented director and a linear polarizer has been considered. It has been shown that every state of light polarization of the incident beam has its own, unique intensity distribution after this optical system. The form of the intensity distribution does not depend on the wavelength of the incident radiation.

We demonstrate the recording of volume phase masks in the bulk of photo-thermo-refractive glass. Recording was produced by exposing the glass to UV radiation through binary amplitude masks. Depending on the profile of the amplitude mask either a binary volume phase mask or a grayscale phase mask may be produced. Volume phase masks have been used to generate Fresnel lenses, convert a Gaussian beam into higher order Hermite-Gauss and Laguerre-Gauss modes, to produce optical vortices, and to create aberration-correc ting optical components. Phase masks have been used for decades for a variety of applications, including improving the depth of field [1-3], manufacture of electronics [4], encryption [5-8], and coronagraphy [9-11]. Conventional fixed phase masks are generally produced by either sculpting the surface of a thin film such as PMMA or by r ecording it in the bulk of a photosensitive material such as DCG or lithium niobate. Active phase masks may also be produced using spatial light modulators. In either case these masks may be used effectively in low power systems as they can be designed to have nearly any phase profile. However, such elements have several drawbacks as well. Absorption in these materials prevents them from being used in high power systems, and thin film and SLM phase masks may also be damaged from mishandling or by placement in high temp erature conditions. In order to have a robust phase mask suitable for use in such systems it is therefore necessary to utilize a low-absorption substrate with the phase mask recorded in the bulk to prevent damage via mishandling. Here we present a method for recording volume phase masks (VPMs) in the bulk of photo-thermo-refractive (PTR) glass. PTR glass is a sodium-potassium-zinc-aluminum-fluorine-bromine-silicate glass doped with cerium, antimony, tin, and silver, with a region of transparency from 350 nm to 2700 nm and a damage threshold of 40 J/cm

Volume Bragg gratings have been successfully used in spectr al beam combining of high po wer fiber lasers with narrow channel separationand in four channel passive coherent beam combining of fiber lasers. Future application of beam combining with kilowatt level lasers requires a more detailed understanding of how to cool the gratings without hurting beam quality. Forced air cooling blown across both surfaces of the grating is both easy and cheap, but has been avoided in the past due to concerns of how the air density fluctuations will hurt beam quality. It is now shown that forced air cooling has no adverse effect on the M 2 parameter due to density fluctuations in the air, and can efficiently cool VBG’s such that no degradation in beam quality is seen due to thermal distortions. Volume Bragg gratings are routinely made with low absorption on the level of 10 -4 cm -1 . To model grating operation for kilowatt level lasers, absorption of the studied grating was artif icially increased by 140 times. Thus the use of 80 W fiber lasers enabled imitation of 11kW beams, and the effects of forced air cooling on the beam quality were measured. Without cooling, the M

Two schemes of the image acquisition through a multimode fiber are suggested. Both are based on the assumption that the input-to-output propagation Green function is stabilized by some or other technique. In both schemes the object is characterized by the transverse distribution of reflection pattern, and the reflected signal is to be collected by a photodetector for further computer processing. The applications for endoscopy are discussed.

Angular Selective Achromatic Diffraction Optical Grating scheme is evaluated theoretically in application for stretching of short optical pulses. Compromise between polarization-sensitivity, broadband operation and Time Delay Dispersion is discussed.

A method is proposed for experimental measurement of the correlation dimensionality of attractions in dynamic systems. This method is based on the recording of holograms in photorefractive crystals and it can operate in real time. There are no limitations on the dimensionality to be measured.

An analysis is made of the possibility of widerange tuning of a polarisation system with the properties of a quarter-wave plate. A method which can be used to tune this system to an unknown wavelength is proposed and its implementation is described.

An analysis is made of the mechanism of formation of a stationary grating in a planar photorefractive waveguide by a travelling interference pattern with the aid of an alternating electric field applied perpendicular to the waveguide layer. A theoretical calculation is reported of the distribution of the space-charge field in a transverse section of the waveguide. Finite drift lengths and trap saturation are taken into account in these calculations, which are carried out on the assumption of a weak contrast in the interference pattern.

Permanent binary phase masks with planar surfaces and high tolerance to laser radiation are recorded in the volume of photo-thermo-refractive glass using the contact copying technique and binary amplitude master masks. Conversion of a Gaussian beam to higher order modes is shown.

Manufacturing limits physical length of volume chirped Bragg gratings used for pulse stretching-compressing. We study theoretically performance of CBG composed of several pieces, demonstrating high tolerance to longitudinal chirp inhomogeneity, to phase steps.

We introduced new axially-symmetric optical beams, which are Self-Fourier-Transformed and are close to waveguide modes. Quality characteristics for those and other beam types were found: Mx2, Power-in-the-Bucket product r·θ/λ etc.

A theoretical investigation is reported of the suppression of noise waves in a thin-layer mutual conjugator. The methods of matrix and wave optics are used to show that the displacement of thin layers from the exact image planes in the direction towards a lens results in mutual phase conjugation of Gaussian beams when the self-oscillation threshold is exceeded slightly.

A double conjugator is proposed: it consists of two thin nonlinear layers with a third-order optical nonlinearity. Phase conjugation is based on the principle of conversion of phase modulation into amplitude modulation. Calculations of the threshold conditions are reported and several ways of reducing the threshold are suggested. The feasibility of using liquid crystals as thin nonlinear layers is discussed.

Beam quality is described by “bucket-f” radius, r_f, and angular radius θ_f, both encapsulating fraction f of total beam power. Dimensionless product r_f*θ_f/λ depends on f and on beam shape.

Optical losses vary with detuning from Bragg resonance due to variation of stored optical power inside grating. Additional modulation of absorption coefficient causes asymmetry in detuning dependence of losses. Experiments confirm analytic theory.

Beam quality parameter Mx2 for Gaussian and super-Gaussian beams distorted by self-phase modulation is calculated analytically. Super-Gaussian beam demonstrates more stable behavior with propagation through Kerr media in comparison with Gaussian one.

Differential equations incorporating self-diffraction have been constructed to describe the recording of a holographic grating by synchronous detection. They have been solved numerically. An experimental study was made of the effect of self-diffraction on the spatial-frequency band of a holographic grating recorded in the ferroelectric Ba2NaNb5O15 and in the sillenite Bi12SiO20. There is a satisfactory correspondence between the theoretical and experimental results. Under otherwise equal conditions, a hologram recorded in the ferroelectric has a spatial-frequency band wider than that in the sillenite.

Multiplexed Bragg grating recorded in photo-thermo-refractive glass can be efficient combiner for coherent locking of high-power lasers. Spectral properties of two-channel combiner are studied theoretically and experimentally. Multi-channel scaling of this approach is discussed.

The higher spatial harmonics of the photorefractive response have been studied theoretically and experimentally for gratings written by phase-locked detection in an alternating external field. The conditions for writing higher spatial harmonics are derived analytically. The amplitude of the second spatial harmonic has been found experimentally as a function of the spatial frequency in two Bi12TiO20 crystals.

A new type of reflective hologram with both high angular and spectral selectivity is suggested. With novel design of crossed gratings inside the volume hologram, unusual angular selectivity is achieved via coupling of four waves. Analytic solution with spectral and angular detuning from Bragg regime is derived. The compensation between these two detuning forms an interesting figure of saddle shape.

Over the last 15 years, a new photosensitive glass called photo-thermo-refractive (PTR) glass has been developed for the recording of volume holographic elements such as volume Bragg gratings. Main advantage of such elements is that they allow obtaining narrowband filters in both spectral and angular spaces [1]. However, the further decrease of the spectral bandwidth of volume Bragg gratings represents a technological issue and is thus limited to values between 50 and 100 pm depending on their central wavelength. For some applications such as LIDARS or the longitudinal mode selection of Nd:YAG lasers [2], bandwidth in the range of a few picometers or tens of picometers would be required. Hence, new technology must be developed in order to achieve ultra-narrowband selectivity. In this paper we present the fabrication of so-called Moire reflecting Bragg gratings (Moire RBG), resulting from the recording of two reflecting Bragg gratings with shifted periods (figure 1). Such structure was widely investigated in the past in germanium doped silica fibers [3]. However, due to the unavailability of bulk photosensitive materials, no experimental demonstration of Moire RBG was performed. PTR glass allows recording of high efficiency reflecting Bragg gratings in a few millimeters glass samples and losses can be kept low below 1%. Hence, PTR glass makes an ideal candidate for the recording of Moire RBG with very high transmission at resonance.

We propose narrow-band moire filter in volume Bragg grating. It can be tunable via transverse degrees of freedom absent in fibers. Filter at 1550 nm with bandwidth of 50 pm and transmission 95% was demonstrated.

We present and study solutions of the equations for counter-propagating waves coupled by Chirped Bragg Gratings (CBG). Analytic expression for amplitude and phase of reflection is found, confirming the results of numerical modeling of CBG.

Effects in composite volume Bragg gratings (VBGs) are studied theoretically and experimentally. The mathematics of reflection is formulated with a unified account of Fresnel reflections by the boundaries and of VBG reflection. We introduce the strength S of reflection by an arbitrary lossless element such that the intensity of reflection is R=tanh(2) S. We show that the ultimate maximum/minimum of reflection by a composite lossless system corresponds to addition/subtraction of relevant strengths of the sequential elements. We present a new physical interpretation of standard Fresnel reflection: strength for TE or for TM reflection is given by addition or by subtraction of two contributions. One of them is an angle-independent contribution of the impedance step, while the other is an angle-dependent contribution of the step of propagation speed. We study an assembly of two VBG mirrors with a thin immersion layer between them that constitutes a Fabry-Perot spectral filter. The transmission wavelength of the assembly depends on the phase shift between the two VBGs. Spectral resolution Deltalambda(FWHM)=25 pm at lambda=1063.4 nm is achieved with the device of small total physical thickness 2L=5.52 mm.

The one-dimensional wave equation describing propagation and reflection of waves in a layered medium is transformed into an exact first-order system for the amplitudes of coupled counter-propagating waves. Any choice of such amplitudes, out of continuous multitude of them, allows one to get an accurate numerical solution of the reflection problem. We discuss relative advantages of particular choices of amplitude. ¶ We also introduce the notion of reflection strength [math] of a plane wave by a nonabsorbing layer, which is related to the reflection intensity [math] by [math] . We show that the total reflection strength by a sequence of elements is bounded above by the sum of the constituent strengths, and bounded below by their difference. Reflection strength is discussed for propagating acoustic waves and quantum mechanical waves. We show that the standard Fresnel reflection may be understood in terms of the variable [math] as a sum or difference of two contributions, one due to a discontinuity in impedance and the other due to a speed discontinuity.

We demonstrate an optical axis grating (OAG) recorded in a nematic liquid crystal that yields a higher than 80% diffraction efficiency and over 800:1 switching contrast between diffraction orders for a laser beam of a red wavelength in a material layer only 1.5 microm thick. The grating was used for combining two laser beams with high efficiency. These observations prove the feasibility of new generation high-efficiency diffractive optical components, which are most promising for infrared and high-power applications owing to their enhanced transparency and reduced thermal effects in thin material layers.

Cholesteric liquid crystals are known to possess bandgap and exhibit strong reflection for one of two circular polarizations of light. We suggest a periodically twisted nematic liquid crystal as a medium, which possesses bandgap and exhibits strong reflection for any polarization of normally incident light. Two possible structures are considered: a sinusoidal modulation profile and a rectangular modulation profile. In both cases, the maximum bandgap of a periodically twisted structure is approximately twice as narrow as that of cholesterics. However, the polarization properties of these structures may make them more advantageous than cholesterics in a variety of applications.

Cycloidal nematic liquid crystal cells are capable of high diffraction efficiency in thin layers of materials comparable to the radiation wavelength. We demonstrate switching between diffraction orders of such grating using phase retarder.

Spectral profile of reflective Volume Bragg Gratings is studied with account of interference effects of Fresnel boundaries, partially or completely uncoated. Small boundary contributions diminish considerably transmissivity in the region designated for 100% transmission.

An analysis is made of the propagation of polarised light in an optical system which consists of a linear polariser and a liquid–crystal layer, of nonuniform thickness, of a liquid crystal in which the director of the molecules is oriented along the tangents to concentric circles. It is shown that there is a one-to-one correspondence between the polarisation of the incident light in the intensity distribution at the output from this optical system.

Recent experiments demonstrated high conversion efficiency in the process of Orientational Stimulated Scattering (OSS) in nematics. This fact makes OSS attractive for beam combining and clean-up. We consider a scheme for such application and study it by numerically modeling the process. As the process of energy transfer goes, the reverse transfer also begins. However, the region of the back-transfer moves inside the cell with constant velocity in +z direction and given sufficient time, leaves the cell. By modeling the OSS of diffracting one-dimensional beams we show the possibility to obtain a maximum 94% fidelity and 96% power transfer in a numerical experiment with 6 individual overlapping pump beamlets. This means that 90% of the total pump power may be converted into the diffraction-limited output. Remarkably, this output suffers very little cross-phase modulation.

Beam clean-up and combining using stimulated orientational scattering in nematics is considered. Dynamics of the process is studied, high conversion efficiency and stability with respect to pump fluctuations is demonstrated. Thus, we have demonstrated the possibility of beam clean-up by modeling the process of SOS in NLC. We showed that high conversion efficiency can be achieved, and that the shape and wave-front of the amplified output signal are robust with respect to amplitude and phase distortions of the input pump. We found that the process is limited in longitudinal direction due to the emerging power back-transfer from amplified signal into the pump wave. In summary, Stimulated Orientational Scattering in nematic liquid crystals promises very good prospects for beam clean-up and combining.

Spectral dispersion of a light beam by a diffraction grating is investigated in order to prove the feasibility of formation of a light 'flash' moving at an arbitrary velocity along a certain axis z. An experimental demonstration is reported of a tilt of the coherence layers relative to the constant-phase planes when light is diffracted by a grating.

A numerical experiment is used to confirm the feasibility of adiabatic energy transfer from a pump (fundamental-frequency) wave to its second harmonic. The reverse transition is also demonstrated.

Rotation of the plane of polarisation during propagation of sagittal rays in a rectilinear multimode fibre was observed experimentally. The angle of rotation was in good agreement with the results predicted on the basis of the Rytov—Vladimirskii—Berry theory.

Teaching optical phenomena with the use of analogies to the motion of bi-frequency pendulum on a rotary platform is described. Adiabatic following in liquid crystals and in quantum mechanics is visualized. Particular examples include also diffraction by an edge and Fourier properties of a step function.

We demonstrate a pair of 90-45-45 prisms from binoculars appropriately attached to serve as Fresnel rhomb, i.e. achromatic quarter-wave plate. One and two Dove prisms with metallic reflection instead of TIR can work as half-wave plate and polarization rotator, respectively; both achromatic.

Effective operation of a space control system requires extremely accurate acquisition, tracking, pointing and discrimination (ATPD) capabilities, and should provide the ability to disrupt or degrade an adversary space operations if needed. We present a laser based system concept that will offer an innovative solutions to satisfy many space control mission needs. A long-range adaptive laser tracking system (ALTS) described here will provide the required capabilities in target tracking and characterization. It is based on an approach that uses the target as one of the mirrors of the laser resonator. Then, due to specificity of laser, the parameters of its emission allow for deriving the complete information on spatial-angular position of the target, its range, velocity, and flight direction. In this paper we discuss the architecture and operational principles of the ALTS capable in performing the required ATPD function for a remote target. A double-cavity laser scheme with its resonators coupled through the phase-conjugate mirror (PCM) is at the heart of the system. Four-wave mixing mechanism is applied here to form the PCM. Such a scheme allows for automatic adaptive operation of the laser with movable mirror. Both, the results of the theoretical analysis and experimental studies of the proposed ALTS system will be presented, as well as the methods of detecting the spatial-temporal characteristics of the target (its position, range, velocity) through analysis of the received signal. In addition the perspectives of using the proposed ALTS for remote target imaging are also discussed.

Angular Selective Achromatic Diffraction Optical Grating (ASADOG) device has been implemented. Surface reflective grating had 1200 lines per mm. Two identical volume holograms were implemented using Photo-Thermo- Refractive (PTR) glass technology, with spatial frequency 1697 lines per mm. Sequential diffraction of incident light by surface grating by first volume grating and then by second one oriented at 90 degrees resulted in angular selection of incident beam, completely achromatic within the spectral range from red to blue including.