Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

Varied line spacing plane holographic grating recorded by using uniform line spacing plane gratings

Uniform line spacing plane gratings are introduced into a recording system to generate aspherical wavefronts for recording varied line spacing plane holographic gratings. Analytical expressions of groove parameters are derived to the fourth order. A ray-tracing validation algorithm is provided based on Fermat's principle and a local search method. The recording parameters are optimized to record a varied line spacing plane holographic grating with the aid of derived analytical expressions. A design example demonstrates the exactness of the analytical expressions and the superiority of recording optics with auxiliary gratings.     

Dispersion control with use of long-period fiber gratings

Chirped long-period fiber gratings are analyzed for management of dispersion in optical fiber communications systems. A ray model is used to derive simple analytic expressions that describe the transmission, chromatic delay, and dispersion properties of chirped long-period fiber gratings. A numerical model based on coupled-mode theory is used to verify the accuracy of the analytic expressions and explore design issues of the chirped long-period grating. With certain reasonable restrictions, chirped long-period gratings are found to be a viable and desirable alternative to existing dispersion compensation techniques.     

Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses

The extraction of the spectrum corresponding to a single extreme-ultraviolet ultrashort pulse embedded in an extended spectrum may alter the duration of the pulse itself. This is due to the spectral filtering of optics and the differences in the optical path of the rays caused by ordinary diffraction when a grating is used. The basic mechanism that leads to the latter effect is the difference of one wavelength of the path length of two rays diffracted at the first order by nearby grating grooves. A study of these effects and some possible solutions obtained from using a pair of diffraction gratings is presented. The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.     

Characterization of chromatic dispersion and polarizationsensitivity in fiber gratings

Fiber gratings have already become key passive components in fiber optic communication systems. We have characterized gratings used in reflection for dispersion compensation and long period gratings used in transmission for gain flattening using a low-loss, low-noise experimental setup having a picometer optical wavelength resolution. Our measurements include reflection or transmission response, group delay and polarization dependent loss. We have scanned the spectrum of our devices using a very narrow linewidth tunable laser. A network analyzer is used for the chromatic dispersion measurements. Time delays corresponding to the design values have been measured within the useful bandwidth of the gratings for dispersion compensation and the devices have been found to have reasonably small ripples that increase in magnitude toward the shorter wavelength range. The long period gratings for gain flattening have very small group delays. Polarization dependent loss has been measured for the first time in these devices. A polarization analyzer was used and Jones matrix analysis was applied to obtain the measurements. The gratings for dispersion compensation have small a polarization dependent loss within their useful bandwidth, while the long period gratings exhibit higher values and a stronger wavelength dependency in the polarization dependent loss     

Screw Dislocations in Light Wavefronts

Abstract

We discuss screw dislocations of a phase surface as the one type of wavefront of a monochromatic wave. The simple method for construction of the optical wavefronts with an isolated screw dislocation is reported. Laser beams with the dislocations of different orders were experimentally achieved by using diffraction on computer-synthesized gratings.     

Compensation of third-order dispersion in a 100 Gb/s single channel system with in-line fibre Bragg gratings

This paper presents a scheme to enhance the performance of an ultrahigh capacity (100?Gb/s) long haul transmission system that makes use of chirped fibre Bragg gratings (FBG) for dispersion slope compensation. It is shown that the FBG effectively compensate the dispersion slope while at the same time providing appropriate in-line filtering. The penalty to the system performance due to unwanted group delay ripple is also discussed.     

Mirror-based double diffraction grating system for coherence generation: additional study of periodicity error

The Lau effect consists of generating spatial coherence by using an extended light source that illuminates a double diffraction grating system. The price of this coherence generation is a huge energy loss caused by the successive amplitude gratings, which are blocking elements. To significantly reduce the energy loss, our approach consists in using a longitudinal mirror system to collect the light rays initially blocked by the gratings of the Lau set-up. This technique offers high power efficiency and can be straightforwardly extended to provide Talbot array illuminators. The impact of periodicity error is studied and illustrations are given at the end.     

Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks

The most technological way of recording blazed concave holographic gratings is by using the direct- and back-reflected beams. Usually plano-concave blanks are used for diffraction grating fabrication. To compensate the refraction at the plane back surface of the blank, one has to use additional elements or two-step recording mountings. Another solution is to use diffraction grating blanks having zero optical power. A number of gratings with different groove frequencies have been fabricated using concave—convex blanks. The theoretical investigation of the aberration properties of the recording mountings, and the experimental study of the grating properties are discussed. Using the CODE V program it is shown that a significant reduction in the aberration size of the virtual recording source can be achieved by optimization of the radius of curvature of the blank back surface. The experimental results confirm the possibility of achieving gratings that can be used in flat-field spectrometers with a limit of resolution of about 2–3 nm even in the case where an aberrated virtual recording source is used.     

Generalized Raytracing and Applications

The paper deals with an enlargement of the common raytracing algorithm. It allows a simultaneous handling of all rays in an infinitesimal neighbourhood of a given ray. The method can be used for calculating the astigmatic foci of wavefronts and for direct computation of derivatives of transverse ray aberrations and wave aberrations with respect to parameters of the system. The formulae are sufficiently general to handle optical systems without rotational symmetry and with aspheric lenses and mirrors.     

Diffraction and Interference of Partially Coherent Light Traversing Two Superposed Sound Fields

The diffraction and interference of a light wave passing through two superposed sound waves have been studied theoretically on the basis of Huygens' principle. As a result of frequency shifts in every deflected light ray caused by the sound waves, the instantaneous intensity resulting from linear superposition of the deflected light rays consists of the d.c. component as well as the a.c. component as a sum of beating signals among those rays, provided that the coherence time of the light is long enough compared with the period of a beating signal under consideration. A general formula for diffraction is derived and two-beam interference is considered as a special case. The resultant formula illustrates that the complex degree of coherence is modulated, after traversing the sound field, with a form of the Bessel function of zeroth-order which varies with Raman-Nath parameters as well as with the separation of two points on the wavefront of the light. This validity will hold so long as the inclination factors for the deflected light rays in Huygens' principle are regarded to be nearly equivalent. The results for progressive and standing sound waves are described as special cases.     

Quasi-achromatic laser Doppler anemometry systems based on a diffractive beam splitter

We propose a new beam-splitter system that makes it possible to use nonstabilized laser diodes for laser Doppler anemometry (LDA) systems by making the system wavelength independent. The beam splitter consists of two linear diffraction gratings that produce two parallel beams with a beam spacing that is wavelength dependent. This ensures passive wavelength compensation for the fringe spacing in the measurement volume. One can choose the distance between the two parallel beams by changing the distance between the two gratings, whereas the distance to the measurement volume can be designed by choice of a condensing lens with the proper focal length. This means that the system can be designed to have a desired fringe spacing in the measurement volume. The gratings are implemented as surface-relief holograms in photoresist, which makes it possible to mass produce the beam-splitter system at low cost through replication of the structure. The method for passive wavelength compensation for the fringe spacing is demonstrated both theoretically and experimentally.     

Tuning of external-cavity semiconductor lasers with chirped diffraction gratings

We present a novel scheme of tunable semiconductor laser based on the use of a chirped grating in an external cavity. The chirped grating is fabricated using a simple holographic technique: two Gaussian beams having wavefronts with different radii of curvature are brought to interfere on a photoresist layer. The tuning properties of chirped gratings have been investigated with semiconductor lasers operated with an external cavity. With this type of grating positioned in Littrow configuration, the wavelength selection can be done by translating the grating without any need to rotate it. This cavity configuration provides a tunable output beam with an angle of propagation that is independent of the wavelength. The translation of chirped gratings was shown to tune a visible diode laser and an infrared diode laser over the same spectral band as the conventional tuning scheme where an unchirped grating is rotated.     

Phase mapping and wavefront analysis based on multi-illumination light fields generated by a spatial light modulator

We present a new multi-illumination technique for the determination of the phase maps of unknown phase objects and wavefronts based on their diffraction patterns. A spatial light modulator is used to generate a sequence of probe-light fields that illuminate the unknown object producing different diffraction patterns. Compared with similar diffraction-pattern-based approaches, our technique benefits from a motionless multiview operation and a significantly improved deconvolution algorithm convergence speed (tens of iterations versus hundreds). Computer simulations indicate that the extra information brought by the different diffraction patterns prevents convergence of the phase retrieval algorithm to spurious local minima solutions and results in faster convergence. We describe an experimental system built based on our approach using readily available, relatively low-cost components. Successful reconstructions of test targets from experimental diffraction patterns confirm the feasibility of the technique. Major sources of error are identified, solutions to these problems suggested, and potential extensions to multiresolution analysis of unknown wavefronts are proposed.     

Generalized Bragg selectivity in volume holography

The diffraction efficiency of holographically recorded volume gratings was extensively studied, and it can be accurately predicted as long as the recording wave fronts are simple. The derivation of the diffraction efficiency when complicated wavefronts or images are involved is much more tedious and less explored. In this work we derive operator expressions that can be used to analyze these processes regardless of the shape of the wavefront and the nature of the optical systems through which they propagate. The compact expressions derived are directly applicable to the analysis of volume holographic processes, and the deterioration of the holographic reconstruction quality is derived as a function of the deviations from the recording parameters. The generalized results obtained reduce to the conventional Bragg effect for plane wave recording and reconstruction. Previously unexplored phenomena are discussed and demonstrated through some simple, and practically useful paradigms, including hologram recording and reconstruction in the Fresnel, Fourier transform, and image plane regions, as well as recording with plane and spherical waves. Some prior experimental results are also interpreted mathematically. In subsequent publications the analysis will be explored further to facilitate its application to more complicated architectures.     

Diffractive Optics From Self-Assembled DNA

An algorithm is presented for assembling tiles into a variable spaced grating, the one-dimensional analog of a Fresnel zone plate. The algorithm supports multi-level gratings. The x-ray properties of such a grating, assumed to be constructed from DNA are estimated, leading to the conclusion that thick structures may be useful for intermediate energy x rays, but that thin structures for soft x rays are best used as disposable masks. The diffraction of cold, coherent atoms is a plausible application for single layer stencils.     

Ray tracing and scalar diffraction calculations of wavefronts,caustics and complex amplitudes in optical systems

The procedures for precise calculation of wavefronts, caustics and complex amplitudes in optical systems are developed. Numerical methods are compared with analytical formulae for caustics. The conditions for the validity of the integration on wavefronts for obtaining the complex amplitudes (and hence intensities defining the PSFs) within scalar diffraction theory are discussed in detail. To illustrate the precision of the results obtained with the developed techniques, an experiment showing quite unexpected results is studied and explained in detail.     

啁啾FBG和DCF对16×10Gb/s系统进行色散补偿的性能研究

对负色散光纤法和啁啾光纤光栅法实现色散补偿的两种方案进行了模拟研究 ,结论是 :(1 )对各信道完全色散补偿的前提下 ,入纤光功率较小时 ,啁啾光纤光栅色散补偿系统误码性能较好 ;入纤光功率较高时 ,用负色散补偿光纤进行色散补偿效果更好 ;(2 )适当的欠补偿比完全补偿效果好 ,入纤光功率一定时 ,用啁啾光纤光栅比用负色散补偿光纤进行欠补偿的效果好     

Beam separator for high-order harmonic radiation in the 3-10 nm spectral region

We present the scheme of a beam separator for ultrashort high-order harmonic radiation below 10 nm. The system consists of a collimating mirror and two plane grazing-incidence gratings in compensated configuration. The first grating acts as the beam separator: it diffracts the extreme ultraviolet (XUV) light into the first order while reflecting the fundamental laser beam into the zero order. The diffracted light goes to a second grating that compensates both for the spectral dispersion and for the temporal broadening of the XUV ultrashort pulse caused by the diffraction at the first grating. The system can be designed for any wavelength in the 3-40 nm region. Since the gratings are operated at extreme grazing incidence, the area of the optical surface illuminated by the fundamental laser pulse is large, and therefore there is no risk of damage of the optical surfaces. The effects on the phase of the ultrashort pulse for narrowband applications are discussed.     

Development of multilayer laminar-type diffraction gratings to achieve high diffraction efficiencies in the 1-8 keV energy region

W/C and Co/SiO(2) multilayer gratings have been fabricated by depositing a multilayer coating on the surface of laminar-type holographic master gratings. The diffraction efficiency was measured by reflectometers in the energy region of 0.6-8.0 keV at synchrotron radiation facilities as well as with an x-ray diffractometer at 8.05 keV. The Co/SiO(2) and W/C multilayer gratings showed peak diffraction efficiencies of 0.47 and 0.38 at 6.0 and 8.0 keV, respectively. To our knowledge, the peak efficiency of the W/C multilayer grating is the highest measured with hard x rays. The diffraction efficiency of the Co/SiO(2) multilayer gratings was higher than that of the W/C multilayer grating in the energy range of 2.5-6.0 keV. However, it decreased significantly in the energy above the K absorption edge of Co (7.71 keV). For the Co/SiO(2) multilayer grating, the measured diffraction efficiencies agreed with the calculated curves assuming a rms roughness of approximately 1 nm.