Binary blazed reflection gratings

A reflection grating with a binary surface profile is presented that has high diffraction efficiency. The measured intensity for the + 1st diffracted order was 77%. The binary grating is composed of a minilattice with feature sizes comparable with the wavelength of the incident light. The overall structure is designed in such a way that it imitates a conventional blazed grating. The grating also has interesting polarization properties. The main part of the TE-polarized light is diffracted into the 1st diffracted order, and most of the TM-polarized light remains in the 0th diffracted order. The measurements of the grating are compared with rigorous diffraction theory and found to be in reasonable agreement.     

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.     

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.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Elastic light scattering from single microparticles on a femtosecond time scale

Experimentally measured and theoretically calculated elastic light-scattering spectra from single microparticles illuminated by 100-fs pulses are presented. Although in the theoretical calculation only a single incoming femtosecond laser pulse was used, the spectral behavior of scattered light shows all the features seen in the experimental spectrum from many femtosecond pulses, including morphology-dependent resonances (MDR's). The good agreement between experimental and theoretical elastic light-scattering data has stimulated a theoretical investigation of the time-dependent behavior of the elastically scattered light from a single microparticle on a femtosecond time scale. Since the spatial pulse length of the incoming laser pulse is smaller than the particle circumference, the temporal behavior of reflection, diffraction, refraction, and coupling into MDR's can be distinguished. Since the time-dependent scattering is strongly dependent on particle size, refractive index, and pulse chirp, it may be possible to encode several bits of information into a single laser pulse and therefore to increase optical data communication rates.     

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.     

Temporal superresolution: An application of frequency filtering by a grating in the resonance domain

Abstract

A diffraction grating in the resonance domain is known to exhibit significant change in diffraction efficiencies with a small change of the grating parameters. It is proposed that this property can be utilized for frequency filtering, when polychromatic light illuminates the grating. As an example, compression of a femtosecond optical pulse is numerically demonstrated with the concept of superresolution. Suppression of zeroth diffraction order by suitably optimized grating structure induces the pulse width to narrow. This scheme considerably simplifies existing optical pulse shaping systems.     

Gratings in a conical diffraction mounting for an extreme-ultraviolet time-delay-compensated monochromator

The conical diffraction mounting in which the direction of incident light belongs to a plane parallel to the direction of the grooves has the unique property of maintaining high diffraction efficiency, even in the extreme-ultraviolet (EUV) region. This property is useful for designing high-throughput time-delay-compensated monochromators for the spectral selection of ultrashort EUV pulses as the high-order harmonics generated by the interaction between an ultrashort laser pulse and a gas jet. The time compensation allows one to exploit the femtosecond scale duration of the harmonics both to have high intensity and to reach an unprecedented temporal resolution for pump and probe experiments. Because two gratings have to be used for time compensation, the high diffraction efficiency becomes an essential requirement, which can be fulfilled by the conical diffraction mounting. Measurements recently accomplished at the Bending Magnet for Emission Absorption and Reflectivity (BEAR) beam line (ELETTRA Synchrotron, Trieste, Italy) for three gratings in the 10-90 nm region are reported here that show a peak efficiency of as much as 0.7 in the first order. A model computing the electromagnetic propagation and the grating efficiency, implemented and tested with the experimental data, permits the study and design of rather complex systems operating in the conical mounting. Basic physical principles and mathematical aspects of the model are discussed here.     

Determination of longitudinal and transverse shifts of three-dimensional Gaussian beams reflected at a grating near an anomaly

Spatial displacements of three-dimensional Gaussian beams diffracted at a reflection grating are studied theoretically and numerically. The complex diffraction coefficients (amplitudes and phases) of the grating diffracted plane waves calculated by a rigorous method for conical diffraction are the basis for this investigation. The classical analytical formula for the longitudinal shift depending on the gradient of the reflection phase is generalized to the simultaneous analytical treatment of the longitudinal Goos—Hänchen like shift as well as a transverse shift. A second method uses the full integration on the whole spectrum of plane waves of the diffracted beam.     

Visual method of measuring reflection-type characteristics of holographic optical elements

A highly diverging laser beam is used to measure angular and spectral selectivities and grating vector direction for reflection-type holographic optical elements (HOE's). The intensity distribution of the beam transmitted from the HOE's reveals dark, ring-shaped patterns. Since these ring patterns are formed as a result of the beam diffracted by the HOE's, the thicknesses and the diameters of the ring patterns convey information on both the angular and the spectral selectivities of the HOE's. In addition the deviation of the ring centers relative to the center of the intensity distribution reveals the grating vector direction. Determination of values related to the ring patterns permits highly accurate measurement of HOE characteristics, such as the upper limit of the diffraction wavelength, the angular and the spectral selectivities, and the grating vector direction. This is proved experimentally.     

Estimation method for the light extraction efficiency of light-emitting elements with a rigorous grating diffraction theory

The light extraction efficiency of a light-emitting element with microstructured surface is analyzed with a rigorous grating diffraction theory. The grating theory reveals an improvement of extraction efficiency due to diffraction of light by the surface microstructure. The simulation results show that the improvement of extraction efficiency is due mainly to the reflected diffraction rather than to the transmitted diffraction. A part of total-internal-reflection light is diffracted into directions at less than the critical angle. Extraction efficiency is improved by multiple reflection and diffraction of light in a high-refractive-index layer. We propose a simple design method for an efficient surface microstructure from the viewpoint of reflected diffraction.     

Non-uniform Transient Gratings Induced by Laser Pulses in Nonlinear Media

The excitation of transient gratings induced by the interference of two equal parts of a short laser pulse in nonlinear media with one- or two-photon absorption is considered. The pulse-induced grating displays completely the pulse self-interference pattern; it is not periodic but has the form of a spatially non-uniform permittivity stratification. The grating amplitudes are described by pulse correlation functions. They contain information on the pulse shape and are sensitive to its phase modulation. The diffraction efficiency of the induced grating is calculated using electrodynamic perturbation theory. It is shown that the measurement of the spectral or angular distribution of the diffracted probe light enables the grating amplitude to be computed. The correlation functions of individual pulses can be determined in this way. Some applications of the pulse-induced gratings are proposed, as is a simplified technique for measuring the pulse width. The practicability of the grating in real nonlinear media is estimated.     

Optical grating diffraction method: from strain microscope to strain gauge

The grating diffraction method for direct strain measurement is reviewed. Two systems which use this method are presented. The first system is a compact strain microscope. A Leitz optical transmitting microscope with white light source is reconstructed by developing a loading and recording system. Gratings with median density of between 40 and 200 lines/mm are used. With the help of a Bertrand lens, the Fourier spectrum of the grating is formed with high image quality on the CCD sensor plane. Software is developed to precisely, quickly and automatically determine the diffraction spot centroids. The second system is a new strain sensor based on a high-frequency grating and two Position Sensor Detectors (PSDs). The grating, attached to the surface of the specimen, is illuminated by a focused laser beam, generally with a frequency of 1,200 lines/mm. The centroids of diffracted beam spots from the grating are automatically determined using two PSD sensors connected to a personal computer. The shift of diffracted beam spots due to specimen deformation is detected. Strain sensitivity of one micro-strain can be obtained, as can a 0.4 mm spatial resolution for strain measurement. The system can be used for both static and dynamic tests.     

Ultrafast coherent population transfer with a train of weak femtosecond pulse pairs

We investigate ultrafast coherent population transfer in a Λ-type three-level system driven by a train of weak phase-locked pump-Stokes femtosecond pulse pairs, where the pump and Stokes pulses in each pair are applied in counterintuitive order, similar to that in the stimulated Raman adiabatic passage technique. It is shown that due to temporal constructive quantum interference and the subsequent coherent accumulation, complete population transfer can be achieved by a few pulse pairs with suitable interpair and intrapair time delays even if a single pair of pulses in the train is so weak that nearly no population transfer can take place. The method is efficient and robust to moderate variations in the interpair and intrapair time delays, number of pulse pairs, and laser intensity, which is particularly favorable to coherent population transfer in quantum systems with weak oscillator strengths.     

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.     

Finite size compression gratings in a large aperture chirped pulse amplification laser system

A simple model is presented to calculate the effects of the finite size of the diffraction gratings in the compressor of a chirped pulse amplification laser system. A wavelength-dependent clipping at the second grating alters the spectral distribution of the compressed pulses, affecting their time domain as well as their spatial distribution in the focal plane. Laser parameters of paramount importance to laser/plasma interaction experiments such as peak intensity, pulse duration, and prepulse levels are affected by the compressor design. Calculations of the effect of spectral clipping on these parameters for Gaussian, sech(2), and top-hat input spectra are discussed, and the benefit of double-pass compared with single-pass compression is also investigated. As an example, with 300-mm gratings and single-pass compression, for a sech(2) spectrum the pulse length of a 400-fs pulse increases to 459 fs, the peak intensity decreases by 25%, and the focal spot size increases by 8% because of the finite size of the gratings.     

Grazing Diffraction by Volume Phase Gratings

Light diffraction by a volume phase grating with slanted fringes is considered. An analytical solution of the system of second-order coupled wave equations is obtained and applied to the problems of grazing diffraction by a transmission grating. It is shown that a strong backward diffracted wave arises, demonstrating that the grating can behave simultaneously as a transmission and a reflection grating. The diffraction efficiency balance and angular selectivity are analysed.     

Fabrication of switchable liquid crystal devices using surface relief gratings in photopolymer

Holographically recorded surface relief gratings in dry, self-developing acrylamide based photopolymer were used to fabricate two types of switchable liquid crystal (LC) device. One is an electrically switchable LC diffraction grating and the other is an electrically switchable polarization rotator. The electrically switchable diffraction grating was characterized by measuring the dependence of the intensity in the first diffracted order on the applied electric field. The polarization rotator was characterized by studying the influence of the applied electric field on the twist angle and the variation of intensity in the zero and the first orders of diffraction.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

Simple three-dimensional laser angle sensor for three-dimensional small-angle measurement

A simple three-dimensional (3D) laser angle sensor for 3D measurement of small angles based on the diffraction theorem and on ray optics analysis is presented. The possibility of using position-sensitive detectors and a reflective diffraction grating to develop a 3D angle sensor was investigated and a prototype 3D laser angle sensor was designed and built. The system is composed of a laser diode, two position-sensitive detectors, and a reflective diffraction grating. The diffraction grating, mounted upon the rotational center of a 3D rotational stage, divides an incident laser beam into several diffracted rays, and two position-sensitive detectors are set up for detecting the positions of +/-1st-order diffracted rays. According to the optical path relationship between the three angular motions and the output coordinates of the two position-sensitive detectors, the 3D angles can be obtained through kinematic analysis. The experimental results show the feasibility of the proposed 3D laser angular sensor. Use of this system as an instrument for high-resolution measurement of small-angle rotation is proposed.