Diffraction of a pulsed plane wave from an amplitude diffraction grating

Abstract

A study of diffraction of a time Gaussian-shaped pulse from an amplitude diffraction grating is presented. The changes of the spectral composition, time intensity and energy of the diffraction pattern are considered. The measurement of the spectral composition of the primary pulse with the help of a diffraction grating based on the measurement of the spatial distribution of energy of the diffraction pattern is discussed.     

Wave Mechanics Applied to Semiconductor Heterostructures

Abstract

In this work we demonstrate the appearance of a pulse crest curvature which differs from wave-front curvature in certain chirped pulse compressors within the femtosecond range. This happens because the spectrum is made to focus on a grating or a holographic optical element, and this cannot be achieved for all wavelengths. The phenomenon is analysed from the viewpoint of geometric diffraction, as a function of chromatism, and is tested by ray tracing.     

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.     

Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Diffraction Grating Characterization Using Multiple-wavelength Excitation of Surface Plasmon Polaritons

Abstract

In this work we have used the optical excitation of surface plasmon polaritons to characterize the profile of a diffraction grating with a large groove-depth-to-pitch ratio at wavelengths spanning the visible spectrum. This provides us with confirmation of the accuracy of the modelling theory used to predict the optical response of a deep grating. In addition it draws attention to a particular wavelength regime which proves sensitive to the higher harmonics of the grating profile.     

Erratum

Abstract

Results of a photon scanning tunnelling microscopy study of the plane diffraction grating with nickel stripes on a quartz substrate are reported. The ripples in the optical images with period of 600 nm have been observed when the plane of incidence of laser beam was perpendicular to the grooves of the grating. The interference patterns for the propagating modes in far field have been detected. They are supposed to be the result of Mie scattering of evanescent wave by the elements of the diffraction grating.     

Theoretical Analysis of the Lau Effect with a Sinusoidal Phase Grating

Abstract

By means of both partial coherence theory and diffraction theory, the Lau effect with a sinusoidal phase grating in a double-grating configuration is analysed. The optical intensity distribution at the observation plane is obtained. This distribution is related to the modulation of the phase grating and the separation of the two gratings. The results are somewhat different from the case of double amplitude gratings.     

Suppression of higher diffraction orders in the extreme ultraviolet with a trapezoidal nano-mirror array

ABSTRACT

Higher diffraction orders from a grating introduce harmonic contamination in ‘monochromatic’ output beams processed by grating monochromators at synchrotron radiation facilities, resulting in imprecise calibration of optical elements and detectors. Suppressing these orders can be achieved with a quasi-random nano-hole array, but its fabrication can be a significant limiting factor for implementation. Here, an advanced type of grating is demonstrated that contains a periodic array of several hundred million trapezoidal nano-mirrors with a grazing-incidence reflection geometry that suppresses higher diffraction orders. Moreover, it reduces the difficulty of fabrication to the level of a traditional grating. It has great potential for harmonic suppression in synchrotron radiation, spectral diagnostics of plasmas, and astrophysics.     

Zeroth-order complex-amplitude modulation with dielectric Fourier-type dififractive elements

Abstract

Diffraction by a lamellar grating with slowly modulated groove width and depth is considered. By mathematical design of the diffractive microstructure the zeroth diffraction order of the carrier grating may be modulated in amplitude and phase and thereby split into some specified on-axis far-zone diffraction pattern. The noise, which in diffractive optics normally appears in the immediate neighbourhood of the signal, is shifted angularly into the surroundings of the higher diffraction orders of the carrier grating. Therefore a large frame of virtually zero intensity can be formed around the original signal without brute force optimization. This is of interest in, for example, several space-invariant optical interconnection and photonic switching schemes that employ diffractive beam-splitter elements.     

Pulsed Laser Written Diffraction Gratings in Liquid Crystal Polymers

Abstract

In this work the writing of diffraction gratings in liquid crystal polymer films is studied, where the exposure mechanism is thermal and takes the material from an opaque to a transparent state. A pulsed ruby laser is used to write gratings and the evolution of diffraction is monitored using a continuous wave laser. The resulting diffraction efficiency is compared with an analytic theory for a range of laser pulse energies and grating spacings. Results from the comparison are very good, and final efficiencies of around 5% are obtained, which is near the theoretical maximum for the material used.     

Optical Transfer Function-based Merit Functions for Automatic Diffraction Grating System Design

Abstract

Two types of variable spacing diffraction grating for use with a Seya-Namioka monochromator system are optimized by two merit functions: a diffraction-based optical transfer function (OTF) and a geometrical optics-based OTF. For the optimization of the system, Powell's generalized least-squares method is adopted.     

A non-contact technique for determining the depth of zero-order gratings

Abstract

In this work we present a simple, non-contact method for characterizing the depth of deep zero-order diffraction gratings using standard visible optics. Form birefringence exhibited by zero-order structures alters the polarization state of light transmitted through them. The amount of change is dependent on several factors including the depth of the grating grooves. By recording the polarization changes of laser light transmitted through the sample we demonstrate how the depth of any grating with a known pitch may be determined. Results for many different gratings have been analysed and show good agreement with groove depths measured from scanning electron micrographs. From these results a universal relationship between the amount of polarization change and the depth of the grating grooves has been determined.     

Coherent control of symmetric and asymmetric diffraction grating via relative phase

ABSTRACT

We present a theoretical model to realize the symmetric and asymmetric diffraction grating in a four-level atomic medium. The proposed atomic medium follows a double lambda configuration where four fields interact with it. We get control over symmetric and asymmetric behavior of the diffraction grating by manipulating the relative phase of the fields. Interestingly, the symmetric and asymmetric diffraction grating become prominent when the vortex beam is used instead of the plane wave. Enhanced first, second, and third-order diffraction gratings are achieved via the vortex beam. Further, we find control over asymmetric diffraction gratings by the relative phase of the fields. Coherent control of asymmetric diffraction grating in negative and positive diffracted angles is also achieved via the relative phase.     

Optics for Neutral Atomic Beams: Reflection and Diffraction of Sodium Atoms by Evanescent Laser Light Fields

Abstract

Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.     

Pitch-modulated phase grating and its application to displacement encoder

Abstract

A binary phase grating with modulated pitch is investigated for a simple displacement encoder. The grating consists of a binary phase grating to eliminate the zeroth-order diffraction, and the pitch of the grating is modulated to compensate the higher harmonics of the encoder displacement signal. Therefore, an undistorted sinusoidal signal as a function of displacement is obtained by simply superimposing a conventional binary grating on the pitch-modulated phase gratings for any air gap between the gratings. The characteristics of the proposed gratings and the encoder signal are investigated by the Fresnel diffraction theory. The proposed grating has been fabricated lithographically, and the signal was examined experimentally. Considering these results, the proposed technique can suppress interpolation error and will be useful for an encoder in precision machining.     

High-sensitivity Diffraction-compensated Moiré Deflectometry

Abstract

The spatial resolution and angular sensitivity of conventional moiré deflectometry are known to obey a conjugate relationship reminiscent of the uncertainty principle so that one cannot be improved without deteriorating the other. This paper looks at the origin of this relationship and suggests ways by which this ‘uncertainty principle’ can be violated. It is shown that a ‘projection’ of the grating which is free from diffraction effects and which, at the same time, contains the deflection information amplified by the ‘optical lever’ distance D between the gratings can be formed if the diffracted beams of order + 1 and ? 1 are separated from other orders and are recombined in certain ways. As a result, the angular sensitivity, which depends on the ratio of the pitch d of the grating to the distance D between the two gratings, can be improved without losing the spatial resolution by multiple diffraction orders. One of the diffraction compensation schemes is experimentally illustrated. It is shown that the ‘uncertainty product’ is improved by more than two orders of magnitude.     

Fresnel Images of a Binary Diffraction Grating with Open Ratio 0·5

Abstract

Analysis of the Fresnel image of the binary-amplitude diffraction grating with open ratio 0·5 is presented. Fresnel images situated at the distance z = Nd²/8λ (N = 1,2…) from the grating which was illuminated by a plane wave were calculated and investigated by experiment. Forms of intensity distributions in the second grating plane are presented, the second grating cooperating with the self-imaging grating.     

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.     

Pd grating obtained by direct micromolding for use in high resolution optical diffraction based sensing

Pd grating patterns have been fabricated using the process of micromolding in capillary employing a Pd alkanethiolate precursor, which could be converted to metal in situ by thermolysis. Thus generated Pd grating were uniform in width (~950?nm) and spacing (~450?nm) over millimeter square areas on glass substrates. Importantly, the pattern when used as an optical grating produced a diffraction pattern with a high resolution (>2000); the intensities of widely separated (diffraction angle, ~26·8°) diffracted spots could be measured using a simple photodiode. By varying the concentration of Pd precursor (2?mM to 25?mM), thickness of the resulting gratings could be adjusted in the range of ~15?C115?nm. By adjusting the grating parameters optimally, a maximum diffraction efficiency of 36% has been achieved. Thus fabricated Pd grating was used as seed catalyst to deposit Cu by electroless plating. The Cu deposition process has also been monitored by employing AFM, SEM and EDS analysis. The diffraction efficiency values corroborate well with the changes in the grating thickness due to Cu deposition. The grating structures presented can be reproducibly fabricated for rapidly emerging optical diffraction based sensing applications. This has been demonstrated in the case of aqueous Cu^2?+? by depositing the latter electrolessly on Pd.     

Fresnel Images of a Binary Diffraction Grating with Open Ratio Less than 0·5

Abstract

An analysis of Fresnel images of the amplitude binary diffraction grating with open ratio α/d < 0·5 is presented. Particular attention is paid to images appearing behind the self-imaging grating at distances z = 0 to d ²/λ. An attempt is made at a systematic examination of Fresnel images that have the form of binary gratings with ratio α′/d′ different from that of the original grating.