Experimental research on the multiorder acoustooptic. The graphs in each figure are indistinguishable color online n 1 diffraction probability amplitude evalution in bragg diffraction. The parameter q of klein and cook, which is a normalized measure of grating. This experiment is part of our level 2 physics laboratory. Thus, we can get sh in nonlinear raman nath diffraction directions under the assumption mentioned above.
At sound frequencies of a few megahertz and lower, raman nath theory determines light diffraction by sound if the interaction length is no longer than about 35 cm. Based on a generating function method, an analytical expression for the raman nath like diffraction. Measurement of the intensity of progressive ultrasonic. To now, each order of diffracted light in ramannath diffraction. In the linear optics, light beam propagating through a structure with periodic refractive index experiences either single order bragg diffraction, when the full vectorial phase matching pm condition is satisfied, or multiorder raman nath diffraction rnd, otherwise. The situation is shown in the figure below, where the acoustic wavevector, k, is longer than the ideal bragg wavevector, k 0. Pdf corrections to ramannath diffraction by volume holograms. Criterion for bragg and ramannath diffraction regimes. If the phase of incident fw period is sharply modulated from 0 to. Rnd is usually described as a travelling thinphasegrating diffraction 411. The graphs in each figure are indistinguishable color online n 1 diffraction probability amplitude evalution in bragg diffraction regime. In this letter, we discuss raman nath acoustooptic diffraction, and a new model of raman nath acoustooptic. Ramannath secondharmonic talbot effect in 1d pplt crystal. We present an analytic theory of the diffraction of matter waves by a lattice in the quasibragg regime, by which we mean the transition region between the longinteraction bragg and channeling regimes and the shortinteraction raman nath regime.
Multifrequency acoustooptic diffraction ieee xplore. In this work, the self diffraction kinetics in the saturation region of brfilms are simulated using selfmatched orders of raman nath diffraction. Osa modeling the selfdiffraction holographic kinetics. The raman nath regime is observed at relatively low acoustic frequencies f and a small acoustooptic interaction length l typically, f diffraction takes place at an arbitrary incidence angle of light fig. Oct 08, 2019 nonlinear raman nath diffraction fringes in the rydberg gas for a large nonlocality degree of the kerr nonlinearity. Ramannath diffraction of light by a travelling sound wave, b standing sound wave. A result shows the dependence of various scattered orders on the incident angle. Effective rabi frequency, losses, and phase shifts. In the linear case raman nath and bragg diffraction regimes are discussed. Numerical simulation of atomic diffraction in the raman nath regime. Evolution of the nonlinear ramannath diffraction from. In this case the propagation angle of the th beam satisfies the relation cos. The variations provide a phasegrating that moves with the ultrasonic velocity.
The ramannath equation for the diffracting system is derived and is shown to. Criteria for ramannath regime diffraction by phase. Raman 1 8 8 8 1 9 7 0 even as science labs run amuck with funds and sophisticated gadgetry we must not forget that the most expensive and precious piece of equipment is still the human mind. Nonlinear raman nath second harmonic generation of hybrid structured fundamental. The grating thickness does not enter rho, so the terms thin and thick are, strictly speaking, irrelevant to the question of which regime is operative. Spatial modulation of secondharmonic generation via. By studying the relations between the power of the diffracted light and its origin in the ultrasonic field, we found that the phase of the diffracted light is modulated temporally and spatially by the ultrasonic wave.
Temporal and spatial modulations of phase of diffracted. Osa lopsided ramannath diffraction in ptantisymmetric. Analysis of kapitzadirac diffraction patterns beyond the. Osa criterion for bragg and ramannath diffraction regimes. Our approach to the infinite system of equations 2 originates from the remark that it connects the seeking amplitudes with opposite parity on the left hand and right hand sides 3 of the. Bragg diffraction and nonlinear raman nath diffraction. This paper analyzes the ultrasonic modulation of coherent light in raman nath acoustooptic diffraction. Popular raman nath approximation, in which the kinetic energy. Based on a generating function method, an analytical expression for the raman nath like diffraction has been derived and compared with earlier work. Our expressions for the optical field diffracted from the acoustic wave assume there is only one diffracted order m1.
Raman nath condition governing the diffraction of the th waves on a npc. The atomic grating is constructed by the coldatomic vapor with two isotopes of rubidium, which is driven by weak probe field and spacedependent. Imaging rules under raman nath conditions are nearly the same as corresponding rules for imaging under bragg conditions. If the phase of incident fw period is sharply modulated from 0. Pdf numerical simulation of atomic diffraction in the. Acustooptic interactions, raman nath and bragg diffraction, klein cook parameter, phase delay. Diffraction of light by adjacent ultrasonic beams and by surface acoustic waves are. Us patent for ramannath diffraction grating patent patent. Diffraction of collinear correlated photon pairs by an. Periodic variations of intensity of diffraction orders in. This type of diffraction occurs at an arbitrary angle of incidence. Raman nath diffraction is observed with relatively low acoustic frequencies, typically less than 10 mhz, and with a small acoustooptic interaction length.
The holes are very closely spaced and form a transmissive optical grating, having dimensions suitable for operating in the raman nath regime. The method includes the steps of directing a first portion of a beam of coherent light at normal incidence to a reflective mirror, propogating an acoustic field within a medium to interact with the first portion of the beam, detecting signals derived from. An optical wavelength selective device is provided that is particularly useful as a demultiplexer. The calculated secondharmonic spectra represent frequency combs. Acoustooptic effect and its use in signal processing abstract 1. Usually, the parameters q 1 and q diffraction, respectively 2,3. Method and apparatus employing zero order ramannath. These are raman nath diffraction and bragg diffraction 4. A method is described for the measurement of the velocity of sound in various liquids, based on the raman nath theory of lightsound interaction. Analysis of kapitzadirac diffraction patterns beyond the raman nath regime bryce gadway, daniel pertot, ren. We study the nonlinear raman nath diffraction nrnd of femtosecond laser pulses in a 1d periodic nonlinear photonic structure.
The diffraction efficiency for the order of m 1 or 1 is maximum when the modulation index. Evolution of the nonlinear ramannath diffraction from near. Comparison shows that the presented approximation works excellent in both, raman nath and bragg regimes of interaction. Jul 01, 1993 a function of 4 variables is defined, which is the solution of the ramannath equations. This atomic grating is achieved by the spatial modulations of the atomic density and frequency detunings in the fourlevel double.
For a given orientation, if the rf frequency is slightly different from that required to match the bragg criterion, diffraction will still occur. Analysis and optimum design of a portable qswitch based on. Finally, we present a method to obtain the raman nath acoustooptic. Raman nath diffraction, optimum interaction length, ultimate diffraction efficiency 1. The schr\\odinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and. Whilst in the socalled intermediate diffraction zone, the number of diffracted photon. Corrections to raman nath diffraction by volume holograms. Pdf corrections to ramannath diffraction by volume.
The ramannath diffraction in acoustooptic effect was studied. Ramannath diffraction grating national research council. Measurement of the intensity of progressive ultrasonic waves. Atomwave diffraction between the raman nath and the bragg regime effective rabi frequency, we present an analytic theory of the diffraction of matter. In addition, the efficient thg may also take place under the condition of. The solution of these equations defines the amplitude of various diffraction orders. Analysis and optimum design of a portable qswitch based. Intensity modulation of raman nath ao modulator the diffraction efficiency for the mthorder raman nath diffraction is l x z. In this article, acoustooptic interaction in raman nath acoustooptic diffraction has been discussed. These are a system of infinite coupled differential equations used to describe the diffraction of light from acoustic waves or thick gratings, or in the theory of the free electron laser, or the interaction of radiation with multilevel systems.
The diffraction of a light beam by two orthogonal sound waves is described. A light beam is perpendicularly incident on the grating. Meanwhile the frequency shifts of the diffracted beams in bo. In the problem of the diffraction of light by a supersonic wave, at normal incidence of the light, the solution of the system of differencedifferential equations of raman and nath, for the amplitudes of the diffracted light beams, is reduced to the integration of a partial differential equation. V and a are the velocity and wavelength of the sound wave, respec.
The ideal raman nath diffraction slightly deviated when the klein cook parameter was increased from 0 to 1 for low phase delay values and for large phase delay, the characteristics of the bessel function disappeared. The firstorder self diffraction holographic kinetics in raman nath thin grating conditions on brfilm shows considerable promise for the object motion detection 2. Bragg diffraction of light by a standing sound wave. A research on light intensity for raman nath diffraction yang guijuan1, hao bin2, wang jun1, shi hua1 1.
In the raman nath approximation, the intensity of the nthorder diffraction peak can be shown to be pro portional to the square of the nthorder bessel function. The equipment used in this experiment is available in most undergraduate physics. Acoustooptic interaction in ramannath acoustooptic diffraction. Great efforts have been devoted to understanding these nonlinear diffraction processes 912, and further interest is focused on their applications in broadband shg 4,6, virtual beam generation,14, and orbital angular momentum oam modulation 15. Ramannath acoustooptical diffraction in antiferromagnet. Atomwave diffraction between the ramannath and the bragg. Analogously, in parametric processes such as second harmonic sh generation light can experience nonlinear diffraction in. Gaussian beam phase change and deflection in ramannath. The schrodinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and. We find that the frequency shifts of the diffracted light cause the periodic variation of the ultrasoundmodulated light intensity with time. Pdf analysis of kapitzadirac diffraction patterns beyond.
Diffraction of light by monofrequent ultrasound general raman nagendra nath theory 8. Pdf nonlinear ramannath diffraction of femtosecond. An analog computer program which calculates the intensity of the light scattered into the various diffraction orders has been adapted for use on a digital computer. We show that for grazing incidence, the use of a moving grating can increase the diffraction angle for raman nath diffraction, but not for bragg diffraction. Additionally, the phase shifts of the diffracted light result in the periodic variation of the ultrasoundmodulated light intensity along the. Modeling the selfdiffraction holographic kinetics in raman. Then the optimum interaction length, the suitable dimensions of the transducer, and the required index difference dominated by the ultrasonic frequency and power for achieving the ultimate efficiency are analyzed. These are raman nath diffraction and bragg diffraction. Higher value of klein cook parameter gave bragg diffraction and ideal bragg diffraction was obtained for q100.
The distribution of the energy in each diffractive order follows bessel function1. Pdf diffraction of light by acoustic waves in liquids researchgate. Nonlinear ramannath second harmonic generation of hybrid. We study kapitzadirac diffraction of a boseeinstein con. Sound velocity and diffraction intensity measurements. However, thin enough gratings will tend to operate in the raman nath regime because the index modulation must be large for a thin grating to produce appreciable diffraction. We find that for sufficiently weak pulses, the usual analytical shortpulse prediction for the raman nath regime continues to hold for longer times, albeit with a reduction of the apparent modulation depth of the standing wave.
The idea is well entrenched in the literature that thin phase gratings whether holographic or acoustically induced should exhibit ramannath behavior and thus give several diffracted waves, and that thick phase gratings should show bragg behavior one diffracted beam and that only for bragg angle incidence. The optimal acoustooptic interaction length in raman nath diffraction is investigated by using deliberately designed apparatus working with pure water. Request pdf raman nath secondharmonic talbot effect in 1d pplt crystal we demonstrate a new method to generate secondharmonic talbot effect through raman nath diffraction in 1d pplt crystal. We find that for sufficiently weak pulses, the usual analytical shortpulse prediction for the raman nath regime continues to hold for lo. Perturbations in the form of holes are etched into the slab waveguide cladding or preferably into the core of the waveguide thereby changing the effective refractive index of regions within the core. This is a demonstration of an experiment on the diffraction of light by ultrasound. Atomwave diffraction between the ramannath and the bragg regime. The diffraction pattern can contain many diffraction orders with symmetrical distribution of light. Nonlinear ramannath second harmonic generation with. We investigate raman nath diffraction corresponding to nearbragg diffraction. Raman nath diffraction is observed with relatively low acoustic frequencies, typically less than 10 mhz, and with a small acoustooptics interaction length.
The device is made from a planar slab optical waveguide material transmissive to light. Osa ramannath nonlinear diffraction in second harmonic. The grating diffracts the light beam into bragg diffraction or raman nath rn diffraction. It was also demonstrated that in case of raman nath diffraction the number of photon pairs in a selected, nth, diffraction order varies with the raman nath parameter changes as an nth order bessel function of the first kind, raised to the fourth power. Experimental demonstration of the raman nath effect. Home proceedings volume 4514 article proceedings volume 4514 article. Light diffraction by ultrasonic pulses at normal incidence is studied as well in the raman nath region low frequencies as in the bragg region high frequencies. Our formula quantitatively correctly describes both raman nath and bragg regimes of interaction, thereby merging them into one essence of diffraction process. A method and apparatus employing zero order raman nath diffraction information to visualize the longitudinal character of an acoustic field. The validity of this raman nath theory was confirmed by the experiments of sanders in 1936 ref.
Gainassisted pt antisymmetry allows us to realize lopsided raman nath diffraction with high diffraction efficiency at the exception point. Introduction the features of ramannath rn acoustooptic diffraction are with short interaction length and multiorder diffraction. In addition, different structured npcs can also be used for shaping the second harmonic sh. Ramannath equations, parametric equations, diffraction in crystals, calculation of mathieu functions. We study kapitzadirac diffraction of a boseeinstein condensate from a standing light wave for a square pulse with variable pulse length but constant pulse area. In this letter, we discuss ramannath acoustooptic diffraction, and a new model of ramannath acoustooptic.
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