Transverse Diffraction Research Articles

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.

Nonlinear Pulse Propagation and Modulation Instability in Periodic Media with and without Defects

The nonlinear propagation of EMW in periodic media is of great interest due to the possibility to accumulate energy in periodic media within the stop band and, therefore, the input intensity levels for observation of nonlinear phenomena are quite low [1]. For resonant interactions, also it is possible to realize matching conditions, which are not possible in uniform media. Both resonant multiwave interactions and selfaction of EMW in nonlinear periodic media have been analyzed [1, 2]. Also, a method based on a slow variation in time was proposed, which seems more adequate than others based on coupled equations [3]. The presence of defects in periodic structure leads to narrow regions of transmission within the stop-band. In this case, the application of coupled equations for counter propagating waves becomes doubtful, and a more general approach is needed [3]. Also, the influence of defects on the dynamics of modulation instability of long pulses is of a great interest. The present paper considers numerical simulations of the pointed above phenomena. For a correct description of the nonlinear dynamics, it is necessary also to take into account the wave dissipation and possible transverse diffraction. The results of simulations demonstrated the essential influence of defects within the periodic structure on the nonlinear propagation of EM pulses, even if the carrier frequency is chosen within the stop band of the structure with a defect. This fact can be explained by a quite wide spectrum of the input pulse, and the “tail” of such a spectrum is within the transmission region due to the defect. This situation is analogous to the nonlinear propagation of short spin-dipole waves in the vicinity of the cut-off frequency [4]. The dynamics of modulation instability also changes in the presence of the defect. The diffraction can affect essentially the modulation instability dynamics.

Analytic expression of the diffraction of a circular aperture

Recurring to the characteristic of Bessel function, we give the analytic expression of the Fresnel diffraction by a circular aperture, thus the diffractions on the propagation axis and along the boundary of the geometrical shadow are discussed conveniently. Since it is difficult to embody intuitively the physical meaning from this series expression of the Fresnel diffraction, after weighing the diffractions on the axis and along the boundary of the geometrical shadow, we propose a simple approximate expression of the circular diffraction, which is equivalent to the rigorous solution in the further propagation distance. It is important for the measurement of the parameter of the beam, such as the quantitative analysis of the relationship of the wave error and the divergence of the beam. In this paper, the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is discussed too.

Long-range self-channeling of infrared laser pulses in air: a new propagation regime without ionization

We report long-range self-channeling in air of multiterawatt femtosecond laser pulses with large negative initial chirps. The peak intensity in the light channels is at least one order of magnitude lower than required for multiphoton ionization of air molecules. A detailed comparison is made between experiments and realistic 3+1-dimensional numerical simulations. It reveals that the mechanism limiting the growth of intensity by filamentation is connected with broken revolution symmetry in the transverse diffraction plane.

Accurate modeling of high frequency microelectromechanical systems (MEMS) switches in time- and frequency-domainc

Abstract. In this contribution we present an accurate investigation of three different techniques for the modeling of complex planar circuits. The em analysis is performed by means of different electromagnetic full-wave solvers in the timedomain and in the frequency-domain. The first one is the Transmission Line Matrix (TLM) method. In the second one the TLM method is combined with the Integral Equation (IE) method. The latter is based on the Generalized Transverse Resonance Diffraction (GTRD). In order to test the methods we model different structures and compare the calculated Sparameters to measured results, with good agreement.

Periodic multiphase nonlinear diffractive optics with curved phases

We describe diffraction for rapidly oscillating, periodically modulated nonlinear waves. This phenomenon arises for example when considering long-time propagation, or through perturbation of initial oscillations. We show existence and stability of solutions to variable coefficient, nonlinear hyperbolic systems, together with 3-scale multiphase infinite-order WKB asymptotics: the fast scale is that of oscillations, the slow one describes the modulation of the envelope, which is along rays for the oscillatory components, and the intermediate one corresponds to transverse diffraction. It gives rise to nonlinear Schrodinger equations on a torus for the profiles. The main difficulty resides in the fact that the coefficients in the original equations are variable: thus, phases are nonlinear, and rays are not parallel lines. This induces variable coefficients in the integro-differential system of profile equations, which in general is not solvable. We give sufficient (and, in general, necessary) geometrical coherence conditions on the phases for the formal asymptotics to be rigorously justified. Small divisors assumptions are also needed, which are generically satisfied.

Paraxial waves in the far-field region

Summary By investigating the changes suffered by a paraxial beam propagating in the near-field and in the far-field regions, it has been found a set of wave equations valid for points gradually closer to the near field. A relevant expression for the validity of the far-field approximation is given from the paraxial Helmholtz equation. It is pointed out that the well-known Fresnel number associated with every transverse diffraction pattern can be interpreted as a magnitude that measures the relative standard deviation of the Fraunhofer pattern and a first-order field, thus reporting on an integral expression suitable for a general case. Finally, the Rayleigh range of the optical beam is deduced from the previously inferred Fresnel number, what has been applied for the cases of a spherical Gaussian beam and a uniform-illuminated circular aperture.

Measurements of angular and spatial characteristics of magnetostatic wave beams by an optical guided-wave probe

Optical measurements of the angular and spatial characteristics of magnetostatic forward volume wave (MSFVW) beams propagating both in a linear and in a non-linear regime in yttrium–iron–garnet (YIG) film have been performed. The MSFVW beams were excited by a single-element microstrip transducer, within the microwave frequency range 2–3 GHz. The measurements were conducted with the help of an optical probing technique based on the magneto-optical (MO) interaction between guided optical waves and the MSFVWs in the YIG film. The MO probing system was built on the principle of transverse Bragg diffraction geometry, allowing us to measure the spatial evolution of the partial plane waves making up the MSFVW beam. In the linear regime, the measurements of the longitudinal profiles of the partial waves have shown that the MSFVW attenuation coefficient can increase following a linear law, from 2 to 10 cm −1, as the MSFVW wave number increases from 200 to 2000 cm −1. Also, it was shown that MSFVW beams with different frequencies can be spatially separated at a small distance from the microstrip transducer (≈2 mm) by using a weak non-uniform magnetic bias field with a gradient of ≈30 Oe/cm. In the non-linear regime, there are, at least, three specific levels of the incident microwave power which correspond to different manifestations of non-linearity of the MSFVW beams. At a certain value of the power, the partial plane waves of the beam can periodically change the direction of propagation (we observed a periodic collision of these waves). A small increase of the power level can lead to a spatial-periodic energy exchange between the different groups of the partial plane waves. At high microwave powers, non-linear MSFVW can excite a discrete spectrum of new spin-wave modes, the in-plane wave number of which is less than the wave number of the MSFVW. These non-linearly excited waves exist within a small spatial region situated near the microstrip transducer.

Fabrication of high-temperature superconducting Josephson junctions on substrates patterned by focused ion beam

High aspect ratio trenches were patterned on (100) LaAlO3 substrates by focused ion-beam milling prior to film deposition. Subsequent YBCO films deposited by pulsed laser deposition were found to break naturally across these trenches. In situ Au was then deposited to connect the separated YBCO electrodes. Junctions were then patterned across the trenches to form a superconductor/normal/superconductor configuration. The resistively shunted junctions exhibited supercurrents up to 86 K. Under microwave irradiation, the junctions exhibited a number of clear Shapiro steps in the I–V characteristics. The transverse magnetic-field diffraction pattern indicted uniform current distribution across the junction.

TRANSVERSE DIFFRACTION EFFECTS OF LIGHT FIELDS ON THE GAIN WITHOUT POPULATION INVERSION

We discussed transverse diffraction effects of probe and driving fields on the gain in the model of Raman driven four level atomic system. The calculated results showed that the spectrum of the probe field has different structure compared with that in plane wave approximation due to the transverse diffraction effects of light fields, and the optimum focal position of a focus lens for the maximum gain is in the vicinity of a sample cell.

Self-focusing of chirped optical pulses in media with normal dispersion

The self-focusing of ultrashort optical pulses in a nonlinear medium with normal dispersion is examined. We demonstrate that chirping the pulse initially can strongly increase the achievable peak intensity by competing with the splitting of the pulse in the time domain. On the one hand, we apply a variational procedure to Gaussian beams, leading to a reduced system of ordinary differential equations that describe the characteristic spatiotemporal evolutions of the chirped pulse. On the other hand, when the chirp induces a temporal compression of the pulse, it is shown by means of exact analytical estimates that a transverse collapse can never occur. In the opposite situation, i.e., when the chirp forces the pulse to expand temporally while it shrinks in the transverse diffraction plane, we display numerical evidence that chirping can generate highly spiky electric fields. We further describe the splitting process that takes place near the self-focusing finite distance of propagation and discuss the question of the ultimate occurrence of a collapse-type singularity.

Stimulated Coherent Emission from Short Electron Bunches in Free Space.

The peculiarities have been studied of the stimulated emission of a sheetlike electron bunch of finite length and transverse size passing through an undulator field. A two-dimensional model, based on a nonstationary parabolic equation, has been formulated and includes the effects of slippage and optical guiding as well as transverse electromagnetic energy diffraction and dissipation. It is shown that the emission from the electron bunch is composed of short coherent pulses (superradiation pulses) which are diffracted after escaping from the channel formed by the electron bunch.

Coherent spontaneous emission from short electron bunches in free space

Abstract We study superradiance of an electron bunch which has a finite transverse size in the frame of a 2-D model. This model includes effects of optical guiding as well as transverse electromagnetic energy dissipation and diffraction. Using a nonstationary parabolic equation we describe SR of a sheet shaped electron bunch in free space. It is shown that the radiation is composed of pulses of electromagnetic radiation which are diffracted after escaping from the channel formed by the electron beam. This process is accompanied by a progressive increase of the electron efficiency. This enhancement is caused by the phenomenon of permanent self supporting resonance due to the variation of the radiation angle and frequency.

Self-focusing of optical pulses in media with normal dispersion

The self-focusing of ultra short optical pulses in a nonlinear medium with normal (i.e., negative) group-velocity dispersion is investigated. By using a combination of various techniques like virial-type arguments and self-similar transformations, we obtain strong evidence suggesting that a pulse propagating in a nonlinear medium with normal dispersion will not collapse to a singularity in the transverse diffraction plane. It is explicitly shown that the pulse spreads out along the "time-direction" and ultimately splits up. The analytical results are supported by direct numerical solutions.

Ultrashort pulsed squeezing by optical parametric amplification.

We investigate temporal effects in pulsed squeezing by parametric amplification, including effects of group-velocity dispersion. Our calculations show that the local oscillator pulse used to detect the squeezed field cannot be made shorter than the inverse phase-matching bandwidth of the generation process without degrading the amount of squeezing detected. This result generalizes an earlier result that showed that in the absence of dispersion, the local oscillator pulse duration should approach zero for optimum squeezing detection. We further show that by using local oscillator amplitude and phase pulse shaping it should be possible to achieve more than 40 dB of detectable quadrature squeezing. This is applicable where it is possible to neglect transverse spatial dimensions and diffraction, such as in a waveguide. We derive the s-parametrized quasiprobability evolution equation for the traveling-wave parametric amplifier. As the Wigner representation results in third-order derivatives, we also use the positive-P representation as an exact representation with equivalent Ito stochastic differential equations. This allows us to compare approximate --- but easily simulated --- Wigner representation results with those using the positive-P representation.

Calculation of a transverse optical mode and diffraction loss in a supercavity

In this paper, we present a simulation of the dynamic procedure of the photon storage in a practical supercavity ( R = 99.99%) pumped by a circular symmetric Gaussian beam. The Fox-Li technique has been used to numerically calculate the field distribution, the diffraction losses, and the round-trip phase shift of TEM 0 n modes. A concept of an effective Fresnel number is put forward. Details of the Fox-Li type calculation are introduced along with the discussions of the convergence in solutions of the iterative equations. The effects of the refraction index of the e-beam and the loss of Compton backscattering by the e-beam inside the cavity are discussed.

Theoretical models of ferroelectric-photonic sensors

Abstract A theoretical model of a nonlinear Fabry-Perot cavity for a Gaussian beam with transverse diffraction is used to simulate the static and dynamic response of optical multistability in ferroelectrics. The model is applied using material parameters of ceramic lead magnesium niobate, Pb(Mg03Nb06Ti0.09)O3, for its application as photonic sensors. The theoretical results are in good agreement with the experimental results.

Spatio-temporal chaos due to attractor-merging in an Ikeda-like system

We report a bifurcation series into spatio-temporal chaos in an Ikeda-like model with a transverse diffraction term. The transitions are quantitatively described by correlation functions and Lyapunov exponents. It turns out that the bifurcations are caused by spatially localized connections of separate attractor regions, thus leading to spatial coexistence and final merging of these different regions. Since this is a generalization of attractor merging in low-dimensional systems to spatially extended systems, the bifurcations display the phenomena and the scaling behaviour of intermittent transitions in low-dimensional systems. Results are discussed with respect to their relevance for nonlinear optical systems in general.

Space domain analysis of micro-IDG structures

The microstrip loaded inset dielectric waveguide has been proposed as a transmission medium alternative to microstrip, and as a useful antenna medium at X-band and millimetric frequencies. In the present analysis we consider the case where a multi-layer, multi-conductor microstrip circuit may be housed within inset dielectric waveguide. A generalised transverse resonance diffraction method is developed in the space domain for analyzing such structures. Experimental and theoretical results for the propagation characteristics of the fundamental and first higher order mode of a few different configurations are presented showing good agreement. >

Rigorous analysis of the higher order modes, impedance and attenuation factor of coupled striplines

The paper presents a rigorous and computationally efficient analysis of coupled striplines of arbitrary dimensions based on the transverse resonance diffraction (TRD) technique. The calculated higher order mode cutoff frequencies, impedance, coupling factors and attenuation factor are shown to give improved accuracy over a wide range of dimensions when compared with purely analytical and numerical approaches. The TRD results are also in excellent agreement with measured values for the higher order mode cutoff frequencies. The design parameters can be computed in a fraction of the time required for numerical based techniques such as finite elements.