Non-paraxial Region Research Articles

Non-paraxial region adaptive aberration compensation using the phase transfer function.

The optical transfer function is crucial for imaging system design and characterization. However, practical optical systems often deviate from linear spatial invariance due to aberrations and field-of-view considerations, posing challenges for optical transfer function characterization and aberration compensation in non-paraxial region imaging. Partitioning the field-of-view into isoplanatic regions and measuring the optical transfer function for each region is a potential solution, but practical implementation is hindered by the lack of field-of-view information. This Letter introduces a compensation method for the phase modulation function based on spatial frequency domain division, specifically tailored for scenarios where high imaging quality is not essential. The proposed method addresses the challenge by filling the phase transfer function in an annular form corresponding to aberrations in different isoplanatic regions, offers a valuable solution for adaptive aberration compensation in non-paraxial region imaging, and presents a practical illustration of its effectiveness.

Slit Diffraction Spectrum Manipulation in Non-Paraxial Regions via the Spatial-Spectral Correspondence Relationship

In the past, a two-dimensional aperture diffraction of light in the non-paraxial region could only be studied using the Huygens integral without functional forms. This work presents a special case—a one dimension slit where the functional form can be obtained. The monochromatic light intensity distributions are investigated in detail. Using the correspondence relationship, the diffracted spectra of polychromatic light in that region can be readily found. Three interesting spectral effects are described: spectral switches, multi-level data transmission, and optical wavelength ruler. Since the functional form is derived without approximation, it is applicable to a region very near to the slit, including the wavelength region or even sub-wavelength scale. Thus, for light with micron-order wavelength (visible to near infrared (NIR) band), these results are valuable to micro- or nano-optics, especially for studies of the spatial intensities or spectral characteristics in the non-paraxial region.

Relativistic longitudinal self-compression of ultra-intense Gaussian laser pulses in magnetized plasma

AbstractThis article presents a preliminary study of the longitudinal self-compression of ultra-intense Gaussian laser pulse in a magnetized plasma, when relativistic nonlinearity is active. This study has been carried out in 1D geometry under a nonlinear Schrodinger equation and higher-order paraxial (nonparaxial) approximation. The nonlinear differential equations for self-compression and self-focusing have been derived and solved by the analytical and numerical methods. The dielectric function and the eikonal have been expanded up to the fourth power of r (radial distance). The effect of initial parameters, namely incident laser intensity, magnetic field, and initial pulse duration on the compression of a relativistic Gaussian laser pulse have been explored. The results are compared with paraxial-ray approximation. It is found that the compression of pulse and pulse intensity of the compressed pulse is significantly enhanced in the nonparaxial region. It is observed that the compression of the high-intensity laser pulse depends on the intensity of laser beam (a0), magnetic field (ωc), and initial pulse width (τ0). The preliminary results show that the pulse is more compressed by increasing the values of a0, ωc, and τ0.

Self‐focusing of a cosh‐Gaussian laser beam in magnetized plasma under relativistic‐ponderomotive regime

The combined effect of relativistic and ponderomotive nonlinearities on the self‐focusing of an intense cosh‐Gaussian laser beam (CGLB) in magnetized plasma have been investigated. Higher‐order paraxial‐ray approximation has been used to set up the self‐focusing equations, where higher‐order terms in the expansion of the dielectric function and the eikonal are taken into account. The effects of various lasers and plasma parameters viz. laser intensity (a0), decentred parameter (b), and magnetic field (ωc) on the self‐focusing of CGLB have been explored. The results are compared with the Gaussian profile of laser beams and relativistic nonlinearity. Self‐focusing can be enhanced by optimizing and selecting the appropriate laser‐plasma parameters. It is observed that the focusing of CGLB is fast in a nonparaxial region in comparison with that of a Gaussian laser beam and in a paraxial region in magnetized plasma. In addition, strong self‐focusing of CGLB is observed at higher values of a0, b, and ωc. Numerical results show that CGLB can produce ultrahigh laser irradiance over distances much greater than the Rayleigh length, which can be used for various applications.

Three-dimensional collimated self-accelerating beam through acoustic metascreen.

We report the generation of three-dimensional acoustic collimated self-accelerating beam in non-paraxial region with sourceless metascreen. Acoustic metascreen with deep subwavelength spatial resolution, composed of hybrid structures combining four Helmholtz resonators and a straight pipe, transmitting sound efficiently and shifting fully the local phase is evidenced. With an extra phase profile provided by the metascreen, the transmitted sound can be tuned to propagate along arbitrary caustic curvatures to form a focused spot. Due to the caustic nature, the formed beam possesses the capacities of bypassing obstacles and holding the self-healing feature, paving then a new way for wave manipulations and indicating various potential applications, especially in the fields of ultrasonic imaging, diagnosis and treatment.

Metascreen-based acoustic passive phased array with sub-wavelength resolution

A phased source array is an array consisting of elementary sources with proper relative phases to steer a wavefront, so as to form desired wave fields of specific property and applications. However, the phased array requires a large number of sources in forming complex wavefront or non-paraxial wave beams, leading to high cost and complexity in the electronics required to operate individual sources of the active array. A passive metascreen is presented here to transmit sound energy from a single source and steer the transmitted wavefront to form desired fields. The metascreen plays a role like a phased array but with a passive way that avoids the complexity of an active array. The screen has a half-wavelength thickness and composes of a series of elements with a dimension of one-tenth of the sound wavelength along the screen. The elements have a hybrid structure designed for high transmission and full range of phase shift. The performance of the screen is numerically simulated and experimentally demonstrated to generate a self-bending beam in non-paraxial region. The screen with its simple configuration and extreme acoustic performance could have applications for sound field shaping in numerous areas where the conventional array would have complexity and limited capability.

Higher-order paraxial theory of the propagation of ring rippled laser beam in plasma: Relativistic ponderomotive regime

This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled laser beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate.

Effects of relativistic and ponderomotive nonlinearties on the beat wave generation of electron plasma wave and particle acceleration in non-paraxial region

In this communication, the combined effect of relativistic and ponderomotive nonlinearities on the generation of electron plasma wave by cross focusing of two intense laser beams at difference frequency (Δω ≈ ω1 − ω2 ≈ ωp) and acceleration of electrons in laser produced homogeneous plasma is analysed in the non-paraxial region. On account of these nonlinearities, two laser beams affect the dynamics of each other, and cross focusing takes place. It is observed that the focusing of laser beams becomes fast in the non-paraxial region by expanding the eikonal and other relevant quantities up to the fourth power of the radial distance (r). Modified coupled equations for the beam width of laser beams, electric field amplitude of the excited electron plasma wave and energy gain at beat wave frequency are derived, when relativistic and ponderomotive nonlinearities are operative. These coupled equations are solved analytically and numerically to study the cross focusing of two intense laser beams in plasma and its effect on the variation of the amplitude of the electron plasma wave and energy gain. It is observed from the results that both nonlinearities significantly affect the amplitude of plasma wave excitation and particle acceleration in the non-paraxial region in comparison to the paraxial region.

Simulation and analysis of nonlinear self-focusing phenomenon based on ray-tracing

The simulation of nonlinear self-focusing phenomenon using ray-tracing method can macroscopically provide an intuitive picture of the propagation of light in a self-focusing material, without adopting paraxial approximation or self-similar hypothesis. In this paper, propagation of light is sampled by discrete slices along a certain direction. Thus nonlinear propagation is turned into the combination of optical modulation of the refractive index on separate slices and linear propagation between each two adjacent slices. On each slice, after calculating the flux, we use a novel algorithm to suppress the quantized errors. For the linear propagating process, Adams method is adopted to solve the ray equations, which solve the problem that the widely used Runge-Kutta method cannot be used in simulation of light in nonlinear materials. The simulation results reveal that there are several foci along the propagating axis and the location of the first focus becomes closer to the incident plane as the power of light goes up. Furthermore, because the program traces real rays, it is possible to reach the non-paraxial region and reveal the phenomenon of ring-structure flux distributions caused by self-focusing. This is significant for the safety of high-power laser systems. Some commercial optical design and simulation software are also based on ray-tracing methods. Thus the systems including both nonlinear and linear materials are possible to simulate, which can guide people to set up the corresponding experimental systems.

Relativistic Filamentation of Intense Laser Beam in Inhomogeneous Plasma

In the paper, relativistic filamentation of intense laser beam in inhomogeneous plasma is investigated based on the nonparaxial region theory. The results show that, relativistic nonlinearity plays a main role in beam filamentation, and plasma inhomogeneity further reinforces the beam filamentation. The combination effects of relativistic nonlinearity and plasma inhomogeneity can generate particularly intense and short pulse laser. However, plasma inhomogeneity leads to obvious filamentation instability.

Generalised radiant emittance in the phase-space representation of planar sources in any state of spatial coherence

The physical meaning of the generalised radiant emittance is not trivial. Indeed, its energy values should describe the local emission properties of planar sources in any state of spatial coherence, but they can take on positive and negative values mainly within the non-paraxial region. The recent phase-space modelling of optical fields in terms of radiant and virtual layers of point sources is used as framework for analysing the nature of the generalised radiant emittance in order to give more insight on its physical meaning.

The splitted beam profile of laser beam in the interaction of intense lasers with overdense plasmas

AbstractIn this paper, the interaction of intense lasers with overdense plasmas is investigated. Based on the modified nonlinear wave equation describing the interaction of intense laser and overdense plasmas in nonparaxial region, due to the influence of off-axis components a2 and a4 in nonparaxial region, we first find the three-splitted laser beam intensity profile, besides, discuss detailed the forming mathematic and some possible physical conditions of the single highly self-focusing beam profile, two-splitted beam, and three-splitted beam profile. In addition, we also investigate the influence of the parameters βE02 and ρ2 on splitted beam profiles.

Filamentation of laser beams and excitation of ion acoustic wave in non-paraxial region

This paper contains the work on the filamentation of a laser beam and its effect on excitation of ion acoustic waves in a hot collision less plasma in non-paraxial region. To consider the non-paraxial region, the amplitude and the eikonal part of the beams are expended in terms of r2 and r4. On account of the non-uniform intensity distribution along the wave front of the laser beam, the ponderomotive force becomes finite. This leads to modification of the plasma density profile in the plane transverse to the beam axis and hence also the modification in the propagation characteristics of the waves propagating in the plasma. It is shown that the Filamentation of the waves can occur and this considerably affects the ion acoustic wave.

Effect of ultrarelativistic laser beam filamentation on third harmonic spectrum

This paper investigates the generation of plasma wave and third harmonic generation in a hot collision less plasma by an intense laser beam. On the account of the V→×B→ force, a plasma wave at 2ω0 (here ω0 is the pump laser frequency) is generated. The solution of the pump laser beam has been obtained within the nonparaxial ray approximation. Filamentary structures of the laser beam are observed due to relativistic nonlinearity. By expanding the eikonal and the other relevant quantities up to the fourth power of r it is observed that the focusing of the laser beams become fast in the nonparaxial region. Interaction of the plasma wave with the incident laser beam generates the third harmonics. The mechanism of the plasma wave, third harmonic generation, and the parameters, which govern the third harmonic yield and hence the spectrum of third harmonics, have been studied in detail. Correlation of the third harmonic spectrum with the filamentation has been pointed out. Therefore, the broadening of the third harmonic spectra can be used as a diagnostic tool to study the presence of the filamentation of laser beams in laser plasma experiments.

Nonparaxial theory of cross-focusing of two laser beams and its effects on plasma wave excitation and particle acceleration: Relativistic case

Cross-focusing of two propagating ultrahigh power laser beams in homogeneous plasma (laser intensity IL>016W∕cm2) has been studied in the nonparaxial region. By expanding the eikonal and other relevant quantities up to the fourth power of r (radial distance), we observed that the focusing of the laser beams becomes fast in the nonparaxial region. The difference in focusing/defocusing of the axial and off-axial rays leads to the formation of a splitted profile of laser beams in the plasma. A remarkable change is also observed in the amplitude of plasma wave excitation and particle acceleration in the nonparaxial region in comparison to the paraxial region.

Effect of laser beam filamentation on plasma wave localization and electron heating

This paper presents the ponderomotive filamentation (single hot spot) of a laser beam, propagating in homogeneous plasma in a nonparaxial region. Electron plasma wave coupling in these filaments has been studied. It is found that initially launched weak plasma wave (small amplitude) gets excited and becomes highly localized (wave packet) with a broad spectrum. By expanding the eikonal and other relevant quantities up to the fourth power of r, it is observed that the focusing of the laser beams becomes fast in the nonparaxial region. The uneven focusing/defocusing of the axial and off-axial rays leads the formation of the splitted profile of laser beams in the plasma. The effects of wave particle interaction are also included in this formalism. The simulation result confirms the presence of chaotic fields, and the interaction of these fields with electrons, leads to velocity space diffusion. The stochasticity in the system is also verified by estimating the Lypunov exponent by slightly varying the laser beam power. The energy of the accelerated electrons on account of the laser beam and plasma wave interaction has been calculated by using the distribution function. For typical laser beam and plasma parameters with wavelength (λ=1064nm), power flux (1016Wcm−2), and initial temperature (Te=2.5keV), the elevated electron temperature was found to be around 4.5keV, after passing through one wave packet.

The RCS of a Cylindrical Array Antenna Coated With a Dielectric Layer

The scattering properties of dielectric coated waveguide aperture antennas mounted on circular cylinders are investigated. Both the single element antenna and the array case are treated. The array antenna consists of 4 /spl times/ 32 rectangular apertures placed in a rectangular grid on the surface of an infinitely long circular cylinder. The problem is formulated in terms of an integral equation for the aperture fields which is solved with the method of moments using rectangular waveguide modes as basis and test functions. An efficient uniform asymptotic technique is used to calculate the excitation vector and the backscattered far-field. The asymptotic solution is valid for large cylinders coated with thin dielectric layers away from the paraxial (i.e. near axial) region. A similar asymptotic solution is used to calculate the mutual coupling in the nonparaxial region. For the self coupling terms and for the mutual coupling in the paraxial region a planar approximation is used with a corresponding spectral domain technique. Numerical results are presented as a function of frequency, angle of incidence, cylinder radius, and electrical thickness of the coating.

Uniform asymptotic solution for the radiation from a magnetic source on a large dielectric coated circular cylinder: Nonparaxial region

An accurate uniform asymptotic technique to calculate the radiated field from a magnetic current moment situated on the surface of a circular cylinder coated with a thin dielectric layer has been developed. Using the Watson transform, a slowly convergent radially propagating series representation for the fields is converted into a rapidly convergent circumferentially propagating series representation. An asymptotic shadow region solution is then obtained by employing the method of steepest descent. By modifying the shadow region solution in an appropriate manner, a uniform lit region solution is obtained that reduces to the geometrical optics solution in the deep‐lit region. The asymptotic solution is valid for large cylinders away from the paraxial region and can be used to calculate the radiation pattern and the scattering from waveguide‐fed apertures. Numerical results are compared to an eigenfunction solution, and a very good accuracy is achieved within the expected region of validity.

High‐frequency approximation for mutual coupling calculations between apertures on a perfect electric conductor circular cylinder covered with a dielectric layer: Nonparaxial region

An asymptotic Green's function technique is presented for the calculation of the surface fields on a perfect electric conductor circular cylinder covered with a dielectric layer. The sources are apertures located on the perfect electric conductor surface. This method is very efficient and valid for large cylinders in terms of wavelengths. The new representation is obtained via Watson's transformation and integral contour deformations. The efficiency of the method results from the circumferentially propagating representation of the Green's function as well as the efficient numerical evaluation of various integrals. Numerical results are presented showing good agreement when compared to other solutions as well as measurements.

Non-paraxial analysis of curved analogue lens with multiple-phase jump

The non-paraxial analysis of the analogue waveguide Fresnel lens with curved entrance diopter and multiple-phase jump is presented. The finite length of the element's pads is included into the design. The alteration of both the curvature and the multiplication factor allows us to reduce off-axis aberration and to overcome the photolithographic resolution limits which seriously affect the fabrication of conventional analogue lenses. In the modelling, a hybrid numerical procedure has been used, which is a combination of ray tracing inside the lens and Fresnel-Huygens integral behind the lens; this procedure has been shown to work reliably in the non-paraxial region. The curved analogue lens based on the assumption of infinitesimal pad's length and the plane analogue lens with multiple-phase jump are also discussed as special cases of the generalized structure. Finally, the possibility of chromatic aberration's reduction is examined.