Spontaneous emission of free electron laser with planar wiggler and ion-channel guiding is calculated analytically and possibility of emission at up-shifted wiggler or ion-channel betatron frequency and their harmonics has been found. To investigate the nonlinear odd harmonics, a set of self-consistent nonlinear differential equations that governs the evolution of radiation and electron beam are derived and solved numerically by Runge-Kutta method. Using the simulation code, gain improvement of third harmonic is studied in the range of microwave frequency by applying ion-channel guiding for a cold beam. It is shown that the combination of the ion-channel and a prebunched electron beam increases the amplitude of the third harmonic of the radiation and decreases its saturation length. The relation between the linear and nonlinear harmonics is discussed.

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Simulation of free electron laser (FEL) with modified wiggler consisting of a conventional planar wiggler with third harmonic field component is presented. A set of self consistent nonlinear differential equations is derived and solved numerically by Runge–Kutta method. The optimum amplitudes of fundamental and third harmonic wiggler filed are obtained to increase the third harmonic radiation in comparison with conventional wiggler and also to have lower electron beam energy compared to conventional wiggler with the same wavelength. For the thermal effect the axial energy spread of electron beam, without any spread in the transverse velocity, is assumed. A peculiar region is found in which there is a sharp increase of the radiation amplitude. Thermal effect of the electron beam was found to be irregular in this peculiar region.

The effect of axial energy spread on the radiation of third harmonic is studied in the free electron laser with planar wiggler and ion-channel guiding. Spread in the longitudinal momentum and so in the initial energy of electron beam, without any spread in the transverse velocity, is assumed in the form of Gaussian distribution function. The technique that is employed is a one-dimensional and steady-state simulation. A set of self consistent nonlinear differential equations that describes the system is solved numerically by Runge-Kutta method. Due to the sensitivity of harmonics to thermal effects, gain improvement of third harmonic radiation is achieved by using ion-channel guiding technique and efficiency enhancement is applied by tapering the magnetic field of wiggler to optimize radiation. The bunching parameter of the electron beam is also studied. It is found that the growth of the magnitude of the bunching parameter that is caused by the ponderomotive wave stops before the saturation point of the radiation. This means that ponderomotive wave saturates at a shorter distance compared to the radiation.

In this paper, a three ringresonator serially coupled is considered as an optical filter. We are going to improve the performance of the designed optical filter by increasing the quality factor and finesse of filtered wavelengths. The first and last rings are coupled to the bus waveguides that carry the input and output fields. The effect of coupling parameters and ring radii on the filtering of operating wavelengths which are between 1545-1550 nm with narrow Free Spectral Range (FSR) less than 0.5 nm is investigated. Using the transfer matrix method, all the rotating and output fields are obtained. FSR, Full Width at Half Maximum (FWHM) and Finesse (F) are evaluated by the wavelength response plots of the output ports obtained in Wolfram Mathematica. The behavior of structure is analyzed by a new approach in order to filter the resonant wavelengths of the transmission channel with higher finesse.

The functionality of most of the metasurfaces that have been investigated so far, especially in illuminations with arbitrarily linearly polarized incident light, are restricted to x- or y-polarized incoming light. In particular, filtering out one of the two orthogonal polarizations of the incoming electromagnetic wave loses the incident light energy and limits the potential performance of the metasurface. In this study, by utilizing the cross-shaped silicon metaatoms that support the simultaneous excitation of electric and magnetic dipoles under the illumination of both x- and y- orthogonal polarizations, we overcome the polarization-restricted functionality of the metalenses. By selecting the metaatoms arrangement in the metalens structure, which follows the hyperbolic phase profiles for both x- and y-polarized incoming light waves at the same time, we obtain the light intensity distribution with the extended depth of focus (EDOF) or enhanced intensities at the focal spot with the focusing efficiency 65% for the numerical aperture of 0.7. Utilizing metaatoms with the ability to control the two orthogonal incoming polarizations develops a new methodology for using the full potential and intensity of the arbitrary polarized incoming light. The present design concept of metaatoms has several advantages that are not limited to metalenses alone but can be applied in all metasurfaces realized to have good efficiency. Finally, the proposed metalenses are suitable for imaging, optical tweezers and lithography applications, where subwavelength light intensity distributions with EDOF are the most desirable property.

Optical metasurfaces with versatile focal properties have great importance and adaptability in photonic systems and potential applications. The unique capability of the ultracompact device in forming and modulating light fields is triggered to configure multifocal setups. This study introduces a geometric metasurface consisting of dielectric cross-shaped metaatoms with a suitable phase profile operating in the visible regime that can transport the conjugate focal spot of the auto-focused Airy beam (AFAB) into real space by adding the proper convex lens profile and resulting in three foci whose positions and intensities can be adjusted without redesigning metaatoms architecture. The cross-shaped meta-atoms with complete control of the amplitude and phase of the incident light have considered diverse functionalities for the x-and y-components of the incident light, generating six focal spots with high adjustable intensities shown in free space. The proposed hybrid metalens has shown robustness against change in geometrical design while controlling multifocal setups, which can be useful in developing polarization-sensitive devices, photonics, medicine, micromachining and imaging applications to realize beneficial results.