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Physical features of spatial-energy characteristics of linearly polarized THz laser beams at sharp and moderate focusing in free space are analyzed both theoretically and experimentally. The Rayleigh-Sommerfeld vector theory is used to model propagation of laser beams excited by quasi-optical waveguide resonator modes in free space. Well-known methods of measuring spatial-energy characteristics of laser beams in the THz range are used in the experimental study. It is shown that the intensity of the total electric field of both combined TE0n + EH2n and EН-1n + EH3n modes (n = 1, 2, 3) in the focal region is defined by all three components and has a dip on the axis for both focusing types. The central maxima of the field of these modes become significantly shifted from the geometric foci of the lenses used as the order n of these modes increases. The EН-11 + EH31 mode has the smallest diameter (2.94λ) of the focal spot in the maximum intensity region at sharp focusing. The TE01 + EH21 mode has the smallest diameter (13.65λ) of the focal spot at moderate focusing. [ABSTRACT FROM AUTHOR]

Subject and Purpose. The problems under consideration concern selection and focusing of higher-order modes in a waveguide-based dielectric laser. The purpose is to clarify the physics underlying the behavior of, and permitting control over, continuous terahertz-frequency laser beams of various spatial polarizations. Methods and Methodology. The mode parameters of the waveguide-based laser resonator involving an inhomogeneous phase-stepped mirror were calculated in a matrix technique. To analyze the propagation and focusing of the laser beams that can be excited in a variety of diffraction zones by the wave modes of a waveguide-based quasi-optical resonator, a vectorial Rayleigh–Sommerfeld theory was used. The pertinent experimental studies were performed with the use of known measurement methods suitable for the terahertz frequency range. Results. A method for selecting the higher-order EH12q-mode of a terahertz-range laser resonator has been suggested, substantiated theoretically and approbated in experiment. It envisages placing an additional element to perform control over the system’s modal structure, namely a (2.3…2.8) λ-wide groove on the surface of one of the resonator mirrors. This measure can significantly increase losses for all undesirable modes. At the same time, the losses for the higher EH12q-mode remain practically unchanged, which creates conditions for its predominant excitation. Theoretical and experimental studies of moderate and ‘sharp’ focusing in free space of higher-order modes with different spatial polarizations of a dielectric waveguide-based resonator have been carried out. Conclusion. As has been shown, the proposed phase-stepped mirror with a groove can effectively select the higher-order transverse modes that may be required. The linearly polarized EH12q-mode has maximum field intensity in the focal region of the lens employed. For azimuthally polarized TE02q- and TE03q-modes the central lobes, noticeably shifted from the focus of the lens, have a field maximum. An increase in the axial intensity is observed upon ‘sharp’ focusing in the field distribution of the radially polarized TM02q- and TM03q-modes. In this case their central lobes, like those of the higher TE0nq-modes, are noticeably shifted from the lens focus.

Subject and Purpose. In this paper, spatial power characteristics of laser beams with inhomogeneous spatial polarization are theoretically investigated depending on whether they have moderate or sharp focusing. The spotlight of the numerical simulation of laser beam focusing in the terahertz range is on the laser waveguide dielectric resonator modes coincident with waveguide eigenmodes. Symmetric and asymmetric modes with both spatially inhomogeneous azimuthal and radial polarizations and homogeneous linear polarization of the field are considered. Methods and Methodology. The study of the electric field components of laser radiation beams in their free space propagation employs Rayleigh-Sommerfeld integrals in nonparaxial approximation. The focusing lens action on the laser radiation is considered using the amplitude-phase correction function. The total intensity distributions of the resonator modes and their particular field components in the lens focal area are examined. Results. Wave beams with inhomogeneous spatial polarization of radiation are needed for meeting important fundamental and applied problems concerning terahertz electromagnetic wave interaction with matter and including diagnostics of material surface, thin films and biological objects, design and development of terahertz systems of information transmission and processing, terahertz communication systems, achievement of subwave resolution in terahertz tomography, etc. The literature on pulsed radiation beam focusing in the terahertz region is available, which cannot be said about continuous radiation beam focusing, data on the subject being practically absent. In the present work, physical features of moderate and sharp focusing of laser beams have been theoretically studied in the case of their excitation by modes of the resonator with a circular dielectric waveguide with different spatial polarizations of the field. The obtained results give a more in-depth view of the focusing features of terahertz laser beams. Conclusions. Physical features have been established for spatial power characteristics of radiation beams with different spatial polarizations of the field in the case of the excitation by modes of the laser cavity upon a circular dielectric waveguide in the terahertz range and with the regimes of moderate and sharp beam focusing in the free space considered.

The possibility for control of tightly focused laser beams excited by the resonator modes of a THz laser based on a hollow circular dielectric waveguide is studied theoretically and experimentally. The wavelength of the radiation under study is 0.4326 mm corresponding to the generation line of the optically pumped HCOOH‐molecule THz laser. The focusing system is implemented by a short‐focus lens covered by absorbing masks in the central region. The focal area parameters were controlled by changing the size of the masks. The electric field components of the laser modes are calculated using the Rayleigh‐Sommerfeld integral transformations under non‐paraxial approximation. The use of absorbing masks made it possible to reduce the beam diameter in the focal region and increase the depth of focus of the linearly polarized EH11‐mode and azimuthally polarized TE01‐mode as well. In this case, despite of the presence of an absorbing mask, the distribution of the total field intensity of the TE01‐mode retained its annular shape, and the field maximum of the EH11‐mode is observed at center of the focal spot. The results of this work can be implemented in medical diagnostics, high‐speed communications, and environmental monitoring. [ABSTRACT FROM AUTHOR]

Subject and ppurpose. In this paper, the spatial-energy characteristics of laser beams with inhomogeneous spatial polarization with their moderate and sharp focusing are theoretically investigated. In the numerical simulation of focusing of wave laser beams in the terahertz range, laser resonator modes based on a circular metal waveguide were used as the radiation under study. These modes coincide with the proper types of oscillations of such a waveguide. For the calculation, we selected symmetric and asymmetric modes with azimuthal, radial, and complex spatial polarization of the field. Methods and methodology. In the study of the propagation of the components of the electric field of laser radiation in free space, Rayleigh-Sommerfeld integrals were used in the nonparaxial approximation. The effect of the focusing lens on the radiation under study was taken into account using the function of amplitude-phase correction. The transverse distributions of the total field intensity and its individual components of the studied resonant modes in the region of the minimum size of the focal spot of focused radiation beams were studied. Results. Wave beams with inhomogeneous spatial polarization of radiation are necessary for solving important fundamental and applied problems. These tasks are associated with the interaction of electromagnetic waves of the terahertz range with matter. For example, diagnostics of the surface of materials, thin films, biological objects, THz transmission systems and information processing, the achievement of subwave resolution THz tomography, terahertz communication systems, etc. The results of studies of focusing features in the terahertz range are practically absent. A theoretical study was made of the physical features of moderate and sharp focusing of laser beams of radiation excited by the modes of a resonator with a circular metal waveguide with different spatial polarization of the field. The results obtained extend knowledge of the focusing features of terahertz laser beams. Conclusions. The physical features of the spatial-energy characteristics are established with moderate and sharp focusing in free space of radiation beams with different spatial polarization of the field. These beams were excited by laser resonator modes based on a circular metal waveguide in the terahertz range.