Image beam from a wire laser

Abstract

We demonstrate the formation of a narrow beam from a long (L λ) laser with subwavelength transverse dimensions (wire laser) as an image of the subwavelength laser waveguide formed by a spherical lens. The beam is linearly diverging with the angle determined by the ratio of the wavelength to the lens radius, while the minimum beam spot size is the same as that of the image of a point source. We realize such a beam experimentally using a terahertz quantum cascade wire laser. , and multi-quantum-well structures [3] have a wire geometry with transverse dimensions smaller than the emission wavelength and a length much larger than the wavelength. The spatial structure of wire laser radiation differs drastically from that of conventional lasers with large apertures. It was found to be highly divergent, with strong intensity modulations observed both in far [4] and near field [5], with the pattern of modulations more dense for longer lasers. It was shown that the far-field pattern of wire lasers is formed by the interference of radiation from the longitudinal distribution of sources along the laser waveguide [6] and is similar to that of antennas of traveling wave. Thus it depends strongly on the longitudinal phase velocity of the waveguide mode. Concentration of radiation into a narrow, axially symmetric beam along the laser axis with the divergence determined by the ratio of the wavelength to the laser length has been predicted by the antenna model for the modes of wire lasers with longitudinal phase velocity close to that of light in air, where all the sources along the laser emit in phase in the direction of the longitudinal axis. However, realization of such modes is hindered due to their low confinement and high radiation losses. Directive emission from wire lasers has been achieved using gratings with appropriate periodicity, acting as a discrete array of phased sources along the laser waveguide [7][8][9][10]. However, this approach not only implies a complicated waveguide design, but also leads to an increase of radiation losses; thus it is not always possible. Transformation of radiation with external optical elements is free from these complications. Beam shaping is a wellestablished technique for lasers with transverse dimensions much bigger than the wavelength [11]. Lenses have been used to collimate the radiation from wire lasers [12] and to provide their optical images [5,13], yet little is known about peculiarities of external transformation of wire laser radiation. In this Rapid Communication we analyze the structure of the beam formed as an image of a wire laser placed on the axis of a spherical lens behind the focal plane (Fig. 1). According to geometrical theory of optical images, the image of the laser is stretched along the lens axis. The length of the image increases with reduction of the distance between the lens and the laser, and the image becomes semi-infinite when the end of the laser touches the focal plane. The distribution of the radiation field in the vicinity of the image of a wire laser ...

Spatial filtering of radiation from wire lasers

“…Assuming the equivalent current of the laser mode in the form of a standing wave along the laser axis, the expression for the far field of a wire laser has been obtained containing only a few integral parameters of the laser mode, such as the first nonvanishing momentum of transverse distribution of equivalent current, laser length and the phase shift between the mode and free space plane wave along the waveguide [3]. Based on this expression, the radia tion field of a wire laser placed along the axis of a spherical lens is calculated using the Fresnel integral over the aperture of the lens [9]. The resulting field distribution in the paraxial approximation is described by the product of a spherical wave from the center of the lens and a structural factor:…”

“…Thus, the beam divergence can be made arbitrarily small by bringing the laser closer to the lens focal point, and filtering the maximum at a larger distance. For comparison, the divergence of the directive beam obtained as an image of a wire laser [9] is determined by the ratio of the wavelength to the lens radius:…”

“…Few results can be mentioned in the field of development of specific methods of transforma tion of radiation of wire lasers. Recently it was proposed to use spherical lenses to form a narrow beam as an image of a wire laser placed on the lens axis [9]. However, the conditions of formation of such a beam include the limitation on the number of interference rings within the lens aperture, thus limiting the fraction of the omnidirectional radiation from a slow mode of a wire laser radiation collected by the lens.…”