Antenna Model for Wire Lasers

Abstract

An antenna model is proposed for long (L ) lasers with subwavelength cross sections (wire lasers). It is shown that the far-field pattern of the wire lasers is determined by the ratio of the wavelength to the length. The radiation of the wire laser is predicted to be concentrated in a narrow beam ' 2=L p for laser modes where the longitudinal phase velocity is in synchronism with the velocity of light in air. Experimental results obtained using a terahertz quantum cascade wire laser are in agreement with the model. DOI: 10.1103/PhysRevLett.96.173904 PACS numbers: 42.60.Jf, 42.25.ÿp, 78.67.-n Is it possible to concentrate radiation from a laser with a subwavelength cross section into a narrow beam? The combination of a small laser aperture with a low beam divergence would open the perspective of local laser excitation of individual nano-objects, which would be of interest in numerous applications such as optical communication, high-density magneto-optic data storage, biological studies, and quantum information. However, the reduction of a laser aperture is known to cause an increase of the beam divergence due to diffraction. The diffraction limited minimum angular size of the beam for radiation with a wavelength for an aperture of size a is determined by ' =a for sources with a > [1]. Thus, for example, in diode lasers, the localization of the optical mode in a thin active region (with the width of the order of several wavelengths) leads to a high beam divergence in the plane perpendicular to the active layer [2]. High efficiency and gain achieved in nanostructure lasers permits laser dimensions comparable to or smaller than the wavelength [3][4][5]. Highly divergent radiation is expected from lasers with subwavelength apertures [4]. The methods used to improve the directivity of laser radiation, using, for example, surface emission [2], an array of lasers [6], or using external optical elements, are all based on the increase of the effective size of an aperture. The recently discovered effects of surface plasmons on the transmission of light through subwavelength apertures [7] also imply an increase of the effective aperture size due to the formation of plasmon-polaron excitations at the surface of a metallic screen. The development of nanotechnologies has brought along new methods to manipulate light on the scales comparable to the wavelength using the concepts of photonic crystals [8], left-handed synthetic materials [9], and onedimensional plasmonic waveguides [10]. These methods however do not solve the problem of the guidance of light in the air outside the artificially fabricated media.In this Letter we propose a method to achieve a high directivity for lasers with subwavelength apertures (wire lasers). The idea is based on an antenna approach to analyze laser modes. Since individual sources in the laser medium emit coherently with their phases determined by the cavity modes, each laser mode can be thought of as a continuous phased array. The different laser modes do not interfere because of their slig...

Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions

“…These values, which are similar to those calculated in Ref. 13, agree quite well with the experimental data, and account for the essential interference phenomena observed. It can also be understood that for the beam patterns presented in Fig.…”

“…Description of the details of this model, however, is outside the scope of this letter and will be presented elsewhere. 13 To obtain some insight into the physical origin of these interference patterns, we use an extremely simplified version of this model. We describe the emission of the laser bar with length L as resulting from a system of two coherent point sources situated at the two laser end facets, radiating into free space at a wave- length .…”

Image beam from a wire laser

“…4(a). Strong modulations of far-field intensity are almost axially symmetrical, with the separation of intensity rings in agreement with the wire laser model [6]. Radiation of the laser was partially blocked by the sample holder, leading to a smaller intensity in the lower part of Fig.…”

“…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.…”

“…Thus the radiation field of a wire laser can be expressed in terms of the field values within the laser waveguide. Like in [6], we assume that each Cartesian component of equivalent current density, corresponding to an optical mode of a wire laser, can be presented by a combination of traveling waves along the laser axis:…”