The observation of far-infrared stimulated emission from shallow donor transitions in silicon is reported. Lasing with a wavelength of 59 &mgr;m due to the neutral donor intracenter 2p(0)-->1s(E) transition in Si:P pumped by CO2 laser radiation is obtained. Populations of D0 and D- center states and the balance of the radiation absorption and amplification are theoretically analyzed.

The need to reach single-mode lasing and minimize at the same time the electrical dissipation of cryogenically operated terahertz quantum cascade lasers may result in small and subwavelength cavity dimensions. To assess the influence of such dimensions on the shape of the laser emission, we have measured the beam pattern of two metal-metal cavity quantum cascade lasers. The patterns show regular angular intensity variations which depend on the length of the laser cavity. The physical origin of these features is discussed in terms of interference of the coherent radiation emitted by end and side facets of the laser bar. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2194889͔The quest for terahertz sources has resulted recently in the development of the terahertz quantum cascade laser ͑QCL͒. 1 At present, continuous-wave ͑cw͒ QCLs in the terahertz range have been demonstrated for frequencies as low as 2.0 THz ͑Ref. 2͒ and 1.9 THz ͑Ref. 3͒ ͑ Ϸ 160 m͒ and for temperatures up to 117 K. 4 These sources are very promising as local oscillators for heterodyne detection 5,6 and for general terahertz imaging applications. 7 The terahertz QCLs which have achieved the highest temperature performance are based on the so-called "metal-metal waveguides" of subwavelength dimensions. 8,9 Such waveguides minimize lasing threshold current densities due to their strong confinement of the mode to the gain region, their low losses, and their enhanced facet reflectivities. 10 Furthermore, the strong confinement has allowed the fabrication of structures with small lateral and transverse dimensions which minimizes electrical power dissipation; this is critical for their cryogenic operation and leads to improved cw performance. It is expected that the emitted beam from a cavity with subwavelength dimensions would be strongly divergent. 10 Study of the beam profile therefore is important to characterize this type of terahertz source.The heterostructure design employed for the terahertz QCLs used in this research is based on resonant longitudinaloptical-phonon scattering to selectively depopulate the lower radiation level. 11,12 The metal-metal waveguide was fabricated using a copper-to-copper thermocompression bonding technique. 8 We will report here results of beam profile measurements on two laser samples with subwavelength dimensions, fabricated from the same wafer. The metal-metal cavities are bonded to an n + GaAs substrate. The front and back facets of the cavities are uncoated. The cavity dimensions and the free space wavelengths are given in Table I, together with the relation between geometry and the Cartesian coordinate system, used to present the experimental data. Figure 1 shows our experimental setup used to measure the beam patterns. The n + GaAs substrate is indium soldered to a copper sample holder, which in turn is attached to the copper cold plate of a helium flow cryostat. The laser bar can be mounted in various orientations with respect to the 50 mm diameter window at a minimum distance of about 10 mm. It has bee...

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...

Far-infrared stimulated emission from optically pumped neutral Bi donors in silicon has been obtained. Lasing with wavelengths of 52.2 and 48.6 μm from the intra-center 2p±→1s(E:Γ8),1s(T2:Γ8) transitions has been realized under CO2 laser pumping. The population inversion mechanism is based on fast optical-phonon-assisted relaxation from the 2p0 and 2s excited states directly to the ground 1s(A) state leading to relatively small population in the intermediate 1s(E), 1s(T2) excited states.

Frequency-tunable radiation from the free electron laser FELIX was used to excite neutral phosphorus and bismuth donors embedded in bulk monocrystalline silicon. Lasing at terahertz frequencies has been observed at liquid helium temperature while resonant pumping of odd parity impurity states. The threshold was about two orders of magnitude below the value for photoionization pumping. The influence of nonequilibrium intervalley TO phonons on the population of excited Bi impurity states is discussed. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1476955͔ Semiconductors doped by shallow level Coulomb centers are promising media for terahertz ͑THz͒ light amplification and stimulated emission. Up to the moment the main activity has been concentrated on phosphorus ͑P͒ and bismuth ͑Bi͒ donors embedded in single crystalline silicon ͑Si͒ excited by CO 2 laser radiation. Both, THz spontaneous and stimulated emission based on intracenter optical transitions, were detected and the involved states have been identified. [1][2][3][4][5] There are two basic mechanisms that may cause the population inversion of charge carriers between the impurity states. The first one is based on the suppression of the acoustical phonons assisted relaxation of the optically excited electrons over the localized states with the increase of the energy gap between the levels. Such a bottleneck effect occurs for the lower excited states of the impurity center. In Si:P it leads to the overpopulation of the 2p 0 state and THz stimulated emission on the 2p 0 →1s(T) transition under optical pumping at cryogenic temperatures (TϽ15 K) ͓Fig. 1͑a͔͒. A similar effect can be expected for Si doped by As, Sb, Li shallow donors as well. Another mechanism for population inversion is predicted in Si:Bi ͓Fig. 1͑b͔͒ due to the strong coupling of both 2p 0 and 2s excited states with the 1s(A) ground state via intervalley TO and LO optical phonon resonant interaction. 6 Spontaneous emission of optical phonons makes the lifetimes of the 2p 0 and 2s states extremely short (10 Ϫ12 s), dumping carriers directly to the ground state. Such a scenario provides the depletion of the 2 p 0 and 2s states and leads to a negligible population of the 1s(E,T) states. Hence, the population inversion between the higher excited states and the 2s, 2p 0 , 1s(E,T) states is expected. 1,5 Recently THz lasing has been obtained from the 2 p Ϯ →1s(E,T) transitions in Si:Bi under CO 2 laser pumping. 5 The drawbacks of the CO 2 laser pumping, which a͒ Electronic mail: heinz-wilhelm.huebers@dlr. de FIG. 1. Scheme of optical and nonradiative transitions in Si:P ͑a͒ and Si:Bi ͑b͒ under intracenter excitation and photoionization pumping: broad arrow down-THz emission; arrow up-FELIX pumping; diagonal solid arrowsacoustical assisted transition; diagonal dashed arrows-low probable acoustical assisted transitions; dashed vertical arrow down-optical phonon assisted transition.