Gain and threshold current density are analyzed for quantum-box lasers where electrons are confined in quantum well three-dimensionally, based on the density-matrix theory of semiconductor lasers with relaxation broadening. The electronic dipole moment and its polarization dependence are first analyzed, and it is shown that the gain becomes maximum when the electric field of light is parallel to the longest side of the quantum box. Calculated gain is about 10 times that of bulk crystal for 100 A × 100 A × 100 A GaAs/Ga 0.8 Al 0.2 As quantum box, and 15 times for Ga 0.47 In 0.53 As/InP quantum box with the same size, respectively. The threshold current density are 45 A/cm2and 62 A/cm2for GRINSCH GaAs/(Ga 0.8 Al 0.2 As-Ga 0.4 Al 0.6 As) and Ga 0.47 In 0.53 As/(Ga 0.28 In 0.72 As 0.6 P 0.4 -InP), respectively, where for the GaInAs/ GaInAsP/InP system the intervalence band absorption and nonradiative recombinations have been assumed to be the same as those obtained for bulk crystals experimentally. These results show the possibility of remarkable reduction in the laser threshold by the quantum-box structures.

Gain and the threshold of three-dimensional quantum-box lasers

The prism coupler, known from experiments on integrated optics, can be used to determine the refractive index and the thickness of a light-guiding thin film. Both parameters are obtained simultaneously and with good accuracy by measuring the coupling angles at the prism and fitting them by a theoretical dispersion curve. The fundamentals and limitations. of this method are discussed, its practical use, and mathematical procedures for the evaluation.

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Measurement of Thin Film Parameters with a Prism Coupler

Integrated optics and new wave phenomena in optical waveguides

Planar optical waveguides consisting of thin dielectric films with metal cladding have been investigated theoretically and experimentally. A computer program was devised to provide the phase and attenuation constants and wavefunctions for TE and TM modes in symmetric and asymmetric guides. Approximate expressions suitable for slide-rule calculation were also derived. Numerical results and illustrations are given for films of photoresist with Al, Ag, and Au cladding. Direct measurements of the attenuation and phase constants at 0.633 microm of numerous experimental waveguides are in reasonable agreement with theory. Attenuations <1 dB/cm, which is sufficiently small for application in devices, were measured. Calculated wavefunctions illustrate the mismatch of modes at transitions between unclad and metal-clad waveguides. Experimentally, we find substantial losses at such abrupt junctions. They can be overcome by simple tapered transitions.

Metal-clad optical waveguides: analytical and experimental study.

Sol-gel silica/titania-on-silicon Er/Yb-doped waveguides for optical amplification at 1.5 μm

We consider thin film light guides consisting of a transparent film of high refractive index deposited on a substrate of lower index. The propagation of light in such a two-dimensional transmission medium can be described within the limits of geometrical optics by an effective index of refraction N. Its value depends on the film thickness. Therefore, a light beam in the thin film guide is refracted or totally reflected at a step of film thickness. We discuss these phenomena (Snell’s law) and demonstrate them experimentally, using ZnS films on glass as guides. As applications, we show a thin film prism and thin film lenses for guided light beams. By properly choosing the film thicknesses at both sides of the step, one can obtain an unusually large positive or negative wavelength dispersion of the refraction or, if desired, achromatic refraction.

Geometrical optics in thin film light guides

In a far infrared molecular laser the traditional pierced output mirror has been replaced by an infrared interference filter, consisting of two metal mesh reflector grids. By adjusting the spacing between the two parallel grids, the reflectance of the filter can be varied. Theory and experiment of this variable reflector are presented. It allows convenient optimization of the coupling conditions of a laser for maximum power output. In contrast to hole coupling, the interference filter provides uniform coupling over the entire cross section of the reflector. This reduces the diffraction losses and improves the angular distribution of the output beam. The variable reflector has also been used to determine the linear gain of the laser.

Variable Metal Mesh Coupler for Far Infrared Lasers

Light-guiding thin films of various materials have been deposited on glass substrates from liquid solutions by slow evaporation of the solvent. The attenuation of the guided light wave in some of these films is as low as that in the best films prepared by other methods. Film deposition from solution is done at or near room temperature. Therefore, this technique allows us to dope the thin films with organic molecules, e.g., laser dyes. The preparation and light-guiding properties of the doped and undoped films are described. The materials studied were epoxy, lead-silica, polyurethane, and Kodak photoresist KPR. Films of the first and second material have shown losses as low as 0.3 dB/cm at wavelengths of 0.633 microm and 1.064 microm, respectively. Films of polyurethane have been prepared with rhodamine 6G doping. When pumped with a pulsed nitrogen laser, the doped films showed optical gains of up to 100 dB/cm. The KPR films have an attenuation of ~1 dB/cm at 1.064 microm. This low optical loss, in combination with the hotographic sensitivity of the KPR, offers the possibility of fabricating integrated optical circuits directly in the photoresist films.

Solution-deposited thin films as passive and active light-guides.

Thin-film optical devices are disclosed which function within the plane of a thin-film as lenses or prisms. They function in two dimensions, since the thin dimension of the film serves to guide the beam with respect to the third dimension. The devices are formed integrally from the body of the thin-film by variations in its thickness either along the path of the light beam or by such variations both along the path of the beam and transversely thereto, with contours of constant thickness intersecting the light path in an orientation affecting change of the direction of propagation of at least a portion of the light. Lenses of increased thickness are convergent if provided with convex contours or divergent if provided with concave contours; but lenses of decreased thickness with respect to the surrounding film are convergent if provided with concave contours and divergent if provided with convex contours. The prisms change the path of the entire beam. They can also be made to provide total internal reflection within the prism or frustrated internal reflection if disposed sufficiently close to another thin-film optical device. It is advantageous for the efficient operation of these devices if the mentioned changes in the film thickness are not abrupt but rather are tapered smoothly over a distance of several wavelengths of the light. This minimizes reflection losses and conversion to other modes.

Reinhard Ulrich

Papers

Geometrical optics in thin film light guides

Variable Metal Mesh Coupler for Far Infrared Lasers

Solution-deposited thin films as passive and active light-guides.

Thin-film optical devices