The foundational Franz-Keldysh effect and Einstein model are applied in this work to characterize semiconductor band-edge absorption-and its departures from ideality. We unify the Franz-Keldysh and Einstein models to fully characterize the field-induced tunneling of photoexcited electrons from degenerate valence bands into the conduction band, with encroachment into the band gap arising as an Urbach tail. Our unified model is implemented for semi-insulating indium phosphide (SI-InP) with strong agreement seen between the theoretical and experimental results for varied photon energies and electric fields.

This work demonstrates the realization of terahertz (THz) spectroscopy on a subwavelength scale. We do so by using dielectric spheres as focusing elements and apertures as spatially constricting elements for THz radiation. Such a configuration forms intense, subwavelength-sized THz microjets. Two implementations are used to demonstrate the effectiveness of THz microjets, as follows: apertured THz plane waves and apertured THz microjets. Seven aperture diameters were chosen for each implementation to discern their capabilities at the subwavelength scale. We investigated the effectiveness of each implementation in mapping the material characteristics of the sample onto the THz beam. Such analyses show that apertured THz microjets were able to map material characteristics (via refractive index and extinction coefficient) onto the beam (via phase and amplitude) effectively and reliably. This is expected as the beam produced by apertured THz microjets has a small cross-sectional area (apertures) and high intensity (THz microjets). Here, we illustrate the capabilities of apertured THz microjets for a biological specimen, being lactose, to show the potential for biological applications. Overall, this work demonstrates the ability of apertured THz microjets to perform THz spectroscopy at a subwavelength scale. Such findings could bring about biological characterization with cellular-scale resolution.

In this work, we explore the band edge absorption characteristics of semiconductors as applied to optoelectronic modulation—with careful consideration to the departures from ideality in the semiconductors. To this end, we develop a rigorous model of electroabsorption in semiconductors that characterizes the electric-field-induced constriction/narrowing of the bandgap and the resulting increase in absorption of photons, whose energies are slightly below the bandgap energy. The model unifies the Franz-Keldysh effect, characterizing the electric-field-induced tunneling of photoexcited electrons from valence band states to conduction band states, and the Einstein model, quantifying the encroachment of valence and conduction band states into the bandgap. Careful consideration is given here to the nonidealities in the semiconductor, which arise within the valence band as degenerate states, due to light and heavy holes, and within the bandgap, as encroaching Urbach tail states. We apply the model in characterizing optoelectronic modulation of 980-nm photons with semi-insulating indium phosphide (SI-InP), and we see strong agreement between our theoretical and experimental results over a wide range of electric fields and photon energies. Ultimately, the findings show that optoelectronic modulation can be had with large modulation depths over short propagation lengths through the semiconductor. This opens the door to highly effective implementations of optoelectronic modulators in emerging free-space optical communication systems—given that such modulators do not allow for prolonged (guided-wave) propagation and have thus exhibited small modulation depths.

In this work, we introduce the concept of a hemispherical retro-modulator for the realization of passive free-space optical communication links. The hemispherical retro-modulator is implemented with a high-refractive-index glass (S-LAH79) hemisphere on a semi-insulating-InP (SI-InP) layer, whose thickness dictates the effectiveness of both retroreflection and modulation. A voltage is applied across transparent indium tin oxide (ITO) and gold (Au) films on either side of the SI-InP layer to bring about the desired modulation. The overall device is designed to enable low divergence on the retroreflected beam, as defined by a small divergence angle, and deep modulation on the retroreflected beam, as a result of electroabsorption in the SI-InP layer. To this end, the device is analysed with a ray-based model for retroflection and a unified Franz-Keldysh/Einstein model for modulation in the SI-InP layer. The theoretical results show strong agreement with the experimental results from our prototype. Moreover, the results show effective retroflection and deep modulation-with an applied electric field of 2.167 kV/cm yielding modulation depths of 13%, 34%, and 50% for our 980-nm photons and SI-InP layer thicknesses of 200, 600, and 1,000 µm, respectively. From this, we deem the SI-InP layer thickness of 600 µm to be optimal given its combined capabilities for retroflection and modulation. Ultimately, the introduced hemispherical retro-modulator is shown to be an effective element for future realizations of passive freespace optical communication links.

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