Metrologia, 47, 5, pp. R15-R32, 2010-08-03 Photometry, radiometry and 'the candela' : evolution in the classical and quantum world Zwinkels, Joanne C.; Ikonen, Erkki; Fox, Nigel P.; Ulm, Gerhard; Rastello, Maria Luisa AbstractThe metrological fields of photometry and radiometry and their associated units are closely linked through the current definition of the base unit of luminous intensity -the candela. These fields are important to a wide range of applications requiring precise and accurate measurements of electromagnetic radiation and, in particular, the amount of radiant energy (light) that is perceived by the human eye. The candela has been one of the base units since the inception of the International System of Units (SI) and is the only base unit that quantifies a fundamental biological process -human vision. This photo-biological process spans an enormous dynamic range of light levels from a few photon interaction involved in triggering the vision mechanism to more than 10 15 photons per second level that is accommodated by the visual response under bright daylighting conditions. This position paper, prepared by members of the Task Group on the SI of the Consultative Committee of Photometry and Radiometry Strategic Planning Working Group (CCPR WG-SP), reviews the evolution of these fields of optical radiation measurements and their consequent impact on definitions and realization of the candela. Over the past several decades, there have been significant developments in sources, detectors, measuring instruments, and techniques, that have improved the measurement of photometric and radiometric quantities for classical applications in lighting design, manufacturing and quality control processes involving optical sources, detectors and materials. These improved realizations largely underpin the present (1979) definition of the candela. There is no consensus on whether this radiant-based definition fully satisfies the current and projected needs of the optical radiation community. There is also no consensus on whether a reformulation of the definition of the candela in terms of photon flux will be applicable to the lighting community. However, there have been significant recent advances in radiometry in the development of single photon sources and single photon detectors and the growth of associated technologies, such as quantum computing and quantum cryptography. The international acceptance of these new quantum-based technologies requires improved traceability and reliability of measurements at the few photons level. This review of the evolution of the candela and the impact of its possible reformulation might lead, in the future, to a reformulation in terms of quantum units (photons). This discussion is timely since redefinitions of four of the other SI base units are being considered now in terms of fundamental constants to provide a more universally realizable quantum-based SI system. This paper also introduces for the first time a fundamental constant for photometry.

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A comprehensive experimental and theoretical study of indirect gap optical absorption in bulk Ge is presented. While this topic was the subject of intense studies from the early days of semiconductor physics, the resonant aspect of the absorption received very little attention until now. This is a unique property of Ge related to the proximity of the direct and indirect gaps.The absorption coefficient was measured over the entire spectral range between the two gaps for comparison with theory. It is shown that the standard textbook expressions, obtained by assuming intermediate states with constant energy, are in very poor agreement with experiment. A theory first proposed by Hartman, which takes into account the energy dependence of the intermediate states, provides a much better account of the photon-energy dependence of the absorption, but the prediction of the experimental absorption strength requires the incorporation of excitonic effects. The latter, however, have only been considered by Elliott in the limit of constant intermediate state energy. A generalization to the case of energy-dependent intermediate states, consistent with Hartman's theory, is presented here. The basic qualitative difference with the classical Elliott theory is that the excitonic character of the intermediate states affects the computed absorption, generating an additional resonant enhancement that is confirmed by the experimental data. The generalized theory presented here agrees very well with the experimental absorption using independently determined band structure parameters.

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