IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 4, DECEMBER 2008 1761 Theory of Superconductive Traveling-Wave Photodetectors Behnood G. Ghamsari and A. Hamed Majedi, Member, IEEE Abstract—This paper studies the theory of traveling-wave pho- todetection in superconductive multilayer optical waveguides, as a general platform for ultrafast, ultrasensitive, and ultralow-noise optoelectronics. The kinetic inductance theory of superconductive thin films and the modified transmission line theory are employed to investigate the distributed photodetection and signal generation mechanisms in superconductive traveling-wave devices. A general model for calculation of the optical responsivity of superconduc- tive traveling-wave photodetectors is developed and operation regimes of interest are highlighted. Moreover, the inclusion of a photoconductive layer in the device structure and some important loading schemes are discussed and their effects on the device per- formance, such as quantum efficiency and electrical bandwidth, are addressed. Index Terms—Superconducting devices, superconductive optical waveguides, superconductive photodetectors, terahertz (THz) pho- tonics, traveling-wave optoelectronic devices. I. INTRODUCTION T HE photoresponse of superconductive structures has been the subject of research both due to its rich physics and its prospective applications in novel devices [1]–[8]. The fast pho- toresponse of superconductors along with their high quantum yield, which arises due to the small Cooper pairing energy in the order of 1 meV, as well as the diminished thermal noise at cryogenic temperatures, are the major causes of attention to superconductive structures as ultrafast, ultrasensitive, and ul- tralow-noise optoelectronic devices. Generally, there are dif- ferent characteristics of a superconductive structure that are per- turbed as a result of optical illumination, such as quasi-particle number density, chemical potential, average energy gap, and ki- netic inductance [1], [2], [9]–[12]. It is also possible that the light changes the thermodynamic phase of a superconductive structure into the normal state, either locally or globally as in nano-wire single photon detectors or transition edge sensors [13]–[15]. In fact, all of these phenomena can be employed in order to detect light. Nevertheless, efficient coupling of the light into the active element is a common key issue in almost all kinds Manuscript received February 16, 2008; revised May 29, 2008. Current ver- sion published December 04, 2008. This work was supported in part by the Canadian Institute for Photonic Innovations (CIPI) and Institute for Quantum Computing (IQC), University of Waterloo, Waterloo, ON, Canada. The work of B. G. Ghamsari was supported in part by the Mike and Ophelia Lazaridis Fel- lowship. This paper was recommended by Associate Editor M. Mueck. The authors are with the Department of Electrical and Computer En- gineering and Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: ghamsari@maxwell.uwaterloo.ca; ahmajedi@maxwell.uwaterloo.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2008.2007238 of photodetectors. This task is much more challenging for super- conductive photodetectors due to the need of cryogenic setups, fabrication difficulties, and the compatibility with the specific optical process which is in charge of the photodetection. The traveling-wave photodetection strategy is one potential remedy which has already proved its merits in semiconductor photode- tectors [16]–[24]. This strategy is provoked even more due to the recent technological achievements suitable for integrating optical waveguides and superconductive structures [25]–[27]. Therefore, integration of superconductive detectors with optical waveguides is not only a solution to the light coupling problem, but also presents a wide range of benefits arising from the dis- tributed nature of photodetection in contrast to the lumped-ele- ment devices. In this paper, we propose the use of the kinetic-inductance of a superconductive thin film which is integrated with an op- tical waveguide and a microwave transmission line as a pho- todetector, namely the superconductive traveling-wave photode- tector (STWPD). The main physical mechanism that contributes to the detection of light in STWPDs, is the modulation of the ki- netic inductance of a superconducting thin film by means of ab- sorption of photons and breaking Cooper pairs. One approach to detect the changes in the kinetic inductance is to monitor the shift in the resonance frequency/transmission phase of a su- perconductive microwave resonator [28]. While this technique hardly lends itself to a traveling-wave device, the alternative ap- proach is to apply a constant external current bias to the film and read out the induced voltage caused by temporal variations of the magnetic flux linkage through the superconductive structure [29]. Therefore, as the light propagates down the optical wave- guide, it is gradually absorbed by the superconductive thin film and generates a voltage at each point along the film. Every point along the length of the device is considered as a detector and the superconductive film plays the role of a series of distributed photodetectors whose contributions can be constructively col- lected by means of a velocity-matched microwave transmission line(Fig. 1). Interestingly, the superconductive film can serve as the transmission line itself. Also, due to their distributed photodetection scheme, STWPDs can provide terahertz (THz) bandwidth which is the direct consequence of the elimination of the limiting RL time-constant in a traveling-wave device. Moreover, an STWPD can be used as a photomixer and/or high-frequency microwave/THz signal generator, provided that the input op- tical field consists of two optical signals with slightly off-tuned frequencies [30]. A thorough investigation of the optical propagation in super- conductive optical waveguides and proper analytical and numer- ical techniques for their analysis and design as well as the ef- 1051-8223/$25.00 © 2008 IEEE