Abstract:
A single photon detector includes a superconductor strip biased near its critical current. The superconductor strip provides a discernible output signal upon absorption of a single incident photon. In one example, the superconductor is a strip of NbN (niobium nitride). In another example, the superconductor strip meanders to increase its probability of receiving a photon from a light source. The single-photon detector is suitable for a variety of applications including free-space and satellite communications, quantum communications, quantum cryptography, weak luminescence, and semiconductor device testing.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present disclosure generally relates to photodetectors and more particularly to single photon detectors. 
     2. Description of the Related Art 
     A photodetector is a device that provides an electrical voltage or electrical current output signal when light is incident thereon. There are two basic types of photodetectors: linear detectors and quantum detectors. Linear detectors provide an output signal that is a linear function of the incident light intensity of average optical power. Quantum detectors provide an output signal upon detection of photons of the incident light. 
     A single-photon detector is a qunatum detector that can detect one incident photon at a time. Commercially available single photon detectors detect photons in the visible and shorter wavelength optical regions of the electromagnetic spectrum. These commercially available detectors include silicon avalanche photodiodes (Si APDs), such as part number C30954 from EG&amp;G Optoelectronics. A typical Si APD has a responsivity of 70 A/W (amps/watt) for photons with wavelengths of 900 nm, which drops to 36 A/W for photons with wavelengths of 1064 nm. Currently available Si APDS are not sensitive enough to detect photons with wavelengths longer than 1100 nm. 
     Characteristics of hot-electron photodetectors that are fabricated from superconducting NbN (niobium nitride) films are discussed in K. S. Il&#39;in, I. I. Milostnaya, A. A. Verevkin, G. N. Gol&#39;tsman, E. M. Gershenzon, and Roman Sobolewski, “Ultimate Quantum Efficiency of A Superconducting Hot-Electron Photodetector,”  Applied Physics Letters  Vol. 73, No. 26 (Dec. 18, 1999), pages 3938-3940 and in K. S. Il&#39;in, M. Lindgren, M. Currie, A. D. Semenov, G. N. Gol&#39;tsman, Roman Sobolewski, S. I. Chereduichenko, and E. M. Gershenzon, “Picosecond Hot-Electron Energy Relaxation in NbN Superconducting Photodetectors,”  Applied Physics Letters  Vol. 76, No. 19 (May 8, 2000), pages 2752-2754. Both publications are incorporated herein by reference. Some of the authors of the above mentioned articles are also inventors of this disclosure. While the first article suggests that “NbN HEPs should be able to detect single quanta of the far-infrared radiation and successfully compete as single-photon detectors with SIS-tunnel devices” ( Applied Physics Letters,  Vol. 73, No. 26 at p. 3940), there is no further relevant disclosure. The second article discusses the intrinsic response times of the hot-electron effect in NbN&#39;s, which applies to both linear and quantum NbN photodetectors. 
     SUMMARY 
     The present disclosure addresses the above mentioned limitation of prior art photodetectors by providing a single-photon, time-resolving detector with good quantum efficiency for photons in the wavelengths from the visible to the far infrared spectral region. 
     In one embodiment, the single-photon detector includes a strip of superconducting material. The superconductor is biased with electrical current that is near the superconductor&#39;s critical current. The superconductor provides a discernible output pulse signal upon absorption of a single incident photon. In one embodiment, the superconductor is a narrow strip of NbN film. In another embodiment, the superconductor has a meandering shape to increase its surface area and thus also the probability of absorbing a photon from a light source. 
     The present single-photon detector can be used in a variety of applications including free-space and satellite communications, quantum communications, quantum cryptography, weak luminescence, and semiconductor device testing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A shows a block diagram of a photon counter using the present superconducting single-photon detector (SSPD). 
     FIG. 1B shows a plan view of an SSPD. 
     FIG. 1C shows a plan view a of an SSPD having a meandering shape. 
     FIGS. 2A-2D graphically illustrate the physical process which the inventors believe gives rise to the voltage that develops across an SSPD upon absorption of a single photon. 
     FIGS. 3A-3L show cross-sectional views of an SSPD being fabricated. 
     FIG. 4A shows a block diagram of an apparatus including the present SSPD. 
     FIG. 4B shows further details of the biasing arrangement for the SSPD shown in FIG.  4 A. 
     FIG. 4C shows a typical current-voltage (I-V) plot for an SSPD at 4.2 Kelvin. 
     FIG. 5 shows plots of the probability of detecting an output pulse from an SSPD as a function of either incident light energy per pulse or, equivalently, the number of photons per device, per pulse using the apparatus shown in FIG.  4 A. 
     FIGS. 6A and 6B show waveforms of a typical output signal of the SSPD used in the apparatus shown in FIG.  4 A. 
     FIG. 7 shows oscilloscope traces of output signals of the SSPD used in the apparatus shown in FIG.  4 A. 
     FIGS. 8A-8C show schematic diagrams of various arrangements for coupling light to an SSPD. 
    
    
     The use of the same reference symbol in different figures indicates the same or identical elements. Further, the figures in this disclosure are schematic representations and not drawn to scale. 
     DETAILED DESCRIPTION 
     FIG. 1A shows a block diagram of a photon counter  10  including a superconducting single-photon detector (SSPD) in accordance with an embodiment of the invention. Referring to FIG. 1A, an SSPD  12  detects photons  16  emitted by a light source  11 , which includes suitable optics (not shown). It is to be understood that light source  11  is not necessarily a part of photon counter  10  and is, for example, a transistor which emits photons when switching. Upon absorption of an incident photon, SSPD  12  in response generates an electrical output pulse signal that is amplified by associated amplifier  13 . Each output pulse signal is recorded and counted by data acquisition system (DAQ)  14  (e.g., a computer equipped with appropriate interfere circuitry and software). 
     In one embodiment, SSPD  12  is a narrow, thin strip of a superconducting material that is electrically biased to provide an output pulse signal upon absorption of a single incident photon. As shown in the plan view of FIG. 1B, SSPD  12 , in this example, is a narrow strip of NbN (niobium nitride) film having a width D 1  of about 200 nm, a length D 2  of about 1 μm, and a thickness of about 5 nm. A direct current (DC) bias source (not shown) provides biasing current to SSPD  12  through gold contact pads  42 . SSPD  12  and contact pads  42  are conventionally disposed on a substrate; suitable substrates include sapphire and quarts for infrared and visible light applications. Silicon can also be used as a substrate, e.g. for infrared applications. SSPD  12  typically, but not necessarily, faces light source  11 . In the absence of incident photons and while SSPD  12  is conventionally cooled to a superconducting state, the voltage across SSPD  12  is zero because SSPD  12  is a superconductor and hence has zero resistance when in the superconducting state. A photon incident on SSPD  12  switches it into the resistive state, thereby developing a voltage drop across SSPD  12  detected by DAQ  14 . 
     As is well known, a superconductor, such as SSPD  12 , remains in a superconducting state only while the amount of current being carried by the superconductor, the temperature of the superconductor, and the external magnetic field surrounding the superconductor are maintained below certain values referred to as critical values. The critical values (i.e., critical current, critical temperature, and critical magnetic field) are characteristic of the superconducting material and its dimensions. To maintain SSPD  12  in the superconducting state in the absence of incident photons, SSPD  12  is maintained at a temperature below 10 Kelvin (the approximate critical temperature of a thin NbN film) such as 4.2 Kelvin and exposed to ambient Earth magnetic field as is conventional with superconductors. The biasing current through SSPD  12  is set just below the critical current to increase its sensitivity, thereby allowing single-photon detection. The critical current of SSPD  12  is experimentally determined by maintaining SSPD  12  well below its critical temperature and critical magnetic field and then increasing the amount of current flown through SSPD  12  until it transitions from a superconducting state (zero resistance) to a resistive state (some resistance). 
     FIGS. 2A-2D graphically illustrate the physical process which the inventors believe gives rise to the voltage pulse that develops across SSPD  12  upon absorption of a single photon. However, understanding of this is not necessary for making or using the SSPD. The dashed arrows in FIGS. 2A-2D schematically represent the flow of the biasing current through SSPD  12 . Referring to FIG. 2A, a photon incident on SSPD  12  creates a hot spot  21 , a region where the temperature of electrons is much higher than SSPD  12 &#39;s ambient temperature. The diameter of hot spot  21  directly depends on the energy of the incident photon. Within a few picoseconds, hot spot  21  diffuses further across SSPD  12  and becomes a larger hot spot  22  (FIG.  2 B). Hot spot  22  defines a region in SSPD  12  that is no longer superconducting. Because hot spot  22  is a resistive region, the biasing current is forced to flow around hot spot  22  and into regions between hot spot  22  and the edges of SSPD  12  that are still superconducting. This increases the current density in the still superconducting regions above the critical current density, thereby destroying superconductivity and creating resistive regions  24  (also known as phase slip centers) (FIG.  2 C). Thus, a resistive region  25  (FIG. 2D) is formed across the entire width of SSPD  12 . Biasing current flowing through resistive region  25  develops a voltage signal across SSPD  12 . 
     Following the formation of hot spot (i.e., resistive) regions is the cooling process associated with the diffusion of electrons out of the hot spot regions and simultaneous reduction of the electrons&#39; temperature via the electron-phonon energy relaxation mechanism. The cooling process takes a few tens of picoseconds and results in the automatic disappearance of the hot spot (and resistive region  25 ) and reestablishment of a superconducting path across SSDP  12 . The hot spot formation and the healing processes result in an output voltage signal having a pulse shape with an intrinsic width of approximately 30 ps. The width of the voltage pulse is determined by the specifics of the superconducting material and the energy of the incident photon. Because the output voltage pulse has a duration of only tens of picoseconds, SSPD  12  (and other SSPDs in accordance with this disclosure) can time resolve incident photon energy, and can distinguish photons arriving at a very high rate (e.g., above 10 9  photons per second). 
     Referring back to FIG. 1B, dimension D 1  of SSPD  12  is, in one embodiment, about 200 nm. If dimension D 1  is significantly wider than 200 nm, a detectable resistive region  25  (FIG. 2D) may not be formed as the biasing current may remain superconducting at all times and be able to flow around the resulting hot spot without exceeding the current density around the hot spot. Dimension D 1  can be increased for detection of very high energy (e.g., ultraviolet) photons. For detecting red to short-infrared photons, a dimension D 1  of 200 nm is suitable for an NbN SSPD. The length of the narrow section, dimension D 2 , is 1 μm in one embodiment. The length of the narrow section does not affect the physical process that gives rise to the output voltage pulse but does change the surface area and hence the overall quantum efficiency of SSPD  12 . The thickness of the narrow section is about 5 nm in one embodiment. The thickness of an SSPD directly affects the hot electron thermalization and relaxation processes, which are responsible for the healing of hot spots. Of course, the dimensions and critical values provided here are specific to the disclosed examples (which are designed to detect red and short-infrared photons) and can be varied depending on the energy levels of the photons of interest and the superconducting material used. For example, the dimensions of SSPD  12  can be modified to detect photons having wavelengths in the ultraviolet, visible, or far infrared spectral region. 
     In general, any thin and narrow strip of superconducting material can be used as an SSPD in accordance with this disclosure. Other metallic superconductors (so-called low-temperature superconductors), such as Nb (niobium), Pb (lead), or Sn (tin) can be fabricated with somewhat wider D 1  dimension for detecting red and short infrared photons. However, these other metallic superconductors are not as time resolving as is NbN because of their significantly longer output voltage response (in nanosecond to even microsecond range) which is due to their slow hot electron relaxation process. Recently discovered high-temperature superconductors, such Y—Ba—Cu—O (yttrium-barium-copper oxide compound), are predicted to require a D 1  dimension on the order of about 10 nm to 100 nm and have a response time on the order of about 1 ps. 
     FIG. 1C shows a plan view of a superconducting single photon detector  101  (SSPD  101 ) of the same type as SSPD  12 . SSPD  101  has a meandering shape to maximize its top surface area and thereby increase its probability of receiving an incident photon from a light source. In one example, SSPD  101  is a continuous NbN film having a width D 5  of about 0.2 μm, a device length D 6  of about 3 μm, and a thickness of about 5 nm. Other meandering shapes (e.g., zigzag shape) can also be used. 
     FIGS. 3A-3L show cross-sectional views of a superconducting single photon detector, such as SSPD  12 , being fabricated in accordance with one embodiment. Steps that are well known and not necessary to the understanding of the fabrication process have been omitted. Further, while specific fabrication process parameters are provided, other embodiments are not so limited because one of ordinary skill in the art can use other fabrication processes to make an SSPD. Referring to FIG. 3A, a 5 nm thick NbN film  32  is deposited on a substrate  31  by reactive magnetron sputtering. The reactive magnetron sputtering process is performed using an LH Z-400 sputtering system of the type supplied by Leybold-Herauss of Germany with the following parameters: 
     residual pressure is 1.3×10 −6  mbar; 
     substrate temperature is 900° C.; 
     partial N 2  pressure is 1.3× −5  mbar; 
     partial Ar pressure is 1.3× −3  mbar; 
     discharge voltage is 260V; 
     discharge current is 300 mA. 
     Substrate  31  is, for example, a 350 μm thick sapphire substrate that is polished on the active side. Other substrates can also be used such as a 125 μm thick Z-cut single crystal quartz polished on both sides. Any high-quality dielectric material that has low microwave loss and good cryogenic properties can be used as a substrate. 
     FIGS. 3B-3D illustrate the formation of alignment structures of NbN  32  for subsequent photolithography and electron beam lithography steps. In FIG. 3B, a 1.0-1.5 μm thick photoresist mask  33  is formed and patterned on NbN  32  by conventional photolithography using the following parameters: 
     photoresist material is AZ 1512; 
     spinning at 3000-5000 rps; 
     baking at 90° C., 30 minutes. 
     A KARL SUSS MA-56 aligner is used to align photoresist mask  33  over NbN  32 . Over the resulting structure, a 100 nm thick gold layer  35  is formed on top of a 5 nm thick titanium layer  34  using a double layer metallization process (FIG.  3 C). Gold layer  35  and titanium layer  34  are formed by vacuum evaporation at room temperature and at a residual pressure of 1.5×10 −5  Torr. Photoresist mask  33  is lifted off by immersing the structure in warm acetone for about 3 minutes or longer, leaving alignment structures consisting of gold layer  35  and titanium layer  34  (FIG.  3 D). 
     FIGS. 3E-3G illustrate the formation of internal contact pads on NbN  32 . In FIG. 3E, a 400 nm thick electron resist mask  36  is formed and patterned on NbN  32  by conventional electron beam lithography using the following parameters: 
     electron resist material is PMMA 950, 475; 
     spinning at 3000 rpm; 
     baking at 130° C., 10-30 minutes; 
     electron beam exposure current is 30 pA; 
     electron beam exposure voltage is 25 kV. 
     The length of the middle section of electron resist mask  36 , shown in FIGS. 3E and 3G as dimension D 2  (also, see FIG.  1 B), can be varied from about 0.15 μm to 10 μm to change the effective length of the SSPD in one embodiment. Electron resist mask  36  is cleaned in an oxygen plasma using the following parameters: 
     O 2  pressure is 10 −2  Torr; 
     residual pressure is 10 −5  Torr; 
     discharge current of 10 mA; 
     process time of 15 seconds. 
     A 400 nm thick gold layer  37  is then formed on top of a 3 nm thick chromium layer  38  using a double layer metallization process (FIG.  3 F). Gold layer  37  and chromium layer  38  are formed by vacuum evaporation using an LH-960 e-beam evaporation system from Leybold-Herauss of Germany at room temperature and at a residual pressure of 2×10 −6  Torr. Electron resist mask  36  is then lifted off, leaving internal contact pads consisting of gold layer  37  and chromium layer  38  (FIG.  3 G). 
     FIGS. 3H-3J illustrate the formation of a silicon dioxide mask (SiO 2 ), a “hard” mask for later ion milling processing steps. In FIG. 3H, electron resist mask  39  is formed on NbN  32  using a process similar to that used to form electron resist mask  36  discussed above. A SiO 2  layer  41  is then vacuum evaporated on the resulting structure as shown in FIG.  3 I. Electron resist mask  39  is lifted off, leaving an SiO 2  mask consisting of SiO 2  layer  41  (FIG.  3 J). The SiO 2  mask, which is transparent to the photons, defines the width of the SSPD. 
     External contact pads, consisting of 200 nm thick gold layer  42  on top of 7-10 nm thick titanium layer  43 , for coupling NbN  32  to external equipment such as a bias source are formed as shown in FIG.  3 K. The external contact pads are formed using a process similar to that used to form gold layer  37  and chromium layer  38 . Portions of NbN  32  between the external contact pads and the alignment structures are then removed by argon ion milling, defining the SSPD device (FIG.  3 L). 
     FIG. 4A shows a block diagram of a pulse counter  60  including an SSPD  12 . In pulse counter  60 , SSPD  12  is a 200 nm wide, 1 μm long, and 5 nm thick NbN film. Light source  11  outputs light pulses  16  to a beam splitter  62 , which splits the light for input to an attenuator  63  and a photodetector  64 . In pulse counter  60 , light source  11  is a laser that generates short light pulses at a repetition rate of about 76 MHz when it is a modelocked IR laser from Coherent Laser Group (MIRA laser) to about 82 MHz when it is a modelocked laser from Spectra Physics (Tsunami laser). Light source  11  can also be a GaAs semiconductor laser modulated from 1 Hz to 3 kHz. The wavelength of the photons from light source  11  is approximately 810 nm in this example. In other experiments, single photon detection was also achieved with photons having wavelengths of 500 nm to 2100 nm. Attenuator  63  is a series of absorbing filters used to reduce the number of photons incident on SSPD  12  to an average of less than one photon per pulse. For example, absorbing filters can be added to or removed from attenuator  63  so that the probability of having a photon in each pulse is 0.01, resulting in an average of one photon every 100 pulses. 
     Photons passing through attenuator  63  are focused onto SSPD  12  using conventional focusing lens  65 . A direct current (DC) bias source  67  provides biasing current to SSPD  12  through a wide-band “cold” bias-T  66  (also shown in FIG.  4 B). The output signal of SSPD  12  is coupled to a “cold” amplifier  68 , through bias-T  66 , for amplification prior to being transmitted outside a cryostat  69 . Cryostat  69  is a conventional liquid helium cryostat that maintains SSPD  12  at a temperature below its critical temperature. Cold amplifier  68 , a conventional cryogenic power amplifier, has a thermal equivalent noise (T noise ) of about 5 Kelvin, frequency range of 1-2 GHz, and gain (K p ) of 30 dB. Bias-T  66 , cold amplifier  68 , and SSPD  12  are conventionally housed within cryostat  69 . The output signal of cold amplifier  68  is further amplified by a power amplifier  70  to boost the output signal of SSPD  12  to a level detectable by a single shot oscilloscope  71 . Power amplifier  70  has a specified peak output power of about 0.2 W, frequency range of 0.9-2.1 GHz, and gain (K p ) of 32 dB. 
     A conventional photodetector  64  detects the split-off light pulses from beam splitter  62  and provides an output signal that triggers oscilloscope  71  to acquire the signal from power amplifier  70 . A CCD video camera  72  takes a picture of the screen of oscilloscope  71 , which is then downloaded to a computer  73  with video capture hardware for analysis. The data acquisition elements which include oscilloscope  71 , CCD video camera  72 , and computer  73  are, like the other depicted elements, exemplary. 
     FIG. 4B shows further details of the electrical biasing arrangement for SSPD  12 . As shown in FIG. 4B, 50-Ohm transmission lines  402  (i.e., transmission lines  402 A,  402 B,  402 C, and  402 D) are used to couple SSPD  12  to bias-T  66 , DC bias source  67 , and cold amplifier  68 . The coupling between SSPD  12  and transmission line  402 A is through a conventional high-bandwidth connection  401 , which is part of the SSPD  12  housing. Bias-T  66  has a DC port and an AC port which are schematically depicted in FIG. 4B as inductor “L” and capacitor “C”. The inductor and capacitor of bias-T  66  are preferably not dependent on temperature. One can also measure the performance of a particular bias-T  66  at cryogenic temperatures and determine the appropriate component values based on how the component values shift with temperature. Appropriate component values in this example are 0.2 μH or greater for inductor “L” and 1000 pF or greater for capacitor “C” at a temperature of about 4 Kelvin. The pulsed voltage output signal from SSPD  12  is applied to the AC port of bias-T  66  and amplified by cold amplifier  68  before being transmitted out of cryostat  69  via transmission line  402 C. Bias current from DC bias source  67  is provided to SSPD  12  through the DC port of bias-T  66 . DC bias source  67  has a variable DC current source  403  for providing bias current, a current meter  406  for reading the supplied bias current, and a voltage meter  405  for reading the voltage across SSPD  12 . DC bias source  67  also includes an adjustable voltage limit  407  to limit the voltage across SSPD  12  when it switches to the resistive state. A typical setting for voltage limit  407  is about 3 mV to 5 mV. The critical current of SSPD  12  is determined by maintaining SSPD  12  well below its critical temperature using cryostat  69  (note that the ambient Earth magnetic field is well below the critical magnetic field of SSPD  12 ). DC current source  403  is then adjusted until SSPD  12  transitions from the superconducting state to the resistive state. The bias current, read using current meter  406 , which transitions SSPD  12  into the resistive state is the critical current. SSPD  12  is normally operated with a bias current that is below the critical current. A typical range of biasing current for SSPD  12  is 40-50 μA. Preferably, the biasing current is set as close to the critical current as possible without falsely transitioning SSPD  12  into the resistive state in the absence of an incident photon. 
     FIG. 4C shows a typical current-voltage plot for SSPD  12  at 4.2 Kelvin. In FIG. 4C, the vertical axis indicates the DC bias current through SSPD  12  (in μA) as measured by current meter  406  while the horizontal axis indicates the DC voltage drop across SSPD  12  as measured by voltage meter  405  (FIG.  4 B). As indicated in FIG. 4C, the critical current of SSPD  12  is approximately 45 μA. As long as the bias current is below the critical current, SSPD  12  remains in the superconducting state represented by the vertical trace beginning at 0 mV. Although the biasing current through SSPD  12  is 40 μA, the voltage across SSPD  12  remains at 0 mV while SSPD  12  is in the superconducting state (because SSPD  12  is a superconductor and hence has zero resistance in the superconducting state). Thus, SSPD  12  remains on operating point “A” under normal conditions. When SSPD  12  absorbs a photon, SSPD  12  can become resistive thereby causing the current through it to drop and the voltage across it to rise. This moves the operating point of SSPD  12  from point “A” to a point “B” on a dashed trace labeled “Meta Stable Region” in FIG.  4 C. Note that points “A” and “B” are connected by a solid 50-Ohm load trace, which reflects the impedance of the 50-Ohm transmission line presented to SSPD  12 . The separation point between the Meta Stable Region and the Normal Resistance Region is the voltage level corresponding to the critical current multiplied by the 50-Ohm load resistance, which comes out to 2.25 mV (i.e., 45 μA×50 Ω=2.25 mV) in the example of FIG.  4 C. For a short time (tens of picoseconds) after absorption of the photon, the operating point of SSPD  12  remains on point “B”. Thereafter, the operating point of SSPD  12  returns to point “A”. If the current through SSPD  12  is increased enough, to slightly above 45 μA in the example shown in FIG. 4C, the bias current will exceed the critical current thereby moving the operating point of SSPD  12  to point “C” on the trace labeled “Normal Resistance Region”. While at operating point “C”, photon detection is not possible because SSPD  12  will remain in the resistive state until its bias current is lowered below the critical current. Note that the voltage across SSPD  12  on point “C” is limited by the setting of voltage limit  407 , which is 3 mV in this example. 
     As will be demonstrated below, single photon detection requires a linear dependence on the number of absorbed photons. For a mean number of m photons absorbed per laser pulse, the probability of absorbing n photons from a given pulse is          P        (   n   )       =           e     -   m            (   m   )       n       n   !                              
     When m&lt;&lt;1,          P        (   n   )       =       m   n       n   !                              
     For the apparatus shown in FIG. 4A, m&lt;&lt;1 can be achieved by adjusting attenuator  63  such that the number of photons incident on SSPD  12  is reduced to an average of much less than one per laser pulse. From the foregoing, the probability of absorbing 1 photon per pulse is 
     
       
           P (1)= m    
       
     
     The probability of absorbing 2 photons per pulse is          P        (   2   )       -       m   2     2                            
     (Of course, P(2) is the probability of absorbing two photons on the same spot on the superconducting film at the same time; otherwise, the two photons would count as two single photons). The probability of absorbing 3 photons per pulse is          P        (   3   )       -       m   3     6                            
     Thus, for m&lt;&lt;1, the probability of detecting one photon per pulse is proportional to m, the probability of detecting two photons is proportional to m 2 , the probability of detecting 3 photons is proportional to m 3 , and so on. 
     FIG. 5 shows plots of the probability of SSPD  12  producing an output voltage pulse in one experiment. In FIG. 5, the vertical axis indicates the probability of SSPD  12  detecting a photon in a single light pulse, based on the number of light pulses detected by pulse counter  60  over a long period of time. The lower horizontal axis indicates the average energy (in femtojoules) of each light pulse focused on SSPD  12  while the upper horizontal axis indicates the computed corresponding number of incident photons per light pulse, per 0.2×1 μm 2 , which is the area of SSPD  12  in the experiment. The critical current, I c , was experimentally determined to be around 45 μA. 
     Trace  501  corresponds to an SSPD  12  that was biased to 0.95 Ic (i.e., 95% of the critical current). Trace  501  shows the linear dependence of detection probability to the average number of photons per pulse, indicating single photon detection. Trace  502  corresponds to an SSPD  12  that was biased to 0.9 Ic. Trace  502  shows a quadratic dependence of detection probability to the average number of photons per pulse, indicating two photon detecting. Further reducing the bias current of SSPD  12  to 0.7 Ic results in trace  503 . Trace  503  shows a cubic dependence of detection probability to the number of photons per pulse, indicating three photon detection. From the foregoing, setting the bias current of SSPD  12  near its critical current allows single photon detection. 
     FIG. 6A shows a waveform of a typical output signal of SSPD  12 . Pulse  91 , which corresponds to a detected incident photon, is readily distinguishable from background noise. As shown in the magnified view of FIG. 6B, pulse  81  has full width half maximum (FWHM) of about 100 ps. The bandwidth of pulse  81  was limited by the bandwidth of the data acquisition equipment used, not by SSPD  12 . In FIGS. 6A and 6B, the vertical axis is in an arbitrary unit of voltage while the horizontal axis is in nanoseconds. An SSPD in accordance with this disclosure simplifies the detection process by providing an output voltage pulse that is readily read using conventional data acquisition techniques. 
     Spectroscopic information about the energy of the detected photon can also be obtained by analyzing the shape of the output signal of an SSPD. A hot electron is created when a photon is absorbed by the SSPD and breaks a so-called Cooper pair. The hot electron collides with other Cooper pairs in the SSPD, thereby breaking the Cooper pairs and creating more hot electrons. Because the number of broken Cooper pairs is proportional to the energy of the incident photon, and the shape of the output voltage pulse depends on the number of hot electrons, the shape of the output voltage pulse depends on the energy of the incident photon. For example, one could integrate the output voltage pulse of SSPD  12  as a function of time and find a correlation between the incident photon energy and the integral of the pulse. 
     FIG. 7 shows traces captured by oscilloscope  71  (FIG. 4A) in one experiment. Trace  701  shows the output signal of photodetector  64  upon detection of light pulses received from beam splitter  62 . Trace  702  shows the amplified output signal of SSPD  12  for incident light pulse powers corresponding to an average of 100 incident photons per device area, per light pulse. In that case, the probability of SSPD  12  producing an output voltage pulse for each incident light pulse is 100%. Trace  703  shows the amplified output signal of SSPD  12  for incident light pulse powers corresponding to an average of 40 photons per device area, per light pulse. Similarly, traces  704 ,  705 ,  706 ,  707 , and  708  show the amplified output signal of SSPD  12  for incident pulse powers corresponding to an average of 10, 5, 5, 1, and 1 photon per device area, per light pulse, respectively. Traces  707  and  708  demonstrate that SSPD  12  has enough sensitivity to detect a single photon. The traces also show that the detected pulse has approximately the same shape and amplitude regardless of how many photons are absorbed. 
     FIGS. 8A-8C show diagrams of various arrangements for coupling light to the SSPD. Note that FIGS. 8A-8C are schematic representations and not drawn to scale (for example, SSPD  12  in actuality has practically zero thickness relative to its substrate). In FIG. 8A, incident light beam  16  passes through an aperture diaphragm  802  in front of a hemispherical lens  803 . Substrate  823  of SSPD  12  functions as an optical extension and is directly bonded to hemispherical lens  803 . Light beam  16  is focused onto SSPD  12  through hemispherical lens  803  and substrate  823 . Hemispherical lens  803  and substrate  823  are preferably of the same material so that the diameter of aperture diaphragm  802  can be maximized. SSPD  12  can also be mounted with its superconducting film directly facing light beam  16  (on the other end of substrate  823 ) by extending hemispherical lens  803 . In FIG. 8B, SSPD  12  receives the incident light beam from a single-mode or multi-mode fiber  805 . Light that is not absorbed by SSPD  12  passes through substrate  823  and into mirror  806  where the light is reflected off a mirrored surface  807  and focused onto SSPD  12 . In FIG. 8C, incident free-propagating light beam  16  passes through anti-reflective coating  808 , substrate  823 , and quartz (or silicon for infrared applications) parabolic lens  810 . Light beam  16  is reflected off mirrored surface  811  and focused onto SSPD  12 . 
     While specific embodiments of this invention have bene described, it is to be understood that these embodiments are illustrative and not limiting. Many additional embodiments that are within the broad principles of this invention will be apparent to persons skilled in the art.