# Patent

## Title
Integrated silicon-based nonlinear photodetector

## Abstract

Disclosed is a system including an integrated silicon-based structure including a microcavity configured to receive optical energy from an input beam carrying an optical signal and absorb the optical energy by a nonlinear multi-photon absorption process. For example, the multi-photon absorption process can be two-photon absorption (TPA). The integrated silicon-based structure further includes electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing an electronic signal indicative of the optical signal. A related method is also disclosed.

## Background
PRIORITY CLAIM
This patent application claims the benefit of the priority date of U.S. Provisional Patent Application No. 61/111,015, filed on Nov. 4, 2008, pursuant to 35 USC 119. The entire content of this provisional application is herein incorporated by reference.


STATEMENT AS TO FEDERALLY FUNDED RESEARCH
This invention was made with government support under Grant No. DMR0819762 awarded by the National Science Foundation and under Contract No. FA9550-07-1-0014 awarded by the U.S. Air Force and under Contract No. W911NF-07-D-0004 awarded by the Army Research Office. The government has certain rights in this invention.


FIELD OF THE INVENTION
The invention relates to an integrated silicon-based nonlinear photodetector suitable for use in silicon photonics and in telecommunications networks.
BACKGROUND
In many applications, including optical telecommunications, it is often desirable to convert an optical signal into an electrical signal. This can be done by photodetection, whereby the optical signal is linearly absorbed in a semiconductor material to create free carriers that cause an electrical response at nearby biased electrodes. Ideally, well established fabrication techniques for silicon, such as complementary metal-oxide-semiconductor (CMOS), could be used to fabricate an integrated photodetector in silicon. Unfortunately, the energy of the indirect electronic bandgap of silicon (1.1 eV) is too large for linear absorption of the energy of photons in the telecommunication band (0.8 eV).
SUMMARY
In general, disclosed herein as a system including an integrated silicon-based structure including a microcavity configured to receive optical energy from an input beam carrying an optical signal and absorb the optical energy by a nonlinear multi-photon absorption process. For example, the multi-photon absorption process can be two-photon absorption (TPA). The integrated silicon-based structure further includes electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing an electronic signal indicative of the optical signal.
Embodiments of the system can include one or more of the following features.
The integrated silicon-based structure can further include an optical waveguide for receiving the input beam carrying an optical signal, with the microcavity being optically coupled to the waveguide to receive the optical energy from the input beam.
The microcavity can include silicon, with the nonlinear multi-photon absorption process taking place in the silicon.
The microcavity can have a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, and wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR, with 1.2 μm<λAIR<2.4 μm. Alternatively, or in addition, the microcavity can have a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, and wherein the system further includes a source for the input beam, and wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR.
For example, Q>100 and VMODE<1000 λAIR3, or more specifically, for example, Q>1000 and VMODE<100 λAIR3, or even more specifically, for example, VMODE<10 λAIR3.
Also, for example, the input beam carrying the optical signal can have a carrier frequency equal to ω, and wherein |ω−ω0|/ω0<10/Q, or more specifically, for example, wherein |ω−ω0|/ω0<5/Q, or even more specifically, for example, wherein |ω−ω0|/ω0<1/Q.
Also, for example, the microcavity can be configured to achieve a conversion efficiency for the multi-photon absorption of the optical energy in the input beam of greater than 15% for an input beam power smaller than 0.2 mW.
The microcavity can be a photonic crystal structure.
The waveguide can be a photonic crystal structure.
The integrated silicon-based structure can be implemented in a Complementary metal-oxide-semiconductor (CMOS) platform.
The input beam carrying the optical signal can have a carrier frequency equal to ω, wherein N photons, with N>1, are absorbed simultaneously by a material in the microcavity during the multi-photon absorption process, and wherein the multi-photon absorption material has an indirect electronic bandgap Eg larger than the energy corresponding to a single photon of frequency ω and smaller than the energy of the N photons absorbed simultaneously by the material.
The integrated silicon-based structure can further include an output optical waveguide optically coupled to the microcavity and configured to output optical energy from the microcavity that is not absorbed by the multi-photon absorption process.
Furthermore, in certain embodiments of the system, the integrated silicon-based structure comprises multiple microcavities each optically coupled to the waveguide and configured to receive optical energy from the input beam and absorb the optical energy by a nonlinear multi-photon absorption process.
In general, in another aspect, disclosed herein is method including: i) directing an input beam carrying an optical signal into an integrated silicon-based structure including a microcavity; ii) receiving optical energy in the microcavity from the input beam and absorbing the optical energy in the microcavity by a nonlinear multi-photon absorption process; and iii) producing an electronic signal in response to the nonlinear multi-photon absorption process in the microcavity, the electrical signal indicative of the optical signal. For example, the multi-photon absorption process can be two-photon absorption (TPA).
Embodiments of the method can include one of more of the following features.
The integrated silicon-based structure can further include an optical waveguide for receiving the input beam carrying an optical signal, with the microcavity being optically coupled to the waveguide to receive the optical energy from the input beam.
The integrated silicon-based structure can further include electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing the electronic signal indicative of the optical signal.
The microcavity can include silicon, with the nonlinear multi-photon absorption process taking place in the silicon.
The microcavity can have a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR, and wherein Q>100 and VMODE<1000 λAIR3. More specifically, for example, Q>1000 and VMODE<100 λAIR3, more specifically, for example, wherein VMODE<10 λAIR3.
The input beam carrying the optical signal can have a carrier frequency equal to ω, and wherein |ω−ω0|/ω0<10/Q. More specifically, for example, wherein |ω−ω0|/ω0<5/Q. Even more specifically, for example, wherein |ω−ω0|/ω0<1/Q.
The input beam carrying the optical signal can have a wavelength in air equal to λAIR, and 1.2 μm<λAIR<2.4 μm.
The microcavity can be configured to achieve a conversion efficiency for the multi-photon absorption of the optical energy in the input beam of greater than 15% for an input beam power smaller than 0.2 mW.
The microcavity can be a photonic crystal structure.
The waveguide can be a photonic crystal structure.
The integrated silicon-based structure can be implemented in a Complementary metal-oxide-semiconductor (CMOS) platform.
The input beam carrying the optical signal can have a carrier frequency equal to a), wherein N photons, with N>1, are absorbed simultaneously by a material in the microcavity during the multi-photon absorption process, and wherein the multi-photon absorption material has an indirect electronic bandgap Eg larger than the energy corresponding to a single photon of frequency ω and smaller than the energy of the N photons absorbed simultaneously by the material.
The integrated silicon-based structure can further include an output optical waveguide optically coupled to the microcavity, and wherein the method can further include outputting optical energy from the microcavity that is not absorbed by the multi-photon absorption process through the output optical waveguide.
Furthermore, in certain embodiments of the method, the integrated silicon-based structure comprises multiple microcavities each optically coupled to the waveguide and configured to receive optical energy from the input beam and absorb the optical energy by a nonlinear multi-photon absorption process.
In another aspect, the method can be used to perform optical performance monitoring (OPM) of one or more channels of an optical telecommunications network.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting.
The term “comprising” in the claims and any variations thereof are used synonymously with the term “including” and variations thereof and are open, non-limiting terms.
The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from this disclosure and from the claims.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1a and FIG. 1b each show a schematic layout of an integrated silicon-based nonlinear photodetector, including an external circuit through which the electrical signal can be characterized. In FIG. 1a, no output port is provided for the input signal, unlike the case in FIG. 1b where an output port is provided.
FIG. 2a shows an overall illustration of an array of all-silicon photodetectors working in parallel. The inset of FIG. 2a illustrates the two-photon absorption process (TPA) in silicon. FIG. 2b and FIG. 2c show two different physical implementations of the integrated silicon nonlinear photodetector. The schematics shown in the inset of each of the FIGS. 2b and 2c depict certain parameters and schematic illustrations of the two implementations.
FIG. 3 is a schematic of an embodiment similar to that shown in FIG. 2c, except that multiple optical microresonators are cascaded in FIG. 3 to increase the overall efficiency of the photodetector.
FIGS. 4a-f show time-dependent responses of an optical microresonator to different sequences of input light pulses. FIG. 4a shows a regular 1 GHz bit-rate signal train that is sent to an integrated photodetector. FIG. 4b shows the corresponding absorbed power Pabs in the microcavity. FIG. 4c shows the change in the refractive index Δn of the microcavity due to the absorbed power. The responses of the same integrated photodetector to a pseudorandom train of optical signals (the temporal profile of this signal train is shown in FIG. 4d) are correspondingly shown in FIGS. 4e and f. 
FIGS. 5 a-c show the plots of conversion efficiency Eabs/Ein as a function of the energy input per bit for optical microresonators with different Q-factors. The insets in FIGS. 5b and 5c magnify the regions of each plot close to the intersection of the two plotting axes.
FIG. 6 is a plot of the maximum absorption efficiency per bit as a function of the heat relaxation constant τth.
FIGS. 7 a-c shows plots of the continuous-wave regime power conversion efficiency as a function of the input power for different Q-factors. The behavior of the microcavity under different levels of preshift Δω (displayed as a ratio Δω/ω) is also shown.



Like reference symbols in the various drawings indicate like elements.
DETAILED DESCRIPTION
Disclosed is an apparatus and method suitable for use as an all-silicon integrated detector to convert optical signals into electrical signals via the nonlinear process of two-photon absorption. This apparatus and method can be used, for example, in telecommunications and silicon photonics.
An integrated photodetector that is composed entirely of silicon is attractive due to well-established fabrication techniques for processing silicon, such techniques can be exploited to readily implement the photodetector in a CMOS platform.
FIGS. 1a and 1b show two different schematic representations of the apparatus. In the first embodiment of an integrated silicon-based detection system 100 shown in FIG. 1a, an input signal light 110 is carried by an optical waveguide 120, which is optically coupled to an optical microresonator 130. As described further below, in preferred embodiments, both the optical waveguide and the optical microresonator are formed in a silicon-based integrated structure. Upon optical coupling of the signal light into the optical microresonator, the optical energy if the coupled light 115 is absorbed by a nonlinear multi-photon absorption process in the silicon in the microresonator to create free carriers 140. These free carriers can be detected, for example, as a photocurrent 150 that flows in an external circuit when an external voltage 160 is applied across a pair of electrodes 170 adjacent to the optical microresonator. The role of the reversed biased p-i-n junction formed at the optical microresonator by the external voltage 160 is twofold. Besides enabling the electrical read-out of the optical signal, the reversed biased p-i-n junction also allows the free carriers generated inside the microresonator to be swept out, when a large enough voltage is applied to the junction. This substantially reduces the optical loss induced by free carrier absorption (FCA), thereby improving the overall performance of the detection system 100.
In another embodiment, an integrated detection system 190 comprising all the elements illustrated in FIG. 1a is shown in FIG. 1b. What distinguishes the apparatus shown in FIG. 1a from that shown in FIG. 1b is the presence of an additional dedicated optical output port, positioned after the optical microresonator 130. Such an output port can be implemented, for example, in the form of another optical waveguide 125, as shown in FIG. 1b. This optical output port enables the transmission of an output signal light 180 that has not been absorbed by the microresonator to be reutilized in a different part of the chip.
Both embodiments of the apparatus shown in FIGS. 1a and 1b can be used as an in-line detector, wherein only a portion of the optical signal light is picked off for analysis. Such analysis can include the monitoring of optical power levels, for example, in one or more different channels in an optical communications network, or the conversion of the optical signal light into electrical signals. In addition, the disclosed apparatus can also be used for Optical Performance Monitoring (OPM) on an all-silicon platform. In general, OPM devices are similar to photodetectors but instead of monitoring the complete and exact bit sequence of a train of optical signals, they perform a comprehensive assessment of the optical signal quality. For more information regarding OPM, see: S. Wielandy et al., J. of Lightwave Tech., 22, 784-793 (2004).
In addition, the apparatus disclosed in FIG. 1a can also be used expressly as an end-point detector for conversion of optical signals into electrical signals.
FIG. 2a shows a schematic illustration of a possible on-chip integration of the photodetector 200. Even though the system depicted in FIG. 2a comprises an array of four all-silicon photodetectors 210, the disclosed apparatus is in no way constrained to operate solely in a multiplex mode for simultaneous detection of optical signal across multiple channels. It does, however, illustrate how readily the disclosed apparatus can be incorporated into, for example, an extensive, multi-channel telecommunication network. Nonetheless, a single all-silicon based photodetector 210 is sufficient by itself to convert an arbitrary train of ultrafast ( ̃10 Gbit/s) and ultralow energy ( ̃1 pJ) light pulses 220 into an electric binary code 230 (represented as a set of 1's and 0's in the figure). The electrical signal is then fed into receiver chip 240, which forms part of a standard electronic circuit.
In certain embodiments of the apparatus disclosed here, the nonlinear multi-photon absorption process can be two-photon absorption (TPA). The inset of FIG. 2a shows a sketch of the two-photon absorption (TPA) process that is employed as the basis for this photodetection scheme. The absorption of one photon in the telecommunication band (1.55 μm or 0.8 eV, the magnitude of which is depicted by the length of arrow 250) in silicon, which has an indirect electronic bandgap 260 of 1.1 eV is insufficient to cause a valence electron, e−, to be promoted into the conduction band to become a free carrier, while leaving a positively charged hole, h+, in the valence band. In TPA, two 0.8 eV photons are absorbed simultaneously by silicon, the sum of the energy of these two photons is now larger than the bandgap of silicon, allowing a valence electron to be liberated as a free carrier. Because TPA relies on nonlinear interactions between the optical field and silicon, TPA is proportional to higher orders of optical intensity. Nonlinear effects like TPA can therefore only be observed in the regime of high optical fields.
In order to obtain dramatic enhancement of the optical field to achieve TPA, modest optical fields typically used in telecommunications and silicon photonics are optically coupled from an optical waveguide into an optical microcavity or a photonic crystal structure, in the apparatus and method disclosed herein.
Details regarding optical coupling, optical microcavities, and parameters related to the description of optical microcavities are given below.
Optical coupling describes the transfer of energy among electromagnetic modes whose respective electromagnetic fields overlap with one another both in space and frequency. Evanescent optical coupling (a particular type of optical coupling) between a waveguide mode and a microresonator mode is used to transfer energy from the optical waveguide to the optical microresonator in certain embodiments of the photodetector. Specifically, the evanescent optical coupling involves coupling between the confined modes in the waveguide and microresonator, respectively, because an evanescent portion of the mode confined to the waveguide extends into the microresonator, and vice-versa with respect to an evanescent portion of the mode confined in the microresonator extending into the waveguide.
One component of the all-silicon nonlinear detector is the optical microresonator. An optical microresonator (or optical microcavity, which terms are used interchangeably herein) is as a structure that confines electromagnetic energy, both spatially and temporally, by resonant recirculation of light, in such a way that the electromagnetic energy is trapped for many optical periods in a volume in which one or more spatial dimensions are of the size of a few wavelengths of light or smaller. Parameters relevant to the microcavities are the quality factor Q, resonant frequency ω0, and modal volume Vmode.
The frequency of the electromagnetic wave confined inside the optical microcavity or optical microresonator is termed the resonant frequency ω0. Another parameter of an optical microcavity is the quality factor Q, defined as




  
    
      
        Q
        =
        
          
            ω
            0
          
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              Electromagnetic
              ⁢
              
                
              
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              field
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              by
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              microresonator
            
            
              Power
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              dissipated
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              microresonator
            
          
        
      
    
    
      
        (
        1
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where ω0 is the resonant frequency. The magnitude of the Q-factor indicates how well the optical microresonator can store optical energy.

The definition of the modal volume employed here is given by the following expression




  
    
      
        
          V
          MODE
        
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              (
              
                ∫
                
                  
                    d
                    
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where n({right arrow over (r)}), E({right arrow over (r)}) stand for the refractive index and the electric field, respectively, at position {right arrow over (r)} in the structure.
With respect to nonlinear effects, TPA is not the only nonlinear phenomenon that can occur in the microcavity. In particular, free-carrier absorption (FCA) can also be included in the description of the system. TPA and FCA introduce two nonlinear absorption mechanisms into the optical microcavity, and their respective rates scale as Q2/VMODE and Q2/VMODE2 (for more information, see: S. F. Preble et al. Opt. Lett. 30, 2891-2893 (2005)).
The presence of free carriers further influences the response and optical properties of the microcavity. For instance, the steady-state population of the electron-hole free carriers generated by TPA modifies the refractive index of the microcavity (a phenomenon known as free carrier dispersion, FCD), blue shifting the resonant frequency of the microcavity. In contrast, the population of phonons generated via relaxation processes (both of interband and intraband character) of the free carriers produced by TPA gives rise to a red shift of the resonant frequency ω0.
Another feature of the integrated photodetector is the optical waveguide. In general, an optical waveguide is a structure that transports electromagnetic energy between two different locations using a physical mechanism that enables electromagnetic energy confinement. In certain embodiments, a dielectric waveguide in which the physical mechanism for electromagnetic energy confinement is total internal reflection can be used (e.g. regions of higher dielectric index material surrounded by a lower dielectric index material). Other types of optical waveguiding mechanism can also be implemented.
There are several ways to construct suitable optical waveguides and optical microcavities. In certain embodiments one or both of such structures can be constructed as, for example, regions of higher dielectric index material surrounded by a lower dielectric index material, such as is typical in optical fibers or planar waveguides. In other embodiments, one or both of such structures can be part of a photonic crystal structure.
Photonic crystals are structures having a periodic variation in dielectric constant. One description of photonic crystals is that the solutions for propagating electromagnetic (EM) modes within the periodic structure give rise to a photonic “band” structure, in which propagating EM modes having frequencies within a “photonic bandgap” cannot exist within the periodic structure. This band theory for EM waves is analogous to the band theory developed for electrons in crystals.
In other applications, a photonic crystal includes a series of defects that combine to form a waveguide within the photonic crystal. The series of defects support EM modes having frequencies within the photonic bandgap that can propagate along the series of defects but are otherwise confined to regions of the photonic crystal in the vicinity of these defects. Defect-based waveguides in photonic crystals can include sharp turns since the photonic bandgap can prevent propagation of the EM radiation away from the waveguide for at least some, if not all, propagation directions. Further description of photonic crystals can be found in, for example, Nelson et al. in U.S. Pat. No. 5,999,308, the contents of which are incorporated herein by reference.
FIG. 2b shows a physical implementation of an embodiment of the all-silicon nonlinear photodetector 210 depicted in FIG. 2a, without the electrodes and other standard electronic components shown in FIGS. 1a and 1b. The gray pattern with different shading intensities depicted in the middle of the figure represents the spatial distribution of the electromagnetic field intensity across the photodetector 210. A silicon photonic crystal (PhC) microcavity 280 is implemented in a hexagonal lattice of air holes 281 in silicon. For ease of visual interpretation, the boundary of the hexagonal lattice is marked with dashed lines to denote the PhC microcavity 280. Exemplary dimensions for the radius of the holes r, is 90 nm, while the periodicity of the lattice, d, can for example be 330 nm. These geometric parameters of the PhC microcavity influence the quality factor Q of the microcavity and also determine the resonant frequency ω0. In particular, dimensions of the microcavity are chosen to have one or more spatial dimensions of the microcavity be the size of a few wavelengths of light or smaller. This enables signal light at the resonant frequency ω0 to be confined effectively, increasing the Q-factor of the microcavity.
The hexagonal lattice of air holes 281 in the silicon define a photonic bandgap structure that prevents electromagnetic modes having a frequency in the photonic bandgap from propagating through hexagonal lattice. In other words, there are no modes having a frequency in the photonic bandgap that have a real-valued wavenumber. The PhC microcavity is formed by a region of defects in the hexagonal lattice. For example, microcavity 280 in FIG. 2b is formed by a region in the silicon where the air holes 281 are absent. As a result, microcavity 280 can support propagating electromagnetic modes having a frequency in the photonic bandgap; however, such modes are substantially confined to the microcavity because of the photonic bandgap formed by the surrounding air-hole lattice structure. An evanescent component of the confined electromagnetic modes extends beyond the microcavity and provides a basis for coupling between microcavity 280 and any nearby microcavities and/or waveguides. Moreover, as explained in greater detail further below, because the electromagnetic modes are substantially confined to the microcavity and because the dimensions of the microcavity are set to be comparable the wavelength of the confined modes (and further because of the large quality factor (Q), and the small modal volumes VMODE), the peak optical field intensity inside the microcavity can become very large, giving rise to nonlinear optical effects like TPA that are otherwise not observed at modest optical power.
An optical waveguide 270 is formed in the area on the Si slab without the air holes. Once again, as a visual aid the area comprising the optical waveguide 270 is demarcated as a rectangle with dashed perimeter, as shown in FIG. 2b. The dimension of this waveguide is defined by the boundary of the air holes bordering it. In the particular configuration (where the waveguide acts simultaneously both as an input and output port) shown in FIG. 2b, the photodetector can be optimized, by a judicious choice of geometric parameters for the size of air holes, the size of the PhC microcavity 280, the separation between the microcavity 280 and the waveguide 270 so that the decay rate of the optical microresonator into the waveguide matches the nonlinear absorption rate of the optical signal light in the microresonator. In certain embodiments, this can lead, in principle, to the complete absorption of the incident power, through a general mechanism often described as “Q-matching”.
The inset of FIG. 2b shows the pertinent parameters and magnitudes of the all-silicon photodetector 210. Sin is the input signal light carried by the optical waveguide 270 portion of the integrated all-silicon photodetector 210. When operating in the configuration in which the optical waveguide 270 acts both as the input and output port, the output light signal Sref is carried also relayed by the optical waveguide 270 out of the photodetector 210. τIO denotes the coupling rate between the optical microcavity 280 and the waveguide 270, while αcav is the electric field amplitude inside the microcavity. The embodiment depicted in FIG. 2b can be implemented in silicon using well-established semiconductor manufacturing techniques for silicon.
The physical implementation of another embodiment of the all-silicon nonlinear photodetector 210 is shown in the main panel of FIG. 2c, again without the electrodes and other standard electronic components shown in FIGS. 1a and 1b. 
The device in FIG. 2c consists of a dielectric optical waveguide 275 coupled to an optical disk microresonator 285. In the presently described embodiment, both elements are composed of silicon. In general, the device shown in FIG. 2c can be implemented with any high index material being surrounded with a low index material. Besides having both 275 and 285 be composed from silicon, and separated by air (the low index medium), the structure can also be implemented by patterning and depositing the silicon (the high index medium), and surrounding the silicon with some other solid, lower-index material (such as SiO2). In either case, the silicon waveguide and microcavity can be grown on a substrate of SiO2 using well-established semiconductor manufacturing techniques. As an example, the structure can be formed with 1000 nm of SiO2, on which 200 nm of silicon is patterned and deposited. In the structure shown in FIG. 2c, an exemplary width of the waveguide and an exemplary radius of the disk of w=290 nm and rd=730 nm, respectively, can be chosen. As described in the preceding figure, the modulating gray pattern depicted in the structures 275 and 285 shows the spatial variation of the electromagnetic field intensity across the device. This spatial depiction of the electric field clearly demonstrates the optical coupling (through evanescent coupling) between the waveguide 275 and the microcavity 285.
The limited spatial dimensions of the components 260, 270, 275, and 285, as explained earlier, enhance the nonlinear effects that occur in a microcavity. The exemplary geometrical parameters used in FIGS. 2b and 2c have been chosen to tune the resonant wavelength of a TM resonant mode of the optical microcavity or the disk to 1.55 μm, the telecommunication wavelength. While the apparatus shown in FIG. 2c is well suited for use in Optical Performance Monitoring (OPM), the apparatus shown in FIG. 2b can also be used.
The kind of symmetric structure shown in FIG. 2c can also operate in the linear regime as a so-called all-pass filter, in which 100% transmission can be achieved for all frequencies. In the linear regime, the signal light intensity is below the threshold intensity required for free carriers creation via TPA in the microcavity. All signal light that is optically coupled into the microcavity is coupled back out into the waveguide without any loss.
In the inset of FIG. 2c, all features are similar to those shown in the inset of FIG. 2b, the difference being a longer waveguide 275 that can also be used to carry the transmitted output signal Strans, coupled out from the microcavity 285, in the same direction as the incoming light signal Sin. The reflected signal Sref carries some of the signal light back in the direction along which the incoming light signal originates.
FIG. 3 is similar to FIG. 2c except for the incorporation of multiple optical microcavities, shown schematically as 285, 286, 287, 288, and 289 in the integrated photodetector 210. The same numerals are used for equivalent structures in FIGS. 2c and 3. Once again, electrodes and other standard electronic circuit components are not shown here. Even though five microcavities are depicted in FIG. 3, it is not a limitation to how this embodiment can operate. Any number of microcavities, appropriate for the photodetector system, can be cascaded in this manner. The cascaded design can increase the overall conversion efficiency of the photodetection system. More than one microcavity (285, 286, etc) is optically coupled to the waveguide 275 in a cascaded manner. The microcavities are all arranged at the same distance away from the plane of the waveguide, equally spaced from one another, and optically coupled to the waveguide to receive optical energy from the input beam Sin. The arrows in FIG. 3 indicate the direction of propagation of the optical signal light.
The input beam (Sin) is guided along the waveguide 275 and optically couples into the first optical microcavity 285. Part of the optical signal light confined in the optical microcavity is absorbed through TPA to create free carriers. The remainder of the unabsorbed optical signal light is optically coupled, without significant losses from the first microcavity, back into the optical waveguide, as shown by the arc-shaped arrows. The out-coupled optical signal 310 propagates for some distance in the optical waveguide, before the optical signal is optically coupled into a second microcavity 286. The second microcavity, located further along in the direction of propagation of the optical light in the waveguide, is arranged at the same distance away from the waveguide as is the first microcavity. Part of the optical light confined in the second microcavity is absorbed via TPA to generate free carriers. The second optical cavity enables more free carriers to be generated from Sin. When electrodes are placed across each of the microcavity (285 and 286), the sum of the electrical signals detected will be greater than that detected when only one microcavity (e.g. 285) is used alone. The efficiency of a system with two microcavities is therefore higher than a system with only one microcavity. A photodetection system can employ one or more (two or more, three or more, four or more, five or more, etc.) of these microcavities to achieve a target efficiency.
If higher efficiency than that afforded by two microcavities (e.g. 285 and 286) is desired, the out-coupled optical light signal 320, which is not absorbed by the second microcavity 286, can be coupled into a third microcavity 287. The output light signal that has interacted with all the microcavities designed for the system is denoted by Strans. It should be noted that when the photodetector 210 is operating in the cascaded mode, the input signal light interacts with all the microcavities that are placed within the evanescent coupling range of the waveguide. However, none of the microcavities interact with each other. Each microcavity operates sequentially, to generate part of an aggregate electrical signal, the sum of which is larger than the signal would be in the non-cascaded case.
In order to obtain accurate information about system performance through the temporal response of the apparatus disclosed herein, in which the time-dependent interplay between all different optical and thermal effects plays a role, a theoretical framework based on a combination of a coupled mode theory (CMT) and a first order perturbation theory is applied. This approach offers an intuitive universal description (i.e., independent of the particular geometry under analysis) of the structures displayed in FIGS. 2b and 2c. Furthermore, it can be shown that the CMT description of the two different geometries shown in FIGS. 2b and 2c can be written in the same manner (despite the absence of any transmitted power in the system rendered in FIG. 2b). The results for the corresponding nonlinear absorption are thus the same in both cases. The specific details of the electric field distribution of each one of these systems are accounted for through a set of parameters introduced into the CMT theory. Hence, without a loss of generality, the results computed for the electric field distribution shown in FIG. 2b are emphasized.
In particular, a parallel implementation of finite-difference-time-domain (FDTD) method is used to compute both the electric field profiles shown in FIGS. 2b and 2c and their corresponding quality factors. Details of both the theoretical framework and the computational method are provided after the system performance is presented.
FIGS. 4a-f summarize the calculated system performance and characteristics for a system with the electric field distribution shown in FIG. 2b, assuming Q=105. An effective lifetime of the carriers and a heat relaxation constant of 80 ps and τth=50 ns, respectively are used for the system, as these parameter values are typical for this class of microresonators. The heat relaxation constant τth, is defined as the average time in which (in the absence of any source of heat input into a system) the temperature of a system is reduced through radiation, convection, and conduction processes by a factor of 1/e=0.3679.
Apart from the quantum efficiency, the power absorbed by the TPA (Pabs) provides an accurate measure for the conversion efficiency between the light pulses and electrical signals. In other words, once the electrons are generated via TPA, they represent an electronic signal in the circuit (represented by 14 in FIG. 1a), in the same way as in any conventional photodetector based on linear absorption. In these calculations and the figures summarizing their results shown below, Pabs only accounts for absorption from TPA processes (i.e., the power absorbed due to FCA is not included).
System Performance with a 1 GHz Optical Signal Train
FIGS. 4a-c show a first set of simulations of the temporal response of the disclosed apparatus in which a continuous train of 0.25 ns-duration light pulses is sent down the waveguide. The time interval between the pulses is 1 ns and the carrier frequency is the same as the resonant frequency ω0 of the microresonator. When the energy of the first pulse of the train sequence starts coupling into the microresonator (t=0), the effects of the nonlinear absorption begin to increase, as shown in FIGS. 4a and 4b. Since the times over which the variation of the refractive index of the microresonator, Δn, changes appreciably are much longer than the duration of each pulse, the temporal profile of the absorbed power Pabs follows the one corresponding to the input pulse. The optical absorbed power raises the temperature of the structure by ΔT (t), which in turn introduces a shift Δn(t) of the refractive index of the microresonator (the contribution to Δn coming from the heating of the microresonator is the dominant mechanism determining Δn).
For times t<<τth, the increase of the temperature in the optical microresonator induced by each one of the subsequent pulses of the input train is added up, giving rise to the staircase-like profile of Δn(t) displayed in the inset of FIG. 4c. The plateau regions in the inset (e.g. the time interval between 1-2 ns, 2-3 ns, and 3-4 ns) correspond to the time interval between light pulses, during which the device does not have enough time to shed its thermal energy via thermalization with the environment. As can be seen in FIG. 4c, the growth of Δn(t) saturates after approximately 100 ns.
In a similar manner, the maxima of Pabs (t) decrease with time, until a steady-state value of 0.03 mW is reached at ±100 ns, which corresponds to ±20% of the maximum input power. In the case of the structure displayed in FIG. 2c, the pulses are transmitted through the system largely unperturbed when the apparatus is operating in the linear all-pass filter regime, and the signal pulses can consequently be reutilized in a different part of the chip. The peak value chosen for Pin(t) (Pinmax=0.15 mW) in FIGS. 4a-c has been optimized to obtain the best possible ratio between the absorbed and input energies (i.e., the best conversion efficiency of the TPA process).
System Performance with a Pseudorandom Sequence of a 1 Ghz Optical Signal Train
In the second set of numerical experiments, the response of the system to a pseudorandom train of 0.25 ns pulses is analyzed. Pseudorandom sequences of signals are routinely employed to test electronic integrated circuits. Therefore, the use of this kind of sequences enables a more rigorous assessment of the performance of the photodetector. The results of the computations are displayed in FIGS. 3d-f. The same physical parameters as those used in FIGS. 4a-c are assumed in this set of simulations. The physical description of the behavior observed in FIGS. 4d-f is similar to the one given above for the case of a continuous train of pulses.
Factors Influencing System Performance
1. Interplay Between Δn(t) and τth 
Two intertwined effects cause the behavior observed in FIGS. 4b and c. On one hand, Δn(t) produced by the temperature rise in the microresonator modifies the resonant frequency of the microresonator, which in turn, feeds back and reduces the optical power that is coupled into the microresonator by the subsequent pulses, decreasing the optical absorption and therefore the rate of growth of ΔT (t). On the other hand, after a time comparable to the heat relaxation constant (τth=50 ns), the optical microcavity starts to exchange thermal energy with its surroundings in a significant way. Both of these mechanisms influence one another until the microresonator reaches an approximate thermal steady-state (Δn≈3.6×10−6 and ΔT≈0.5K in this case).
2. Preshift Δω
In contrast to the results shown in FIGS. 4 a-c, a preshift do has been introduced into the frequency of the input signal used in the calculations shown in FIGS. 4e-f, so the signal carrier frequency ω is not the same as the resonant frequency ω0 of the microresonator. The typical absorbed power can be improved by choosing Δω=−ωΔnc, where Δnc is the steady-state value of the Δn(t) obtained from the former set of simulations corresponding to a continuous train of pulses (see FIGS. 4a-c).
In the system depicted by FIGS. 4d-f, as the microresonator absorbs optical energy, the shift of the refractive index (or equivalently the shift of the resonant frequency) induced by the warming of the system starts to compensate the original input preshift Δω, producing an increase in the maxima of Pabs (t) with time (see FIGS. 4e and 4f). The result is a steady-state in which the system improves the self-alignment of its resonant frequency with that of the external source, producing an increase in the absorbed power once the system reaches the approximate thermal steady-state. Thus, for instance, if the average power of the considered pseudorandom sequence were the same as the one corresponding to the periodic sequence displayed in FIG. 4a, this self-alignment would be nearly optimal. As shown in FIG. 4e, values for the maxima of Pabs (t) between 0.021 and 0.031 mW are achieved in this case. It should be noted that since in a pseudorandom train of pulses the time interval between consecutive pulses changes with time, the maxima of Pabs (t) of various pulses varies, even for times longer than the heat relaxation constant of the structure.
3. Pulse Energy and Q-Factor
In order to quantitatively analyze the mentioned variation of Pabs(t) over long time periods, the dependence of the energy absorbed per pulse, Eabs, as a function of the energy of each input pulse Ein, is shown in FIG. 5. Note that for Q=105, values of Eabs/EL, up to 0.15 can be reached for input pulse energies of 0.015 pJ without any significant difference between the most and the least absorbed pulses. Additionally, FIG. 5 provides a complete picture of the overall performance of the photodetection scheme, providing universal design guidelines for the photodetection approach.
4. Thermal Relaxation Constant σth 
The range of values for the maximum absorption efficiency, Eabs/EL, that enables the practical implementation of the photodetection scheme disclosed here can only be achieved using optical microresonators characterized by a small enough thermal relaxation constant τth. This fact is illustrated in FIG. 6, for a system with Q=105 where the maximum value for Eabs/Ein, per bit is plotted as a function of the thermal relaxation constant τth. The figure shows that the performance of the photodetector decreases drastically as τth becomes larger. Moreover, as it can be shown that τth increases with the modal volume of the optical microresonator, only microphotonic structures able to confine light into subwavelength volumes (as those shown in FIGS. 2b, 2c, and 3) are suitable for this class of devices.
An Embodiment of the Apparatus for Operation in the Continuous-Wave Regime
Besides the embodiments of the photodetector detailed above which are able to detect a train of ultrafast optical pulses, continuous wave (cw) optical signals can also be detected by the systems disclosed here.
FIG. 7 displays the dependence of the ratio between the absorbed power by TPA (Pabs) and the input power (Pin) as a function of Pabs for different values of the Q-factor of the optical microresonator. In all calculations, most of the free carriers are assumed to have been swept away from the microresonator. Each panel also renders the corresponding results computed for several values of the preshift Δω of the carrier frequency with respect to the resonant frequency of the system ω0. As can be observed in this figure, for each Q value, there is an optimal value of Δω0 (approximately given by Δω0=ω0/Q) which optimize the ratio Pabs/Pin and for which no optical bistability effects are observed. A bistable system has an output that can take one of two distinct stable values at a particular input level. Note that in this case these bistability effects are produced by the shift of the refractive index due to the thermal effects produced by TPA. Optical bistability is detrimental to the performance of the photodetection scheme, and should thus be avoided.
The optimal Δω0 actually corresponds to the maximum value of the frequency preshift Δω that can be introduced in the carrier frequency before the microresonator start showing optical bistability properties. On the other hand, this Δω0 is large enough to partially compensate the shift of the refractive index of the microresonator due to thermal effects produced by TPA, and, thus, it improves the ratio Pabs/Pin with respect to the one obtained when Δω=0. The optimal input power found from the numerical analysis for each Q-value power scales roughly as Q1/2.
The high values of the ratio Pabs/Pin computed for the optimal Δω corresponding to each one of the Q-values considered in FIG. 7 (Pabs/Pin=0.07, 0.02 and 0.008 for Q=103, Q=104, and Q=105, respectively) indicates the potential application of the novel photodetection scheme in the cw regime.
However, it should be noted that in the cw regime, the change of the refractive index in the microresonator is dominated by thermal effects, where the relevant time scale is given by the heat relaxation constant τth. Heat relaxation constants of τth  ̃50 ns has been experimentally obtained in structures similar to the ones considered here (see T. Tanabe et al. Opt. Lett. 30, 2575-2577 (2005), and S. F. Preble et al. Opt. Lett. 30, 2891-2893 (2005)). In order to reach the cw operation regime, the duration of each pulse should be  ̃τth, and therefore the time-interval between pulses should be  ̃100 ns. Alternatively, the corresponding bit rate  ̃1/100 ns=10 MHz, which makes the application of the cw regime described here only suitable for the photodetection of trains of optical pulses with bit rates up to  ̃10 MHz.
The theoretical framework and the computational methods used to obtain the system performance parameters pertinent to the apparatus and method disclosed herein are fully described below.
Time-Dependent Coupled-Mode Theory
To accurately compute the temporal response of the class of systems disclosed here, a theoretical framework based on a combination of a coupled mode theory (CMT) and a first order perturbation theory is applied.
Insets of FIGS. 2b and 2c display the different magnitudes and parameters used in this description. In both insets, αcav(t) stands for the electric field amplitude inside the microresonator, normalized so that |αcav(t)|2 corresponds to the electromagnetic energy stored in the microresonator. τIO governs the coupling strength between the cavity and the microresonator, while SIN(t), SREF(t), and STRANS(t) denote the amplitude of the input, reflected and transmitted pulses, respectively (STRANS(t) only appears in FIG. 2c). These quantities have been normalized so that |sIN(t)|2, |sREF(t)|2, |sTRANS(t)|2 and are the input, reflected and transmitted powers, respectively. By using energy conservation arguments, it can be shown that the temporal evolution of αcav(t) in the two different geometries displayed in FIGS. 2b and 2c can be described in a unified manner by means of the following nonlinear differential equation,




  
    
      
        
          
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                      lin
                    
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        (
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where ω0 and Δω are the resonant frequency of the system and the frequency preshift of the external source, respectively. γlin corresponds to the sum of all the energy decay rate mechanisms of the microresonator in the linear regime: it includes the decay rate into the waveguide (γIO), the radiative losses (γrad) and the losses associated with linear absorption in the material (γabs), γTPA and γFCA, which are functions of the energy stored in the microresonator (|αcav|2), represent the two nonlinear absorption mechanisms of interest in this case, i.e., both TPA and FCA, respectively. The specific expressions for both γTPA and γFCA can be obtained by integrating the local absorption rates due to TPA and FCA over the geometry of the microresonator, given by γTPA({right arrow over (r)})=( 1/2)β′({right arrow over (r)})∈0n2({right arrow over (r)})|{right arrow over (E)}({right arrow over (r)})|2 and γFCA({right arrow over (r)})=σ({right arrow over (r)})N({right arrow over (r)}), respectively.

In these expressions, β′ ({right arrow over (r)}) is the material dependent strength of the TPA process, n2 ({right arrow over (r)}) is the dielectric constant distribution of the microresonator, {right arrow over (E)}({right arrow over (r)}) is the complex electric field profile of the resonant mode of the structure, ∈0 is the permittivity of free space, σ′({right arrow over (r)}) is the free-carrier cross-section, and N({right arrow over (r)}) represent the free carriers density inside the microresonator. Note that both n2({right arrow over (r)}) and {right arrow over (E)}({right arrow over (r)}) correspond to unperturbed (i.e., in the linear regime) local refractive index and electric field, respectively.
From the first order perturbation theory, it can be deduced that the magnitudes Δ nth and Δ nfc appearing in the right-hand side of Eq. (1) correspond to the spatial averages of the refractive index changes in the microresonator due to thermal effects and the presence of free carrier (free carrier dispersion), respectively. Specifically, Δ nth and Δ nfc can be written as Δ nth(t)=−1/nSi(dnSi/dT)Δ T(t) and Δ nfc (t)=−1/nSi(dnSi/dN) N(t), with Δ T(t) and Δ N(t) being the spatial average of the temperature increase in the microresonator and the free carriers density, respectively. The temporal evolution of these magnitudes is determined by the following differential equations (which, as can be observed, are in turn coupled to the one given in Eq. 1),




  
    
      
        
          
            
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                t
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              th
            
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                abs
              
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                  fc
                
              
            
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                _
              
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                t
                )
              
            
          
          +
          
            
              ζ
              N
            
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                
                
                  
                    a
                    cav
                  
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                    t
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              4
            
          
        
      
    
    
      
        (
        5
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where τth defines the heat relaxation constant corresponding to the specific geometry under study. ξth depends both of the details of the specific geometry of the microresonator and the thermal conductivity of Si (for more information, see: P. Barclay et al., Opt. Express 13, 801-820 (2005)). In this work, the phenomenological values used for τth and ξth correspond to the ones measured experimentally in similar structures (for more information, see: T. Tanabe et al., Opt. Lett. 30, 2575-2577 (2005), S. F. Preble et al., Opt. Lett. 30, 2891-2893 (2005), and P. Barclay et al., Opt. Express 13, 801-820 (2005)).
τfc denote the effective lifetime of the free carriers, which in our calculations has also been obtained from the available experimental results (for more information, see: T. Tanabe et al., Opt. Lett. 30, 2575-2577 (2005), S. F. Preble et al., Opt. Lett. 30, 2891-2893 (2005), and P. Barclay et al, Opt. Express 13, 801-820 (2005)), while ξN depends exclusively on the geometry of the microresonator and it is proportional to the two-photon absorption coefficient of Si (for details on this parameter, see: P. Barclay et al., Opt. Express 13, 801-820 (2005)).
Finite-Difference-Time-Domain Calculations
A parallel implementation of finite-difference-time-domain (FDTD) method is used to compute both the electric field profiles shown in FIGS. 2b and 2c and their corresponding quality factors. This numerical method produces virtually exact results, apart from the discretization. The simulations were performed using a resolution of 40 pts per α, which is found to give results with less that 0.1% of relative error. The results presented here correspond to two-dimensional (2D) simulations of the analyzed structures. In order to obtain an accurate estimation of the performance of the actual three-dimensional (3D) counterparts of the structures considered here, the electric field profile in the perpendicular direction to the plane shown in FIGS. 2b and 2c is assumed to be roughly the same as the mode profile computed for the 2D case. Specifically, it is assumed that the extension of the mode profile in the third dimension is about α/2. This fact does not affect the generality of the results disclosed here, since it is possible to design true 3D structures with 2D electric field cross sections very similar to the ones shown here.
A number of embodiments of the apparatus and the method have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Therefore, other aspects, advantages, and modifications are within the scope of the following claims.

## Claims

1. A system comprising:
an integrated silicon-based structure comprising an optical waveguide for receiving an input beam carrying an optical signal and a microcavity optically coupled to the waveguide and configured to receive optical energy from the input beam and absorb the optical energy by a nonlinear multi-photon absorption process,
the integrated silicon-based structure further comprising electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing an electronic signal indicative of the optical signal.

2. The system of claim 1, wherein the microcavity comprises silicon and wherein the nonlinear multi-photon absorption process is in the silicon.

3. The system of claim 1, wherein the microcavity has a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, and wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR, with 1.2 μm<λAIR<2.4 μm.

4. The system of claim 3, wherein Q>100 and VMODE<1000 λAIR3.

5. The system of claim 4, wherein Q>1000 and VMODE<100 λAIR3.

6. The system of claim 5, wherein VMODE<10 λAIR3.

7. The system of claim 4, wherein the input beam carrying the optical signal has a carrier frequency equal to ω, and wherein |ω−ω0|/ω0<10/Q.

8. The system of claim 7, wherein the input beam carrying the optical signal has a carrier frequency equal to ω, and wherein |ω−ω0|/ω0<5/Q.

9. The system of claim 8, wherein the input beam carrying the optical signal has a carrier frequency equal to ω, and wherein |ω−ω0|/ω0<1/Q.

10. The system of claim 1, wherein the microcavity has a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, and wherein the system further comprises a source for the input beam, and wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR.

11. The system of claim 1, wherein the microcavity is configured to achieve a conversion efficiency for the multi-photon absorption of the optical energy in the input beam of greater than 15% for an input beam power smaller than 0.2 mW.

12. The system of claim 1, wherein the microcavity is a photonic crystal structure.

13. The system of claim 1, wherein the waveguide is a photonic crystal structure.

14. The system of claim 1, wherein the integrated silicon-based structure is implemented in a Complementary metal-oxide-semiconductor (CMOS) platform.

15. The system of claim 1, wherein the input beam carrying the optical signal has a carrier frequency equal to ω, wherein N photons, with N>1, are absorbed simultaneously by a material in the microcavity during the multi-photon absorption process, and wherein the multi-photon absorption material has an indirect electronic bandgap Eg larger than the energy corresponding to a single photon of frequency ω and smaller than the energy of the N photons absorbed simultaneously by the material.

16. The system of claim 1, wherein the integrated silicon-based structure further comprises an output optical waveguide optically coupled to the microcavity and configured to output optical energy from the microcavity that is not absorbed by the multi-photon absorption process.

17. The system of claim 1, wherein the multi-photon absorption process is a two-photon absorption (TPA).

18. The system of claim 1, wherein the integrated silicon-based structure comprises multiple microcavities each optically coupled to the waveguide and configured to receive optical energy from the input beam and absorb the optical energy by a nonlinear multi-photon absorption process.

19. The system of claim 1, further comprising an external voltage source configured to apply an external voltage across the electrodes to extract a photocurrent from the integrated silicon-based structure in response to the non-linear multi-photon absorption process and produce the electronic signal indicative of the optical signal.

20. The system of claim 19, wherein the external voltage is configured to enable an electrical readout of the optical signal.

21. The system of claim 19, wherein the external voltage applied across the electrodes causes the integrated silicon-based structure to form a reversed biased p-i-n junction.

22. The system of claim 21, wherein the reversed biased p-i-n junction sweeps out free carriers generated inside the microcavity.

23. Apparatus comprising:
an integrated silicon-based structure comprising an optical waveguide for receiving an input beam carrying an optical signal and a microcavity optically coupled to the waveguide and configured to receive optical energy from the input beam and absorb the optical energy by a nonlinear multi-photon absorption process,
the integrated silicon-based structure further comprising electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing an electronic signal indicative of the optical signal,
wherein the microcavity comprises silicon and wherein the nonlinear multi-photon absorption process is in the silicon, and
wherein the micro cavity has a resonant frequency ω0, a quality factor Q, and a modal volume VMODE, and wherein the input beam carrying the optical signal has a wavelength in air equal to λAIR, with 1.2 μm<λAIR<2.4 μm, and wherein Q>100 and VMODE<1000 λAIR3.

24. The apparatus of claim 23, further comprising an external voltage source configured to apply an external voltage across the electrodes to extract a photocurrent from the integrated silicon-based structure in response to the non-linear multi-photon absorption process and produce the electronic signal indicative of the optical signal.

25. The apparatus of claim 24, wherein the external voltage is configured to enable an electrical readout of the optical signal.

26. The apparatus of claim 24, wherein the external voltage applied across the electrodes causes the integrated silicon-based structure to form a reversed biased p-i-n junction.

27. The apparatus of claim 26, wherein the reversed biased p-i-n junction sweeps out free carriers generated inside the microcavity.

28. A system comprising:
an integrated silicon-based structure comprising a micro cavity configured to receive optical energy from an input beam carrying an optical signal and absorb the optical energy by a nonlinear multi-photon absorption process,
the integrated silicon-based structure further comprising electrodes responsive to the nonlinear multi-photon absorption process in the microcavity for producing an electronic signal indicative of the optical signal,
wherein the microcavity comprises silicon and wherein the nonlinear multi-photon absorption process is in the silicon.

29. The system of claim 28, wherein the integrated silicon-based structure further comprises an optical waveguide for receiving the input beam carrying an optical signal, and wherein the microcavity is optically coupled to the waveguide to receive the optical energy from the input beam.

30. The system of claim 28, further comprising an external voltage source configured to apply an external voltage across the electrodes to extract a photocurrent from the integrated silicon-based structure in response to the non-linear multi-photon absorption process and produce the electronic signal indicative of the optical signal.

31. The system of claim 30, wherein the external voltage is configured to enable an electrical readout of the optical signal.

32. The system of claim 30, wherein the external voltage applied across the electrodes causes the integrated silicon-base structure to form a reversed biased p-i-n junction.

33. The system of claim 32, wherein the reversed biased p-i-n junction sweeps out free carriers generated inside the microcavity.