1. INTRODUCTION

The advent of quantum optics and quantum information processing goes hand in hand with the search for adequate active and passive components operating on the single-photon level at telecommunication wavelengths [1–4]. Among a variety of approaches, a hybrid arrangement of integrated single-photon sources, reconfigurable photonic circuitry, and detectors on a single chip is particularly promising with respect to complexity, compactness, reproducibility, stability, and ease of fabrication [5–9]. Such a platform will stimulate the implementation of optical quantum computing and other challenging nanophotonic experiments in the near future [10–14].

For on-chip single-photon detectors (SPDs), waveguide-integrated devices have been demonstrated [15–20] that rely on a temporary breakdown of superconductivity in a current-biased nanowire. The absorption of light triggers an external readout circuitry, sensitive down to the single-photon level [21,22]. Superconducting nanowire single-photon detectors (SNSPDs) aim to satisfy the stringent requirements imposed by quantum optical protocols in terms of crucial performance metrics, namely efficiency, the absence of noise, low recovery times for high detection rates, and precise timing accuracy [23–28]. Concerning the efficiency, the KLM protocol demands an overall efficiency of unity for source, on-chip manipulation, and detectors [23], while other protocols are less demanding. Varnava et al. report on a necessary overall efficiency of 66.6%, and Gong et al. propose a scheme that requires the product of the source and detector efficiencies to exceed 50% [28]. In addition, a scalable fabrication method within the ubiquitous silicon-on-insulator (SOI) platform is desirable. The high refractive index of silicon allows for compact photonic devices, and the fabrication is compatible with the complementary metal–oxide–semiconductor standard, the prevalent technology in electronics.

Experimental measurement and analysis of the absorption efficiency and the detector reset dynamics demonstrated that the geometry of the nanowire has a major influence on the attainable detection efficiency and timing properties. Long nanowires increase the absorption [29], but the simultaneously increased kinetic inductance renders the device slow [30,31], effectively limiting the maximum count rate. Reducing the length of the nanowire has more advantages than only increasing the possible count rate. It reduces the detector footprint, minimizes external influence of the environment, and reduces the emergence of imperfections as constrictions in the nanowire [32]. However, in order to capitalize on these advantages, the absorption in the nanowire with reduced length necessarily needs to be restored. This is a prime challenge for which modern nanophotonics, fortunately, offers some solutions.

Akhlaghi et al. exploited the concept of perfect absorption for this purpose, relying on a U-shape nanowire wrapped around a one-dimensional (1D) photonic crystal (PhC) cavity [19]. While the authors demonstrate near-perfect absorption, the long nanowire renders the detector rather slow. In a previous publication [33], we extended the concept to shorter nanowire designs, giving the detector a compact microbridge geometry. In this approach, a short nanowire ($\approx 2\mathrm{\mu m}$) made from niobium nitride (NbN) is placed atop a photonic waveguide in a perpendicular orientation. The short nanowire design allows extraordinary fast recovery times of 500 ps due to the reduced kinetic inductance of the wire [34]. Straight nanowire geometries are supposed to avoid current crowding, in contrast to the typical U-shape nanowire geometry. This furthermore allows the detector to be operated at increased bias currents, which enhances the internal quantum efficiency (IQE) [35,36]. In addition, the dark count rate is greatly reduced due to the small active area of the nanowire and the filtering effect of the cavity.

However, in the perpendicular orientation, the absorption is limited by the subwavelength dimensions of the nanowire, amounting to around 5% per each passing of light in the waveguide [33]. To mitigate the reduction in the absorption efficiency, the microbridge nanowire is placed inside an 1D PhC cavity to enhance the absorption in a particular wavelength range. The cavity has been designed with the concept of a perfect absorber in mind. Although 30% on-chip detection efficiency (OCDE) for such a compact detector in a cavity has been achieved, the proposed configuration had a fundamental drawback. The supporting structure underneath the nanowire that is required to offer the nanowire a mere structural support leads to substantial outscattering losses, leading to a reduced enhancement of the OCDE [33]. Therefore, these devices were fast but fundamentally limited in their efficiency by outscattering losses.

To mitigate these problems, we describe in this paper the design, simulation, and experimental characterization of a novel detector design surpassing these shortcomings in terms of efficiency while preserving the timing characteristics. The key to success was a fundamental change to a design that relies entirely on a photonic crystal-based architecture. This lowers possible scattering losses to a minimum. As demonstrated before [19], by employing the concept of critical coupling, suitably photonic crystal cavities can be designed that ultimately lead to the observed outstanding absorption characteristics. While we focus here on the discussion of the detector concept and the key performance metrics, extensive device characterization and additional details are presented in Supplement 1.

2. DEVICE CONCEPT

Our novel detector design combines both high efficiencies and short recovery times by embedding a short nanowire inside a two-dimensional (2D) double heterostructure PhC cavity [37], as depicted in Fig. 1. The main building block of the cavity is a defect line PhC waveguide formed by removing one row of holes in a triangular lattice of air holes etched into a silicon (Si) slab. A cavity is formed by locally altering the lattice constant in the direction of the defect line on both sides of the nanowire [38–40] [see Fig. 1(a)]. Since the change in lattice constant is on the order of 10 nm, it is barely visible in the scanning electron microscope (SEM) image [Fig. 1(b)]. The cavity region is a triangular lattice PhC with a lattice constant $a_c$ in the direction of the defect line, which is equal to the lattice constant in the vertical direction, $a_v=a_c$ (compare Fig. S1 in Supplement 1).

 

Fig. 1. (a) Illustration of the detector. Dark areas correspond to the front and back reflector with modified lattice constants. The change in the lattice constant is exaggerated in comparison to the real device for better visibility. (b) A colorized SEM image of the SNSPD viewed from the top. The nanowire (red) is integrated into an asymmetric heterostructure PhC cavity by locally altering the lattice constant in the direction of the defect line. (c) An SEM image showing the detector as well as the gold contact pads (yellow) and the photonic circuitry (blue).

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Attached to the cavity region are two reflector regions with deformed triangular lattices and a lattice constant $a_r<a_c$. In the vertical direction the lattice constant $a_v$ is kept unchanged in order to achieve lattice matching [39]. The localized mode forming inside the cavity region is confined in-plane by index confinement, perpendicular to the defect line by the photonic band gap (PBG), and in the direction of the defect line by the mode gap [38,39]. Due to the induced deviation of the lattice constant in the direction of the defect line, the photonic bands in the cavity and reflector regions are slightly detuned against each other. This creates a small frequency range at which there are no propagating solutions in the reflector region but still propagating modes in the cavity region. This confines local resonator modes inside the cavity region. The back reflector of this cavity is made sufficiently large to entirely suppress transmission through it, i.e., the length is much longer than the decay length of the evanescent modes. The front reflector has a much smaller length such that light from the injecting waveguide can evanescently couple to the cavity and excite the resonant mode.

In this configuration, the nanowire can be placed atop the PhC slab in between the holes. An additional support structure is obsolete, overcoming the fundamental limitations governing the initial design [33]. The cavity-integrated SNSPD is connected to a SOI nanophotonic strip waveguide via an injector region, as shown in Fig. 1(b), with an increased lattice constant. The interface between the nanowire and the electrical biasing and readout circuitry is provided by gold contact pads. As will be elucidated in the following section, careful tuning of the cavity parameters is required to obtain perfect absorption of all incident photons. For this purpose, we rely on the concept of critical coupling.

3. CAVITY DESIGN AND SIMULATION RESULTS

Similar to a critically coupled ring resonator [41], we can realize perfect dissipation in the cavity for a precisely adjusted coupling of the waveguide to the cavity. The theory of near perfect absorption in waveguide-integrated SNSPDs using a PhC has been introduced and discussed in detail in the original paper by Akhlaghi et al. [19] and adapted for application of subnanosecond recovery time SNSPDs in our recent publication [33]. For this reason, we focus here only on the most crucial aspects to explain the cavity design procedure. Additional details are provided in Supplement 1.

The condition for maximal dissipation is derived within the framework of temporal coupled mode theory (TCMT) [19,42–44]. The net damping rate of the cavity mode in the TCMT can be expressed in terms of the loss into the adjacent waveguide, radiative losses, and the desired absorption in the nanowire $\mathrm{\Gamma }={\mathrm{\Gamma }}_{\mathrm{wg}}+{\mathrm{\Gamma }}_{\mathrm{rad}}+{\mathrm{\Gamma }}_{\mathrm{nw}}={\mathrm{\Gamma }}_{\mathrm{wg}}+{\mathrm{\Gamma }}_{\mathrm{diss}}$.

Perfect dissipation inside the cavity is achieved when the condition of zero back reflection $R=0$ at resonance is satisfied. The reflectance $R(\omega )$, expressed in terms of quality factors $Q_i={\omega }_0/2{\mathrm{\Gamma }}_i$, is written as [43]

At resonance $(\omega ={\omega }_0)$, the reflectance equals zero for $Q_{\mathrm{diss}}=Q_{\mathrm{wg}}$. This constitutes the key design criteria: the losses due to dissipation in the cavity, which originate from absorption of light in the nanowire, should be equal to the radiative losses of the cavity into the mode supported in the waveguide from the injector region. This point of operation is commonly referred to as critical coupling. To prevent energy from coupling to radiative modes inside the cavity instead of being absorbed in the nanowire, the condition $Q_{\mathrm{rad}}\gg Q_{\mathrm{nw}}$ has to be fulfilled [43]. In the following, we demonstrate that all these requirements can be met by a suitable design.

Three separate simulations are needed by the TCMT to determine the near perfect absorption condition. For this purpose, we aim to evaluate the individual quality factors from the analysis of suitable subsystems. This approach allows us to analyze and optimize each element of the detector individually, greatly reducing the simulation overhead. A sketch of the detector’s cavity and the design parameters can be found in Supplement 1, together with details on the simulation procedure.

First, a symmetric cavity, i.e., identical front and back reflectors with a length of eight lattice constants each and without nanowire, is considered in order to design the resonance wavelength. The resonance wavelength and the radiative quality factors of the fundamental mode $M_0$ are plotted versus the lattice constant in Fig. 2(a). A linear dependence of the resonance wavelength on the lattice constant is observed over a wide spectrum from 1500 nm to 1600 nm. The radiative quality factor $Q_{\mathrm{rad}}$ is already around ${10}^4$ for the smallest lattice constant, which is in good agreement with the condition $Q_{\mathrm{rad}}\gg Q_{\mathrm{nw}}$. To set the detector at an operating wavelength of 1540.7 nm, we choose a lattice constant of $a_c=400\mathrm{nm}$ ($a_r=390\mathrm{nm}$), resulting in $Q_{\mathrm{rad}}=\mathrm{12,500}$.

 

Fig. 2. (a) Resonance wavelength (black hexagons) and quality factor (red squares) of mode $M_0$ for the symmetric cavity as a function of the lattice constant in the cavity region $a_c$. The lattice constant in the reflector region is chosen as $a_r=a_c-10\mathrm{nm}$. The resonance wavelength depends linearly on $a_c$. The black ellipse denotes the selected value for the lattice constant in further simulations. (b) The quality factor of the fundamental cavity mode $M_0$ for a varying front reflector length $n_{\mathrm{rl}}$ (red squares) and nanowire width (black hexagons). For a nanowire width of 70 nm and a front reflector length of $n_{\mathrm{rl}}=2$, the resonant absorption condition is satisfied (blue dashed line). (c) The numerical full-wave simulation of the complete detector compared to the TCMT approach. The electric field profiles are shown at the peak of resonance $M_0$ (right) and $M_1$ (left) in a cut plane in the middle of the waveguide. The results in (b) and (c) are obtained for the parameters corresponding to the marked data points in (a) with $a_c=400\mathrm{nm}$.

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Second, the length of the front reflector is varied for a fixed and sufficiently large back reflector (eight lattice constants long), resulting in the quality factor $Q_{\mathrm{wg}}$. Figure 2(b) shows in red the quality factor as a function of the length in discrete steps ($n_{\mathrm{rl}}$ as an integer multiple of $a_r$). The quality factor increases with a longer front reflector and saturates at a length of four, while the resonance wavelength stays approximately constant.

Third, in the final simulation step, the nanowire is added to the symmetric cavity considered in the first step to determine the absorption. The corresponding data is shown in Fig. 2(b) in black (front and back reflector with a length of eight lattice constants). To achieve near perfect absorption, the dissipative quality factor $Q_{\mathrm{diss}}$ of the cavity including the nanowire has to match $Q_{\mathrm{wg}}$ for a chosen length of the front reflector. We find a good agreement for a front reflector length of two unit cells and a nanowire width of 70 nm, resulting in $Q_{\mathrm{wg}}=611$ and $Q_{\mathrm{diss}}=596$. In this configuration, the absorption efficiency at resonance amounts to 95.1%. We associate the remaining 4.9% to outscattering losses, which occur mainly in the silicon dioxide (${\mathrm{SiO}}_2$) buffer layer [45], which could be further reduced by releasing the PhC from the substrate.

A full-wave simulation of the complete detector including the nanowire, the waveguide, and the transition from the strip waveguide to the PhC has been performed to evaluate the accuracy of the obtained results with the TCMT. In this full-wave simulation, all the geometrical details of the optimized device are considered. Light is injected to the strip waveguide from the negative $x$ direction and a numerical computation of transmitted and reflected fields, as well as the radiative losses and the absorption in the nanowire has been performed.

The full-wave simulation results show an 85.1% absorption peak. A comparison to the TCMT approach in the spectral region around the resonance wavelength of 1542.5 nm is presented in Fig. 2(c). The figure also shows the field distribution at resonance. It is possible to observe that the maximum absorption obtained with the TCMT is overestimated by 10%, if compared with the full-wave simulation results. Both the full-wave simulation and the TCMT approach reveal a similar full width at half-maximum (FWHM) of the resonance of 4.3 nm and 5.1 nm, respectively. An additional simulation of the coupling losses between the strip and the PhC waveguide allowed us to confirm that this deviation can be mainly attributed to the coupling losses between the strip and the PhC waveguide, which have not been included in the TCMT simulation and have been estimated to be of 9.5%.

At a wavelength of 1531 nm, another resonance with a decreased maximal absorption can be observed. We attribute this resonance to the presence of the higher-order mode $M_1$, with a decreased quality factor $Q_{\mathrm{rad}}$ with respect to $M_0$ and therefore increased radiative losses. The field amplitude of this mode is shown in Fig. 2(c) as well. The overlap of these two resonances results in the observed double hump structure. While mode $M_1$ features an asymmetric field profile with decreased field amplitude at the position of the nanowire, the field of mode $M_0$ is strongly enhanced at the location of the nanowire. We emphasize the fact that, of course, the second resonance is not predicted in the TCMT as it has also not been considered in this theory.

4. EXPERIMENTAL RESULTS

We realized several 2D cavity detectors, based on the design concept outlined above, with varying periodicities of the PhC. The nanowires are fabricated from nominal 4 nm thick NbN, deposited on SOI (220 nm Si, 3 μm buried oxide layer, Si substrate). For the devices presented here, the nanowire width is around 70 nm, confirmed by SEM imaging. Waveguides are fully etched into the top Si layer, with a width of 500 nm.

Strongly and weakly coupled cavities have been fabricated by adjusting the length of the front reflector to achieve the coupling strength necessary for resonant absorption ($Q_{\mathrm{diss}}=Q_{\mathrm{wg}}$), i.e., the regime of critical coupling. The experimental quality factors of isolated cavities are between 4000 and 8000, meeting the condition $Q_{\mathrm{rad}}\gg Q_{\mathrm{nw}}$. Details concerning fabrication as well as the design parameters for the presented devices are provided in Supplement 1.

We characterize our detectors in a closed cycle cryostat with a base temperature of 1.6 K. Focusing grating couplers on the chip allows us to couple light from a fiber array into the photonic circuitry and to estimate the on-chip photon flux at the detector via a calibrated light source method [46] using a balanced waveguide design [33,47]. Electrical connection for detector biasing and readout is provided by contact probes. For our fabricated devices, we find a critical current density on the order of $5\mathrm{MA}{\mathrm{cm}}^{-2}$ at 1.6 K (see Fig. S18b in Supplement 1).

A. On-Chip Detection Efficiency

In contrast to the system detection efficiency (SDE), which would also include fiber-to-chip coupling losses, for waveguide-integrated devices the detection of single photons already propagating inside the waveguides [denoted here as the on-chip detection efficiency (OCDE)] represents the parameter of interest [16]. The detection efficiency is measured by registering the count rate (CR) of the device under test upon propagation of a calibrated continuous wave (CW) photon flux toward the detector. The detection spectrum for three different devices at wavelengths around 1520 nm is shown in Fig. 3(a). For the best device, a maximum OCDE of $66.9\pm 14.8\%$ (see Supplement 1 for details on uncertainty estimation) is obtained at a bias current of $0.75I_{\mathrm{C}}$ (device #1).

 

Fig. 3. (a) Spectrally resolved OCDE for three selected devices. #3 is a detector that is coupled more strongly to the waveguide, showing a broader resonance. Please note that devices #1 and #3 are characterized at a normalized bias current that is lower than the maximal possible, while device #2 is measured at the maximum bias current. The solid lines are Lorentzian fits to the data over a spectral range where a fit is applicable. The device parameters are listed and elucidated in Supplement 1. (b) OCDE as a function of the normalized bias current at the individual resonance wavelength for the same devices as in (a). (c) The resonance wavelength ${\lambda }_{\mathrm{res}}$ versus the lattice constant $a_c$ ($a_r=a_c-10\mathrm{nm}$) as obtained from the Lorentzian fits in (a). The solid lines represent a linear fit to the data points for devices with identical hole radii $r$ and represent a guide for the eye. The legend indicates the hole radii and the length of the front reflector.

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Considering the fiber-to-waveguide coupling losses, this results in a SDE of 0.5%. By using more elaborate coupling schemes as tapered couplers [48], the coupling efficiency and hence the SDE can be significantly enhanced.

As expected from the simulations, the OCDE reaches high values on resonance. The resonance FWHM of device #1 amounts to 4.3 nm at a wavelength of 1503 nm, corresponding to a quality factor of 350. This has to be compared to the simulation, which has been predicting a quality factor of 301 for this geometry. The simulation and experiment agree reasonably well. Further optimizing the device parameters might result in an improved match between the designed and fabricated quality factors.

A broader resonance (with reduced OCDE) is obtained for enhanced coupling of the cavity to the waveguide [device #3 in Fig. 3(a)], featuring a FWHM of 13.2 nm at the resonance wavelength of 1524 nm. This corresponds to a quality factor of 115.

As simulated, both resonances $M_0$ and $M_1$ are clearly visible in the spectrum for every device in Fig. 3(a). However, the resonance wavelengths are shifted to lower values with respect to the simulations [compare Fig. 2(c)]. This arises from deviations in the fabrication with respect to the etch depth and the hole radii, as discussed in the supplementary information of [33]. To account for this difference, the resonance wavelength can be shifted by adapting the cavity lattice constant, as shown in Fig. 3(c). Continuous and reliable tuning of the resonance wavelength ${\lambda }_{\mathrm{res}}$ is possible by changing the lattice constants of the cavity and reflection regions simultaneously. From the linear fits, we obtain the change in ${\lambda }_{\mathrm{res}}$ to 2.9 nm and 3.1 nm per 1 nm variation in the lattice constant $a_c$ for hole radii of 100 nm and 110 nm. These measurements agree in good accuracy with simulated values, 4 nm and 3.1 nm per 1 nm change in $a_c$, respectively.

Studies of the reset dynamic of the detector evidenced that our short detectors show a switching current in the presence of light, smaller than the critical current determined in absence of a photon flux [30]. This behavior, called latching, cannot be attributed to a mere heating effect but to the low kinetic inductance of the nanowire. The kinetic inductance represents the charge carrier inertia under the influence of an external electric field and depends on the nanowire geometry

The dark count rate (DCR) is measured at blocked laser output, while the fiber array remains aligned to the grating couplers. As determined in detail for one device, not a single dark count was measured during the total integration time of 2 h per bias current in Fig. 3(b), resulting in an upper limit for the DCR of 0.1 mcps (millicounts per second). The reasons for a low DCR in the PhC microbridge SNSPDs are discussed in Supplement 1.

The noise-equivalent power (NEP) is calculated from the OCDE and DCR as ${\mathrm{NEP}}_{\mathrm{OCDE}}=h\nu \sqrt{2\mathrm{DCR}}/\mathrm{OCDE}<2.7\times {10}^{-21}\mathrm{W}/\sqrt{\mathrm{Hz}}$. This is, to our knowledge, the lowest value reported for telecommunication wavelengths until now [49]. Taking the considerable coupling losses into account, the NEP is in addition calculated with the SDE as reference. Accordingly, a value of ${\mathrm{NEP}}_{\mathrm{SDE}}=h\nu \sqrt{2\mathrm{DCR}}/\mathrm{SDE}<3.7\times {10}^{-19}\mathrm{W}/\sqrt{\mathrm{Hz}}$ is reported.

B. Timing Characteristics

The recovery time ${\tau }_{\mathrm{rec}}$ of a SNSPD is the finite time span it takes until the next photon can be detected with the original detection efficiency [50]. Subnanosecond recovery times are a highly desirable property for single-photon detectors used in time-multiplexing schemes and in high rate routing and communication. Relying on 4 GHz amplifiers, we perform interarrival time measurements in a start-multistop measurement procedure [51–53] using a fast sampling oscilloscope.

A detector click is used as an initial trigger signal to obtain a histogram of the time delays between this initial signal and subsequent detector pulses. The results for the 3 μm long nanowire of device #3 are depicted in Fig. 4, together with a selection of pulse traces and their averaged voltages. We define ${\tau }_{\mathrm{rec}}$ as the plateau in the interarrival times, corresponding to an almost complete return of the bias current to the nanowire. Following this definition, we obtain a recovery time of $\sim 480\mathrm{ps}$, implying that maximum count rates in the GHz range are possible and might still be limited by the readout circuitry, i.e., the 4 GHz bandwidth of the amplifiers.

 

Fig. 4. Interarrival times in a start-multistop measurement (blue) and pulse shape (red) of device #3. The bin width of the histogram amounts to 25.8 ps. One thousand voltage traces have been evaluated for the averaged pulse shape (white).

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A slight peak of counts after $\sim 5\mathrm{ns}$ and a dip around 16 ns have been observed within the latching-limited operation $I_B<I_{\mathrm{latch}}$ and the electrical circuitry in use (4 GHz amplifiers). This might be interpreted as afterpulsing of the detector [54,55] (details in Supplement 1). Nevertheless, the effect is not strong and can likely be addressed by improvements in the biasing circuitry. A fast operation with negligible afterpulsing distinguishes our single-nanowire high-speed SNSPDs from parallel nanowire architectures; for example, superconducting nanowire avalanche photodetectors (SNAPs) [56].

The timing jitter of the detector is a further crucial performance metric for SPDs, especially for correlation measurements [9]. The short nanowire length should result in a low geometric jitter [57]. We determine the jitter using a picosecond pulsed laser as input and record a histogram of the signal variation compared to the excitation pulse. For device #2, we obtain a value of 29 ps (see Supplement 1), similar to the 1D cavity embedded detectors (32 ps) [33]. Further improvement can be expected from the use of cryogenic amplifiers [58].

5. DISCUSSION

With a maximum of 67%, the OCDE is only slightly lower than 85% as obtained in the full-wave simulations (see Section 3). We attribute the reduced detection efficiency to the latching-limited operation, i.e., non-saturated IQE due to a reduced bias current, to increased losses at the injector region, and to a mismatch between coupling to nanowire and waveguide, i.e., imperfect critical coupling. Especially not fully etched holes in the PhC can lead to additional outscattering losses. By increasing the kinetic inductance of the nanowire, the IQE can be increased while turning the detector slower.

Furthermore, variations of the presented design enable novel applications for integrated nanophotonics. By embedding the detector in a side-coupled cavity, high quality factors can be achieved, which renders the resonance sharper [59]. Consequently, accurate on-chip spectrometers with high extinction ratios (ERs) are conceivable. This design can represent a more compact alternative to on-chip spectrometers as arrayed waveguide gratings (AWGs) [60]. In particular, the combination with integrated active optical elements is worthwhile in order to tune the resonance to a desired wavelength. High modulation rates of electro-optical elements [61] can be combined with the presented fast detection rates to realize spectroscopic time-multiplexed SPDs on a single chip.

6. CONCLUSION

In summary, we demonstrated superconducting nanowire single-photon detectors embedded into a 2D heterostructure PhC cavity, with detection efficiencies up to 67% in latching-limited operation at telecommunication wavelengths and recovery times below 500 ps. Combining the detector with a 2D cavity enhances the absorption, while maintaining the advantages of short nanowires in terms of high detector speed, vanishing dark counts, and compact integration. By changing the periodicity of the PhC, the resonance wavelength can be continuously tuned. Temporal coupled mode theory is able to address the task of designing a suitable cavity, as confirmed by full-wave finite element method simulations.

Our overhauled design approach reduces outscattering losses compared to the previous cavity-enhanced detectors and can readily be combined with single-photon emitters integrated into on-chip cavities [62]. Detector arrays can be used to build complex architectures out of functional monolithic optical elements on a single chip.