1. Introduction

2. SNSPD Design and Materials

The SNSPD design is depicted in figure 1. The structure presented contains an alternating SiO2/TiO2 DBR on top of a 200 nm gold mirror as the cavity. The proposed design also utilizes a total of 4 layers of nanowires, for single photon detection. As shown in figure 1, there is one layer of nanowire placed in Region 1 (upper region) and three layers of nanowires stacked in Region 2 (lower region). Each nanowire has a thickness of 7 nm, and all layers, including the dielectric and the gold mirror, are tuned to maximize absorption resonance at the position where the nanowires are placed.

Figure 1. Schematic of the simulated structure. Nanowires are 7nm thick and have SiO2 spacers in between one another. In the simulation, the photon source is normally incident onto the structure as shown.

Figure 1. Schematic of the simulated structure. Nanowires are 7nm thick and have SiO2 spacers in between one another. In the simulation, the photon source is normally incident onto the structure as shown.

3. Simulation and Results

3.1. Band selection DBR

The DBR employed in the proposed SNSPD differs from conventional ones, where each layer's thickness is typically set as $\frac{\lambda }{4n}$, with $\lambda$ being the target wavelength and $n$ representing the real part of the refractive index of the dielectric material employed. Through the utilization of a modified DBR design, where the layers with higher refractive index possess a thickness less than $\frac{\lambda }{4n}$, and layers with lower refractive index have a thickness greater than $\frac{\lambda }{4n}$, together with appropriate adjustments in the thickness of dielectrics within the three initial and final layers, it becomes possible to mitigate the adverse effects of higher-order interference as well as high-order modes of constructive interference that causes unwanted spectral ripples in conventional DBR [20,21]. Since the DBR serves both as a mirror and a filter, reflecting photons within the 1070 to 1400 wavelength range while allowing photons with wavelengths > 1400 to pass through, high-order modes of constructive interference must be mitigated to ensure high transmittance in the desired wavelength range. The reflectance-wavelength graphs of a conventional DBR targeting 1230 nm and a modified DBR, with a structure shown in figure 2a, are depicted in figure 2b.

Figure 2. (a) Schematic of the simulated modified DBR. In this design, the gold mirror, some of the SiO2 above the gold mirror, and all layers of the proposed SNSPD’s nanowires are removed; (b) The reflectance as a function of wavelength for conventional and modified DBR.

Figure 2. (a) Schematic of the simulated modified DBR. In this design, the gold mirror, some of the SiO2 above the gold mirror, and all layers of the proposed SNSPD’s nanowires are removed; (b) The reflectance as a function of wavelength for conventional and modified DBR.

As shown by figure 2b, the modification does not heavily influence the reflectance in the region near the target wavelength. While the modified DBR’s ability to eliminate higher order interference is compromised with the addition of thick SiO2 layers and the gold mirror below it, the modified DBR still proves to work better than conventional DBR designs.

With the DBR acting as a mirror and a filter that primarily reflects light with wavelengths ranging from 1070 to 1400 nm, it is possible to create two well separated absorption bands through the addition of a gold mirror and three layers of NbN nanowires below the DBR. Since gold has high reflectance in the infrared region, it reflects most of the photons passing through the dielectric stack.

3.2. Dual-band mirror using modified DBR + Gold

In order to identify the optimum position to place the nanowires, the electric field intensity within the dielectrics is calculated, as shown in figure 3. The electric field colormap demonstrates the principle concept behind a dual-spectral SNSPD. Thanks to the DBR above the gold mirror, most photons with wavelengths ranging from 1070 to 1400 nm are reflected in the first few layers of the dielectric stack.

Figure 3. FDTD simulated electric field intensity profiled by the wavelength and the Z position in the dielectric layers above the gold mirror of the SNSPD. The NbN nanowires are then positioned at places with the strongest electric field intensity. In this colormap, it is obvious that the first few layers of the dielectric stack filtered out most photons with wavelengths from 1070 to 1400 nm before they reached the layers below.

Figure 3. FDTD simulated electric field intensity profiled by the wavelength and the Z position in the dielectric layers above the gold mirror of the SNSPD. The NbN nanowires are then positioned at places with the strongest electric field intensity. In this colormap, it is obvious that the first few layers of the dielectric stack filtered out most photons with wavelengths from 1070 to 1400 nm before they reached the layers below.

The reason for the electric field intensity variation that creates bubble-like structures in the colormap is due to the interference introduced by thicker layers of SiO2, such as the layers with thicknesses of 550 nm and 740 nm. At times, the interference pattern introduced by these layers might lead to low nanowire absorption at certain wavelengths. Thus, thicker dielectrics in the SNSPD should be carefully tuned and optimized to a specific desired thickness, maximizing the absorption resonance at the region where the nanowires are placed.

Another point to note in the electric field intensity colormap shown in figure 3 is that photons with wavelengths > 1400 nm still have considerable electric field strength in multiple layers of the dielectric stack due to the gold mirror’s high reflectance. This effect is one of the limitations of this device. Due to the strong electric field in the uppermost SiO2 layer, when a NbN nanowire is inserted in Region 1, it will also absorb some photons with longer wavelengths. To mitigate this effect, three layers of nanowires are stacked in the SiO2 layer between the gold mirror and the DBR.

3.3. Dual-spectral SNSPD

After inserting 4 layers of NbN nanowires with a thickness of 7 nm into the structure according to the design shown in figure 1, figure 4 illustrates the absorbance of each nanowire.

Note: as shown in figure 1, Region 1 (upper region) consists of NbN1, and Region 2 (lower region) contains NbN2, NbN3, and NbN4.

Figure 4. The absorbance of each nanowire is shown. The absorbance of NbN1, or the uppermost nanowire in the SNSPD design, peaks at 1143 nm with a value of 0.788. As for NbN2, the nanowire demonstrates an absorbance > 0.2 for wavelengths from 1450 to 2000 nm. For NbN3, its absorbance is > 0.178 for wavelengths from 1440 to 2000 nm. Finally, NbN4 exhibits an absorbance > 0.163 for wavelengths ranging from 1435 nm to 2000 nm.

Figure 4. The absorbance of each nanowire is shown. The absorbance of NbN1, or the uppermost nanowire in the SNSPD design, peaks at 1143 nm with a value of 0.788. As for NbN2, the nanowire demonstrates an absorbance > 0.2 for wavelengths from 1450 to 2000 nm. For NbN3, its absorbance is > 0.178 for wavelengths from 1440 to 2000 nm. Finally, NbN4 exhibits an absorbance > 0.163 for wavelengths ranging from 1435 nm to 2000 nm.

Figure 4 highlights the effect of the DBR, which blocks most photons with wavelengths 1070~1400 nm from reaching nanowires positioned in Region 2. Also, while the DBR employed in this design has high reflectance from 1070 to 1400 nm, since it remains challenging to control the phase dispersion and interference introduced by the dielectric stack [13], the absorption band in the shorter wavelength region is very limited. On the contrary, a gold mirror has not only good reflectance in the infrared region but also ignorable phase dispersion, enabling a relatively constant absorbance for wavelengths from 1440 nm onwards.

Figure 5 shows the total absorbance of nanowires placed in Region 1 and Region 2.

Figure 5. The absorbance of nanowires in Regions 1 and 2 is shown. Region 1 exhibits a peak absorbance at 1143 nm, reaching a value of 0.788, and Region 2 has a total absorbance > 0.55 for all wavelengths ranging from 1440 to 2000. The total absorbance of all 4 layers of nanowires combined demonstrates high SDE.

Figure 5. The absorbance of nanowires in Regions 1 and 2 is shown. Region 1 exhibits a peak absorbance at 1143 nm, reaching a value of 0.788, and Region 2 has a total absorbance > 0.55 for all wavelengths ranging from 1440 to 2000. The total absorbance of all 4 layers of nanowires combined demonstrates high SDE.

From figure 5, the dual-spectral characteristic of the SNSPD can be readily observed. The nanowire in Region 1 primarily absorbs photons with wavelengths around 1143 nm and the nanowires in Region 2 (NbN2–NbN4) are responsible for absorbing photons with wavelengths from 1440 to 2000 nm.

To demonstrate the effect of multilayer nanowires, figure 6 depicts the simulated absorbance when just two NbN nanowires are utilized. Compared to the original dual-spectral SNSPD, this new design removes two nanowires in Region 2, leaving the detector with a nanowire in the uppermost SiO2 layer and another between the modified DBR and the gold mirror. Figure 6 shows the simulated absorbance of these two nanowires.

Figure 6. Simulated absorbance of the upper and lower nanowires in a SNSPD structure reduced to just two nanowires. The peak absorbance of the upper nanowire has a value of 0.794 at the wavelength 1151 nm. The lower-positioned nanowire has an absorbance > 0.355 for wavelengths 1460 to 2000 nm.

Figure 6. Simulated absorbance of the upper and lower nanowires in a SNSPD structure reduced to just two nanowires. The peak absorbance of the upper nanowire has a value of 0.794 at the wavelength 1151 nm. The lower-positioned nanowire has an absorbance > 0.355 for wavelengths 1460 to 2000 nm.

After comparing the two absorbance-wavelength graphs in figure 6 to those in figure 5, it is evident that the addition of more nanowires in Region 2 successfully decreases the uppermost nanowire’s high absorbance at certain wavelengths > 1400 nm, creating a more desirable dual-spectral SNSPD with the capability to distinguish between photons with wavelengths in distinct absorption bands.

4. Discussion

While this work describes a SNSPD design sensitive to photons with wavelengths ranging from 1070 to 2000 nm, it is important to note that this device is tunable. By changing the target wavelength of the DBR and placing the nanowires at the position with the strongest absorption resonance, it is possible to change the target wavelength of the SNSPD. For example, using the structure depicted in figure 7a, the simulated absorbance for Region 1 and Region 2 are shown in figure 7b.

Figure 7. (a) Schematic of an alternative SNSPD design targeting different wavelengths; (b) The absorbance as a function of wavelength for Region 1 and Region 2 of the SNSPD.

Figure 7. (a) Schematic of an alternative SNSPD design targeting different wavelengths; (b) The absorbance as a function of wavelength for Region 1 and Region 2 of the SNSPD.

5. Conclusions

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