# Wavelength Selection for Satellite Quantum Key Distribution
## 5 Results and Discussion
### Wavelength Selection Through Atmospheric Turbulence
The \(\lambda\) (\(\mu\)m) that produces the highest rate for each \(D_{r}\) is shown next to each data point. Blue points correspond to a \(w_{0}\) of 10 cm and red points correspond to a \(w_{0}\) of 35 cm. When \(w_{0}\) is 10 cm, the secret key rates are similar for both Tucson and Waterford, despite very different atmospheric conditions,  
Figure 5: Variation of secret key rate with coherence length in (**a**) Tucson and (**b**) Waterford using the optimum \(w_{0}\), \(D_{r}\) and \(\lambda\) values for each region of the electromagnetic spectrum. with marginally higher secret key rates for the Tucson scenario. Visible wavelengths produce the highest secret key rates for lower \(D_{r}\) values due to the smaller spot size at the receiver. As \(D_{r}\) increases, the optimal \(\lambda\) transitions to the NIR region at 3 m,and the SWIR at 6 m, where a rate of 0.0262 bits/use is obtainable at \(\lambda=1.556\)\(\upmu\)m. When \(w_{0}\) is 35 cm, the larger \(w_{0}\) decreases the beam spread, and the NIR region outperforms the visible region at smaller \(D_{r}\) values. An advantage for the NIR region encompasses the high-performance, cost-effective optical components are readily available from the semiconductor industry [23; 66]. This is demonstrated by the Micius satellite, which utilizes NIR wavelengths ranging from 810 nm to 850 mm [11; 12]. Several challenges exist in implementing the optimized longer wavelength regions, SWIR and MWIR, particularly for larger receiver diameters and beam waists. For example, an initial beam waist of 10 cm (35 cm) and wavelength \(\sim\)1.55 \(\upmu\)m (\(\sim\)3.70 \(\upmu\)m) requires a 6 m diameter receiver. Practical difficulties in implementing larger telescopes include supporting large, heavy optical components which are prone to imperfections, including distortion and aberrations, along with the expense and difficulty of manufacturing suitable high-quality reflective mirrors. These practical limitations in the receiver were ignored in the modelling under the assumption that they would be overcome in the future with advances in technology. Figure 6: The effect that increasing the initial beam waist and receiver diameter has on the maximum secret key rate and optimum wavelength selection in (**a**) Tucson and (**b**) Waterford. Points show wavelengths, in \(\upmu\)m, that produce the maximum secret key rate for each initial beam waist and receiver size. Alternatively, a small receiver diameter combined with a large initial beam waist could serve a multitude of wavelengths in the visible and NIR with a slightly lower performance. At 1 m, the NIR region is optimum (at a \(\lambda=0.867\) um), while at 2 m, the SWIR region (at a \(\lambda=1.556\) um) achieves a secret key rate of 0.0271 bits/use which is close to the maximum value. Many optical devices are optimised for the telecommunication channel at \(\lambda=1.556\) um, which makes it the most practical channel for high-performance satellite QKD. The SWIR region has been studied extensively in the literature, for channels around 1.55 um [61; 67]. This is due to the maturity of optical components with widespread use in the telecommunications industry. The telecom band is the standard choice in optical fibre communication (both classical and quantum) and is fully compatible with integrated silicon photonics. Additionally, off-the-shelf single-mode fibre (SMF) has low absorption at 1550 nm wavelengths, and SMF coupling is optimized here. This is vital when considering the size, weight and power (SWAP) requirements for satellite QKD transmitters and optical payloads. As the beam waist requirement increases, the transmitter payload increases in SWAP requirements which is detrimental for satellite missions. The advantage at telecom wavelengths includes the significant advances in existing technologies and miniaturization with dedicated satellite missions (QUBE) for developing the integration of all optical components of a QKD system on a photonic integrated circuit (PIC) [68].