# Research on Key Technologies of Quantum-Safe Metro-Optimized Optical Transport Networks
## 2 Methods
### Time-Domain Scrambling/Descrambling Combined with DS-QKD
The scrambling implementation employs independent temperature-controlled modules (TCMs) for each fiber deliver, enabling the dynamic adjustment of cavity parameters to achieve temporal-domain signal scrambling. The FPCs have been modularized, with a working temperature ranging from 0 \({}^{\circ}\)C to 50 \({}^{\circ}\)C. For subsequent experiments, the ambient temperature is maintained at room temperature, specifically within the range of 20 \({}^{\circ}\)C to 25 \({}^{\circ}\)C.  
This scrambling mechanism induces waveform reconstruction through two primary effects:  
Figure 4: System schematic diagram of an OSU combined with DS-QKD. Figure 5: Schematic diagram of the time-domain scrambling/descrambling of the OSU optical signal through a TCM. Temporal rearrangement of optical pulses, creating new waveform configurations;  
Controlled inter-symbol interference through adjacent-bit overlap. The resultant signal mixture exhibits enhanced resistance to eavesdropping attempts due to the following:  
Non-linear cross-interaction between overlapping bits;  
Noise-equivalent signal degradation from timing jitter;  
Irreversible scrambling transformations. The above scrambling process can be mathematically modeled as a convolution operation between the input optical signal \(z_{\text{osu}}(t)\) and the FPC's impulse response \(h(t)\) as follows:  
\[z^{\prime}_{\text{osu}}(t)=\int_{-\infty}^{\infty}z_{\text{osu}}(\tau)h(t-\tau) d\tau=z_{\text{osu}}(t)\otimes h(t) \tag{5}\]  
where \(z^{\prime}_{\text{osu}}(t)\) is the time-scrambled signal and \"\(\otimes\)\" is the convolution operation. \(z_{\text{osu}}(t)\) is the input OSU optical signal. \(h(t)\) is the FPC impulse response, and its inverse Fourier transform is expressed as  
\[h(t)=\int_{-\infty}^{\infty}r(\omega)\exp{(-i\omega t)}d\omega \tag{6}\]  
where the frequency response of FPC \(r(\omega)\) is denoted as  
\[r(\omega)=\frac{r_{1}-r_{2}\exp(i2\omega nd\cos\theta_{0})}{1-r_{1}r_{2}\exp( i2\omega nd\cos\theta_{0})} \tag{7}\]  
Let \(r_{1}\) and \(r_{2}\) be the reflectance of the two surfaces of the FPC, respectively. The optical frequency, denoted as \(\omega\), is defined by the equation \(\omega=2\pi/\lambda\), where \(\lambda\) represents the wavelength of light in a vacuum, \(n\) denotes the refractive index of the FPC substrate, and \(d\) denotes the thickness of the FPC substrate. The angle of incidence, \(\theta_{0}\), is the angle at which the optical signal enters the FPC. It can be seen from Equations (6) and (7) that the impulse response of the FPC \(h(t)\) is correlated with \(r_{1}\), \(r_{2}\), \(n\), and \(d\). In subsequent experiments, we ensured that \(\theta_{0}\) was \(0^{\circ}\) and the incident polarization had no influence on the experimental data. To achieve time-domain randomization of the OSU optical signal, a TCM can be used to adjust the optical thickness of the FPC \(nd\). The OSU optical signal after \(N\)-level cascaded FPC scrambling is denoted as  
\[z^{{}^{\prime}}_{\text{osu}}(t)=z_{\text{osu}}(t)\otimes h_{1}(t)\otimes h_{2 }(t)\otimes\ldots\otimes h_{N}(t) \tag{8}\]  
The OSU optical signal reflected from the FPC array of the scrambler is denoted as  
\[ \begin{split} z^{{}^{\prime\prime}}_{\text{osu}}(t)=z_{\text{osu }}(t)\otimes h_{1}(t)&\otimes h_{2}(t)\otimes\ldots\otimes h_{N} (t)\otimes h^{{}^{\prime}}_{1}(t)\otimes h^{{}^{\prime}}_{2}(t)\otimes\ldots \otimes h^{{}^{\prime}}_{N}(t)\\ &=z_{\text{osu}}(t)\otimes H(t)\otimes H^{\prime}(t)\end{split}  \tag{9}\]  
where \(H(t)=h_{1}(t)\otimes h_{2}(t)\otimes\ldots\otimes h_{N}(t)\) is the impulse response of the scrambler and \(H^{\prime}(t)=h^{{}^{\prime}}_{1}(t)\otimes h^{{}^{\prime}}_{2}(t)\otimes \ldots\otimes h^{{}^{\prime}}_{N}(t)\) is the impulse response of the descrambler. The solution to time scrambling signal interference follows a principle similar to that in [18], which is based on the thermal light effect and uses a dynamic reconfigurable code synchronization solution as a key approach. Let \(H^{\prime}(t)=H^{*}(-t)\).