Experimental Characterization and Model Validation of Interference in Classical-QKD Coexistence Transmission

1. Problem Statement

Quantum Key Distribution (QKD) offers physically guaranteed secure communication but faces significant challenges when deployed over existing optical fiber networks alongside high-power classical data channels. While dedicated dark fibers maximize secret key rates (SKRs), infrastructure optimization requires coexistence of quantum and classical signals within the same link.

The primary obstacle to this coexistence is the massive power disparity between classical and quantum channels, which induces severe degradation through:

• Amplified Spontaneous Emission (ASE): Can be mitigated via filtering.
• Non-linear Effects: Unmitigable in silica-core fibers, specifically:
  • Spontaneous Raman Scattering (SpRS): A broadband, bidirectional effect requiring significant spectral separation between classical and quantum channels.
  • Four-Wave Mixing (FWM): A narrowband effect that becomes dominant when the quantum channel is placed adjacent to high-power classical channels propagating in the same direction (co-propagation).

There is a critical need for accurate theoretical models to predict noise levels and SKRs in these coexistence scenarios to guide network design.

2. Methodology

The authors employed a combined approach of experimental characterization and semi-analytical modeling to validate noise estimation techniques.

• Experimental Setup:

  • SpRS Characterization: A narrow-linewidth tunable light source (TLS) swept from 1350–1680 nm (6 dBm launch power) to act as a pump. Classical transmission was emulated using a C-band ASE-loaded spectrum. Measurements were taken in both co-propagating and counter-propagating configurations using an Optical Spectrum Analyzer (OSA).
  • FWM Characterization: Conducted in the C-band with the quantum channel (194.7 THz / 1539.8 nm) placed between high-power unmodulated Continuous Wave (CW) tones at $\pm 50$ and $\pm 100$ GHz. CW signals were spectrally filtered to suppress crosstalk before transmission through Single-Mode Fiber (SMF) spools of varying lengths.
  • Fiber Parameters: Experiments utilized SMF with a measured attenuation profile and standard parameters ($\beta_2 = -21.1$ ps$^2$/km, $\gamma = 1.3$ W$^{-1}$km$^{-1}$).

• Theoretical Model:

  • The study utilized a comprehensive semi-analytical model (previously developed in Ref. [3]) to estimate the Power Spectral Density (PSD) of non-linear noise.
  • The model relies on classical power spectra and fiber parameters (SpRS efficiency, attenuation profiles, dispersion, and non-linearity coefficients).
  • Two theoretical approaches were compared against data: the exact FWM solution and a linearly-averaged approximation for computational efficiency.

3. Key Contributions

• Comprehensive Experimental Validation: The paper provides the first experimental validation of a specific semi-analytical model for both SpRS and FWM noise in QKD coexistence scenarios.
• Dual-Regime Analysis: It distinctively characterizes the two dominant non-linear regimes:
  1. Multi-band transmission: Where SpRS is the limiting factor.
  2. C-band co-propagation: Where FWM is the limiting factor.
• Model Accuracy Verification: It demonstrates that the theoretical model accurately predicts noise PSD across different fiber lengths, power levels, and propagation directions, including the behavior of the linearly-averaged FWM approximation.

4. Key Results

• SpRS Efficiency (Fig. 2a):
  • Measured SpRS efficiency increases for pumps at lower wavelengths due to reduced effective area and is higher in the Stokes region.
  • Implication: QKD schemes placing classical signals at lower frequencies suffer SpRS impairments even with spectral separations $>200$ nm.
• Multi-band SpRS Noise (Fig. 2b):
  • Counter-propagation: Noise in the O- and E-bands plateaus as SpRS becomes negligible, limited only by background noise and Rayleigh backscattering (measured efficiency: -42.32 dB/km).
  • Co-propagation: Unfiltered ASE dominates, necessitating notch-filtering for QKD transmission.
  • Agreement: Theoretical predictions matched experimental data with minor divergences only in the lower E-band under high C-band loading.
• FWM Noise (Fig. 2c):
  • Measured FWM noise (after subtracting linear contributions) showed excellent agreement with the exact theoretical solution.
  • The linearly-averaged approximation also demonstrated high accuracy across the dataset, despite smoothing out rapid oscillations, making it suitable for efficient numerical computation.

5. Significance

This work is significant for the practical deployment of QKD in real-world optical networks:

1. Infrastructure Optimization: It validates that QKD can coexist with classical traffic without dedicated dark fibers, provided non-linear effects are accurately modeled and managed.
2. Network Design Guidelines: The results confirm that spectral separation strategies must account for SpRS in multi-band scenarios, while channel allocation in the C-band must carefully manage FWM risks when quantum channels are adjacent to high-power classical signals.
3. Predictive Capability: The validated semi-analytical model allows network operators to accurately estimate Secret Key Rates (SKRs) for various transmission configurations, facilitating the transition from theoretical quantum networks to scalable, integrated infrastructure.

The research was supported by the European Union's QuNEST project (Grant Agreement No. 101120422).