Adjust the parameters below to calculate the squeezing and anti-squeezing spectra from a single-mode optical parametric oscillator (OPO) or optical parametric amplifier (OPA). The plot shows how the quadrature variance (normalized to vacuum noise) varies with frequency.
Note: The squeezing spectrum shows the noise variance of the squeezed quadrature (blue) and anti-squeezed quadrature (red) as a function of frequency. At DC (zero frequency), maximum squeezing is achieved. At frequencies much larger than the cavity linewidth, the spectrum approaches the vacuum noise level (0 dB). The pump parameter σ determines the degree of squeezing: as σ approaches 1 (threshold), squeezing increases but bandwidth decreases.
The squeezing and anti-squeezing spectra from a single-mode optical parametric oscillator (OPO) or optical parametric amplifier (OPA) are calculated using the following formulas:
1. Pump Parameter:
\[ \sigma = \frac{P}{P_{\text{th}}} \]
where \(P\) is the pump power and \(P_{\text{th}}\) is the threshold power.
2. Normalized Frequency:
\[ \Omega = \frac{\nu}{\nu_{\text{FWHM}}} \]
where \(\nu\) is the analysis frequency and \(\nu_{\text{FWHM}}\) is the full-width at half-maximum of the cavity resonance.
3. Squeezed Quadrature Variance [1]:
\[ V_- = 1 - \frac{\eta T}{T + \alpha} \cdot \frac{4\sqrt{\sigma}}{\Omega^2 + \left(1 + \sqrt{\sigma}\right)^2} \]
4. Anti-Squeezed Quadrature Variance [1]:
\[ V_+ = 1 + \frac{\eta T}{T + \alpha} \cdot \frac{4\sqrt{\sigma}}{\Omega^2 + \left(1 - \sqrt{\sigma}\right)^2} \]
5. Conversion to Decibels:
\[ V_{\text{dB}} = 10 \log_{10}(V) \]
6. Linear Entropy [2]:
\[ S_L = 1 - \frac{1}{V_- \cdot V_+} \]
Parameters: