Coupled Parametric Oscilators Proof of Concept in Radio Frequency


Optical Paramteric Oscillators (OPO) oscillate at a specific frequency by means of a non-linear interaction. A pump input laser with frequency \(\omega_p\) is converted through the non-linear interaction into a signal and idler frequencies, such that \(\omega_p = \omega_i + \omega_s\). Both frequencies can resonate in the cavity (doubly-resonant) or just one (singly-resonant).

The light generated by the OPO is “squeezed” - one quadrature is attenuated and the other amplified, which is useful for various scientific purposes.

By coupling two oscillators together, we create more modes. Unlike regular oscillators, where usually only one mode can oscillate due to mode competition, paramteric oscillators can (and must) oscillate in multiple modes. Active mode-locking can be used to create a source for broadband squeezed-light.

Demonstration of these effects using optical components is difficult and time consuming, we use radio components to simulate the same behavior in Radio Frequency domain (RF). RF components are easy and quick to set up, and can capture the same behavior.

Theoretical Background

Parametric Oscillator

An optical parametric oscillator consists of an optical resonator and a non-linear medium, a pump wave is inserted into the resonator, the resonator is noisy and thus many frequencies are present. Through the non-linear interaction the pump wave amplifies resonant frequency-pairs that satisfy the conditions \[\omega_p = \omega_s + \omega_i\] \[\varphi_p = \varphi_s + \varphi_i\] Where \(\omega_j\) is the frequency of the wave and \(\varphi_j\) is the phase.

The optical resonator resonates in at least one of the generated frequencies. The non-linear interaction in the medium leads to amplitude gain for the signal and idler waves and attenuation of the pump wave (parametric amplification). If the amplification is enough to overcome the losses, the resonator will resonate in one of the generated frequencies (singly-resonant) or both (doubly-resonant). A special case is when the idler and signal frequencies are degenerate. \[\omega_s = \omega_i = \omega_p/2\] Our setup is doubly resonant, meaning that the pump, signal and idler frequencies are all a multiple of the base frequency of the resonator. \[\omega_0 = \frac{c}{nL}\] The generated frequency can be tuned by changing the phase-matching conditions of the OPO, thus making the OPO a source of tunable radiation, also, as explained in the next section, the light produced is “squeezed”.