Influence of phonon harmonicity on spectrally pure resonant Stokes fields

Due to their highly coherent emission, tunability, and compactness, integrated single-frequency diamond Raman lasers are interesting tools for applications in integrated quantum technology, high-resolution spectroscopy, or coherent optical communications. While the fundamental emission linewidth of these lasers can be Fourier limited, their thermo-optic characteristics lead to drifts in their carrier frequency, posing important challenges for applications requiring ultrastable emission. We propose here a method for measuring accurately the temperature-dependent index of refraction of diamond by employing standing Stokes waves produced in a monolithic Fabry-Pérot diamond Raman resonator. Our approach takes into account the influence of temperature on the first-order phonon line and the average lattice phonon frequency under intense stimulated Raman scattering conditions. We further utilize this model to calculate the value of the average phonon frequency and then the temperature-dependent thermo-optic coefficient. The theory is accompanied by the demonstration of tunable Fourier-limited Stokes nanosecond pulses with a stabilized center frequency deviation of less than $4$ MHz.

Figure 1

(a) Schematic depiction of main thermal effects influencing the resonant Stokes frequency in a monolithic Raman resonator, and (b) depiction of the temperature effect on the photon and optical phonon energies.

Figure 2

Schematic layout of the experimental setup: A monolithic diamond resonator is pumped by a frequency-doubled Q-switched Nd:YAG laser. The output Stokes nanosecond pulse was characterized temporally and spectrally with a set of four high-resolution Fizeau interferometers, and a photodiode (PD) connected to a large bandwidth 16 GHz oscilloscope. HWP1, HWP2: half-wave plates; PBS: polarizing beam splitter; FL: focusing lens; PM: power meter.

Figure 3

Active temperature stabilization of the Stokes resonant frequency over more than 16 h. The RMS fluctuation of the Stokes frequency is less than 4 MHz. Inset: Measured Stokes field spectrum.

Figure 4

(a) Stokes center frequency (${\nu }_S$) detuning as a function of measured diamond temperature. Dashed blue line represents the tuning range (FSR) of the Stokes frequency as a function of temperature. (b) Measured tuning slope for each FSR as a function of temperature. (c) Calculated average phonon frequencies by solving Eq. (16).

Figure 5

Calculated thermo-optic coefficient of diamond as a function of temperature between 300 and 370 K using the solutions of Eq. (16).