Influence of phonon harmonicity on spectrally pure resonant Stokes fields
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2022-08-03 |
| Journal | Physical review. A/Physical review, A |
| Authors | Georgios Stoikos, E. Granados |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis research introduces a novel, highly accurate methodāthe āresonant Stokes fieldā methodāto determine the temperature dependency of diamondās refractive index (thermo-optic coefficient), critical for ultra-stable integrated photonics.
- Core Problem Addressed: Existing models for diamondās thermo-optic coefficient (TOC) are inaccurate, especially above 300 K, hindering the development of ultra-stable diamond lasers and quantum devices.
- Methodology: The study employs a monolithic Fabry-PĆ©rot (FP) diamond Raman resonator, measuring the shift in the Stokes resonant frequency (Ī½S) as a function of temperature (T). This shift is directly linked to the materialās opto-mechanical properties.
- Stability Achievement: The monolithic resonator demonstrated exceptional frequency stability, achieving Fourier-limited Stokes nanosecond pulses with a center frequency deviation of less than 4 MHz RMS over 16 hours under active temperature stabilization.
- Key Finding (Phonon Harmonicity): By fitting the measured tuning slope (dĪ½S/dT), the average lattice phonon frequency (ħĻ(T)) was retrieved, showing a linear decrease with temperature (805 cm-1 at 300 K to 740 cm-1 at 370 K).
- TOC Calculation: The calculated thermo-optic coefficient (1/n * dn/dT) is approximately 3.5 x 10-6 K-1 at room temperature, but exhibits severe nonlinearity in the 200 K to 400 K range, tending asymptotically toward 8 x 10-6 K-1 above 400 K.
- Material Parameters: The model allowed for the estimation of the GrĆ¼neisen parameter (Ī³) for diamond as 4715, and the 0 K Raman shift (ħĻ0) as 600 cm-1.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Type | Synthetic Cuboid | N/A | CVD material used for monolithic FP resonator. |
| Resonator Dimensions | 7 x 2 x 2 | mm3 | Physical size of the diamond crystal. |
| Crystal Orientation | (110) axis | N/A | Beam propagation direction. |
| Pump Wavelength | 532 | nm | Frequency-doubled Nd:YAG laser. |
| Stokes Wavelength | 573 | nm | First Stokes order output. |
| Raman Frequency Shift | 1332 | cm-1 | Giant shift characteristic of diamond. |
| Raman Gain (532 nm) | >40 | cm/GW | High gain property. |
| Pump Pulse Duration | 10 | ns | Temporal envelope of the pump laser. |
| Pump Repetition Rate | 100 | Hz | Pulse repetition frequency. |
| Pump Energy | 50 | ĀµJ | Energy per pulse. |
| Pump Intensity (Waist) | 0.1 | GW/cm2 | Intensity focused inside the crystal (50 Ā± 5 Āµm waist). |
| Free Spectral Range (FSR) | ~8 | GHz | FSR at 573 nm. |
| Stokes Linewidth (FWHM) | 100 Ā± 20 | MHz | Measured average linewidth. |
| Center Frequency Stability (RMS) | <4 | MHz | Achieved stability over 16 hours using active temperature control. |
| Temperature Stability (Oven) | <0.01 | Ā°C | Standard deviation of the high precision oven. |
| Average Tuning Slope (dĪ½S/dT) | -2.3 | GHz/K | Measured frequency-temperature tuning slope within one FSR. |
| Raman Phonon Line Slope (dĪ½R/dT) | +0.23 | GHz/K | Temperature dependence of the first-order Raman phonon line (300 K to 400 K). |
| Thermo-Optic Coefficient (300 K) | 3.5 x 10-6 | K-1 | Calculated value (1/n * dn/dT) at room temperature. |
| Thermo-Optic Coefficient (Asymptotic) | 8 x 10-6 | K-1 | Value approached above 400 K. |
| GrĆ¼neisen Parameter (Ī³) | 4715 | N/A | Estimated material parameter. |
| Debye Temperature (ĪD) | 1880 | K | High characteristic temperature of diamond. |
Key Methodologies
Section titled āKey MethodologiesāThe study utilizes Stimulated Raman Scattering (SRS) in a monolithic FP resonator combined with perturbation theory and thermal models to extract material parameters.
- Monolithic Resonator Setup: A synthetic CVD diamond cuboid (7 x 2 x 2 mm3) with uncoated end-faces (R ā 18%) serves as the monolithic Fabry-PĆ©rot resonator. The crystal is housed in a high-precision oven capable of temperature stabilization <0.01 Ā°C.
- SRS Generation: The resonator is pumped by a frequency-doubled Nd:YAG laser (532 nm, 10 ns, 100 Hz). The pump polarization is aligned parallel to the (111) axis to maximize SRS efficiency.
- Frequency Measurement: The resulting 573 nm Stokes output is filtered, and its center frequency deviation (dĪ½S) is measured as the oven temperature (T) is adjusted in 10 mK increments.
- Resonance Condition Modeling: The Stokes resonant frequency (Ī½S) is modeled based on the FP resonance condition, which depends on the physical length L(T) (thermal expansion) and the refractive index n(Ī»S, T) (thermo-optic effect).
- Tuning Slope Calculation: Perturbation theory is applied to the resonance condition to derive the approximate tuning slope (dĪ½S/dT), which is a function of the thermal expansion coefficient (Ī±) and the thermo-optic coefficient (1/n * dn/dT).
- Phonon Frequency Retrieval: The temperature-dependent part of the refractive index (nT(T)) is modeled using a Bose-Einstein distribution, which incorporates an average phonon frequency ħĻ(T). The measured tuning slope (dĪ½S/dT) is fitted to this model to retrieve the temperature-dependent average phonon frequency ħĻ(T).
- GrĆ¼neisen Parameter Estimation: The thermal-expansion contribution to the phonon frequency (Ī(1)(T)) is related to the GrĆ¼neisen parameter (Ī³) and the thermal expansion coefficient (Ī±). By analyzing the linear decrease of the fitted ħĻ(T), the GrĆ¼neisen parameter (Ī³ = 4715) and the 0 K Raman shift (ħĻ0 = 600 cm-1) are estimated.
- TOC Calculation: The final thermo-optic coefficient is calculated by differentiating the Bose-Einstein model for nT(T) using the experimentally derived ħĻ(T) values.
Commercial Applications
Section titled āCommercial ApplicationsāThe highly stable, spectrally pure, and tunable laser source developed, coupled with the accurate material characterization, supports several advanced technological fields:
- Integrated Quantum Technology: Providing ultra-stable, narrow-linewidth light sources necessary for quantum computing and quantum memory applications, particularly those utilizing diamond color centers (e.g., NV or SiV centers).
- High Resolution Spectroscopy: The generation of Fourier-limited Stokes pulses with stabilized center frequency deviation (less than 4 MHz) is ideal for high-precision spectroscopic measurements.
- Coherent Optical Communications: Stable, single-frequency emission is a prerequisite for high-speed, coherent communication systems.
- Temperature-Sensitive Photonic Devices: The derived, accurate temperature-dependent thermo-optic coefficient is essential for modeling and designing integrated photonic devices in diamond that require thermal stability or precise thermal tuning.
- Diamond Laser Development: Enabling the design of next-generation diamond Raman lasers with reduced thermal lensing effects and improved frequency stability, suitable for high-power operation (up to kW average power).
- Quantum Sensing: Utilizing diamond resonators for applications requiring highly stable optical fields for sensing magnetic or electric fields.
View Original Abstract
Thanks to their highly coherent emission and compact form factor, single axial mode diamond Raman lasers have been identified as a valuable asset for applications including 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 ultra-stable 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-Perot (FP) diamond Raman resonator. Our approach takes into account the influence of the temperature on the first-order phonon line and the average lattice phonon frequency under intense stimulated Raman scattering (SRS) conditions. We further utilize this model to calculate the temperature-dependent thermo-optic coefficient and the Gruneisen parameter of diamond in the visible spectral range. 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.