Raman-lasing threshold power is increased through suitable choice of dimensions.
NASA’s Jet Propulsion Laboratory, Pasadena, California
A generic design has been conceived to suppress the Raman effect in whispering-gallery-mode (WGM) optical resonators that have high values of the resonance quality factor (Q). Although it is possible to exploit the Raman effect (even striving to maximize the Raman gain to obtain Raman lasing), the present innovation is intended to satisfy a need that arises in applications in which the Raman effect inhibits the realization of the full potential of WGM resonators as frequency-selection components. Heretofore, in such applications, it has been necessary to operate high-Q WGM resonators at unattractively low power levels to prevent Raman lasing. (The Raman-lasing thresholds of WGM optical resonators are very low and are approximately proportional to Q–2.)
Heretofore, two ways of preventing Raman lasing at high power levels have been known, but both entail significant disadvantages:
- A resonator can be designed so that the optical field is spread over a relatively large mode volume to bring the power density below the threshold. For any given combination of Q and power level, there is certain mode volume wherein Raman lasing does not start. Unfortunately, a resonator that has a large mode volume also has a high spectral density, which is undesirable in a typical photonic application.
- A resonator can be cooled to the temperature of liquid helium, where the Raman spectrum is narrower and, therefore, the Raman gain is lower. However, liquid-helium cooling is inconvenient.
The present design overcomes these disadvantages, making it possible to operate a low-spectral-density (even a single-mode) WGM resonator at a relatively high power level at room temperature, without risk of Raman lasing.
The present design exploits the following two physical principles:
- There is a wavelength interval between the optical pump signal (in this case, the optical signal at the desired resonance frequency) and the Raman signal emitted by the resonator material in response to the pump signal. For a CaF2 resonator, this wavelength interval is ≈80 nm; for a diamond resonator, this wavelength interval is ≈400 nm.
- In a single-mode resonator, there is a cutoff frequency — a minimum frequency at which the optical mode is still confined and has high material-limited value of Q. At lower frequency, Q is limited by leakage of the partially confined mode to the environment.
The essence of the present design is to choose the dimensions of a single-mode WGM resonator to place the cutoff frequency between the pump and Raman frequencies. For example, if the resonator is to be made of diamond and to have a resonance wavelength of 1,550 nm, then its dimensions should be chosen to place the cutoff wavelength between 1,550 nm and the Raman wavelength of 1,550 + 400 = 1,950 nm. Preferably, the cutoff wavelength should be set at or near 1,750 nm. The basic inequality that expresses the required relationship among the wavelengths and dimensions for a WGM resonator like the one in the figure is
λp < 2L(2εh/R)1/2 < λR,
where λp is the pump wavelength, L is the axial length of the resonator, ε is the relative permittivity of the resonator material, h is the radial depth of the groove that separates the resonator from the rest of the rod of resonator material, R is the radius of the rod, and λR is the Raman wavelength.
In a resonator designed in this way, the value of Q at the Raman lasing wavelength is a fraction, 1/ρ, of the value of Q in an otherwise identical WGM resonator that has not been designed to place the cutoff wavelength between the pump and Raman wavelengths. Consequently, the Raman-lasing threshold power is about ρ2 times as high as it is in the absence of this innovation.
This work was done by Anatoliy Savchenkov, Andrey Matsko, Dmitry Strekalov, and Lute Maleki of Caltech for NASA’s Jet Propulsion Laboratory. NPO-43334
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