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We have presented theoretical as well as experimental studies of light attenuation resulting from fundamental scattering in crystalline WGM resonators. We show that the spontaneous Raman scattering results in the fundamental restrictions of the resonator quality factor at low temperatures. Stimulated Raman scattering also restricts the quality factor at any temperature if the power of the light used in the resonator exceeds the threshold of the stimulated process.

Chapter 5

Photon–phonon interactions in

crystalline resonators

There are three major scattering mechanisms in optical fibers. These mechanisms are named after Rayleigh, Raman, and Brillouin. If the intensity of light in fiber is high enough, a stimulated process may occur in which the scattered wave is amplified at the expense of the input beam. All three scattering mechanisms are present in WGM crystalline resonators. Rayleigh scattering is caused by non-propagating, frozen density fluctuations and is theoretically absent in pure crystals at low temperatures. At higher temperatures there may still be Rayleigh scattering due to microscopic temperature fluctuations. Raman scattering is caused by interaction of photons and vibrational states of molecules of which the crystal is made, or optical phonons. Brillouin scattering is an interaction between photons and acoustic phonons, or scattering from density fluctuations caused by acoustic waves. In a stimulated Brillouin scattering, the energy is transferred from the optical beam to the acoustic wave through electrostriction and the frequency of phonons is clamped to a specific value defined by energy and momentum conservation. It depends on optical wavelength, material composition, and, to some extent, temperature and pressure. While spontaneous scattering events limit the optical Q factor of a resonator, stimulated process is useful in that it enables WGM-based Raman and Brillouin lasers, which are expected to have very good characteristics as compared to the counterparts based on the fiber-ring resonators. Advantages include lower threshold and higher conversion efficiency as well as narrow linewidth. Raman and Brillouin lasing in crystalline WGM resonators are demonstrated in this work for the first time.

Results presented in this chapter are based on papers published in Optics Letters, Journal of Optical Society of America B and Physical Review Letters (submitted) [5, 6, 7]. Reproduced with permission from OSA.

5.1

Stimulated Raman scattering.

5.1.1

Introduction

Scattering of light by optical phonons was experimentally discovered by Raman and Krishnan in liquids, and independently by Mandelshtam and Landsberg in crystals [90, 91]. Lasers based on the stimulated Raman scattering (SRS) effect have found numerous applications in material science, molecular spectroscopy, and in many biological studies. SRS can be used to convert one optical frequency into another, making it possible to access virtually any wavelength within the Raman- active material’s transparency window. Generation of stimulated Raman scattering requires high levels of optical power, which may be reduced if a Raman-active medium is placed into an optical resonator. In this case, Raman laser characteristics are also defined by the properties of the resonator. Existing configurations include Raman lasers based on variations of Fabry-Perot cavities [92], Bragg grating resonators [93], fiber-ring cavities [94] and WGM resonators [72, 95]. The latter, while being compact and fiber compatible, exhibit the lowest lasing thresholds as extremely high optical power density in the cavity is easy to achieve. For example, in a 100µm fused silica WGMR with

Q= 5×108_{, injected power of 1 mW builds up to intensity of 12 GW/cm}2_{. The high optical Q factors}

of WGMRs make it possible to easily achieve high intracavity power to enhance nonlinear effects [96, 33, 27, 31, 94]. Low threshold makes miniaturization of a Raman laser possible. The recently demonstrated [95] integrated Raman laser based on a fused silica microsphere has a lasing threshold on the order of 100µW, owing mostly to high intracavity intensity buildup factor. However, the Q factor of fused silica cavities is subject to degradation due to atmospheric water and is limited to about eight billions for mm-sized resonators by material purity achievable with today’s technology. Fluorite cavities have certain advantages over their fused silica counterparts. The lower loss of the crystalline material allows for higher Q factors and the associated intracavity optical power buildup which, along with a higher Raman gain of the fluorite (Sec. 4.2), lead to lower thresholds of Raman lasing. This material may easily be superpolished to subnanometer surface roughness as demonstrated in Sec. 4.1, and the resulting surface does not absorb water vapor. The refractive index of fluorite is smaller than that of fused silica, making it possible to use common optical fibers to couple light in and out of the cavity. A coupling efficiency exceeding 80 % is routinely achieved in our lab. Finally, it is possible to use diamond machining techniques to produce fluorite cavities with a predesigned spectral response and single-mode cavities (Sec. 3.1).

We demonstrate efficient and ultralow threshold Raman lasing with ultrahigh Q CaF2whispering

gallery mode (WGM) resonators. Continuous wave emission threshold is shown possible below 1µW with a 5 mm cavity, orders of magnitude lower than in any other non-WGMR Raman source. Achieving a low lasing threshold may be possible by increasing the Q factor, as opposed to decreasing the cavity diameter. Indeed, the threshold of Raman lasing in a WGM cavity is given by the following

formula [87]: Pth= π2_n2 ξgcQSQP Vm λPλS