Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator

Abstract

In whispering gallery mode (WGM) resonators light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase matching conditions for optical parametric down conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons' angular momenta and predicts a very low parametric oscillations threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in Lithium Niobate. We demonstrated a single-mode, strongly non-degenerate OPO with a threshold of 6.7 µW and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs and opens the perspectives for their applications in quantum and nonlinear optics, particularly for the generation of squeezed light. WGM resonators have found applications in many areas of photonics, including quantum and nonlinear optics, spectroscopy, biophysics and optomechanics (see [1][2][3] and references therein). These areas benefit from a high quality factor (Q) and strong field confinement of WGM resonators in two different aspects. First, WGM resonators provide strong coupling of the confined field to other systems such as quantum dots [4], atoms [5], mechanical oscillators [6] or other cavities [7]. Second, WGM resonators provide strong nonlinear coupling between optical fields. Here the possibilities lie in utilizing either third order nonlinear effects in fused silica [8][9][10], or nonlinear effects in crystalline materials [11][12][13][14].In this letter we demonstrate optical parametric oscillations with extremely low thresholds and narrow linewidths in a crystalline WGM disk resonator. This is achieved by taking advantage of the strong second-order optical nonlinearity of Lithium Niobate and of the high quality factor of our WGM resonator, limited by the material absorption only. This research is motivated by the perspective to develop a miniature, stable, narrow-line tunable OPO for spectroscopy applications, to study the OPO dynamics far above the threshold, and by the wide and successful use of conventional OPOs for the generation of non-classical light.To achieve efficient parametric processes in a nonlinear material phase matching conditions have to be fulfilled. For parametrically interacting plane waves in a bulk material, these phase matching conditions correspond to conservation of energy and linear momentum of pump (p), signal (s) and idler (i) photons:In spherical geometry the orbital angular momentum of the photons is conserved, along with the energy. This gives rise to WGM selection rules for the PDC process and determines the OPO threshold in-coupled pump power for various modes [15]:where c is the speed of light, λ p is the pump wavelength n = n e (λ p ) = n o (λ s ) is the phase-matched refractive index, and ...

Nonlinear and Quantum Optics with Whispering Gallery Resonators

“…Further selection rules are discussed in [317][318][319][320] 11 . In particular, it is shown [318][319][320] that in large resonators the overlap integral s 123 factors into the radial and angular parts as a very good approximation. The angular part yields Clebsch-Gordan coefficients á ñ l l m m l m , ;…”

“…As a result, the c 2 ( ) factor in (21) 11 Note that [320] required a corrigendum [321]. 12 In equation (6) of [319], the numerical factor should be 4, not 8. 13 Reference [323] quotes µ V R p 1.83 as calculated in [322], but [322] only provides a plot for V p (R) in its figure 3.…”

Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

“…One of the mirrors of the signal cavity is not fixed and can act then as a mechanical oscillator forced by the radiation pressure exerted from the light contained in the cavity. OPOs based on dual semi-monolithic cavities [81] can implement this exact setup, but other platforms such as crystalline whispering gallery mode resonators [66][67][68][69][70][71][72][73][74][75][76][77][78] or superconducting circuits [27,44,59,79,80] are already at a point where the model analyzed in our work can be studied experimentally.…”

“…In particular, miniaturized whispering gallery mode resonators can be fabricated directly with the typical crystalline materials possessing secondorder optical nonlinearity, such that light can be downconverted while circulating on the resonator [66][67][68][69][70][71][72][73][74][75][76][77][78]. A completely different, but equally realistic implementation could consist on a superconducting circuit in the degenerate parametric oscillation configuration [79] coupled to a drum-shaped capacitor acting as a the mechanical degree of freedom [27,44,59] (see also [80] for a recent circuit QED proposal).…”

Observation of second-order hyper-Raman generation in LiNbO_3 whispering-gallery mode disk resonators

“…Dramatic improvement in the efficiency of nonlinear frequency conversion processes, including Raman scattering [7,8], parametric oscillations [9,10], and second [11,12] and third [13] harmonic generation using WGMRs have been recently demonstrated. In this manuscript, we report observation of nonlinear conversion of a strong pump field (λ p = 1064 nm) into several optical fields of higher frequencies.…”