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 ...