Optical frequency comb generation from a monolithic microresonator

arXiv:0708.0611v1 [physics.optics] 4 Aug 2007 Optical frequency comb generation from a monolithic microresonator P. Del’Haye,1 A. Schliesser,1 O. Arcizet,1 T. Wilken,1 R. Holzwarth,1 and T.J. Kippenberg1, ∗ 1Max Planck Institut f¨ur Quantenoptik, 85748 Garching, Germany Optical frequency combs[1, 2, 3] provide equidistant frequency markers in the infrared, visible and ultra-violet[4, 5] and can link an unknown optical frequency to a radio or microwave frequency reference[6, 7]. Since their inception frequency combs have triggered major advances in optical frequency metrology and precision measurements[6, 7] and in applications such as broadband laser-based gas sensing[8] and molecular fingerprinting[9]. Early work generated frequency combs by intra-cavity phase modulation[10, 11], while to date frequency combs are generated utilizing the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized[12]. Here, we report an entirely novel approach in which equally spaced frequency markers are generated from a continuous wave (CW) pump laser of a known frequency interacting with the modes of a monolithic high-Q microresonator[13] via the Kerr nonlinearity[14, 15]. The intrinsically broadband nature of parametric gain enables the generation of discrete comb modes over a 500 nm wide span (≈70 THz) around 1550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3×10−18. In contrast to femtosecond mode-locked lasers[16] the present work represents an enabling step towards a monolithic optical frequency comb generator allowing significant reduction in size, cost and power consumption. Moreover, the present approach can operate at previously unattainable repetition rates[17] exceeding 100 GHz which are useful in applications where the access to individual comb modes is required, such as optical waveform synthesis[18], high capacity telecommunications or astrophysical spectrometer calibration[19]. Optical microcavities[20] are owing to their long tem- poral and small spatial light confinement ideally suited for nonlinear frequency conversion, which has led to a dramatic improvement in the threshold of nonlinear op- tical light conversion[21]. In contrast to stimulated gain, parametric frequency conversion[22] does not involve cou- pling to a dissipative reservoir, is broadband as it does not rely on atomic or molecular resonances and consti- tutes a phase sensitive amplification process, making it uniquely suited for tunable frequency conversion. In the case of a material with inversion symmetry - such as silica - the non linear optical effects are dominated by the third order non linearity. The process is based on four-wave mixing among two pump photons (frequency νP ) with a signal (νS) and idler photon (νI) and results in the emer- gence of (phase coherent) signal and idler sidebands from the vacuum fluctuations at the expense of the pump field (cf. Fig.1). The observation of parametric interactions requires two conditions to be satisfied. First momentum conservation has to be obeyed. This is intrinsically the case in a whispering gallery type microcavity[20] since the optical modes are angular momentum eigenstates and have (discrete) propagation constants βm = m R resulting from the periodic boundary condition, where the integer m designates the mode number and R denotes the cav- ity radius. Hence the conversion of two pump photons (propagation constant βN) into adjacent signal and idler modes (βN−∆N, βN+∆N, ∆N = 1, 2, 3 . . .) conserves mo- ∗Electronic address: tjk@mpq.mpg.de mentum intrinsically[14] (analogous reasoning applies in the case where the two annihilated photons are in differ- ent modes, i.e. for four-wave mixing, cf. Fig. 1b). The second condition that has to be met is energy conser- vation. As the parametric process creates symmetrical sidebands with respect to the pump frequency (obeying hνI + hνS = 2hνP , where h is the Planck constant) it places stringent conditions on the cavity dispersion that can be tolerated since it requires a triply resonant cavity. This is a priori not expected to be satisfied, since the distance between adjacent modes νFSR = |νm −νm+1| (the free spectral range, FSR) can vary due to both ma- terial and intrinsic cavity dispersion which impact neff and thereby render optical modes (having frequencies νm = m · c 2π·R·neff , where c is the speed of light in vacuo) non-equidistant. Indeed, it has only recently been possi- ble to observe these processes in microcavities (made of crystalline[15] CaF2 and silica[14, 23]). Importantly, this mechanism could also be employed to generate optical frequency combs: the initially generated signal and idler sidebands can interact amo

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