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An entirely novel comb generator based on the silica WGM cavities described in chapter 1 was reported at the Max Planck Institute of Quantum Optics in 2007. This has allowed a dramatic reduction in size and enabled access to ultra-high repetition rates, exceeding 40 GHz, while normal mode-locked lasers typically only offer rates below 1 GHz. The approach is based on the χ(3) nonlinearity of the device’s host material, giving rise to parametric frequency conversion1. The cavities’ high optical finesse and small mode volume make them uniquely suited for optical frequency conversion [298] due to the significantly reduced threshold power for nonlinear optical processes.

Figure 3.1 illustrates the comb generation process. A high-Q (Q _∼108) WGM resonance of a 75µm-diameter toroidal microcavity is pumped with a monochromatic laser in the 1550 nm-range at a power of about 60 mW. Such a power corresponds to an intracavity intensity of more than 1 GW/cm2, and thus far exceeds the threshold for parametric oscillations [75]. In this case, a comb-like spectrum consisting of several bright emission lines spaced by about 7 nm (cf. figure 3.1) is measured using an optical spectrum analyzer. This spacing corresponds approximately to the cavity FSR

νFSR = c

2πRneff

, (3.2)

with the cavity radiusRand neff the effective refractive index. The observed process is very efficient, generating strong (typically > 1 mW or 0 dBm) sidebands spanning several hundreds of nanometers of spectral width.

The underlying physical mechanism is a cavity-enhanced cascaded four- wave mixing (FWM) process. It is mediated by the intensity-dependent refractive index of silica as introduced in subsection 1.5.3. At low pump powers this process gives rise to a single pair of signal and idler sidebands at frequencies νS and νI, respectively. In a quantum picture, this corresponds to the conversion of two pump photons into a pair of signal and idler photons, and energy conservation requiresνS+νI =νpump+νpump. If idler, signal and

pump frequencies all coincide with optical modes of the microresonator, this mechanism is resonantly enhanced by the cavity. This effect was observed both in silica microtoroidal resonators [75] and crystalline CaF2 WGM res-

onators [299] at very low thresholds (tens of µW). We have also been able to generate frequency combs from the crystalline resonators introduced in section 2.9.

At higher powers, the generation of sidebands can cascade via non-degen- erate four-wave mixing among pump and first-order sidebands. This gives rise to higher order sidebands, as shown in figure 3.1. Energy conservation (for example,νpump+νI =νII+νS) again ensures that the difference of pump and first-order sidebands _|νpump−νI| = |νS −νpump| is exactly transferred 1_{This process has also been referred to ashyperparametric frequency conversion [297].}

Figure 3.1: Frequency comb generation in an optical microresonator. (a) Optical mi- crograph of a silica toroid employed for frequency comb generation, and a spectrum measured at the output of the tapered optical fiber. The individual modes are approx- imately spaced by the FSR (7 nm) of the cavity. Below the pump line at 1550 nm, amplified spontaneous emission due to the employed erbium-doped fiber amplifier is also observed. (b) Principle of the comb generation process, involving both degenerate (top panel) and non-degenerate four-wave mixing (bottom panel) processes.

to all higher-order inter-sideband spacings. If the cavity exhibits a suffi- ciently equidistant mode spacing, the frequencies of higher-order sidebands remain resonant with the corresponding WGMs. The cavity then resonantly enhances successive four-wave mixing to higher orders, leading to the gen- eration of phase-coherent sidebands with equal spacing over a large spectral range—an optical frequency comb. However, dispersion due to the cavity geometry or material may render the cavity resonances non-equidistant (cf. figure 3.2). If the resulting walk-off of the cavity modes from the oscillat- ing sidebands therefore exceeds the WGMs’ linewidth, the broadening of the comb ceases [299].

Dispersion in a microcavity arises from both its geometry and the intrinsic dispersion of the resonator’s material. Advantageously, these two contribu- tions can cancel if they are of similar magnitude but opposite sign. This is indeed the case for silica WGM cavities in the 1550-nm spectral window. Measurements have verified that the WGM of a cold cavity deviate by only around 20 MHz from equidistance over a 100-nm span. This deviation is still comparable to the width of slightly overcoupled WGM resonances as typically used in this work. Furthermore, non-linear mode pulling (self- and cross-modulation) can contribute to compensate residual dispersion [75].

Figure 3.2: The role of dispersion in optical frequency comb generation. Cavity dispersion renders the free spectral range (FSR) dependent on the optical frequency. As a conse- quence, the cavity resonances (blue Lorentzians), are not equidistant in frequency space, while the generated optical sidebands are. If the walk-offexceeds the WGMs’ linewidth, the cavity enhancement of the four-wave mixing process is reduced. Therefore, uncom- pensated cavity dispersion can eventually limit the comb bandwidth.