Hybrid Electro-Optically Modulated Microcombs

Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microresonators (“microcombs”) has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: Combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spanning spectra but mode spacings beyond electronic detection limits. However, it has not yet been possible to achieve these two key requirements simultaneously, as will be critical for most microcomb applications. Here we present a route to overcome this problem by interleaving an electro-optic comb with the spectrum from a parametric microcomb. This allows, for the first time, direct control and stabilization of a microcomb spectrum with large mode spacing ($>140\mathrm{GHz}$) with no need for an additional mode-locked laser frequency comb. The attained residual 1-sec instability of the microcomb comb spacing is ${10}^{-15}$, with a microwave reference limited absolute instability of ${10}^{-12}$ at a 140 GHz mode spacing.

Figure 1

Experimental scheme of electro-optically modulated microcombs. (a) Setup for generation and stabilization of microcombs with electro-optical modulation. $\mathrm{PD}=\mathrm{\text{photodiode}}$, $\mathrm{EOM}=\mathrm{\text{electro-}}$optic modulator, $\mathrm{cw}=\mathrm{\text{continuous-wave}}$ and $\mathrm{PLL}=\mathrm{\text{phase-locked}}$ loop. (b, c)Photograph and microscope image of the employed whispering-gallery mode microrod resonator with a radius of $230\mu \mathrm{m}$ (143 GHz mode spacing). (d) Scheme of electro-optically generated sidebands around each microcomb mode. The low-frequency beat note $f_{\mathrm{beat}}$ between the sidebands is used to control and stabilize the comb spacing.

Figure 2

Optical microcomb spectra with and without electro-optic modulation sidebands. (a) Optical comb from a microrod resonator with 143 GHz mode spacing. The launched power into the tapered optical fiber is $\sim 250\mathrm{mW}$. (b) Same comb spectrum filled with sidebands from the electro-optic modulator. (c) Zoom into the combined spectra with and without electro-optic modulation. Both the 143 GHz microcomb spacing as well as the 23 GHz electro-optic modulation sidebands are visible. The third-order electro-optic sidebands are nearly overlapping and cannot be distinguished by the optical spectrum analyzer (resolution $\sim 3\mathrm{GHz}$). The beat note between these central sidebands is used for measurement and stabilization of the microcomb mode spacing.

Figure 3

Frequency stability of the free-running and stabilized microcomb. (a) Allan-deviation measurements with different gate times. The fractional (absolute) 1-sec-instabilities of the microcomb mode spacing are $\sigma =2.5\times {10}^{-8}(3.6\mathrm{kHz})$ in the free-running case, $\sigma =1\times {10}^{-12}(140\mathrm{mHz})$ for the out-of-loop measurements, and $\sigma =1.2\times {10}^{-15}(170\mu \mathrm{Hz})$ for the in-loop measurement. Note that the out-of-loop stabilities are limited by the synthesizer that produces $f_{\mathrm{eom}}$ (shown by the purple circles), which also limits the stability of the reference comb (black upside-down triangles). All fractional frequency instabilities are given at the microresonator mode spacing frequency of 143 GHz. (b) Measurement of the stabilized electronic spectrum of the in-loop beat note $f_{\mathrm{beat}}$ in Fig. 1d. (c) Out-of-loop mode-spacing beat note against a fiber-laser reference comb. This beat note is generated by beating two adjacent microcomb lines against a stabilized reference comb, followed by generation of the difference frequency of these two beats. This beat note depends only on the microcomb and reference comb mode spacings and not on their offset frequencies.

Figure 4

Subharmonic stabilization of a microcomb. (a) Principle of generation and stabilization of eletro-optic sidebands at a subharmonic frequency of the microcomb spacing. A fast photodiode [PD1 in (c)] simultaneously detects $f_{\mathrm{beat}1}$ and $3\times f_{\mathrm{eom}}$. The subsequently generated difference frequency $f_{\mathrm{beat}1}-3\times f_{\mathrm{eom}}$ is used to stabilize the microcomb spectrum at exactly 6 times the electro-optic modulation frequency. This scheme provides a continuous optical comb with a spacing of $f_{\mathrm{eom}}$. The corresponding mode spacing stability is shown in Fig 3a. (b) Crossing of $f_{\mathrm{beat}1}$ and $3\times f_{\mathrm{eom}}$ when changing the launched optical power. The subharmonic lock point corresponds to $f_{\mathrm{beat}1}-3\times f_{\mathrm{eom}}=0$. The total mode-spacing tuning range is around 1.5 MHz, with a slope of $-5.7\mathrm{kHz}/\mathrm{mW}$. (c) Setup for the subharmonic comb stabilization. LP designates low pass filter.