Coherent terahertz-to-microwave link using electro-optic-modulated Turing rolls

Arising from modulation instability, Turing rolls in optical Kerr microresonators have been used in the generation of optical frequency combs and the synthesis of microwave and terahertz frequencies. In this work, by applying electro-optic modulation on terahertz-frequency Turing rolls, we implement electro-optic frequency division with a microcomb to synthesize variable low-noise microwave signals. We also actively stabilize the terahertz oscillations to a microwave reference via intracavity power modulation, obtaining fractional frequency instabilities that are better than those of the free-running situation by up to six orders of magnitude. This study not only highlights the extraordinary spectral purity of Turing-roll oscillations but also opens the way for bidirectional terahertz-to-microwave links with hybrid optical-frequency-comb techniques.

Figure 1

Low-noise microwave synthesis with the TR-EOFD technique. (a) The schematic layout of the TR-EOFD setup. (b) The phase-noise spectra of computed fundamental quantum noises and simulated technical noises of a terahertz TR oscillation, a single-soliton DKS oscillation, and a microwave synthesized with the TR-EOFD scheme. The synthesized microwave has a frequency that is the same as the DKS repetition rate (12 GHz in the simulations, details of which are presented in Appendixes pp1 and pp2). The arrows indicate the phase-noise reduction due to the frequency division.

Figure 2

Experimental realization of the TR-EOFD scheme. (a) An ECDL is locked to a microresonator mode with the PDH technique to generate a TR microcomb. After amplification using an erbium-doped fiber amplifier (EDFA), the microcomb is phase modulated by three EOMs. An optical bandpass filter (BPF) with a passband centered at 1549.5 nm is used to filter out the overlapping EOCs to generate a beat frequency around 10 MHz. The PLL servo phase locks $f_{\mathrm{mod}}$ to the TR oscillation frequency, thus generating low-noise microwaves whose phase noises are measured with a phase-noise analyzer (PNA). (b) The optical spectra of the original TR microcomb and the combs after electro-optical modulation at three different modulation frequencies. The two first-order TR sidebands are in dark red (dark gray). (c) A photo of the ${\mathrm{MgF}}_2$ microresonator. (d) The laser-sweeping spectra of the mode resonance and the generated microcomb power and the corresponding PDH error signal. The PDH modulation frequency is 9 MHz. (e) Electrical spectra of the free-running $f_{\mathrm{rf}}$ and the phase-locked $f_{\mathrm{mod}}$ measured with an electrical spectrum analyzer.

Figure 3

Phase-noise spectra (solid lines, from bottom to top) of synthesized microwave signals of 5.3, 10.3, and 16.9 GHz, as well as the 0.372-THz TR oscillation, respectively. The noise peaks around 1 kHz are caused by the phase noise of the pump laser. The dotted lines (from bottom to top) are the phase-noise spectra of the uncontrolled $f_{\mathrm{mod}}$ with the corresponding microwave frequencies and the phase-noise spectrum of $f_{\mathrm{rf}}$ when the PLL is deactivated, respectively. At frequencies above 100 Hz the THz-oscillation phase-noise measurement is limited by the multiplication noise of the uncontrolled $f_{\mathrm{mod}}$.

Figure 4

Phase-coherent microwave-to-THz link based on actively frequency stabilized Turing rolls. (a) The optical spectra of the TRs before (top) and after (bottom) the electro-optic modulation. (b) Spectrum of $f_{\mathrm{rf}2}$ when the PLL is activated. (c) Measured frequencies of $f_{\mathrm{rf}2}$ without (top) and with (bottom) the PLL control. (d) The histogram of the counted frequencies with the PLL activated. The standard deviation is indicated. (e) Computed modified Allan deviations of the frequency traces presented in (c). The error bars are too small to be visible.

Figure 5

The profiles of the intracavity field amplitude of the simulated TRs with three different $D_2$ settings. The values of $D_2$ and the numbers of TRs are shown in the corresponding panels. The insets plot the relative intracavity powers of the pumping laser and the first-order TR sidebands.

Figure 6

Numerically simulated quantum-noise-limited phase-noise spectra (solid lines) for three different TR oscillation frequencies show that the phase-noise levels are independent of the roll number $m$. The theoretical estimation (dashed line) is also presented for comparison.

Figure 7

(a) Spectrum of the laser RIN that is used for technical noise simulation. (b) Spectrum of the computer-generated laser phase noise that is for numerical simulation. (c) Phase-noise spectra of the TR oscillation simulated with input noise of only laser RIN (dashed line), only laser phase noise (dotted line), and both laser RIN and phase noise (solid line).

Figure 8

Simulated technical phase-noise spectra of the DKS oscillation, the TR oscillation, and the TR-EOFD-synthesized microwave with the same frequency as the DKS oscillation when $\frac{D_2}{2\pi }$ is set to (a) 10 kHz and (b) 0.4 kHz.

Figure 9

Computed fundamental phase noises including the thermorefractive noise and the quantum noise of a microwave that is synthesized with the TR-EOFD scheme. The TR oscillation has a roll number of 16. The frequency of the synthesized microwave is equal to ${\nu }_{\mathrm{FSR}}$.