Globally Stable Microresonator Turing Pattern Formation for Coherent High-Power THz Radiation On-Chip

In nonlinear microresonators driven by continuous-wave (cw) lasers, Turing patterns have been studied in the formalism of the Lugiato-Lefever equation with emphasis on their high coherence and exceptional robustness against perturbations. Destabilization of Turing patterns and the transition to spatiotemporal chaos, however, limit the available energy carried in the Turing rolls and prevent further harvest of their high coherence and robustness to noise. Here, we report a novel scheme to circumvent such destabilization, by incorporating the effect of local mode hybridizations, and we attain globally stable Turing pattern formation in chip-scale nonlinear oscillators with significantly enlarged parameter space, achieving a record-high power-conversion efficiency of 45% and an elevated peak-to-valley contrast of 100. The stationary Turing pattern is discretely tunable across 430 GHz on a THz carrier, with a fractional frequency sideband nonuniformity measured at $7.3\times {10}^{-14}$. We demonstrate the simultaneous microwave and optical coherence of the Turing rolls at different evolution stages through ultrafast optical correlation techniques. The free-running Turing-roll coherence, 9 kHz in 200 ms and 160 kHz in 20 minutes, is transferred onto a plasmonic photomixer for one of the highest-power THz coherent generations at room temperature, with 1.1% optical-to-THz power conversion. Its long-term stability can be further improved by more than 2 orders of magnitude, reaching an Allan deviation of $6\times {10}^{-10}$ at 100 s, with a simple computer-aided slow feedback control. The demonstrated on-chip coherent high-power Turing-THz system is promising to find applications in astrophysics, medical imaging, and wireless communications.

Popular Summary

As data networks expand to support ever-increasing demand, communication devices that can handle vast amounts of information are essential. While the bulk of this information is shuttled via fiber-optic networks that support terabits per second, the final connection to the end user is often via a wireless link. To keep up with fiber-optic data rates, this link must operate at frequencies of around 1 THz. But long-distance, high-capacity, THz wireless communication is limited by insufficient transmitter power and instabilities in the electromagnetic carrier signal. As a step toward solving these issues, we have developed a stable THz transmitter that operates on a microchip at room temperature.

We combined a microscale cavity, which generates a coherent set of THz frequency lines known as a frequency comb, with a photomixer, a device that generates THz radiation by combining two frequency lines. This generates stable, coherent, near-milliwatt-level THz radiation on a single chip at room temperature. Modal interactions in the microcavity stabilize the pattern of frequency lines across a broad spectrum and parameter space. The stationary pattern is discretely tunable across 430 GHz. We observed record-high power-conversion efficiency between the pump and primary frequency lines at 45%, with an elevated peak-to-valley contrast of 100.

Figure 1

(a) Stability diagram of the Turing pattern in the anomalous GVD regime. Light blue shows the region of the stable Turing pattern, yellow shows the region of breathers and spatiotemporal chaos, and red shows the region of the soliton and soliton molecules. (b) Pump-to-comb power-conversion efficiency along the white dashed line in (a), showing only 8% maximum power conversions to the Turing pattern before destabilization and transition to chaos happens. (c) Simulation of the Turing roll in the normal dispersion microresonator ($1300{\mathrm{fs}}^2$), where the Turing roll is excited by local mode hybridization. The red arrow points to the mode where local dispersion disruption is introduced in the Lugiato-Lefever model. It shows an apparent asymmetry and can be tuned further into resonance without triggering the subcomb growth and the associated Turing pattern destabilization, expanding the stability zone and opening the route to harness Turing pattern’s high coherence and exceptional robustness at high optical powers. Note that the pump-resonance detuning used in the simulation is referenced to the cold cavity resonance frequency.

Figure 2

(a) Turing rolls generated from ring resonators with different radii. Even though the GVD of the ring resonators differ by less than $2{\mathrm{fs}}^2/\mathrm{mm}$, the ${\mathrm{TM}}_{11}\text{−}{\mathrm{TM}}_{21}$ mode hybridization positions (red dashed lines) with respect to the pump (blue lines) shift because of the change in the ring radii, resulting in abrupt dispersion variations locally and very different spontaneous Turing patterns. The Turing-roll repetition rates are 1.72 THz ($12\times \mathrm{FSR}$) for the $160\mu \mathrm{m}$ radius ring, 0.64 THz ($5\times \mathrm{FSR}$) for the $180\mu \mathrm{m}$ radius ring, and 1.72 THz ($15\times \mathrm{FSR}$) for the $200\mu \mathrm{m}$ radius ring. (b) Pump-cavity transmission as a function of the pump wavelength, labeling the detunings where different Turing-roll stages are generated. Inset: The cold resonance of the pump mode, measuring a loaded Lorentzian linewidth of 500 MHz and a loaded quality factor of $3.7\times {10}^5$. (c) Total cavity transmission as a function of the pump wavelength in the range where the Turing roll is generated. Compared to the pump-cavity transmission, the total cavity transmission shows a less apparent decrease as the pump is tuned into the resonance, confirming an efficient power conversion from the pump to the generated Turing lines. (d) Example Turing-roll spectra at different stages. At stage V, even a highly depleted pump close to the resonance is observed in the measurement, illustrated in the dashed box.

Figure 3

(a) IAC traces of the Turing rolls at different stages. The red dashed lines are the ideal traces calculated from the spectra, while the black curves are the measured traces. As the sidebands grow, the deviations between the measured and calculated IAC traces also increase. (b) To examine the emergence of incommensurate subcombs, RF amplitude noise spectra of the Turing rolls (black curve) along with the detector background (red curve) are measured up to 3 GHz, 6 times the cavity linewidth. No apparent amplitude noise is observed, verifying the existence of the commensurate subcombs. Inset: Zoom-in RF amplitude noise spectra up to 250 MHz, at the instrumentation detection noise floor. (c) To probe the equidistance of the Turing rolls, the beat notes between the three Turing-roll sidebands (pump, $m=1$, and $m=2$) and the adjacent fiber-laser frequency-comb lines are measured, and the ratio errors are presented. The small deviation from the ideal ratio $R$ of 2 [$R$ defined in the main text as $({\delta }_2-{\delta }_0)/({\delta }_1-{\delta }_0)$] verifies the Turing pattern’s excellent uniformity. The average nonuniformity is measured at 125 mHz, or $7.3\times {10}^{-14}$ when referenced to the Turing pattern repetition rate at 1.72 THz. (d) The linewidth of the first sideband is measured at 500 kHz, limited by the coherence of the pump laser, by the self-heterodyne technique at different stages. No linewidth broadening is observed, independently confirming that the coherence of the Turing roll is maintained at all evolving stages. (e) Power fluctuation of individual sidebands at the stages I (left) and V (right) with a sampling rate of 250 MHz, ruling out the possibility of breathing solutions.

Figure 4

Long-term frequency fluctuation of the first sideband with respect to the pump in the free-running mode, showing the repetition rate fluctuation of 160 kHz over 20 minutes. The left inset shows the linewidth of the beat note with a sweep time of 200 ms, measuring a narrow FWHM linewidth of 9 kHz; the right inset shows the frequency stability of the beat note, measuring an Allan deviation of $1.15\times {10}^{-8}·\sqrt{\tau }$ when referenced to the THz carrier.

Figure 5

(a) Long-term frequency fluctuation of the first sideband with respect to the pump engaging (blue) and without engaging (red) the computer-aided slow feedback control, counted with a gate time of 1 second. (b) Allan deviation of the stabilized THz frequency, measuring a plateau of $1.2\times {10}^{-8}$ for gate times shorter than 5 seconds and a roll-off of $6\times {10}^{-8}/\tau$ for longer gate times.

Figure 6

(a) Scanning electron micrographs of the fabricated plasmonic photomixer with a logarithmic spiral antenna integrated with plasmonic contact electrodes on an $\mathrm{ErAs}:\mathrm{InGaAs}$ substrate. Scale bars from left to right: $100\mu \mathrm{m}$, $10\mu \mathrm{m}$, and $3\mu \mathrm{m}$. (b) Turing-roll repetition rate, and hence the generated THz frequency, can be tuned by changing the pump wavelength and the resonator temperature. (c) THz radiation power as a function of optical pump power. Power-conversion efficiency of 1.1% can be obtained with an optical pump power of 54 mW.