Millimeter-wave frequency synthesizer based on microcomb photomixing, and associated methods

A millimeter-wave frequency synthesizer generates a millimeter wave by photomixing two Kerr-soliton microcombs. A single-frequency laser beam is modulated to create first and second pump components having first and second pump frequencies. The first pump component excites a first microresonator to create a first microcomb while the second pump component excites a second microresonator to generate a second microcomb. A pair of comb lines from the two microcombs is detected to generate a low-frequency beat note that is phase-locked by identically tuning the pump frequencies. Another pair of comb lines is detected with a high-speed photodiode to generate the millimeter wave. The frequency of the millimeter wave is based on (i) the difference between the pump frequencies, (ii) the difference between the repetition rates, and (iii) the index of the comb lines that are photomixed to generate the millimeter wave.

BACKGROUND

Millimeter-wave frequency synthesizers generate stable and tunable millimeter waves for applications including radar, spectroscopy, and wireless communications. Conventional frequency synthesizers are based on electronics, and usually incorporate a voltage-controlled oscillator, harmonic generators, and phase-locked loops.

SUMMARY

The present embodiments include an architecture for millimeter-wave frequency synthesis that is based on photomixing of two Kerr-soliton microcombs having different repetition rates and different pump frequencies. Advantageously, the present embodiments synthesize millimeter waves with respect to a microwave frequency standard such that the millimeter waves inherit the phase noise, accuracy, and frequency stability of the standard. While the millimeter-wave region of the electromagnetic spectrum occurs between 30 and 300 GHz, the present embodiments can be used to synthesize electromagnetic waves with higher frequencies (e.g., up to 1 THz) or lower frequencies (e.g., down to 1 GHz).

The present embodiments advantageously use nonlinear optical techniques to overcome several limitations of all-electronic millimeter-wave frequency synthesis. In addition to improved tuning range and noise, the recent development of microresonator-based dissipative Kerr solitons (DKS) enables compact and efficient frequency-comb generation, which makes a chip-scale millimeter-wave frequency synthesizer possible. Initial results from a dual-microresonator chip-scale system are presented below.

To assist with synthesis of the highest frequencies (i.e., over 100 GHz), a high-speed modified uni-traveling carrier photodiode may be used for photomixing. This type of photodiode has been recently shown to operate at frequencies up to 160 GHz (−3 dB bandwidth), and has a theoretical transit-time limited bandwidth of several hundred gigahertz. However, the present embodiments may implement photomixing with another type of high-speed photodiode without departing from the scope hereof.

In embodiments, a method for millimeter-wave frequency synthesis includes modulating a single-frequency laser beam to generate a multi-component pump beam having a first pump component at a first pump frequency and a second pump component at a second pump frequency. The method also includes simultaneously coupling the multi-component pump beam into first and second microresonators such that (i) the first microresonator converts the first pump component into a first microcomb having a first repetition rate and (ii) the second microresonator converts the second pump component into a second microcomb having a second repetition rate different from the first repetition rate. The method also includes detecting a first pair of comb lines of the first and second microcombs to generate a low-frequency beat note, the first pair of comb lines having an identical first index. The method also includes stabilizing a difference between the first and second repetition rates by phase-locking the low-frequency beat note to a phase-lock reference signal, said phase-locking including identically tuning the first and second pump frequencies prior to said simultaneously coupling. The method also includes photomixing a second pair of comb lines of the first and second microcombs to generate a millimeter wave, the second pair of comb lines having an identical second index different from the first index. A millimeter-wave frequency of the millimeter wave is based on (i) a difference between the first and second pump frequencies, (ii) the difference between the first and second repetition rates, and (iii) the second index.

In other embodiments, a millimeter-wave frequency synthesizer includes a modulator that modulates a single-frequency laser beam to generate a multi-component pump beam having a first pump component at a first pump frequency and a second pump component at a second pump frequency. The millimeter-wave frequency synthesizer also includes a first microresonator that, when excited by the multi-component pump beam, converts the first pump component into a first microcomb having a first repetition rate. The millimeter-wave frequency synthesizer also includes a second microresonator that, when excited by the multi-component pump beam, converts the second pump component into a second microcomb having a second repetition rate different from the first repetition rate. The millimeter-wave frequency synthesizer also includes a low-speed photodiode that detects a first pair of comb lines of the first and second microcombs to generate a low-frequency beat note, the first pair of comb lines having an identical first index. The millimeter-wave frequency synthesizer also includes a phase-lock loop that stabilizes a difference between the first and second repetition rates by phase-locking the low-frequency beat note to a phase-lock-loop reference signal. The phase-lock loop includes a frequency shifter that identically tunes the first and second pump frequencies prior to exciting the first and second microresonators. The millimeter-wave frequency synthesizer also includes a high-speed photodiode that photomixes a second pair of comb lines of the first and second microcombs to generate a millimeter wave. The second pair of comb lines has an identical second index different from the first index. A millimeter-wave frequency of the millimeter wave is based on (i) a difference between the first and second pump frequencies, (ii) the difference between the first and second repetition rates, and (iii) the second index.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1illustrates a method for synthesizing millimeter waves by photomixing a first microcomb100(1) and a second microcomb100(2). The first microcomb100(1) has a plurality of first-comb lines102that are equally spaced in frequency by a first repetition rate frep(1). Each of the first-comb lines102is uniquely identified by a first index n, which may be any positive integer, negative integer, or zero. For clarity inFIG. 1, only the first-comb lines102(−1),102(0),102(+1), and102(+10) are labeled. However, there may be thousands of first-comb lines102, or more, extending to higher and lower frequencies than shown inFIG. 1. The first microcomb100(1) is generated by coupling a first pump beam into a first microresonator, which coherently transfers energy from the first pump beam to the first-comb lines102. The first index n is defined such that a zeroth first-comb line102(0) with n=0 has a frequency that equals a first pump frequency fP(1)of the first pump beam. With this definition of n, the first-comb lines102have first-comb frequencies fn(1)given by
fn(1)=fP(1)+nfrep(1)(1)

Similarly, the second microcomb100(2) has a plurality of second-comb lines112that are equally spaced in frequency by a second repetition rate frep(2)that is different from the first repetition rate frep(1). Each of the second-comb lines102is uniquely identified by a second index m, which may be any positive integer, negative integer, or zero. For clarity inFIG. 1, only the second-comb lines112(−1),112(0),112(+1), and112(+10) are labeled. However, there may be thousands of second-comb lines112, or more, extending to higher and lower frequencies than shown inFIG. 1. The second microcomb100(2) is generated by coupling a second pump beam into a second microresonator, which coherently transfers energy from the second pump beam into to the second-comb lines112. The second index m is defined such that a zeroth second-comb line112(0) with m=0 has a frequency that equals a second pump frequency fP(2)of the second pump beam. With this definition of m, the second-comb lines112have second-comb frequencies fm(2)given by
fm(2)=fP(2)+mfrep(2).  (2)
Thus, a zeroth second-comb frequency f0(2)of the zeroth second-comb line112(0) equals the second pump frequency fP(2), i.e., f0(2)=fP(2).

The microcombs100(1) and100(2) may be photomixed by spatially overlapping on a photodiode. Interference between the microcombs100(1) and100(2) gives rise a spectrum of beat notes with frequencies:
fb(n,m)=|fn(1)−fm(2)|=|fP(1)+nfrep(1)−fP(2)+mfrep(2)|.  (3)
Considering only the beat notes for which the indices m and n are equal, Eqn. 3 simplifies to:
fb(n)=|ΔfP+nΔfrep|  (4)
where ΔfP=fP(1)−fP(2)is the difference in first and second pump frequencies and Δfrep=frep(1)−frep(2)is the difference in first and second repetition rates. A beat note whose frequency is given by Eqn. 4 is described herein as being generated by a pair of comb lines having the same index n, i.e., the first-comb line102(n) and the second-comb line112(n). Accordingly, each first-comb line102(n) has a unique corresponding second-comb line112(n). Note that Eqns. 3 and 4 do not include beat notes between the first-comb lines102, which occur at the first repetition rate frep(1)and its harmonics, and beat notes between the second-comb lines112, which occur at the second repetition rate frep(2)and its harmonics.

It is also assumed that ΔfPand Δfrephave different signs, which occurs when (i) fP(1)>−fP(2)and frep(1)<frep(2)(as shown inFIG. 1) or (ii) fP(1)<fP(2)and frep(1)>frep(2). When |ΔfP|≈|Δfrep|, some of the beat-note frequencies fb(n) may be small enough (typically 50 GHz or less) to detect electronically using a conventional photodiode (e.g., PIN photodiodes). Such a conventional photodiode is referred to herein as a “low-speed photodiode”, and a beat note whose frequency fb(n) is low enough to be detected with a low-speed photodiode is referred to herein as a “low-frequency beat note”. As an example of a low-frequency beat-note, consider ΔfP=+50.0 GHz and Δfrep=−49.9 GHz. In this case, the beat note generated by the pair of comb lines102(+1) and 112(+1) has a frequency fb(+1)=100 MHz.FIG. 1illustrates this example by showing the beat-note frequency fb(+1)=|ΔfP+Δfrep| between the comb lines102(+1) and 112(+1). As another example, consider ΔfP=−35.0 GHz and Δfrep=+34.0 GHz. In this case, the pair of comb lines102(−1) and112(−1) generates a low-frequency beat note at fb(−1)=1 GHz. Note that the pump frequencies fP(1)and fP(2)and repetition rates frep(1)and frep(2)may be selected such that a different pair of comb lines (i.e., for n≠±1) generates a low-frequency beat note.

In some embodiments, the microcombs110(1) and110(2) are configured by selecting values of fP(1), frep(1), fP(2), and frep(2)such that the low-frequency beat note as a frequency of 50 GHz or less, and therefore can be detected using a low-speed photodiode. In some of these embodiments, the microcombs110(1) and110(2) are configured such that the low-frequency beat note has an even smaller frequency, such as 1 GHz or less.

In some of the present embodiments, it is assumed that |ΔfP|<frep(1)/2 and |ΔfP|<frep(2)/2. In this case, the first-comb line102closest in frequency to the zeroth second-comb line112(0) is the zeroth first-comb line102(0), and vice versa. With this assumption, the low-frequency beat note will be formed by the pair of comb lines having the same index n=+1 or n=−1. When this assumption is not met (i.e., |ΔfP|>frep(1)/2 and |ΔfP|>frep(2)/2, the low-frequency beat note may be formed by a pair of comb lines having the same index n≠±1.

For most values of n, the beat-note frequencies fb(n) are too high to be detected with a low-speed photodiode. For example,FIG. 1shows the beat-note frequency fb(+10), which is generated by the pair of comb lines having n=+10. Assuming ΔfP=+50.0 GHz and Δfrep=−49.9 GHz, fb(+10)=449 GHz. The beat note can be detected using a high-speed photodiode that can detect frequencies up to several hundred gigahertz, or more. For example, the high-speed photodetector could be a modified uni-traveling carrier photodiode. However, another type of high-speed photodiode or photodetector may be used without departing from the scope hereof. A beat note whose frequency fb(n) is too high to be detected with a low-speed photodiode, yet small enough to be electronically detected by a high-speed photodiode, is referred to herein as a “high-frequency beat note”. WhileFIG. 1shows a high-frequency beat note being generated by a pair of comb lines whose frequencies are higher than the frequencies f0(1)and f0(2), the high-frequency beat note could alternatively be generated by a pair of comb lines whose frequencies are lower than the frequencies f0(1)and f0(2).

In the present embodiments, both a low-frequency beat note and a high-frequency beat note are detected using different spectral portions of the microcombs110(1) and110(2). By phase-locking the low-frequency beat note to a microwave frequency reference, the frequency characteristics of the frequency reference are transferred to all of the beat notes, including the high-frequency beat note. Therefore, a millimeter wave synthesized using the present embodiments inherits the accuracy and stability of the frequency reference. Herein, the term “frequency characteristics” includes any metric that quantifies timing and/or frequency performance of the frequency reference. Examples of frequency characteristics include, but are not limited to, Allan variance, fractional frequency instability, absolute frequency accuracy, phase noise, and timing jitter.

FIG. 2is a functional diagram of a millimeter-wave frequency synthesizer200that implements the photomixing shown inFIG. 1.FIG. 2illustrates how a low-frequency beat note may be detected and phase-locked to a microwave frequency reference such that the frequency characteristics of the microwave frequency reference are transferred to a high-frequency beat note. For clarity inFIG. 2, optical signals are indicated by solid lines, low-frequency (i.e., microwave frequencies or less) electrical signals are indicated by dashed lines, and high-frequency millimeter waves are indicated by dotted lines.

The millimeter-wave frequency synthesizer200includes a laser202that outputs a continuous-wave (cw) single-frequency laser beam203. The laser202may be a diode laser, fiber laser, external-cavity laser, or any other kind of coherent light source that can generate the cw single-frequency laser beam203. The single frequency of the laser beam203may correspond to any wavelength that can be used to pump a microresonator to generate a microcomb. In particular, the wavelength may be near 1550 nm, in which case the optical components inFIG. 2may be fiber-optic-based, thereby benefitting from low-loss and readily available telecom optical fiber and associated components. However, the wavelength may lie elsewhere in the infrared, or a different region of the electromagnetic spectrum (e.g., optical, ultraviolet, etc.), without departing from the scope hereof. Accordingly, optical components inFIG. 2may be free-space or fiber-optic-based.

The millimeter-wave frequency synthesizer200also includes a modulator204that, when electrically driven with a modulation signal235, converts the cw single-frequency laser beam203into a multi-component pump beam205having a first pump component at a first pump-component frequency and a second pump component at a second pump-component frequency (see the first pump component402(1) and second pump component402(2) inFIG. 4). In one embodiment, the modulator204is an intensity modulator and the modulation signal235has a frequency of ΔfP/2. In this embodiment, the amplitude of the modulation signal235(i.e., the modulation depth) may be selected such that the ±1 sidebands have more power than all other components of the multi-component pump beam205. The ±1 sidebands serve as the first and second pump components and are separated in frequency by ΔfP. In another embodiment, the modulator204is a phase or frequency modulator that is also driven at a frequency of ΔfP/2 and with a modulation depth such that the ±1 sidebands have more power than all other components of the multi-component pump beam205. In yet another embodiment, the laser202is a diode laser whose drive current is modulated at the frequency ΔfP/2 to generate the ±1 sidebands. In this embodiment, the modulator204is not needed. A different modulation scheme or frequency-generation technique may be used to create the first and second pump components from the laser beam203without departing from the scope hereof.

As shown inFIG. 2, a modulation frequency synthesizer234generates the modulation signal235. The modulation frequency synthesizer234may be referenced to a time base230, such as a microwave frequency reference (e.g., a rubidium standard), atomic clock (e.g., based on cesium), quartz oscillator, hydrogen maser, etc. In this case, the modulation signal235inherits the frequency characteristics of the time base230. Driving the modulator204with this time-base-referenced modulation signal235thereby ensures that the frequency difference ΔfPbetween the first and second pump components is fixed with respect to the time base230.

The millimeter-wave frequency synthesizer200also includes a frequency shifter208that, when electrically driven by a drive signal237having a frequency fs, identically shifts both of the first and second pump-component frequencies by fs. Specifically, the frequency shifter208(i) shifts the first pump-component frequency by fssuch that the first pump component has the first pump frequency fP(1)and (ii) shifts the second pump-component frequency by fssuch that the second pump component has the second pump frequency fP(2). Thus, the term “identically” means that the frequency shifter208simultaneously shifts the frequencies of the first and second pump components by the same amount, thereby ensuring that ΔfPis unaffected. The output of the frequency shifter208is a frequency-shifted pump beam209.

In one embodiment, the frequency shifter208is a single-sideband carrier-suppressed modulator. In another embodiment, the frequency shifter208is an acousto-optic modulator or electro-optic modulator. The frequency shifter208may be another type of modulator or frequency-shifting optical component without departing from the scope hereof. The drive signal237is generated by a variable-frequency oscillator236that is controlled to change the frequency of the drive signal237. For example, the variable-frequency oscillator236may be a wideband voltage-controlled oscillator (e.g., capable of generating 100 GHz/μs scans over a 4 GHz range). If additional optical power is needed, an amplifier206may be used to amplify the multi-component pump beam205after the modulator204. Alternatively or additionally, an amplifier210may be used to amplify the frequency-shifted pump beam209after the frequency shifter208. Each of the amplifiers206and210may be a semiconductor optical amplifier, a fiber amplifier (e.g., an erbium-doped fiber amplifier) or another type of optical amplifier known in the art.

In some embodiments, the frequency shifter208precedes the modulator204, in which case the frequency-shifted pump beam209is single-frequency. In these embodiments, the laser beam203is first frequency-shifted according to the drive signal237, after which it is modulated according to the modulation signal235. In other embodiments, the modulator204is replaced by a second laser whose output is offset-locked to the laser beam203by ΔfP. The outputs of the laser202and the second laser may be combined to form the multi-component pump beam205. Alternatively, the second laser may be offset-locked to the frequency-shifted pump beam209(i.e., after the frequency shifter208). Another phase-locking technique may be used to create the first and second pump components without departing from the scope hereof.

The frequency shifter208outputs a frequency-shifted pump beam209that is split into two paths by a splitter212. In the first path, a first microresonator214(1) is pumped by the first pump component to generate the first microcomb100(1) ofFIG. 1. In the second path, a second microresonator214(2) is pumped by the second pump component to generate the second microcomb100(2) ofFIG. 2. The microcombs100(1) and100(2) are combined by a splitter216that outputs a first photomixing signal217(1) to a low-speed photodiode220and a second photomixing signal217(2) to a high-speed photodiode258. Each of the photomixing signals217(1) and217(2) contains portions of both microcombs100(1) and100(2). To improve the signal-to-noise ratios of the beat signals, a first filter218(1) may be used to selectively transmit to the low-speed photodiode220only the one pair of comb lines that generate a low-frequency beat note221. Similarly, a second filter218(2) may be used to selectively transmit to the high-speed photodiode258only the one pair of comb lines that generate a high-frequency beat note260. The low-frequency beat note221has a low beat frequency fb(low)while the high-frequency beat note260has a high beat frequency fb(high). The beat frequencies fb(low)and fb(high)are both examples of beat-note frequencies described by Eqn. 4.

To phase-lock the low-frequency beat note221, it is first compared to a phase-lock-loop (PLL) reference signal233using a phase detector224. For example, the phase detector224may be a digital phase/frequency detector used for digital PLLs, or a mixer used for analog PLLs. The phase detector224outputs a phase error signal225that is processed by a servo circuit226to generate a correction signal227that controls the variable-frequency oscillator236to change the frequency of the drive signal237. A PLL frequency synthesizer232generates the PLL reference signal233. The PLL frequency synthesizer232may be referenced to the time base230, thereby ensuring that the low beat frequency fb(low)inherits the frequency characteristics of the time base230when the low-frequency beat note221is phase-locked.

To further appreciate how the phase-lock loop of the low-frequency beat note221is closed, we refer to Jordan R. Stone et al., “Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs”, Phys. Rev. Lett. 121, 063902 (2018). In this publication, the authors demonstrated that for certain detunings, the repetition rate of a microcomb varies linearly with pump frequency. Applying this to the present embodiments, the first microresonator214(1) has a first tuning coefficient K1such that frep(1)=K1fP(1)and the second microresonator214(2) has a second tuning coefficient K2such that frep(2)=K2fP(2). The microresonators214(1) and214(2) are configured and operated with different repetition rates and/or dispersion profiles such that K1≠K2. Thus, when the pump frequencies fP(1)and fP(2)are tuned identically, the difference in repetition rates will change by Δfrep∝(K1−K2) while the difference in pump frequencies ΔfPremains fixed. Accordingly, when the low-frequency beat note221is phase-locked, both fb(low)and ΔfPwill inherit the frequency characteristics of the time base230. From Eqn. 4, it therefore follows that Δfrepwill also inherit the frequency characteristics of the time base230, as will the high beat frequency fb(high).

When the low-frequency beat note221is phase-locked, the high-frequency beat note260serves as a synthesized millimeter wave. Although not shown inFIG. 2, the synthesized millimeter wave may be filtered, amplified, conducted along a transmission line (to a load), or otherwise used as needed for the application at hand.

In some embodiments, the millimeter-wave frequency synthesizer200includes a ramp generator238that outputs a ramp signal239to the frequency shifter208. The ramp generator238may be an arbitrary waveform generator or function generator. The ramp signal239may be configured to initiate soliton propagation (i.e., microcomb generation) in the microresonators214(1) and214(2). For example, the ramp signal239have a slope and temporal duration to simultaneously ramp (i) the first pump frequency from blue-detuning to red-detuning, relative to a cold cavity resonance frequency of the first microresonator214(1) and (ii) the second pump frequency from blue-detuning to red-detuning, relative to a cold cavity resonance frequency of the second microresonator214(2). Although not shown inFIG. 2, each microresonator214may be located proximate to a thermoelectric cooler that, when electrically driven, heats or cools the microresonator214. Changing the temperatures of the microresonators214shifts their resonance frequencies, thereby ensuring that the same ramp can be used to simultaneously initiate soliton propagation in both of the microresonators214(1) and214(2).

As shown inFIG. 2, the ramp signal239is added to the correction signal227using an adder circuit240. The ramp signal239is only applied while initiating soliton propagation (i.e., no correction signal227is applied oscillator236during this process). Once soliton propagation has been successfully initiated in both of the microresonators214(1) and214(2), the ramp signal239is stopped and the correction signal227is started. In an embodiment, the adder circuit240is replaced by a switch that is controlled to switch between the correction signal227and the ramp signal239. Other techniques to initiate soliton propagation and transition to phase locking may be used without departing from the scope hereof.

The present embodiments may be used with any type of microresonator capable of generating Kerr microcombs. For example, each of the microresonators214(1) and214(2) may be a ring resonator, a whispering gallery mode resonator, a microsphere, or a compact fiber cavity. Each of the microresonators214(1) and214(2) may be fabricated from calcium fluoride (CaF2), magnesium fluoride (MgF2), silica, aluminum nitride, diamond, silicon, silicon nitride (Si3N4), or another material used for Kerr-comb generation. The microresonators214(1) and214(2) may be stand-alone optical components or fully integrated into a photonic integrated circuit.

EXPERIMENTAL DEMONSTRATION

FIG. 3shows a setup used to experimentally demonstrate the present embodiments. The pump source consists of a cw laser at 1560 nm, an intensity modulator, a single-sideband suppressed-carrier (SSB-SC) modulator and an erbium-doped fiber amplifier (EDFA). Two sidebands separated in frequency ΔfP=50 GHz are generated through carrier-suppressed intensity modulation, and further serve as the pumps for two microresonators. The SSB-SC modulator is driven by a voltage-controlled oscillator (VCO), and fast pump frequency sweeping is realized by applying a ramp signal to the VCO.

FIG. 4shows the optical spectrum of the pumps generated by the pump source ofFIG. 3. The pump source generates a first pump component402(1) and a second pump component402(2) that are separated in frequency by ΔfP. The pump beam is further amplified by a high-power EDFA and sent to two silicon nitride microresonators. The free spectral range (FSR) of the two microresonators is 950 GHz and 1 THz, respectively. Their resonance is thermally tuned to match the above-mentioned two sidebands. If an appropriate ramp signal is applied to the VCO, soliton frequency combs could be generated in both microresonators.

FIG. 5shows the spectra of 950 GHz and 1 THz soliton microcombs generated by the microresonators ofFIG. 3. The two optical frequency combs are combined together by a 3-dB coupler.FIG. 6shows the spectra ofFIG. 5in more detail. The frequency spacing for different pair of comb lines can be expressed as ΔfN=ΔfP±NΔfrep, where ΔfP≈50 GHz is the FSR difference and N is an integer. In the higher-frequency side of the pump, spacing of the first pair is Δf1=ΔfP−Δfrep≈100 MHz. This pair of comb lines is selected by optical filter1and detected by a low-speed photodiode. The beat signal is phase-locked to a low-frequency reference to stabilize Δfrep. Other pairs for N>1 are selected by optical filter2. After photodetection with a high-speed MUTC photodiode, a millimeter-wave signal at ˜N×50 GHz could be generated. Also, their frequency can be tuned by changing the pump frequency difference ΔfP.

Frequency stability and tunability are two figures of merit for the millimeter-wave frequency synthesizer200. Using the setup ofFIG. 3, we take the beat signal of the fourth pair of comb lines. Their frequency difference is approximately 150.8 GHz, and we use a harmonic mixer to down-convert this 150.8-GHz signal to 124.8 MHz.FIG. 7shows the spectrum of the down-converted signal at 124.8 MHz. A single-frequency signal with SNR>65 dB is observed.FIG. 8shows the measured Allan deviation (ADEV) of the 150.8-GHz signal. At an averaging time of one second, the ADEV is 3×−12. The ADEV floor occurs at averaging times between 0.3 and 10 seconds, and may result from noise from the optical fiber.

FIGS. 9 and 10illustrating coarse and fine frequency tuning of the setup ofFIG. 3. InFIG. 9, the frequency of a millimeter-wave signal is tuned from 150 GHz to 163 GHz in steps of 1 GHz. It should be noted that neither of the resonators lost soliton state during tuning.FIG. 10shows bidirectional linear tuning of the 150.8162 GHz signal in steps of 150 Hz, which is measured by a frequency counter with a gate time of 1 second.

The two microresonator rings inFIG. 3may be integrated on one chip, an important step towards chip-scale integration of the whole system. As shown inFIG. 11, the 3-dB couplers inFIG. 3are replaced by two multi-mode interference (MMI) couplers. The resonances of the microresonators can be tuned by applying different voltage to the on-chip heaters.FIG. 12illustrates the generated 950 GHz and 1 THz soliton combs. As an example, the third pair of comb lines are selected by an optical bandpass filter and a millimeter-wave signal at 146.968 GHz is generated after photodetection by the high-speed photodiode.FIG. 13shows the spectrum of the millimeter-wave signal after frequency down-conversion.