Towards high-power, high-coherence, integrated photonic mmWave platform with microcavity solitons
Beichen Wang, Jesse S. Morgan, Keye Sun, Mandana Jahanbozorgi, Zijiao Yang, Madison Woodson, Steven Estrella, Andreas Beling, Xu Yi
aa r X i v : . [ phy s i c s . a pp - ph ] S e p Towards high-power, high-coherence, integrated photonic mmWave platform withmicrocavity solitons
Beichen Wang , ∗ , Jesse S. Morgan , ∗ , Keye Sun , Mandana Jahanbozorgi , ZijiaoYang , Madison Woodson , Steven Estrella , Andreas Beling , † and Xu Yi , , ‡ Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904, USA. Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA. Freedom Photonics LLC, Santa Barbara, California, USA. ∗ These authors contributed equally to this work.Corresponding authors: † [email protected], ‡ [email protected]. (Dated: September 28, 2020) Abstract:
Millimeter-wave (mmWave) technology continues to draw large interest due to its broadapplications in wireless communications, radar, and spectroscopy. Compared to pure electronicsolutions, photonic-based mmWave generation provides wide bandwidth, low power dissipation,and remoting through low-loss fiber. However, at high frequencies, two major challenges exist forthe photonic system: the power roll-off of the photodiode, and the large signal linewidth deriveddirectly from the lasers. Here, we demonstrate a new photonic mmWave platform by combiningintegrated microresonator solitons and high-speed photodiodes to address the challenges in bothpower and coherence. The solitons, being inherently mode-locked, are measured to provide 5.8dB additional gain through constructive interference among mmWave beatnotes, and the absolutemmWave power approaches the theoretical limit of conventional heterodyne detection at 100 GHz.In our free-running system, the soliton is capable of reducing the mmWave linewidth by two ordersof magnitude from that of the pump laser. Our work leverages microresonator solitons and high-speed modified uni-traveling carrier photodiodes to provide a viable path to chip-scale high-power,low-noise, high-frequency sources for mmWave applications.
Introduction
Millimeter-waves (mmWaves) provide key advantages incommunication bandwidth, radar resolution, and spec-troscopy thanks to their high carrier frequencies . Pho-tonic oscillators operate at frequencies of hundreds ofTHz, and the frequency of the electrical signal producedby, e.g. heterodyne detection of two lasers, is only limitedby the photodiode bandwidth. However, at mmWave fre-quencies, the output power of the photonic system suffersfrom the power roll-off associated with the photodiode’sbandwidth. In terms of signal coherence, stabilizing thefrequency difference of two lasers to a low frequency ref-erence is challenging for mmWaves due to the high fre-quency.The recent development of dissipated Kerr solitonsin microresonators provides an integrated solution toaddress the challenges of photonic-generated mmWavesin both power and coherence. These solitary wavepackets achieve mode-locking by leveraging Kerr nonlin-earity to compensate cavity loss and to balance chro-matic dispersion . Microresonator solitons have beenapplied to metrology , optical communications andspectroscopy in the form of microresonator-based fre-quency combs (microcombs) . Due to the miniaturizeddimension, the repetition rate of microresonator solitonsranges from a few GHz to THz . Direct detection ofthe solitons with a fast photodiode produces mmWaveat the repetition frequency of the solitons. When com-pared with the conventional two laser heterodyne detec-tion method, the soliton mode-locking provides up to6 dB gain in mmWave output due to the constructive interference among beatnotes created by different pairsof neighboring comb lines . This additional gain is ofgreat importance at high frequencies, since it can relaxthe bandwidth requirements in the photodiode. In termsof signal coherence, recent studies have shown that thephase noise of the soliton repetition frequency at 10’sof GHz can be orders of magnitude smaller than thatof its pump laser . When microresonator solitonsare married with integrated lasers , amplifiers , andhigh-speed photodiodes through heterogeneous or hy-brid integration, a fully integrated mmWave platformcan be created with high power, high coherence per-formance and the potential for large scale deploymentthrough mass production (Fig. 1).In this letter, we demonstrate high power, high coher-ence photonic mmWave generation at 100 GHz frequencythrough the combination of integrated microresonatorsolitons and a modified uni-traveling carrier photodiode(MUTC PD). A 5.8 dB increase of mmWave power is ob-tained by using microresonator solitons when comparingto the output power of conventional heterodyne detec-tion. Importantly, the power level we achieve with mi-croresonator solitons is approaching the theoretical limitof heterodyne detection, which assumes an ideal photo-diode with zero power roll-off in its frequency response.The system also achieves a maximum mmWave power of7 dBm, one of the highest powers ever reported at 100GHz . For our free-running system, the 100 GHz signalhas Lorentzian and Gaussian linewidth of 0.2 kHz and4.0 kHz, respectively, which is two orders of magnitudesmaller than that of the pump laser. The dependence of Imaging
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FIG. 1:
Artistic conceptual view of fully integrated mmWave platform based on microresonator soli-tons.
The microresonator solitons are generated by pumping a high-Q Kerr microresonator with a continuous-wave(cw) laser. Photodetecting the solitons generates the mmWave signal at the soliton repetition frequency (combspacing). Soliton mode-locking can provide up to 6 dB more power than that of conventional two laser heterodynedetection, and it is also capable of reducing the mmWave linewidth. By leveraging advances in photonic hetero-geneous integration, all critical components, including pump laser, semiconductor optical amplifiers (SOAs) andultrafast photodiodes (PDs), can potentially be integrated with the Kerr microresonators on the same chip. The in-tegration will enable arrays of coherent mmWave sources, which can generate mmWave signals over a broad rangeof frequencies. Such a mmWave platform can advance applications in high-speed wireless communication, sub-THzimaging and spectroscopy, and high resolution ranging.output power on the number of comb lines and chromaticdispersion is carefully studied both theoretically and ex-perimentally. Our demonstration paves the way for afully integrated photonic microwave system with solitonmicrocombs and high-speed photodiodes.
Results
In conventional heterodyne detection, mmWaves aregenerated when two laser lines mix with each other ona photodiode and create one beat note. However, whenusing an optical frequency comb, each comb line will beatwith its two adjacent neighbour lines to create beatnotesat the comb repetition frequency. For a comb that con-sists of N comb lines, ( N −
1) beat notes will be createdat the comb repetition frequency. Therefore, for the sameaverage optical power, the comb can produce up to twicethe number of beatnotes per laser line than heterodynedetection, and thus generate twice the AC photocurrent.The output power from the photodiode at the comb rep-etition frequency can be described as : P P D = I DC R L (cid:20) N − N (cid:21) × Γ , (1)where I DC is the average photocurrent, R L (50 Ω) is theload resistor, and N ≥ ∼ . µm and ∼ µm diameter PDs used in this work at 100 GHz.Clearly, the power at the limit of N → ∞ is 4 times(6 dB) higher than the power of heterodyne detection,where N = 2. In practice, however, conventional frequency combs arenot the best candidates to achieve the 6 dB gain formmWave generation due to their low repetition frequen-cies. Previously, two attempts with electro-optics modu-lation frequency combs were reported, where line-by-lineamplitude and phase shaping was used to remove theunnecessary comb lines and increase the repetition ratefrom 20 GHz to 100 and 160 GHz . This post spec-tral filtering nonetheless increases the complexity andcost of the system. Conversely, microresonator solitonshave comb repetition rates ranging from a few GHz to1 THz, and can be directly applied to mmWave gen-eration. MmWave generation with soliton microcombsin tapered-coupled microtoroid resonator , from dual-comb structure , and from a pair of comb lines havebeen shown, but there was no investigation into the out-put power.The dissipated Kerr solitons used in this work are gen-erated in an integrated, bus-waveguide coupled Si N micro-ring resonator with free spectral range (FSR) of ∼
100 GHz. The single soliton state with a 35.4 fs pulsewidth is generated and its squared hyperbolic secantspectral envelope is characterized by an optical spectrumanalyzer (Fig. 2 a ). The comb is then amplified by anerbium-doped fiber amplifier (EDFA) and sent to thephotodiode, and an optical programmable waveshaper(WS) is used to compensate the group velocity disper-sion and to suppress spontaneous emission (ASE) noisefrom the EDFA. The inset of Fig. 2 a shows the opticalspectrum after the amplification and dispersion compen-sation. The photodiode used in this work is based on the
178 188 198 208 P o w e r ( d B / d i v ) Photocurrent (mA)1 102 Mm W a v e po w e r ( d B m ) -25-20-15-10-5051015 5.8 dB 3 4 5 6 7 8 9 m m)107 8 11 I n c r ea s e ( d B ) m m @ -3.6 V (a)(d) (e) Exp. (solitons) Calc. (solitons) Exp. (heterodyne) Calc. (heterodyne) Ideal (heterodyne) ( d B / d i v ) Sech fitting P o w e r m m (b) (c) m m 400 m m Frequency (THz)
RBW3 kHz11 m m @ -3.0 V + 99.7590 GHzMHz Mm W a v e po w e r ( d B m ) -20 -10 0 10 20-80-60-40-20 Pump (filtered)
GaussianLorentzian -100 1000-70-50-30-1010 kHz
FIG. 2:
Summary of featured experimental data of 100 GHz mmWave generation. (a)
Optical spectrumof single soliton state from the microresonator. The spectrum has sech spectral envelope (fitting shown in dashedred line). The pump laser is suppressed by a fiber Bragg grating filter. Inset shows the optical spectrum of solitonfrequency comb after amplification and dispersion compensation. (b) Microscopic image of integrated Si N mi-croresonator with 100 GHz free spectral range (FSR). (c) Microscopic images: front of photodiode die zoomed inon single 7 µ m device (left), and back of photodiode die flip-chip bonded to aluminum nitride submount (right). (d)
100 GHz mmWave output power measured for microresonator solitons (red) and optical heterodyne detectionof two cw-lasers (blue). The mmWave output power from the soliton is ∼ . (e) Down-converted electrical spectrum of 100 GHz signal generated with free-running microresonator solitons (red). In-set shows the fitting with Lorentzian (black) and Gaussian (dashed green) lineshapes and the corresponding 3-dBlinewidths are 0.2 kHz and 4 kHz respectively. As a comparison, the signal generated from heterodyne method isshown in blue trace. The PD diameter and bias voltage are indicated in each panel.charge-compensated modified uni-traveling carrier pho-todiode (MUTC PD) structure. MUTC PDs operateunder the principle of single carrier transit, and com-pared to traditional p-i-n photodiodes, isolating electronsfor this transit process eliminates the dependency on theslower-traveling holes leading to higher-speed operation.To further enhance performance and limit thermal degra-dation, the PDs are then flip-chip bonded to a ceramicsubstrate made of gold transmission lines grown on alu-minum nitride submount (AlN) . Pictures of the mi-croresonator and a PD die are shown in Fig. 2 b and Fig.2 c , respectively. Details of microresonator solitons and photodiodes are described in the Materials and Methodssection.To characterize the 6 dB power increase from the mi-croresonator solitons, the PD output powers are mea-sured for both microresonator soliton detection and het-erodyne detection on four of our PDs with 7, 8, 10, and11 µm diameters. The heterodyne measurements are per-formed using two continuous-wave lasers with the sameoptical power and polarization. A variable optical atten-uator is used to control the optical power illuminating onthe PD. In the linear region of PD operation, the 100 GHzmmWave powers at different photocurrents are shown in Exp.Calc. 11 m m @ -2.2 VDispersion compensation (ps/nm) Mm W a v e po w e r ( d B m ) -5 -4 -3 -2 -1 0 1-35-25-15-5 (c) m m @ -2.1VNumber of comb lines2 6 10 14 18 22 26-73-68-63-53-58 P o w e r ( d B / d i v ) Mm W a v e po w e r ( d B m ) (a) (b) @@@@ -48 Exp.Exp.Exp.Exp. Calc.Calc.Calc.Calc.
22 comb lines m A12 m A8 m A4 m A Frequency (THz)
FIG. 3:
MmWave power versus number of comb lines and dispersion. (a)
MmWave power at 100 GHzfor different number of comb lines at four different photocurrents. The measurements agree very well with the the-oretical calculation based on equation (1), which are shown in dashed lines. (b)
Corresponding optical spectra oftwo, twelve and twenty-two comb line measurements in panel (a). (c)
MmWave power versus dispersion compensa-tion added by waveshaper, d c . The maximum output power is reached at d c = − .
95 ps/nm, where the dispersionfrom fiber and EDFA is completely compensated. A theoretical curve from equation (2) is shown in dashed line andagrees very well with the measurement. The PD diameter and bias voltage are indicated in each panel.Fig. 2 d for the 7- µm device. The DC photocurrent is adirect measurement of the optical power illuminating onthe PD. In the experiment, the coupling distance fromfiber to PD is increased for a uniform illumination, re-sulting in 1 mA photocurrent for 11 mW optical inputpower. The mmWave power generated from the microres-onator solitons is measured to be 5.8 dB higher thanthat of heterodyne detection. This power increase is ap-proaching the 6 dB theoretical limit, and is verified onall four PDs with different diameters (shown in the insetof Fig. 2 d ). As a result of the 6 dB power increase, themmWave power generated using microresonator solitonsis within 1 dB of the theoretical power limit of hetero-dyne detection (solid black line in Fig. 2 d ), where thedetector is assumed to be ideal and has no power roll-offat mmWave frequency. It shall be noted that no opti-cal spectrum flattening is applied in our measurement.For 5.8 dB power improvement, a 3 dB bandwidth of 7comb lines is required for the Sech or Gaussian spectralenvelope. As discussed in the Materials and Methodssection, the shape of the spectral envelope has little ef-fect on mmWave power when the number of comb linesis large.The electrical spectrum of the 100 GHz mmWave sig-nal is measured and shown in Fig. 2 e . Limited by theavailable bandwidth of our electrical spectrum analyzer,we down convert the 100 GHz mmWave by sending itto an RF mixer to mix it with the fifth harmonic of a20.2 GHz local oscillator. The mixer generates a differ-ence frequency at ∆ f = 5 f LO − f r . ∆ f is measured to be1.2410 GHz, and we can derive the mmWave frequency as f r = 99 . e (red trace). The signal is fitted with a Lorentzian,and the 3-dB bandwidth is 0 . e ). Note that the soliton repetition rate is sub- ject to fluctuations (laser frequency drift, temperature,etc.), and the central part of the signal is Gaussian with3-dB linewidth of 4 kHz. This narrow linewidth at 100GHz frequency is obtained for a free-running microcav-ity soliton, which is driven by a pump laser with signif-icantly broader linewidth ( ∼
200 kHz, New Focus 6700series specification). To compare the signal coherencebetween conventional heterodyne method and the soli-ton method, the heterodyne signal of beating the pumplaser and another 6700 series New Focus laser is also mea-sured and shown in Fig. 2 e (blue trace). At the sameRBW, the heterodyne signal has poor coherence and itsfrequency is drifting > a . Three representative opticalspectra for 2, 12, and 22 comb lines are shown in Fig.3 b . The measured mmWave power follows the calcu-lated curves. Interestingly, a 3 or 5 dB increase of poweronly requires 4 or 9 comb lines. This relatively small de-mand for comb lines relaxes the microresonator solitonrequirement in terms of its optical bandwidth. Photocurrent (mA)1 10 20 30 Mm W a v e po w e r ( d B m ) -20-15-10-50510 8 m m @ -3.6 VMax: 7.0 dBm SolitonsHeterodyneCounter limitGate Time t (s)10 -4 -2 -6 Offset frequency (Hz)1k 10k 100k 1M
SSB pha s e no i s e ( d B c / H z ) A ll an D e v i a t i on ( H z ) (b)(a) (c)SolitonsHeterodyneLocal oscillatorESA sensitivity limit FIG. 4:
Measurement of mmWave power, mmWave phase noise and Allan deviation. (a)
Maximumpower of 7 dBm is reached at 22.5 mA and − . µm device. (b) Phase noises of the free-running soliton-based mmWave (red) and the heterodyne mmWave (blue) at 100 GHz. The measurement sensitiv-ity floor is set by both the ESA sensitivity limit (dash green), and the local oscillator phase noise (dash black). (c)
Allan deviation of the free-running soliton-based mmWave (red) and the heterodyne mmWave (blue).The increase of mmWave power only happens whenthe beatnotes generated by different pairs of comb linesare in constructive interference. This is not always thecase if there is dispersion between the microresonator andthe PD. This effect is studied by applying programmabledispersion using a waveshaper. The measurement ofmmWave power versus waveshaper dispersion is shownin Fig. 3 c . The effect can be calculated analytically byadding phase to each comb line, and will modify equation(1) to: P P D = I DC R L " (cid:2) ( N − πcdf r /f p (cid:3) N sin (cid:2) πcdf r /f p (cid:3) × Γ , (2)where c is the speed of light, and d = d + d c is theaccumulated group velocity dispersion between the mi-croresonator and PD. d denotes the offset dispersionin the system introduced by fibers and amplifiers, and d c represents the dispersion compensation added by thewaveshaper. The derivation of equation (2) is shown inthe Materials and Methods section. The measurementand theory prediction agree very well when an offset dis-persion of d = 1 .
95 ps/nm is included. The offset disper-sion exists in our system because of the 70 meter fiberused to connect the microcomb lab and photodetectorlab (contributing 1.26 ps/nm), with the rest of the dis-persion coming from the fibers in the EDFA. N is used asa free parameter for fitting the experimental curve, and N = 15 is used for the dashed line in Fig. 3 c . The fitted N should be interpreted as the effective number of comblines to account for the spectral envelope shape. Whenthe entire system is fully integrated, the overall length ofwaveguides will be well below a meter, and the dispersionwill not impact the mmWave power.We obtain a maximum output power of 7 dBm at 22.5mA for the 8 µm device shown in Fig. 4a, due to theoptimized light coupling from the size match of the 8 µ m spot-size collimated fiber and diameter of the PD’sabsorber. Using equation (1) we find that the ideal het-erodyne response for this 8 µm device would need 26.7mA to achieve 7 dBm, which means we can produce thesame power at lower average photocurrent using solitonexcitation. The 7 dBm saturation power is recorded at-3.6 V bias. Increasing the reverse bias can improve thesaturation power, however, ultimately this can cause PDthermal failure , which is due to the raise in junctiontemperature from the dissipated power in the PD (re-verse bias × average photocurrent). One advantage ofusing solitons is that they can generate the same RFoutput power at a lower photocurrent than the two-laserheterodyne method, and thus can reduce the dissipatedpower and allow the PD to be operated further below thepoint of thermal failure.We further characterize the phase noise of themmWaves generated from the free-running microcavitysolitons, and compare it to the phase noise from the het-erodyne method. Similar to the linewidth measurement,the 100 GHz mmWave signal is down converted in anRF mixer where it is mixed with the fifth harmonic ofa 20.2 GHz local oscillator. To minimize the effect offrequency drifting in the phase noise measurement, thefrequency of the down-converted signal is further divideddown electrically by a factor of 14 and 100 for the solitonand heterodyne, respectively. The phase noise is thenmeasured in the electrical spectrum analyzer with directdetection technique, and the result (at 100 GHz) is shownin Fig. 4b. Due to the large frequency drift, the hetero-dyne phase noise below 20 kHz offset frequency cannotbe accurately characterized and thus is not presented.The soliton phase noise beyond 100 kHz is potentiallylimited by the measurement sensitivity, which is set bythe noise floor of the spectrum analyzer (dash green),and the phase noise of the local oscillator (Keysight,PSG E8257D) used to down-convert the mmWave (dashblack). The measurement shows that the free-runningsolitons can reduce the mmWave phase noise by > EDFA WS VOA RF PMPhotodiode Probe Bias-teeSMEDFACW laser PC CavityPC TECAmpVCO fP f L fP f L +f VCO fP EDFA BPFBPFPM FBG PD Oscilloscope DC RF
FIG. 5:
Experimental setup.
The microresonator solitons are generated in a SiN resonator which is coarselytemperature controlled by thermoelectric cooler (TEC). The pump laser is the first modulation sideband of a phasemodulated (PM) continuous wave (cw) laser, and the sideband frequency can be rapidly tuned by a voltage con-trolled oscillator (VCO). The frequencies of the cw laser and phase modulation are f L and f VCO1 , respectively. Thepump laser is then amplified by an erbium-doped fiber amplifier (EDFA), and the amplified spontaneous emissionnoise is filtered out by a bandpass filter (BPF). At the output of the resonator, a fiber-Bragg grating filter is usedto suppress the pump. The microresonator solitons are then amplified, dispersion compensated by a waveshaper(WS), and sent to the photodiode. The configuration also includes polarization controllers (PC), variable opticalattenuator (VOA), source meter (SM), and RF power meter (RF PM).dB from the heterodyne method. The reduction of phasenoise from the pump laser frequency to the soliton repe-tition rate is a result of the noise transfer mechanism inmicroresonator solitons . Our observation is in agree-ment with the previous reports for microresonator soli-tons at X-band and K-band repetition frequencies .The phase noise of soliton-based mmWaves can be fur-ther reduced in the future by using a pump laser withhigher stability , tuning the soliton into quiet operationpoint , and implementing better temperature control ofthe entire system. For instance, compact external-cavitydiode laser has achieved Lorentzian linewidth of 62 Hzrecently . Using this laser to drive the soliton couldfurther reduce the free-running mmWave phase noise.Finally, the Allan deviations of the mmWave generatedfrom the soliton and the heterodyne detection are mea-sured by counting the frequency of the down-convertedsignal on a zero dead-time counter (Fig. 4c). At 1ms gate time, the Allan deviation of the soliton-basedmmWave reaches the minimum of < , or dualmicrocavity soliton methods . Discussion
In summary, we have demonstrated high-power,high-coherence mmWave generation at 100 GHz byusing integrated microresonator solitons and MUTCPDs. Extending the frequency to several hundred GHzis possible. For the microresonator solitons, the highestrepetition rate reported is 1 THz , while demonstratedMUTC PDs have detection capabilities of at least 300GHz . As the microresonator solitons consume verylittle pump power, and most of the pump transmitsthrough the waveguide , it is possible to recycle the pump laser power to drive the next microresonatorsolitons (Fig. 1). Two tandem microresonator solitonsdriven by the same pump laser have been reportedpreviously . The proposed platform has the poten-tial to be fully integrated on a single chip which canenable large-scale mmWave arrays. The four criticalcomponents: laser, Kerr microresonator, amplifier,and ultrafast photodiode, have all been shown to becompatible with Si N photonic platforms throughheterogeneous integration. Once all components arefully integrated, we expect that the platform can delivera new paradigm regarding scalable, integrated photonicstechnologies for applications at very high frequencies,and thus provide a path to compact, low-noise high-frequency sources for spectroscopy, ranging, and wirelesscommunications. Materials and Methods
Microresonator soliton generation.
The dissipated Kerrsolitons used in this work are generated in an integrated, bus-waveguide coupled Si N micro-ring resonator. The resonator hasa free spectral range (FSR) of ∼
100 GHz, and an instrinsic qual-ity factor of 2 . × and loaded quality factor of 2 . × . TheSiN resonator has a cross-section, width × height, of 1 . × . µ m ,and is coupled to a bus-waveguide of the same cross-section. Theresonator radius is 0.24 µ m, and the soliton-generation mode hasanomalous dispersion of ∼ is applied toovercome the thermal complexity when accessing the red-detunedsoliton existence regime. The detailed experimental setup is shownin Fig. 5. The pump laser is derived from the first phase modulatedsideband of a continuous wave laser, and the sideband frequencycan be rapidly tuned by a voltage controlled oscillator (VCO). Thepump laser scans its frequency at the speed of ∼
20 GHz/ µ s, andthe scan is stopped immediately once the pump laser frequencyreaches the red-detuned regime of the resonator. The optical spec-trum has a 3-dB bandwidth of 5 . Modified uni-traveling carrier photodiode.
The charge-compensated modified uni-traveling carrier photodiode (MUTCPD) operates under the principle of single carrier transit, and com-pared to traditional p-i-n photodiodes, isolating electrons for this transit process eliminates the dependency on the slower-travelingholes leading to higher-speed operation. To accomplish this, thephoton absorption process which generates electron-hole pairs inthe PD absorber layer, occurs close to the p-contact layer allowingthe excess holes to be quickly collected in response to the p-typematerial dielectric relaxation time. To further enhance the speedof the PD response, by step grading the doping of the partially-depleted absorber, an electric field is generated which acceleratesthe electrons through the absorber and towards the transparentand depleted drift layer. To prevent electric field collapse at theheterointerface of the absorber and drift layer, a fully-depleted ab-sorber layer and a moderately doped cliff layer help to maintainelectric field strength and accelerate the electrons into the driftlayer . Once in the drift layer, electron space-charge effects aremitigated or charge-compensated by the light n-type doping in thedrift layer . Fabrication flow of the PDs and similar PD epitaxiallayering structures have been reported previously , and so has theAlN submount . The MUTC PDs used in this experiment havedemonstrated dark currents as low as 200 pA at -2 V, 3-dB band-width of up to 145 GHz (4- µm diameter PD), responsivity of 0.2A/W at 1550-nm, and -2.6 dBm maximum output power at 160GHz at -3 V bias . They have also been investigated as viable re-ceivers for soliton applications ranging from 50-500 GHz . The3-dB bandwidth at 5 mA and -3 V bias for the 7, 8, 10, and 11- µm diameter PDs used in this experiment are 92 GHz, 90 GHz, 70GHz, and 70 GHz, respectively. Note that in Fig. 2 d ideal hetero-dyne power calculated using equation (1) where N = 2, assumes100% modulation depth; however, measured modulation depth ofthe signal was 89% leading to the observed mismatch in measuredand calculated heterodyne power. MmWave linewidth reduction.
Our observation of linewidthreduction is in agreement with previous reports of microresonatorsolitons at X- and K-band repetition frequencies . The solitonrepetition frequency equals to the cavity free-spectral range (FSR)at the wavelength of soliton spectral envelope center. Both Ra-man self-frequency shift and dispersive wave recoils can affectthe soliton envelope center wavelength , and they are functionsof laser-cavity frequency detuning. This can be clearly seen in Fig.2 a , as our soliton’s envelope center is to the red side of the pumplaser. Because of the chromatic dispersion, the FSR at differentwavelengths is different, and thus the variation of the pump laserfrequency, f p , will alter the soliton spectral envelope center, andchange the soliton repetition rate, f r . To the first order, the trans-fer of frequency variation from the pump ( δf p ) to the repetitionrate ( δf r ) can be described as δf r = ∂f r ∂f p × δf p , where δ denotesthe variation. For both silica and silicon nitride resonators, thistransfer coefficient ∂f r ∂f p has been measured to be on the level of10 − , and thus the soliton repetition rate linewidth is muchsmaller than that of the pump laser. The characterization of phasenoise reduction from pump laser frequency to repetition frequencyis currently unavailable in our system, as the frequency drift of ourpump laser is too large for phase noise measurement. MmWave power versus dispersion.
Optical pulses that prop-agate in an optical fiber will acquire addition phase due to groupvelocity dispersion in the fiber. Suppose the center frequency ofthe pulse is ω p , then the component at frequency ω will acquire arelative phase after propagation of distance z : E ( z, ω ) = E (0 , ω ) exp[ − i D λ λ πc ( ω − ω p ) z ] + c.c., (3)where E (0 , ω ) = E / √ N exp( − iωt ) is the electrical field of light atfrequency ω and position z = 0, normalized to the photon numberper unit time. Here we have assumed a flat spectrum for the comb,and N as the total number of comb lines. D λ is the group velocitydispersion parameter, and D λ ≈
18 ps/nm/km for SMF-28 fiber at1550 nm. For soliton frequency combs, ( ω − ω p ) / π = n × f r for the n -th comb line from the spectral envelope center, where f r is thecomb repetition frequency. Therefore, the photocurrent generated in the photodiode is I ≡ I DC + I AC = | E | = | N X − N E (0 , ω ) exp[ − iπcf r f p n D λ z ] + c.c. | = | E | + | E | (cid:2) ( N − πcD λ zf r /f p (cid:3) N sin (cid:2) πcD λ zf r /f p (cid:3) cos (2 πf r t ) + ..., (4)where we have used the P nk = m ar k = a ( r m − r n +1 ) / (1 − r ) toderive the term of cos (2 πf r t ), and we have set 2 N + 1 = N .Higher harmonics of the repetition frequency are neglected as theyare beyond the detection limit of our photodiode. Considering I DC as the average photocurrent flowing through the load resistor R L ,the detected mmWave power at frequency f r is yielded as: P f r = I DC R L Γ2 " (cid:2) ( N − πcdf r /f p (cid:3) N sin (cid:2) πcdf r /f p (cid:3) , (5)where we have defined d = D λ z as accumulated dispersion, and Γis the PD power roll-off at the repetition frequency. This equationis the same as equation (2) in the main text. When dispersion isvery small ( d → P f r = I DC R L Γ2 (cid:20) N − N (cid:21) , (6)which is equation (1) in the main text. MmWave power versus optical spectral envelope.
In thissection, we calculate the impact of the optical spectral envelopeon the mmWave power. For simplicity, we assume that the opticalenvelope is symmetric along the envelope center, and we assumeno accumulated dispersion. For the n -th comb line, we have: E ( ω n ) = f ( n ) E √ N e − iω n t + c.c., (7)where function f ( n ) is real and it describes the spectral envelope.We focus on the case where the number of comb lines is large, sothat we can assume the envelope is smooth, and | f ( n +1) − f ( n ) | ≪ f ( n ). The photocurrent is then expressed as: I = | E | = | N X − N f ( n ) E √ N e − iω n t + c.c. | = | E | N N X − N f ( n )+ 2 | E | N cos (2 πf r t ) × N − X n = − N f ( n ) f ( n + 1) + ..., (8)where we have neglected higher harmonics of the repetition fre-quency again. The sum can be simplified by using the symmet-ric envelope condition, f ( − n ) = f ( n ), and we can substitute f ( n + 1) = f ( n ) + ∆ f ( n + 1 / f ( n + 1 /
2) is the dif-ference between f ( n + 1) and f ( n ), and ∆ f ( x ) is an odd function.Therefore, we have: N − X n = − N f ( n ) f ( n + 1) = N X n = − N f ( n ) f ( n + 1) − f ( N ) f ( N + 1)= N X n = − N f ( n ) [ f ( n ) + ∆ f ( n + 1 / − f ( N ) f ( N + 1)= N X n = − N f ( n ) + N X n = − N f ( n )∆ f ( n + 1 / − f ( N ) f ( N + 1) ≈ N X n = − N f ( n ) − f ( N ) f ( N + 1) , (9) where we have used f ( n )∆ f ( n +1 /
2) approximated to an odd func-tion when the spectrum is broad, and thus | f ( n +1) − f ( n ) | ≪ f ( n ),and ∆ f ( n + 1 / ≈ ∆ f ( n ). It is clear that when N and N are very large, the sum is dominated by the total optical power, P N n = − N f ( n ), and is almost irrelevant to the function of the en-velope. The mmWave power can be expressed as: P f r = I DC R L " − f ( N ) f ( N + 1) P N − N f ( n ) . (10)When N → ∞ , f ( N ) f ( N + 1) ≪ P N − N f ( n ), and the powergain relative to the heterodyne detection approaches 6 dB regard-less of the spectral envelope f ( n ). It shall be noted that this resultonly applies to the case where the spectral envelope is symmetricand smooth, otherwise the approximation used in equation (9) willfail. Data availability.
The data that support the plotswithin this paper and other findings of this study areavailable from the corresponding author upon reasonablerequest.
Acknowledgement
The authors thank Ligentec and VLC Photonics for res- onator fabrication, Q.F. Yang at Caltech for helpfulcomments during the preparation of this manuscript,and gratefully acknowledge the support from the Na-tional Science Foundation and Defense Advanced Re-search Projects Agency (DARPA) under HR0011-15-C-0055 (DODOS). X.Y. is also supported by Virginia SpaceGrant Consortium.
Competing interests
The authors declare no competing interests.
Author Contributions
X.Y. and A.B conceived the concept. B.W. and J.S.M.performed the experiment, with assistance from K.S.,M.J. and Z.Y. J.S.M., M.W. and S.E. fabricated themodified uni-traveling carrier photodiode. B.W., J.S.M.,A.B. and X.Y. analyzed data. All authors contributed tothe writing of the manuscript. Cooper, K. B. et al.
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