A pulsed optoelectronic microwave source with high power and frequency tunability

Domain: physics
Published: 2026-02-21
Editorial outcome: minor_revision

Abstract
Microwave sources are central to modern technologies ranging from radar and directed energy to medical applications, yet conventional electronic approaches face long-standing trade-offs between output power and tunability. Optoelectronic techniques offer a promising alternative by combining the broad bandwidth of optical systems with the high power-handling capability of wide-bandgap semiconductors. Here we show an optoelectronic microwave source based on fast-response silicon carbide, enabling picosecond-scale control of photogenerated carrier lifetime while sustaining power-handling capacities up to 55 MW. The system generates continuously tunable pulsed microwave emission across the P–L band, delivering peak output power exceeding 1 MW over the 0.25–1.3 GHz range and exhibiting stable nanosecond-scale pulse operation. The generated pulses exhibit low timing jitter and highly efficient power combining in array operation. These results demonstrate a scalable route toward high-power, broadband, and flexible microwave sources, enabling applications that demand simultaneous control over frequency, energy, and spatial distribution.

Introduction
High-power microwave (HPM) sources are crucial for applications in directed energy1, detection and localization1,2, particle acceleration3, medical treatments4,5, microwave heating6–8, and plasma generation9,10. Among these, detection, localization, and directed-energy applications impose strict requirements on the operating bandwidth and frequency agility of microwave sources to accommodate multi-band demands such as radio communication (~0.4–1 GHz), Wi-Fi (2.4 GHz), GPS (1.5 GHz), airborne navigation, and satellite links within the L-band. Multi-frequency microwave heating and plasma sources provide significantly improved heating performance and control flexibility compared to fixed-frequency methods. Similarly, high-intensity, tunable pulsed electric fields (PEFs) offer emerging strategies for tumor ablation. Consequently, the development of waveform-modulation and radiation technologies that simultaneously provide wide bandwidth and high power has become a critical focus in microwave research, enabling multifunctional system integration, enhanced operational effectiveness, and expanded application targets11–14(Fig. 1f).

Purely electronic microwave sources include vacuum and solid-state types, with vacuum electronic devices (VEDs) and solid-state power amplifiers (SSPAs) as core components (Fig. 1a). VEDs convert electron beam kinetic energy into microwave energy via beam–wave interaction, achieving gigawatt-level peak powers and Ka-band frequencies3,15. However, the center frequency, dictated by the slow-wave structure (SWS), restrict their adaptability across scenarios and targets16,17. Traveling wave tubes (TWTs), a subset of VEDs, offer limited tunability, with relative bandwidths up to 77%18–21. Yet, backward-wave oscillations and thermal issues limit their peak power to ~10 kW22,23. Overall, their single-frequency output and bulky size make VEDs ill-suited for integrated, multifunctional P–L-band applications.

To enhance flexibility, SSPAs have been used to achieve frequency-tunable outputs24,25, SSPAs tune microwave frequency via gate-controlled carrier modulation. In particular, high electron mobility transistors (HEMTs), based on two-dimensional electron gases (2DEGs) (Fig. 1a), offer faster response than traditional metal–oxide–semiconductor field-effect transistors (MOSFETs). However, single HEMT devices are limited to kilowatt-level power, with maximum relative bandwidths of 10% (kW-level) and 40% (100-W-level)26–32. Compared with purely electronic approaches (Fig. 1b), the optoelectronic method provides broader frequency coverage and greater tunability while maintaining megawatt-level peak power33–38.

Here, we show a high-power microwave source based on optoelectronic technology (Fig. 1c). The overall architecture of the optoelectronic microwave source (OEMS) is described, followed by an explanation of its submodules, including fast-response materials, high-voltage-resistant devices, and high-power system components. Finally, the application of the array configuration is discussed. The OEMS demonstrates higher frequency–peak-power performance than traditional electronic microwave sources (Fig. 1d). Moreover, in optoelectronic systems, the photoconductive semiconductor architecture of the OEMS mitigates the limitations on source–drain spacing and output power imposed by carrier transit time, thereby enabling higher output power (Fig. 1e). A detailed comparison of performance metrics is provided in Supplementary Note 19.

Results
Overall architecture of the OEMS

In contrast to sub-nanosecond pulse sources relying on nonlinear photoconductive mechanisms, which suffer from limited operational flexibility [S22–S26], this study adopts a linear photoconductive strategy, wherein the core principle is to amplify radio-frequency signals via an electrical–optical–electrical conversion pathway. The conceptual schematic and overall architecture of the OEMS are illustrated in Fig. 2a,b. GHz-range microwave output is achieved through a combination of optical modulation, amplification, optoelectronic conversion, and array-based radiation. The laser source employs a master oscillator power amplifier (MOPA) architecture, wherein a modulated seed converts weak electrical signals into tunable optical pulses. A narrowband laser diode (LD) generates the initial pulsed beam, followed by pre-amplification to enhance the initial power level. An electro-optic modulator (EOM) applies optical carrier modulation, accurately tailoring the signal to the GHz-range with a bandwidth of up to 10 GHz. A subsequent acousto-optic modulator (AOM) tailors the temporal envelope, enabling tunable repetition rates from 10 Hz to 10 kHz and pulse durations ranging from sub-nanoseconds to 1 µs39. Together, these components generate a clean and reconfigurable seed pulse, enabling precise control over the center frequency, pulse width, and repetition rate of the OEMS output.

The seed pulses subsequently undergo multi-stage fiber amplification (AMP-1/2/3), employing polarization-maintaining, highly doped fibers with progressively increasing core diameters to boost peak output power. A Pockels cell–based repetition-rate reducer ensures synchronization and polarization stability. Final amplification is conducted via a cascaded Nd:YAG solid-state stage, pulse-pumped to generate high-energy pulse clusters. The amplified optical pulses are coupled into a power-delivery fiber and distributed across multiple photoconductive channels.

The system circuitry can be modeled as a series network comprising a high-voltage supply, an energy storage capacitor, a photoconductive semiconductor device (PCSD), and an output load. Detailed material and device designs of the PCSD are represented in the following sections. An RF transmission structure located at the device output delivers microwave power to the load. A suspended-plate antenna array is integrated at the terminal stage, powered and monitored by a custom constant-current voltage source to enable multi-channel radiation. A detailed schematic of the full system layout is available in Supplementary Note 1.

When the incident laser modulates the material resistance (R SiC), it alters the voltage division between R SiC and R load, thereby inducing a variation in the load voltage and generating high-power GHz-range RF signals. Equation (1) captures the relationship among the material resistance R SiC, substrate thickness d, electrode area S 0, and photogenerated carrier concentration n(t), whereas Eq. (2) describes the relation between the output voltage V out and the bias voltage V bias. Detailed derivations and symbol definitions are provided in Supplementary Note 2.

R SiC(t) = d / (n(t)qμ n S 0) = d / (qμ n η(1-R)(1-e^-2αd) R t^-1 P(s)e^-(s-t)/τ 0 ds) (1)

V out = V bias * (R load / (R load + R SiC(t))) (2)

Fast-response materials for OEMS

The wide-bandgap semiconductor SiC is employed due to its favorable properties, enabling exceptional performance in high-voltage and high-temperature environments40–42. For photogenerated carriers, both their generation and capture are essential to achieving high power and fast response43. By adopting a shallow donor-deep acceptor (SDDA) complementary doping scheme, shallow energy levels (Nitrogen, Ec-0.05~0.09 eV) ionize electrons in the dark state, which are then captured by traps to maintain high insulation (Supplementary Note 3). Upon exposure to extrinsic light (1064 nm), electrons trapped in deep acceptor levels (Vanadium, Ec-0.81~0.97 eV) transition to the conduction band, generating free carriers (Fig. 3a). The material’s optical absorption depth is on the millimeter scale44,45, ensuring conduction between the electrodes.

To maximize OEMS output in the P–L band, the total response time is designed to fall between 100 and 150 ps (Fig. 3b). In the photodiode mechanism46–49, the total response time is given by τ total = sqrt(τ tr^2 + τ RC^2), where τ tr and τ RC denote the carrier transit time through the depletion region and the circuit response time, respectively. In comparison, the total response time of the OEMS is determined by τ total = sqrt(τ 0^2 + τ RC^2), where τ 0 represents the carrier lifetime. With an interstage capacitance of 1.6 pF and an N/V doping ratio of 0.4, both the circuit response time and carrier lifetime are ~80 ps, yielding a total response time of 113 ps. For millimeter-scale dimensions, the OEMS exhibits a total response time ~1% that of the photodiode (Fig. 3c). As previously noted, the OEMS overcomes the trade-off between material thickness and response frequency, making it well suited high-frequency response in millimeter-scaled devices.

Carrier lifetime was tested for two designed substrate samples, Sample 1 and Sample 2 (Supplementary Note 4). The capture times of the V acceptor level for the two samples were 8.4 ps and 80.2 ps, respectively (Fig. 3d). The OEMS incorporating Sample 2 exhibited predicted voltage responses of 100% and 50% at laser frequencies of 0.25 GHz and 2.5 GHz, respectively (Fig. 3e). Sample 1 is predicted to extend frequency response up to 10 GHz; however, output amplitude would decrease markedly, and planar electrodes should be used to reduce capacitance.

Furthermore, several strategies can effectively facilitate frequency extension in regimes with short carrier lifetimes. First, optimizing doping levels and introducing efficient recombination centers enhance transient photoconductivity and improve high-frequency response. At a fixed concentration, recombination centers with large electron capture cross-sections can enhance the device’s high-frequency performance (Fig. 3f). Second, device design should simultaneously increase the overall doping concentration to reduce conduction resistance and minimize load impedance, thereby enhancing power output (Fig. 3g). Finally, optimizing the external electrode layout and RF transmission pathway can further extend the circuit bandwidth into higher frequency regimes50,51. Further technical details are provided in Supplementary Note 5.

High-voltage and high-current devices for OEMS

A device with opposing electrodes has been developed (Fig. 4a), in which the laser is incident through a transparent electrode into the substrate. Compared to planar electrodes, this configuration prevents surface flashover breakdown, offering advantages in blocking voltage and operational lifetime. To mitigate collision ionization induced by high current density, the incident light is confined to a low-field region away from the electrode edges. Consequently, during device operation, the peak electric field and peak current density do not coincide, as shown in Fig. 4b. The dark-state breakdown voltage of the 0.5 mm vertical device was tested (Supplementary Note 6), with breakdown occurring at the electrode edge when the bias voltage reached 46 kV (Fig. 4c).

The optical coupling structure is illustrated in Fig. 4d. A comparison was conducted between a single-reflection configuration and a short-cavity, multiple-pass design employing total internal reflection (Supplementary Note 7). For a cavity length of 10 mm, the total-internal-reflection scheme enhances optical intensity by a factor of 3.5 relative to single reflection. However, the associated round-trip delay of 170 ps introduces group delay dispersion and potential saturation, thereby limiting the high-frequency response. Given the OEMS’s emphasis on broadband performance and waveform fidelity, the single-reflection configuration was selected. An AZO layer (150 nm thick), deposited on the front surface of the SiC substrate, yields a theoretical optical coupling efficiency of 98%, with an experimentally measured value of 95% (Fig. 4e). Under a substrate thickness of 1.5 mm and an N/V doping ratio of 0.4 (1×10¹⁷/2.5×10¹⁷ cm⁻³), the average optical absorption is ~23% (Fig. 4f).

The output peak currents under varying bias voltages and light intensities are shown in Fig. 4g. The output amplitude increases linearly with bias voltage (1–3 kV) and approximately proportionally with incident light intensity (0.1–34 mJ). Simulation results indicate that, when triggered by a single-pulse laser with 35 mJ energy and a 7 ns pulse width, the device reaches a minimum on-resistance of 5.3 Ω (Supplementary Note 8). Finally, the conduction current under illumination was measured with a bias voltage of 30 kV and a circuit load of 11.3 Ω. The results show a maximum conduction current of 1.86 kA, with a power capacity of 55 MW and a minimum on-resistance of 4.83 Ω (Fig. 4h), positioning the PCSD among high-performance photoconductive devices (Fig. 4i).

Integrated performance of the OEMS

The coaxial tapered structure provides a 3 dB bandwidth of 0–3 GHz (Supplementary Note 9), enabling low-loss RF power transmission within the PCSD. Figure 5a displays the time-domain output waveforms of the OEMS. At a bias voltage of 22 kV and a trigger energy of 30 mJ (Supplementary Note 10), the 1 GHz microwave pulse achieves a peak power of 1.36 MW and an intra-pulse average power of 0.68 MW (Supplementary Note 11). The pulse width is 30 ns, with a repetition rate of 100 Hz. As shown in Fig. 5b, the peak power decreases with increasing frequency, primarily constrained by the overall response time of the OEMS. Overall, the OEMS achieves megawatt-level peak power while offering continuous and flexible frequency tunability across the P–L band, fulfilling the demands of high-power, multi-parameter microwave systems.

To evaluate the spectral purity of the generated microwave pulses, the FFT-derived power spectrum is shown in Fig. 5c. Harmonic components are suppressed by more than −14 dB relative to the fundamental frequency, and the measured 3 dB bandwidth of the main spectral line is 27 MHz, consistent with the 30 ns pulse width (Supplementary Note 12). A slight waveform broadening caused by voltage division within the series circuit is identified as the primary source of second-harmonic content. These harmonics contribute negligibly to the peak power, ensuring that the actual power at the target frequency closely matches the value calculated using the voltage-based method.

At megawatt output levels, potential sources of harmonic or nonlinear contributions include the voltage-division network, carrier dynamics in the material, parasitic circuit elements, and optical/electrical saturation effects. Among these, series load division is currently the most probable origin of harmonic generation. Material doping and device-level parasitics may introduce frequency-dependent nonlinearities in the output voltage. Additionally, when the incident optical energy exceeds 12 mJ within a 10 ns pulse and the bias field surpasses 30 kV/mm, nonlinear phenomena such as optical saturation and carrier velocity saturation are expected to become prominent. In the current OEMS system, however, both the optical power and electric field strength operate within the linear regime. Detailed saturation thresholds are provided in Supplementary Note 13.

Array application of the OEMS

In large-scale array power synthesis, the standard deviation of time jitter is a critical performance metric and is determined by the stability of the trigger laser. To achieve synthesis efficiency above 95% at 2 GHz, the time jitter must remain below 20 ps (Supplementary Note 15). The 2 GHz optical signal was characterized within an 8 ns amplitude-flat region (Fig. 6a). As shown in Fig. 6b, at an optical energy of 24 mJ, the time jitter of the optical signal is 11 ps, meeting the phase-control requirements for efficient array synthesis. By applying an FFT to the absolute time-jitter sequence, the modified phase-noise power spectrum over the (0, 2 GHz] range was obtained (Supplementary Note 16), and the relationship is expressed as σ abs^2 = 1/ω 0^2 * ∫ f 0^2 L(f)df. As shown in Fig. 6c, periodic spurious peaks introduced by the measurement window appear at 120 MHz and its harmonics, while the noise spectrum exhibits <−85 dBc/Hz near 87 MHz. This noise is attributed to active-device noise within the optical amplification chain and trigger jitter from the synchronized driving signals. Future work will focus on reducing phase noise within the sub-100 MHz region.

The measurement setup is shown in Fig. 6d (Supplementary Note 14). When the four elements radiated sequentially, the average far-field amplitudes were 257.9 mV, 253.9 mV, 239.2 mV, and 256.7 mV, respectively. When radiating simultaneously, the array produced an average far-field amplitude of 1.02 V (Fig. 6e), corresponding to a spatial synthesis efficiency of 98.6%. The amplitude stability of the single-path and array-combined signals was better than ±9.5% and ±7.36%, respectively (Supplementary Note 17). In addition, the measured radiation pattern gain closely agrees with the simulation results (Fig. 6f). These results demonstrate that the OEMS not only offers modularity, compactness, and tunable-frequency waveform generation but also achieves high-efficiency, high-power array synthesis, thereby enabling the development of integrated, multifunctional microwave systems.

Methods
Device configuration and fabrication

The 4H-SiC material was selected with an optimized nitrogen/vanadium (N/V) doping ratio of 0.4 (1×10¹⁷/2.5×10¹⁷ cm⁻³). The wafer was cut along the a-plane (1120-plane) to eliminate micropipes, from which a substrate measuring 8 mm × 8 mm with a thickness of 1.5 mm was obtained. The photoconductive device consists of the substrate, electrodes, and an optical coupling structure. A face-to-face electrode configuration is employed on both sides of the substrate, consisting of an annular multilayer metal electrode (Ti/Ni/Au with respective thicknesses of 30 nm, 80 nm, and 100 nm, patterned by photolithography) and a circular transparent electrode. The outer diameters of the metal and transparent electrodes are 3.5 mm and 2 mm, respectively. The bilayer electrode structure is annealed at 900 °C for 2 min to ensure a reliable ohmic contact. The transparent electrode is composed of aluminum-doped zinc oxide (Al:ZnO, AZO), with a thickness of 150 nm, selected based on thin-film interference considerations to enhance the transmittance of normally incident laser light. The bottom AZO layer is heavily doped to reduce the space-charge region at the AZO/SiC junction, thereby lowering the conduction resistance [S27]. In the axial illumination configuration, the two electrodes are directly aligned, yielding an effective illuminated area of 9.62 mm² and an interstage capacitance of ~1.8 pF. To optimize optical efficiency, the incident laser beam is collimated to minimize divergence loss, and a single-reflection scheme incorporating a terminal mirror is used to improve optical energy utilization. After encapsulation, the overall dimensions of the photoconductive semiconductor device (PCSD) are approximately 2 × 2 × 3 cm³.

PCSD testing setup

The test circuit used for dark DC breakdown measurements consists of a SiC substrate with a pair of opposing electrodes, with a substrate thickness of 0.5 mm. A 1:5 closed-loop magnetic voltage transformer (XF) is employed, and the high-voltage power supply is charged through a ceramic energy-storage capacitor (C1, 50 kV, 2 nF). The voltage across the device under test is monitored using a high-voltage probe.

The circuit used for evaluating the power capacity of the PCSD includes six 40 kV, 1 nF ceramic capacitors connected in parallel, six 50 Ω resistors, and a current-viewing resistor (CVR). During the photoconductive switch test, the ceramic capacitor bank charges the high-voltage supply. Upon laser triggering, the capacitor discharges through the device, which is modeled as a variable resistor. The CVR serves as a low-value, high-bandwidth resistor (2 GHz; T&M SSDN-10, New Mexico, USA). The output signal is recorded using a 4 GHz bandwidth oscilloscope (LeCroy WR9404M, New York, USA). A 1064 nm Nd:YAG laser with a 7 ns pulse width and a 2 mm beam diameter is used for excitation.

Array synthesis testing setup

Time interval error (TIE) is used to quantify time jitter, with its standard deviation computed from 1×10⁴ data points. Approximately 50 peak amplitudes are recorded to evaluate amplitude fluctuations. The pulsed laser is collimated, expanded, and split into five paths; four illuminate the photoconductive devices, and one is used for real-time intensity monitoring. The PCSD is connected to the high-voltage supply at the input and to a suspended plate antenna at the output through an L29 connector. Far-field measurements are performed at 1.37 m at 1.3 GHz. The transmitting and receiving antenna gains are 15.5 dB and 7.15 dB, respectively. After 40 dB and 20 dB attenuation, the signal is delivered to the oscilloscope via a 20 m SMA cable, resulting in a total link attenuation of ~83.01 dB. Array synthesis efficiency is obtained from the average far-field amplitude over more than 50 repeated measurements.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors experimentally demonstrate a microwave source capable of generating GHz microwave pulses with a peak power of 1 MW, at a 100 Hz repetition rate. Their system is tunable (across 1 GHz) and displays time jitter below 20 ps. The modus operandi, in a nut shell, is that a high-peak-power, modulated, tunable and pulsed laser illuminates a semiconductor wide bandgap material and generates a microwave via a photoconductive mechanism. They also propose a model that provides a relatively satisfying agreement with experiments.\nMany applications in microwave engineering are in need of such powerful sources. From that perspective, this work certainly has merit. However, I think that the paper is not very clear, and I fail to see the broad impact needed to be published in a journal like Nature Communications.\nAdditionally, I would like the authors to consider the points below:\n- I can see and appreciate the efforts from the authors to provide as much information as needed, but as a result, the paper ends up being extremely dense and quite poorly written. An obvious illustration of this shortcoming is the very first sentence of Section 2, which is “The relationship among the material resistance ( RSiC ), substrate thickness ( d ), electrode area ( S0 ), and photo-generated carrier concentration ( n t( )) is expressed in Equation (1), while the relationship between the output voltage (Uout ) and the bias voltage (Ubias ) is described in Equation (2).” How is the reader even expected to understand what these parameters are about, just immediately after reading the general introduction?\n- Along the same line, the paper lacks a clear figure for the full microwave generator (NdYAG laser system at input, GHz microwave at output). One has to go through a large number of auxiliary figures and text to self-build a coherent, synthetic idea of the architecture of the proposed generator. The reader is referred to Fig S10 (the 10th figure of the supplementary material) for a general architecture, and even that figure looks quite incomplete to me.\n- As a minor point, the authors present their system as a “An optoelectronic microwave source with high power and frequency tunability”. This can be misleading as from this title alone, one can think that their system outputs a continuous wave signal. The title should reflect the fact that the source is pulsed.\n- Authors claim that their systems output pure microwaves but offer no proof of such purity (purity is different from the stability of the pulse train). From the time traces, I would guess that the microwaves are not very pure.\n- The authors indicate that the time jitter for the pulses is less than 20 ps. The authors have to indicate clearly the bandwidth over which this time jitter is integrated.\n- The authors should carefully proofread their references (for example, we have the occurrence “F. P. G. de Arquer, null”)\n- There are several other typos in the text (for example, “Collecter” and “meterial”, just in Fig. 1).", "reviewer_2": "The work An optoelectronic microwave source with high power and frequency tunability by Niu et al. describes an optoelectronic microwave source (OEMS) with impressive performance such as high output powers > 1MW simultaneously with broad tunability from 0.25 to 1.3GHz. This is achieved by utilizing photoelectric conversion effects in doped Silicon Carbide structures. The authors compare their OEMS with state-of-the-art high power RF amplifiers and show that their device boasts significant improvements in both output power and tunability. Furthermore the authors use a series of OEMS an a phased array application and show that low timing jitter, which is critical for large-scale array synthesis. Overall this work is very impressive, from detailed experimental results to theoretical analysis and tables for comparisons. I believe this work can be accepted for publication in Nature Communications as is – however I do have some minor questions for the authors and which may give insight into additions into the manuscript.\n1. How is the optical to electronic coupling optimized? You mention that the optical absorption length is ~mm, but are there other considerations?\n2. By reducing the carrier lifetime you show that the device can have nearly flat gain over a broader frequency range, however the output power is reduced relative to a longer carrier lifetime. Are there ways to increase the output power while operating at small carrier lifetimes to further extend the tunability of the OEMS?\n3. For the phase array application you discuss timing jitter, and so it is maybe related, but can you discuss how the phase noise from the OEMS. For applications like datacomm, will this have noticeable affects?\n4. Since the optical to electrical conversion occurs during the duration of the pulse, how do you characterize the ~1MW output power – is the pulse duration and repetition rate considered? How does the system function with a CW optical signal? Can you modify the design to accommodate CW light?\n5. Results are shown for amplification of single tone RF waveforms. Is the output affected if the RF signal to be amplified has a nonzero bandwidth, for ex: 500MHz center frequency and 500MHZ bandwidth signals.\n6. How do you characterize and control nonlinear affects especially at such high RF powers?"}, "author_response": "Responses to Reviewer#1 (Manuscript Number: NCOMMS-25-59617-T)\nReviewer # 1 (Remarks to the Author)\nThe authors experimentally demonstrate a microwave source capable of\ngenerating GHz microwave pulses with a peak power of 1 MW, at a 100 Hz\nrepetition rate. Their system is tunable (across 1 GHz) and displays time jitter\nbelow 20 ps. The modus operandi, in a nut shell, is that a high-peak-power,\nmodulated, tunable and pulsed laser illuminates a semiconductor wide bandgap\nmaterial and generates a microwave via a photoconductive mechanism. They also\npropose a model that provides a relatively satisfying agreement with experiments.\nResponse: We sincerely thank the reviewer for the thoughtful and constructive\ncomments. We have carefully considered all suggestions and have revised the\nmanuscript accordingly. Below, we provide a point-by-point response. Additions\nto the Supplementary Informations are marked in green text, modifications added\nto the revised manuscript are shown in blue text, and major changes made directly\nwithin the main manuscript are indicated in red text.\nWe hope that the revisions satisfactorily address the reviewer’s concerns.\nShould any further clarification or discussion be needed, we would be more than\nhappy to respond.\nComment. 1: Many applications in microwave engineering are in need of such\npowerful sources. From that perspective, this work certainly has merit. However,\nI think that the paper is not very clear, and I fail to see the broad impact needed\nto be published in a journal like Nature Communications.\nResponse：We thank the reviewer for highlighting the importance of clarity. To\nmore effectively present the broad impact and improve narrative readability, we\nhave implemented two revisions:\n(1) Application-oriented overview and illustration — now incorporated in the\nrevised Introduction and Fig. 1f: High-power microwave (HPM) sources are\ncrucial for applications in directed energy [1], detection and localization [1, 2],\nparticle acceleration [15], medical treatments [3, 4], microwave heating [5–7], and\nplasma generation [8, 9]. Among these, detection, localization, and directed-energy\napplications impose strict requirements on the operating bandwidth and\nfrequency agility of microwave sources to accommodate multi-band demands such\nas radio communication (~0.4–1 GHz), Wi-Fi (2.4 GHz), GPS (1.5 GHz), airborne\nnavigation, and satellite links within the L-band. Multi-frequency microwave\nheating and plasma sources provide significantly improved heating performance\nand control flexibility compared to fixed-frequency methods. Similarly, high-\nintensity, tunable pulsed electric fields (PEFs) offer emerging strategies for tumor\nablation. Consequently, the development of waveform-modulation and radiation\ntechnologies that simultaneously provide wide bandwidth and high power has\nbecome a critical focus in microwave research, enabling multifunctional system\nintegration, enhanced operational effectiveness, and expanded application targets\n[10–13] (Fig. 1f).\nFig.1 (f) Application domains and development directions of HPM sources.\n(2) Refined narrative structure — added in the third-to-last paragraph of the\nIntroduction and shown in Fig. 2(a). The manuscript is now organized following\nthe progression: overall OEMS architecture, key submodules (fast-response\nmaterials, high-voltage-tolerant devices), system-level performance, phased-array\napplication. Details of the laser-source engineering, which are not the main focus\nof this work, are kept only to the extent necessary for understanding the system.\nThese changes help readers grasp the main storyline and focus on the core\ncontribution: the optoelectronic conversion mechanism.\nFig.2 (a) Conceptual schematic\nComment. 2: I can see and appreciate the efforts from the authors to provide as\nmuch information as needed, but as a result, the paper ends up being extremely\ndense and quite poorly written. An obvious illustration of this shortcoming is the\nvery first sentence of Section 2, which is “The relationship among the material\nresistance (R ), substrate thickness (d), electrode area (S ), and photo-generated\nSiC 0\ncarrier concentration (n(t)) is expressed in Equation (1), while the relationship\nbetween the output voltage (U ) and the bias voltage (U ) is described in\nout bias\nEquation (2).” How is the reader even expected to understand what these\nparameters are about, just immediately after reading the general introduction?\nResponse： We appreciate the reviewer’s point. To improve readability, we now\nintroduce the physical mechanism first, followed by a complete list of parameters,\nand finally present the mathematical derivation of the governing equations.\nThe system circuitry can be modeled as a series network comprising a high-\nvoltage supply, an energy storage capacitor, a photoconductive semiconductor\ndevice (PCSD), and an output load. Detailed material and device designs of the\nPCSD are presented in the following sections. …When the incident laser\nmodulates the material resistance ( ), it alters the voltage division between\nand , thereby inducing a v\n𝑹𝑹\nar𝐒𝐒𝐒𝐒i𝐒𝐒ation in the load voltage and generating\nh\n𝑹𝑹\ni𝐒𝐒g𝐒𝐒𝐒𝐒h-pow\n𝑹𝑹\ne𝐥𝐥r𝐥𝐥 𝐥𝐥G𝐥𝐥Hz-range RF signals. Equation (1) captures the relationship among\nthe material resistance , substrate thickness , electrode area , and photo-\ngenerated carrier conce\n𝑹𝑹\nn𝐒𝐒t𝐒𝐒r𝐒𝐒ation , whereas Eq\n𝒅𝒅\nuation (2) describ\n𝑺𝑺\ne𝟎𝟎s the relation\nbetween the output voltage and the bias voltage . Detailed derivations and\nout 𝒏𝒏(𝒕𝒕) bias\nsymbol definitions are provided in Supplementary Note 2.\n𝑽𝑽 𝑽𝑽\nSupplementary Note 2：\nWhen an optical pulse with a spatially uniform intensity illuminates the surface\nof the material, the rapid generation of photocarriers sharply increases the\nconductivity of the SiC photoconductive semiconductor, causing its resistance to\ndrop abruptly and driving the device into the conductive state. The temporal\nevolution of the photocarrier concentration is governed by the continuity equation\n(Eq. (1)), with the definitions and units of all parameters summarized in Table S1.\n∂n(t) n(t)\n=G(t)− （1）\n∂t τ\nr\nUsing the Laplace transform, the general solution of Eq. (1) can be expressed as\nEq. (2). Here, the carrier lifetime characterizes the net recombination rate and\nserves as a key parameter governi\n𝝉𝝉\nn𝒓𝒓g the carrier dynamics.\nt\nn(t)= ∫ G(s)e(s−t)/τ rds （2）\n−∞\nThe photocarrier generation rate is proportional to the incident optical power\n, the optical absorptivity , and the quantum efficiency . It is given by Eq.\n(3). The quantum efficiency is defined as the ratio of the number of\n𝑷𝑷(𝒕𝒕) 𝑨𝑨 𝜼𝜼\nphotocarriers generated per second to the number of absorbed photons, whereas\n𝜼𝜼\nthe absorptivity is defined as the fraction of incident photons absorbed by the\nmaterial and is influenced by the surface refractive index and impurity-doping\n𝑨𝑨\nconcentrations.\nP(t)η\nG(t)= ⋅A ，A=(1−r)⋅(1−e−ad) （3）\nWdLhυ\nBy combining the conductivity relation with Eqs. (2) and (3), the time-varying\nresistance of the material can be expressed as\nd d d d2hν\nR (t)=ρ(t) = = =− （4）\nSiC S\n0\nσ(t)WL n(t)qµWL quηA∫ t P(s)e(s−t)/τ rds\n−∞\nSince the device output voltage corresponds to the voltage across the load in\nseries with the photoconductive semiconductor, the output voltage can be written\nas\nR\nV ≈V ⋅ load =V ⋅ Φ (f) （5）\nout bias R +R bias structure\nload SiC\nwhere is the DC bias provided by the pulsed energy-storage source, and\nis th\n𝑽𝑽\ne𝒃𝒃 𝒃𝒃𝒃𝒃lo𝒃𝒃ad resistance. The function therefore represents the\n𝑹𝑹 fr𝒍𝒍e𝒍𝒍q𝒃𝒃u𝒅𝒅ency–power transfer characteristics 𝝓𝝓 𝒃𝒃o𝒕𝒕f𝒓𝒓 𝒔𝒔𝒔𝒔t𝒕𝒕h𝒔𝒔e𝒓𝒓 𝒔𝒔( s 𝒇𝒇 y ) stem, incorporating the\ncombined influence of the RF transmission structure and device geometry on the\noutput microwave power.\nTable. S1 Physical quantities related to the time-varying resistance of the\nphotoconductive semiconductor\nSymbol Physical meaning Unit\nn(t) Carrier concentration /m3\nG(t) Photocarrier generation rate /s∙m3\nτ Carrier lifetime s\nr\nP(t) Optical power J/s\nSubstrate length, width, thickness, and\nW/L/d/S m\n0\nilluminated area\nA Optical absorptivity -\nr Substrate reflectivity -\nη\nQuantum efficiency -\n∂ Absorption coefficient /m\nρ/σ Resistivity / conductivity Ω∙m，S/m\nhv Photon energy J\nComment. 3: Along the same line, the paper lacks a clear figure for the full\nmicrowave generator (NdYAG laser system at input, GHz microwave at output).\nOne has to go through a large number of auxiliary figures and text to self-build a\ncoherent, synthetic idea of the architecture of the proposed generator. The reader\nis referred to Fig S10 (the 10th figure of the supplementary material) for a general\narchitecture, and even that figure looks quite incomplete to me.。\nResponse：We sincerely thank the reviewer for this valuable suggestion. In\nSection 3.1 of the revised manuscript, we have added a system-level architecture\ndiagram and expanded the description of the MOPA-based laser source. This\nallows readers to clearly follow the entire process from laser excitation to GHz\nmicrowave generation.\nSection 3.1:\nThe conceptual schematic and overall architecture of the OEMS are illustrated\nin Fig. 2a,b. GHz-range microwave output is achieved through a combination of\noptical modulation, amplification, optoelectronic conversion, and array-based\nradiation. The laser source employs a master oscillator power amplifier (MOPA)\narchitecture, wherein a modulated seed converts weak electrical signals into\ntunable optical pulses. A narrowband laser diode (LD) generates the initial pulsed\nbeam, followed by preamplification to enhance the initial power level. An electro-\noptic modulator (EOM) applies GHz-range modulation, accurately imprinting the\nRF signal onto the optical carrier with support for a dynamic bandwidth of up to\nenvelope, enabling tunable repetition rates from 10 Hz to 10 kHz and pulse\ndurations ranging from sub-nanoseconds to 1 µs [39]. Together, these components\ngenerate a clean and reconfigurable seed pulse, enabling precise control over the\ncenter frequency, pulse width, and repetition rate of the OEMS output.\nThe seed pulses subsequently undergo multi-stage fiber amplification (AMP-\n1/2/3), employing polarization-maintaining, highly doped fibers with progressively\nincreasing core diameters to boost peak output power. A Pockels cell–based\nrepetition-rate reducer ensures synchronization and polarization stability. Final\namplification is conducted via a cascaded Nd:YAG solid-state stage, pulse-pumped\nto generate high-energy pulse clusters. The amplified optical pulses are coupled\ninto a power-delivery fiber and distributed across multiple photoconductive\nchannels.\nFig.2 (a) Conceptual schematic and (b) overall architecture of the OEMS.\nThe system circuitry can be modeled as a series network comprising a high-\nvoltage supply, an energy storage capacitor, a photoconductive semiconductor\ndevice (PCSD), and an output load. Detailed material and device designs of the\nPCSD are presented in the following sections. An RF transmission structure\nlocated at the device output delivers microwave power to the load. A suspended-\nplate antenna array is integrated at the terminal stage, powered and monitored by\na custom constant-current voltage source to enable multi-channel radiation. A\ndetailed schematic of the full system layout is available in Supplementary Note 1.\nAdditional details and schematic illustrations of system components have also\nbeen added to Supplementary Note 1 and Section 2.1 of the Methods.\n1）Laser Modulation and Amplification.（Supplementary Note 1）\nThe acousto-optic modulator (AOM) used in the system has an operating\nbandwidth of 200 MHz and an extinction ratio of ~50 dB, while the electro-optic\nmodulator (EOM) provides a 10 GHz operating bandwidth with a 20 dB extinction\nratio. The driving signals for the EOM are generated by an arbitrary waveform\ngenerator (AWG) and a power amplifier (PA). A pulse-delay generator\nsynchronizes the LD output pulses with the AOM modulation waveform to ensure\ntemporal overlap. During amplification, a 2 nm narrowband bandpass filter (BP)\nis inserted to suppress amplified spontaneous emission (ASE).\nFig. S1. System overview. High-peak-power laser source: modulated laser seed, multi-stage\nfiber amplification, and cascaded solid-state amplifiers[S1]. Single PCSD and RF link:\noptically coupled structure, SiC photoconductive substrate, and a series voltage-division\ncircuit formed by the PCSD and the RF transmission structure. Radiation system: fiber\nsplitting network, suspended-plate antennas, and a custom constant-current voltage supply.\nThe first-stage fiber amplifier (AMP-1) employs a customized integrated fiber\ndevice architecture, boosting the average power to 160 mW. The second-stage\namplifier (AMP-2) uses a polarization-maintaining ytterbium-doped fiber with a\n15/130 µm core/cladding diameter as the gain medium, increasing the average\nsignal power to 2.0 W. The main amplifier (AMP-3) adopts a 30/250 µm\npolarization-maintaining, highly doped ytterbium-doped fiber as the gain medium.\nA backward-pumping configuration is used, with pump light supplied by two\nwavelength-stabilized, continuous-wave multimode laser diodes.\nPolarization purity of the amplified pulse cluster is further improved using a\ncombination of a half-wave plate (HWP1) and a polarization beam splitter (PBS1).\nTo obtain higher peak power during amplification, the repetition rate of the pulse\ncluster is reduced and synchronized with the pulsed-pump scheme. A Pockels cell\nassembly—comprising HWP2, an electro-optic switch (EOS), and PBS2—is\nemployed to decrease the pulse-cluster repetition rate from 25 kHz to the 100 Hz\nlevel under timing-signal synchronization. The resulting pulse cluster is then\ninjected into the Nd:YAG solid-state gain medium for further amplification,\nyielding a final output pulse-cluster energy of 30 mJ.\n2）Device Configuration and Fabrication (Section 2.1)\nThe 4H-SiC material was selected with an optimized nitrogen/vanadium (N/V)\ndoping ratio of 0.4 (1×10¹⁷ / 2.5×10¹⁷ cm⁻³). The wafer was cut along the a-plane\n(112 ˉ0-plane) to eliminate micropipes, from which a substrate measuring 8 mm\n× 8 mm with a thickness of 1.5 mm was obtained. The photoconductive device\nconsists of the substrate, electrodes, and an optical coupling structure. A face-to-\nface electrode configuration is employed on both sides of the substrate, consisting\nof an annular multilayer metal electrode (Ti/Ni/Au with respective thicknesses of\n30 nm, 80 nm, and 100 nm, patterned by photolithography) and a circular\ntransparent electrode. The outer diameters of the metal and transparent electrodes\nare 3.5 mm and 2 mm, respectively. The bilayer electrode structure is annealed at\n900 °C for 2 minutes to ensure a reliable ohmic contact. The transparent electrode\nis composed of aluminum-doped zinc oxide (Al:ZnO, AZO), with a thickness of\n150 nm, selected based on thin-film interference considerations to enhance the\ntransmittance of normally incident laser light. The bottom AZO layer is heavily\ndoped to reduce the space-charge region at the AZO/SiC junction, thereby\nlowering the conduction resistance [S27]. In the axial illumination configuration,\nthe two electrodes are directly aligned, yielding an effective illuminated area of\n9.62 mm² and an interstage capacitance of approximately 1.8 pF. To optimize\noptical efficiency, the incident laser beam is collimated to minimize divergence loss,\nand a single-reflection scheme incorporating a terminal mirror is used to improve\noptical energy utilization. After encapsulation, the overall dimensions of the\nphotoconductive semiconductor device (PCSD) are approximately 2 × 2 × 3 cm³.\n3）Array radiation and power synthesis. （Supplementary Note 1）\nTo realize an N-element array topology, the output energy of the seed source is\ndoubled by increasing the number of cascaded solid-state amplification stages. The\namplified laser is coupled into a power-delivery fiber and, after fiber splitting,\ndistributed to N independent PCSD and their associated links. Each RF\ntransmission stage is terminated with a suspended-plate antenna to enable high-\npower, broadband radiation, with the antenna enclosure filled with SF₆ gas to\nenhance the power-handling capability of the array aperture. A custom constant-\ncurrent voltage supply feeds all photoconductive devices in parallel, while real-\ntime monitoring of the terminal voltage provides a reliable indication of the\noperating state of each semiconductor element.\nReference：\n[S27] Zheng Z, Huang W, Han W-W, et al. Analyzing the Effects of Aluminum-Doped ZnO\nand Ag Layers for the Transparent Electrode Vertical PCSS[J]. IEEE Transactions on\nElectron Devices, 2020, 67(6): 2414~2417.\nComment. 4: As a minor point, the authors present their system as a “An\noptoelectronic microwave source with high power and frequency tunability”.\nThis can be misleading as from this title alone, one can think that their system\noutputs a continuous wave signal. The title should reflect the fact that the source\nis pulsed.\nResponse：We thank the reviewer for this precise comment. To avoid any\nambiguity regarding continuous-wave operation, we have revised the title to: “A\npulsed optoelectronic microwave source with high power and frequency tunability.”\nThe current OEMS operates in a short-pulse regime; CW operation is discussed\nonly as a potential extension. We have clarified in both the Abstract and the\nDiscussion that the output microwave pulse width is 30 ns with a repetition rate of\nThe revised text now reads:\nAbstract: The OEMS generates a pulsed, broadband photoelectric response\nacross the P–L band, with peak-to-peak output power surpassing 1 MW over a\nfrequency range of 0.25–1.3 GHz and a relative bandwidth of 135%. The pulses\nexhibit a 30-ns FWHM pulse width at a pulse-repetition frequency of 100 Hz.\nDISCUSSION: As a result, the OEMS generates MW-level peak-power\nmicrowave pulses over the 0.25–1.3 GHz range with continuous frequency\ntunability within the P–L band; the pulses have a 30-ns FWHM duration at a\npulse-repetition frequency of 100 Hz.\nComment. 5: Authors claim that their systems output pure microwaves but\noffer no proof of such purity (purity is different from the stability of the pulse\ntrain). From the time traces, I would guess that the microwaves are not very pure.\nResponse：We appreciate the reviewer’s insightful distinction between purity\nand stability. We have added the FFT amplitude spectrum, spectral linewidth, and\nharmonic suppression ratio to explicitly quantify signal purity. Furthermore, in\nconnection with Reviewer #2’s comments on nonlinear effects (see Response A6 to\nReviewer #2), we explain that series voltage division and waveform distortion are\nthe primary sources of harmonic generation. We additionally clarify that these\nharmonics contribute minimally to the peak power, which is why the measured\npower at the target frequency agrees with the voltage-based calculation.\nThese revisions are included in Section 3.4 of the revised manuscript:\nFig.5 (a) Output waveforms of OEMS at modulation frequencies of 0.5-1.5 GHz. (b) Frequency\nspectra of the output signal. (c) Frequency-powert characteristic of the OEMS.\nFig. 5a displays the time-domain output waveforms of the OEMS. At a bias\nvoltage of 22 kV and a trigger energy of 30 mJ (Supplementary Note 11), the 1\nGHz microwave pulse achieves a peak power of 1.36 MW and an intra-pulse\naverage power of 0.68 MW (Supplementary Note 12). The pulse width is 30 ns,\nwith a repetition rate of 100 Hz. As shown in Fig. 5c, the peak power decreases\nwith increasing frequency, primarily constrained by the overall response time of\nthe OEMS. Overall, the OEMS achieves megawatt-level peak power while offering\ncontinuous and flexible frequency tunability across the P–L band, fulfilling the\ndemands of high-power, multi-parameter microwave systems.\nTo evaluate the spectral purity of the generated microwave pulses, the FFT-\nderived power spectrum is shown in Fig. 5b. Harmonic components are suppressed\nby more than −14 dB relative to the fundamental frequency, and the measured 3\ndB bandwidth of the main spectral line is 27 MHz, consistent with the 30 ns pulse\nwidth (Supplementary Note 13). A slight waveform broadening caused by voltage\ndivision within the series circuit is identified as the primary source of second-\nharmonic content. These harmonics contribute negligibly to the peak power,\nensuring that the actual power at the target frequency closely matches the value\ncalculated using the voltage-based method.\nAt megawatt output levels, potential sources of harmonic or nonlinear\ncontributions include the voltage-division network, carrier dynamics in the\nmaterial, parasitic circuit elements, and optical/electrical saturation effects.\nAmong these, series load division is currently the most probable origin of\nharmonic generation. Material doping and device-level parasitics may introduce\nfrequency-dependent nonlinearities in the output voltage. Additionally, when the\nincident optical energy exceeds 12 mJ within a 10 ns pulse and the bias field\nsurpasses 30 kV/mm, nonlinear phenomena such as optical saturation and carrier\nvelocity saturation are expected to become prominent. In the current OEMS\nsystem, however, both the optical power and electric field strength operate within\nthe linear regime. Detailed saturation thresholds are provided in Supplementary\nNote 14.\nSupplementary Note 13:\nThe power spectrum of the output signal shows that second-order harmonics\nare present within the 0.5–1 GHz range. These harmonics originate primarily from\nvoltage division across the series resistance, which causes a slight temporal\nbroadening of the output waveform compared with an ideal sinusoid. The\nresulting waveform distortion and the corresponding frequency spectrum are\nillustrated in Fig. S21.\nBecause these harmonic components contribute negligibly to the peak-to-peak\nvoltage, the power at the target frequency can be well approximated using the\nvoltage-derived peak-to-peak power.\nFig. S21 Origin of the second-order harmonic. (a) Output waveform containing the second\nharmonic. (b) Corresponding frequency spectrum.\nComment. 6: The authors indicate that the time jitter for the pulses is less than\n20 ps. The authors have to indicate clearly the bandwidth over which this time\njitter is integrated.\nResponse：We thank the reviewer for the insightful comments regarding the\ndefinition of jitter and the corresponding bandwidth. Considering the limitations\nimposed by the low-duty-cycle pulsed operation [S28], we extract zero-crossing\ntiming information using the oscilloscope time-domain method and compute the\nmodified phase-error power spectrum following Ref. [S29]. The standard\ndeviation of the time jitter is written in its conventional form:\n1 f\nσ 2 = ∫ 0S (f)df （6）\nabs w 2 0 φ\n0\nwhereσ denotes the oscilloscope-measured time-jitter standard deviation,\nabs\nand are the fundamental frequency of the test signal and its angular\n𝒇𝒇fr 𝟎𝟎 equen𝝎𝝎cy 𝟎𝟎 , respectively, and S (f) is the single-sideband phase-noise power\nφ\nspectral density. The modified phase-error power spectrum L(f) is defined as\nL(f)=1/2S (f) [S29], and corresponds directly to the output provided by\nφ\nlaboratory phase-noise analyzers.\nWe have revised the manuscript accordingly based on this theoretical\nframework (see Section 3.5 and Fig. 6 in the revised version). Additional details,\nincluding the construction and validation of the jitter-to-phase-noise model, are\nprovided in Supplementary Note 17 (“Phase noise characteristics of the OEMS”).\nSection 3.5:\nIn large-scale array power synthesis, the standard deviation of time jitter is a\ncritical performance metric and is determined by the stability of the trigger laser.\nTo achieve synthesis efficiency above 95% at 2 GHz, the time jitter must remain\nbelow 20 ps (Supplementary Note 16). The 2 GHz optical signal was characterized\nwithin an 8 ns amplitude-flat region (Fig. 6a). As shown in Fig. 6b, at an optical\nenergy of 24 mJ, the time jitter of the optical signal is 11 ps, meeting the phase-\ncontrol requirements for efficient array synthesis. By applying an FFT to the\nabsolute time-jitter sequence, the modified phase-noise power spectrum over the\n(0, 2 GHz] range was obtained (Supplementary Note 17), and the relationship is\nexpressed as σ 2 =1/w 2∫ 02L(f)df . As shown in Fig. 6c, periodic spurious peaks\nabs 0\n0\nintroduced by the measurement window appear at 120 MHz and its harmonics,\nwhile the noise spectrum exhibits <−85 dBc/Hz near 87 MHz. This noise is\nattributed to active-device noise within the optical amplification chain and trigger\njitter from the synchronized driving signals. Future work will focus on reducing\nphase noise within the sub-100 MHz region.\nReference：\n[S28] R&S FSWP Phase Noise Analyzer and VCO Tester Specifications, 6th ed., Rohde\n& Schwarz GmbH & Co. KG, Munich, Germany, 2024, p. 31.\n[S29] Galton, Ian, Weltin-Wu, et al. Understanding Phase Error and Jitter: Definitions,\nImplications, Simulations, and Measurement[J]. IEEE Transactions on Circuits & Systems,\n2019, Vol.66(1): 1-19.\nComment. 7: The authors should carefully proofread their references (for\nexample, we have the occurrence “F. P. G. de Arquer, null”.\nResponse：We have thoroughly checked all references and corrected\nformatting issues. A small number of references have also been added or\nstreamlined to ensure relevance and completeness (see updated reference list).\nComment. 8: There are several other typos in the text (for example, “Collecter”\nand “meterial”, just in Fig. 1).\nResponse：We sincerely apologize for the oversight. The entire manuscript,\nincluding all figures and tables, has now been carefully reviewed. Spelling errors\nhave been corrected, and the content has been verified to ensure accuracy and\ncompliance with journal standards.\nResponses to Reviewer#2 (Manuscript Number: NCOMMS-25-59617-T)\nReviewer # 2 (Remarks to the Author)\nThe work An optoelectronic microwave source with high power and frequency\ntunability by Niu et al. describes an optoelectronic microwave source (OEMS) with\nimpressive performance such as high output powers > 1MW simultaneously with\nbroad tunability from 0.25 to 1.3GHz. This is achieved by utilizing photoelectric\nconversion effects in doped Silicon Carbide structures. The authors compare their\nOEMS with state-of-the-art high power RF amplifiers and show that their device\nboasts significant improvements in both output power and tunability.\nFurthermore the authors use a series of OEMS an a phased array application and\nshow that low timing jitter, which is critical for large-scale array synthesis. Overall\nthis work is very impressive, from detailed experimental results to theoretical\nanalysis and tables for comparisons. I believe this work can be accepted for\npublication in Nature Communications as is – however I do have some minor\nquestions for the authors and which may give insight into additions into the\nmanuscript.\nResponse: We sincerely appreciate the reviewer’s careful evaluation and\npositive assessment of our work, which is greatly encouraging to us. We have\ncarefully considered each of your insightful comments and suggestions. These\npoints are highly valuable for further strengthening the manuscript, improving its\nlogical rigor, and enhancing its engineering relevance. We provide detailed point-\nby-point responses and corresponding revisions below.\nComment. 1: How is the optical to electronic coupling optimized? You mention\nthat the optical absorption length is ~mm, but are there other considerations?\nResponse：In this work, optoelectronic coupling primarily refers to the process\nof optical transmission and absorption within the semiconductor. Our design\nincorporates the following strategies:\n（1）Axial illumination: Lateral illumination may induce current crowding\nnear the electrode edges and increase the risk of localized breakdown. We\ntherefore adopt axial illumination combined with optimized electrode layout to\nachieve a more uniform carrier distribution and a better-controlled electric field.\n（2）Front-surface antireflection via AZO: A single-layer AZO (Al:ZnO)\ncoating is deposited on the SiC front surface. Using the transfer matrix method,\nthe optimal antireflection thickness is determined as d≈150nm. Both simulation\nand measurements confirm a theoretical transmittance of 98% and a measured\ntransmittance ≥95%, significantly reducing reflectivity and improving optical\ncoupling efficiency.\n（3）Beam shaping and spot-size matching: A collimation unit is attached to\nthe fiber output, forming a ~2 mm optical spot on the substrate surface, well\nmatched to the active region.\n（4）Trade-off between back-reflection and optical cavity design: We\ncompared single-pass reflection with short-cavity multiple-round-trip (fully-\ntrapped) configurations. With a cavity length of 5–10 mm, the trapped-cavity\nscheme increases the effective incident intensity by ~3–4× relative to single-pass\noperation. However, the associated round-trip delay (100–170 ps) introduces\ngroup-delay and saturation risks, which limit the high-frequency performance.\nTherefore, while a fully-trapped cavity benefits low-frequency power and energy\nutilization, the OEMS—prioritizing broadband response and waveform fidelity—\nadopts the single-pass reflection scheme.\nSection 3.3:\nThe optical coupling structure is illustrated in Fig. 4d. A comparison was\nconducted between a single-reflection configuration and a short-cavity, multiple-\npass design employing total internal reflection (Supplementary Note 7). For a\ncavity length of 10 mm, the total-internal-reflection scheme enhances optical\nintensity by a factor of 3.5 relative to single reflection. However, the associated\nround-trip delay of 170 ps introduces group delay dispersion and potential\nsaturation, thereby limiting the high-frequency response. Given the OEMS’s\nemphasis on broadband performance and waveform fidelity, the single-reflection\nconfiguration was selected. An AZO layer (150 nm thick), deposited on the front\nsurface of the SiC substrate, yields a theoretical optical coupling efficiency of 98%,\nwith an experimentally measured value of 95% (Fig. 4e). Under a substrate\nthickness of 1.5 mm and an N/V doping ratio of 0.4 (1×10¹⁷ / 2.5×10¹⁷ cm⁻³), the\naverage optical absorption is approximately 23% (Fig. 4f).\nTo improve readability, detailed derivations of the transfer matrix and optical\ncavity are moved to Supplementary Note 7, while the main text retains only the\ndesign principles and key numerical values.\nSupplementary Note 7：\nThe optical coupling structure of the PCSD consists of three layers:\n(1) air ( ),\n(2) an A\n𝒏𝒏\nl𝟏𝟏-d\n=\nop\n𝟏𝟏\ned ZnO (AZO) thin film ( , ,\n),\nand 𝒏𝒏𝟐𝟐 = 𝟏𝟏.𝟖𝟖𝟎𝟎𝟖𝟖+𝒃𝒃𝒌𝒌𝟐𝟐 𝒌𝒌𝟐𝟐 = 𝟎𝟎.𝟎𝟎𝟎𝟎𝟎𝟎 𝒅𝒅 =\n𝟏𝟏𝟎𝟎𝟎𝟎 𝒏𝒏𝒏𝒏\n(3) the SiC substrate .\nFor a laser waveleng\n(\nt\n𝒏𝒏\nh 𝟑𝟑o\n=\nf\n𝟐𝟐.𝟔𝟔𝟎𝟎)\n,\nthe total optical transmittance and\nreflectance at normal incidence are calculated using the transfer matrix method,\nλ = 1064nm 𝑻𝑻\nwhich accounts for interference in the AZO film and transmission into the SiC\n𝑹𝑹\nsubstrate.\nThe phase thickness of the AZO layer is expressed as\n2πn d\nδ= 2 ， （28）\nλ\nand the characteristic admittances (equivalent to refractive indices) are：\nq =n,q =n ,q =n . （29）\n0 1 2 2 s 3\nThe characteristic matrix of the AZO layer is\n i \ncosδ sinδ\n \nM = q . （30）\n 2 \n \niq sinδ cosδ \nand a substrate of admittance , the amplitude reflection t and transmission\n𝒒𝒒 co𝟎𝟎e fficients r are given by： 𝒒𝒒𝒃𝒃\nq M +q q M −M −q M\nr = 0 11 0 s 12 21 s 22 ， （31）\nq M +q q M +M +q M\n0 11 0 s 12 21 s 22\n2q\nt = 0 . （32）\nq M +q q M +M +q M\n0 11 0 s 12 21 s 22\nThe corresponding reflectance and transmittance are：\nn\nR=|r|2，T = 3 |t|2=n |t|2 (n =1). （33）\nn 3 1\nThe calculated dependence of AZO transmittance on film thickness is shown in\nFig. S11. The transmittance reaches maxima at d = nd its odd multiples;\nat d = 150 nm, the theoretical transmittance is 98%, and the measured value\n150 nm a\nexceeds 95%.\nTo evaluate the transient optical absorption coefficient and the total absorption\nof the SiC substrate, Eq. (34) - (36) were used. In the calculation, the fitted\nabsorption coefficient was set to , the surface reflectivity to\n−𝟏𝟏𝟏𝟏\n,\nand the AZO film thickness to 150 nm. The time-dependent absorption\n𝜶𝜶 = 𝟏𝟏×𝟏𝟏𝟎𝟎 𝑹𝑹 =\nprofile is shown in Fig. S12. With a bottom reflective layer, a 1.5-mm-thick VCSI\n𝟎𝟎.𝟎𝟎𝟎𝟎\n4H-SiC substrate exhibits an average optical absorption of approximately 23%.\nα=∑ n ⋅σ = N σ （34）\ni ij VA VAn\n (1−R)2exp(−2αd)\nR = R+  （35）\nΣ  1−Rexp(−2αd) \n(1−R)(1−e−2αd)\nA=1−R = （36）\nΣ 1−Re−2αd\nFig. S12 Time-domain evolution of the total optical absorption as a function of incident\nintensity 𝑨𝑨\nTwo optical-cavity configurations were evaluated: a single-pass reflection\ngeometry and an all-internal multiple-reflection cavity[S30]. For a cavity of length\n, the round-trip time is dt =2L/c, and the incident Gaussian pulse has a FWHM\nof 1.18 ns.\n𝑳𝑳\nLet denote the incident power in the single-pass configuration, and the\neffectiv 𝑷𝑷 e𝟏𝟏 accumulated incident power after reflections in the cavity (with 𝑷𝑷𝒏𝒏\napproaching the absorption limit). For cavity lengths of 5–10 mm, the total\n𝒏𝒏 𝒏𝒏 = 𝟐𝟐𝟎𝟎\naccumulated power increases by a factor of 3–4 compared to the single-pass\nscheme, while introducing 100–170 ps of optical delay (Fig. S13c).\nThus, the all-internal cavity is advantageous for enhancing low-frequency\noutput by reducing the on-state resistance but becomes detrimental for high-\nfrequency response due to the added group delay and saturation. For broadband\nand tunable operation, the single-reflection configuration offers the optimal trade-\noff.\nP =e−(x/0.5)2 （37）\nn n−1 cavity\nFig. S13 Optical cavity configurations and their performance. (a) Single-pass reflection\nconfiguration. (b) All-internal multiple-reflection cavity. (c) Influence of cavity length on\naccumulated incident power and optical delay in the all-internal cavity.\nReference：\n[S30] Wang L, Chu X, Yi M, Yao J, Xun T, Yang H. Vertical SiC Photoconductive Switch\nwith Axial Optical Internal Reflection Trap[J]. IEEE Transactions on Electron Devices,\n2022, 69(9): 5028~5034.\nComment. 2: By reducing the carrier lifetime you show that the device can have\nnearly flat gain over a broader frequency range, however the output power is\nreduced relative to a longer carrier lifetime. Are there ways to increase the output\npower while operating at small carrier lifetimes to further extend the tunability of\nthe OEMS?\nResponse：We thank the reviewer for raising this important point. A short\ncarrier lifetime broadens the frequency response and yields flatter gain, but also\nreduces steady-state carrier density and increases on-state resistance, thereby\nweakening load voltage division and decreasing output power. To simultaneously\nmaintain short lifetime and enhance output power, we propose three strategies\nfocused on increasing transient conductivity and reducing RF power loss. These\nare detailed in Supplementary Note 5.\n(1) Material engineering: enhancing transient conductivity under short carrier\nlifetime\n1) Increasing internal quantum efficiency. Preserving the carrier lifetime while\nincreasing the internal quantum efficiency leads to a corresponding increase in the\nmaterial conductivity. This requires maximizing the total N and V doping\nconcentration (with an equal or reduced N/V ratio) before reaching the solubility\nlimit, ensuring sufficient photo-excitable electrons. Higher conductivity increases\nthe OEMS broadband output power and raises the optical saturation threshold.\nThe impact of total doping concentration on the frequency–power characteristics\nis shown in Fig. S6a.\nThe solubility limit of V in SiC is – [S31], [S32]. Beyond\n𝟏𝟏𝟏𝟏 𝟏𝟏𝟏𝟏 −𝟑𝟑\nthis threshold, V-rich clusters form and may act as initiation points for micropipes\n𝟑𝟑×𝟏𝟏𝟎𝟎 𝟎𝟎×𝟏𝟏𝟎𝟎 𝐜𝐜𝐦𝐦\nand structural defects, while also introducing stress into the SiC lattice. In contrast,\nN exhibits much higher solubility (up to the range), making donor-level\n𝟏𝟏𝟏𝟏 −𝟑𝟑\nenhancement more readily achievable.\n𝟏𝟏𝟎𝟎 𝐜𝐜𝐦𝐦\n2) Introducing effective recombination centers. A second route is to increase the\nrecombination rate, transitioning the device from high low-frequency gain to a\nbroadband, flatter gain profile. Enhancing recombination requires trap centers\nwith large electron capture cross-sections. Beyond V acceptors, deep-level traps\nreported in 4H-SiC—such as Z1/Z2, EH3, and EH6/7—provide significantly\nlarger capture cross-sections (Table S3) [S33, S34].\nHigh-purity semi-insulating (HPSI) SiC studies show trap activation energies of\n0.55–1.65 eV and defect densities of – [S35], all exhibiting\n𝟏𝟏𝟎𝟎 𝟏𝟏𝟎𝟎 −𝟑𝟑\nacceptor-like electron trapping behavior. Tailoring SiC growth conditions\n𝟏𝟏𝟎𝟎 𝟖𝟖×𝟏𝟏𝟎𝟎 𝐜𝐜𝐦𝐦\n(temperature, Si/C ratio) offers a pathway to deliberately introduce intrinsic deep\nlevels for background-carrier capture [S36]. If similar traps could be incorporated\ninto V-doped SiC, the resulting recombination centers would offer improved\nelectron-capture capability. The influence of electron capture cross-section on\noutput power at fixed defect density is shown in Fig. S6b, demonstrating strong\npotential for improving high-frequency response.\nTable. S3 Energy levels and electron capture cross-sections of major electron traps in n-\ntype 4H-SiC [S33]\nTrap type Energy level below the conduction Electron capture cross-\nband（eV） section（cm2）\nEH1 0.36 10-15\nZ1/Z2 0.65 10-14\nEH3 0.79 10-14\nEH5 1 10-16\nEH6/7 1.48 10-14\nFig. S6 Influence of (a) total N/V doping concentration and (b) electron capture cross-section\non the frequency–power characteristic of the OEMS.\n(2) Increasing the nonlinearity threshold of voltage division: co-optimizing\nmaterial conduction and load impedance\nCurrent saturation in the present system is primarily governed by the voltage-\ndivision ratio between the photoconductor and the load. Simulations and\nmeasurements show that reducing the load resistance alone (with high on-state\nresistance) yields negligible power benefit, and increasing doping alone (with large\nload resistance) still results in saturation once entering the nonlinear division\nregion.\nSignificant improvement appears only when the on-state resistance is reduced\nbelow and the load resistance is co-optimized to below (Fig. S7–S8). This\nmotivates a sequential strategy: first minimize the on-state resistance via doping\n𝟎𝟎𝛀𝛀 𝟐𝟐𝟎𝟎𝛀𝛀\nand recombination optimization, then reduce the load resistance accordingly.\nBecause the series RC time constant τ = R C decreases with load\ncircuit load PCSD\nresistance, this approach also enhances the circuit bandwidth.\nFig. S7 Dependence of peak output power on the minimum SiC on-state resistance and the\nload resistance.\nFig. S8 Effective output power for different N/V doping ratios (corresponding to different on-\nstate resistances) and load-resistance values.\n(3) Extending electrode and transmission-link bandwidth\nThe circuit bandwidth can be expanded from 2 GHz toward ~4 GHz by\noptimizing both electrode geometry and the external RF path (Fig. S9). Key design\nprinciples include:\n1) Minimizing interstage capacitance by tailoring electrode area and substrate\nthickness, with stacked-electrode geometries as a possible solution [50].\n2) Optimizing the RF transmission structure to balance breakdown strength,\noutput power, and bandwidth, while suppressing parasitic elements to achieve\nefficient P–S-band transport. Reducing the effective shunt capacitance at the feed\nreduces reflections and supports a transmission bandwidth of ~4 GHz.\nReaching still higher frequencies (e.g., 10 GHz) requires transitioning from the\nvertical-electrode architecture to a planar configuration [51], which reduces\ninterelectrode capacitance and therefore raises the intrinsic response limit. The\ntrade-off is a lower breakdown strength due to increased susceptibility to surface\nflashover.\nFig. S9 Bandwidth extension enabled by RF-transmission-path engineering.\nThe corresponding revisions are also reflected in Section 3.3 and Fig. 4 of the\nrevised manuscript:\nFurthermore, several strategies can effectively facilitate frequency extension in\nregimes with short carrier lifetimes. First, optimizing doping levels and\nintroducing efficient recombination centers enhance transient photoconductivity\nand improve high-frequency response. At a fixed concentration, recombination\ncenters with larger electron capture cross-sections can significantly enhance the\ndevice’s high-frequency performance (Fig. 3f). Second, device design should\nsimultaneously increase the overall doping concentration to reduce conduction\nresistance and minimize load impedance, thereby enhancing power output (Fig.\n3g). Finally, optimizing the external electrode layout and RF transmission pathway\ncan further extend the circuit bandwidth into higher frequency regimes [50, 51].\nFurther technical details are provided in Supplementary Note 5.\nReference：\n[S31] M. Bickermann et. al., “Incorporation of boron and vanadium during PVT growth of 6HSiC\ncrystals”, Journal of Crystal Growth, Vol. 233, pp. 211 – 218, 2001\n[S32] J. R. Jenny, et. al., “Deep level transient spectroscopic and Hall effect investigation of the\nposition of the vanadium acceptor level in 4H and 6H-SiC”, Applied Physics Letters, Vol. 68, Issue 14,\npage 1963, 1996\n[S33] S. Sasaki, K. Kawahara, G. Feng, G. Alfieri and T. Kimoto, “Major deep levels with the same\nmocrostructures observed in n-type 4H-SiC and 6H-SiC”, Journal of Applied Physics, Vol. 109, Paper\n013705, 2011\n[S34] C. Longneaud, J. Kleider, P. Kaminski, R. Koslowski and M. Miczuga, “Characterization of\nthe defect levels in semi-insulating 6H-SiC by means of photoiinduced transient spectroscopy and\nmodulated photocurrent technique”, Journal of Physics: Condensed Matter, Vol. 21, Paper 045801,\n2009\n[S35] W. C. Mitchel, et al, “Compensation mechanism in high purity semi-insulating 4H-SiC’,\nJournal of Applied Physics, Vol. 101, Paper 053716, 2007\n[S36] Hiromi Kaneko, Tsunenobu Kimoto. Formation of a semi-insulating layer in n-type 4H-SiC\nby electron irradiation[J]. Applied Physics Letters,2011,Vol.98(26): 262106-262106(3).\n[50] Linglong Zeng, Xinyue Niu, Fuyin Liu, et al. “Dual-Stacked SiC Vertical Photoconductive\nSwitch for Modulation Bandwidth Extension of Frequency-Agile Power Microwave”[J]. IEEE\nElectron Device Letters,2024,Vol.45(6): 992-995.\n[51] Chu, Xu, He, et al. Wide-range Frequency-Agile Microwave Generation up to 10 GHz based\non Vanadium-compensated 4H-SiC Photoconductive Semiconductor Switch[J]. IEEE Electron\nDevice Letters,2022,Vol.43(7): 1.\nComment. 3: For the phase array application you discuss timing jitter, and so it\nis maybe related, but can you discuss how the phase noise from the OEMS. For\napplications like datacomm, will this have noticeable affects?\nResponse：We appreciate the reviewer’s suggestion regarding phase-noise\ncharacterization. Due to the very low duty cycle of our system (repetition rate ~100\nHz, pulse width ~100 ns), commercial phase-noise analyzers (e.g., R&S FSWP-26)\ncannot be directly applied because they require a duty cycle ≥0.01% [S28].\nTherefore, we adopt the modified phase-error power spectrum method [S29],\nusing the zero-crossing time-jitter sequence to evaluate the phase-noise\ncharacteristics.\nDetails are provided in Supplementary Note 17：\nTo evaluate phase noise at low duty cycles, we introduce a modified phase error\npower spectrum concept [S28, S29], discuss its theory and model, validate the\naccuracy of the “time-domain to frequency-domain” inversion, and then calculate\nthe phase error power spectrum based on the signal’s time jitter sequence. Finally,\nwe analyze the phase noise characteristics of the signal.\n（1）Theory and Model of the Modified Phase Error Power Spectrum\nLetτ represent the zero-crossing time of the n-th signal transition. Ideally,\nn\nτ =nT /2, where T =2π/ωis the nominal period of the oscillating signal. Phase\nn 0 0 0\nerror causes a deviation of the zero-crossing from the ideal position, and the actual\nzero-crossing time can be rewritten as:\nφ(τ )\nτ =nT /2+∆τ ，∆τ =− n （45）\nn 0 n n ω\n0\nwhere ∆τ is the deviation from the ideal zero-crossing time, which is\nn\nproportional to the phase errorϕ(τ ) at the sampling pointτ , known as absolute\nn n\njitter or aperture jitter.\nLet the total measurement time be , the signal frequency be f , and the zero-\n0\ncrossing sampling rate be 2f . The two-sided time-averaged power spectrum of\n0 𝑻𝑻\nphase error, S (f), is defined as:\nφφ\n T 2 ∞ 2 f\nS φφ (f)=   T li → m ∞ T 0 ∑φ T (τ n )e−j2πfnT 0 , f < 2 0 ， （46）\n\n\nn=−∞\n0，otherwise\nand the single-sided time-averaged power spectrum of phase error S (f) is\nφ\ndefined as:\nS (f)=2S (f)， f ≥0. （47）\nφ φφ\nThe modified phase error power spectrum L(f) is defined as follows (and\ncorresponds to the output of laboratory phase-noise measurement instruments):\nφ\n(zero-crossing error). A more intuitive expression of absolute time jitter and phase\nnoise is:\n1 f\nσ 2 = ∫ 0S (f)df （49）\nabs w 2 0 φ\nsampling, zero-crossing detection, frequency spectrum inversion, and time jitter\nquantization, reflecting the distribution of phase noise components in the input\nsignal’s frequency domain.\nThe calculated results are shown in the figure below. The input signal is a\nsinusoidal signal with 100 MHz phase noise, and the red circles correspond to the\nnoise frequency positions calculated from the time error sequence.\nFig. S32 Time error sequence and phase noise calculation results.\nThe random drift within the measurement window (8.33 ns) weakens the\nspurious peak at 120 MHz, and the main peak of the noise spectrum smoothly\nunfolds at the set frequency of 100 MHz, with a reduced attenuation rate as\nfrequency increases. This single-point noise analysis provides a reference for the\nactual noise distribution.\nTable. S6 Model Parameter Settings\nMeasurement Phase Noise Time Error (ps)\nWindow Width Measurement\nWindow Drift Amplitude\n(ns) Pulse Count\n(rad) (Normalized)\n0.4π 8.33 200 0.02/2π 10\n（2）Oscilloscope Background Noise Influence\nThe modulation signal from the electro-optic modulator (EOM) is a continuous\nwave output with good phase stability in the initial signal, as shown below.\nComparison results show that the time jitter measured by the FSWP-26 is 173 fs,\nwhile the oscilloscope measures 538 fs, indicating that the oscilloscope introduces\nbackground noise of several hundred femtoseconds during the measurement. The\nactual signal time jitter is therefore smaller than the oscilloscope's measured value.\nFig. S33 (a) Phase noise of the EOM measured by the FSWP-26, (b) Time jitter sequence\nmeasured by the oscilloscope.\n（3）Time Jitter Sequence and Phase Noise Power Spectrum of the Signal\nThe signal modulation frequency is set to 2 GHz, with a measurement window\nwidth of 8.33 ns. The measurement results are shown in Fig. S34(a)-(c). From the\ncalculated phase noise power spectral density , a comb-like structure is\n𝑳𝑳(𝒇𝒇)\nobserved with approximately 120 MHz spacing, which is caused by frequency-\ndomain periodic aliasing effects due to the 8.33 ns sampling window. The output\nsignal peaks at 87 MHz, indicating the presence of the dominant spurious noise at\namplitude becomes slower compared to Fig. S32(c), indicating the presence of\nother dispersed noise within the 1 GHz range. Additionally, the noise level in the\n1–2 GHz range increases by approximately 10 dBc/Hz compared to Fig. S32(c),\nwhich corresponds to white noise introduced by the actual signal and the\nmeasurement process.\nFig. S34 (a) Actual measured waveform, (b) Time error sequence, (c) Predicted phase noise\nresults.\nThe signal stability places high demands on the consistency of the\nsynchronization trigger circuit. Measurements show that the pulse width jitter of\nthe trigger signal controlling AOM modulation and the subsequent amplification\nis approximately 26.64 ps (multiplicative term, not contributing to signal phase\njitter). This trigger jitter directly affects the first and last sub-pulse waveforms of\nthe signal and indirectly influences the phase stability of the output signal in the\nvery low-frequency range. When stricter consistency is required, further\noptimization of the timing stability of the trigger circuit is necessary.\nIn summary, the measured 11 ps is the absolute time jitter, and the \"modified\nphase noise power spectrum\" concept is used, with an integration frequency range\nof (0, 2 GHz]. The output signal achieves a peak at 87 MHz (<-85 dBc/Hz), which\noriginates from active device noise in the optical amplifier chain and trigger\njitter from the synchronized drive signal. A comparison of the phase noise\ncharacteristics of our system and optical microwave technology is shown in Table\nS7. The noise in the hundred MHz range limits the system’s noise performance,\nwhich may restrict applications such as data communication. Future work will\nfocus on reducing phase noise in the hundred MHz range.\nTable. S7 Comparison of Phase Noise in Optical Microwave Technology\nGeneration Method Phase Noise (dBc/Hz)\nDistributed-feedback (DFB) laser -80@10kHz，\n[S37] -109@100kHz\nBeating\nDual-frequency Er:Yb:glass laser\nmethod -100@10kHz\n[S38]\nNd:YAG solid-state laser [S39] -90@10kHz\n-160@10kHz\nOptoelectronic oscillator (OEO) [S40-S42] -129@10kHz\n-101@10kHz\nOur work <-85 dBc/Hz@87MHz\nThe key results appear in Section 3.5 and Fig. 6 of the revised manuscript:\nIn large-scale array power synthesis, the standard deviation of time jitter is a\ncritical performance metric and is determined by the stability of the trigger laser.\nTo achieve synthesis efficiency above 95% at 2 GHz, the time jitter must remain\nbelow 20 ps (Supplementary Note 16). The 2 GHz optical signal was characterized\nwithin an 8 ns amplitude-flat region (Fig. 6a). As shown in Fig. 6b, at an optical\nenergy of 24 mJ, the time jitter of the optical signal is 11 ps, meeting the phase-\ncontrol requirements for efficient array synthesis. By applying an FFT to the\nabsolute time-jitter sequence, the modified phase-noise power spectrum over the\n(0, 2 GHz] range was obtained (Supplementary Note 17), and the relationship is\nexpressed as σ 2 =1/w 2∫\nf02L(f)df\n. As shown in Fig. 6c, periodic spurious peaks\nabs 0\n0\nintroduced by the measurement window appear at 120 MHz and its harmonics,\nwhile the noise spectrum exhibits <−85 dBc/Hz near 87 MHz. This noise is\nattributed to active-device noise within the optical amplification chain and trigger\njitter from the synchronized driving signals. Future work will focus on reducing\nphase noise within the sub-100 MHz region.\nReference：\n[S28] R&S FSWP Phase Noise Analyzer and VCO Tester Specifications, 6th ed., Rohde & Schwarz\nGmbH & Co. KG, Munich, Germany, 2024, p. 31.\n[S29] Galton, Ian, Weltin-Wu, et al. Understanding Phase Error and Jitter: Definitions,\nImplications, Simulations, and Measurement[J]. IEEE Transactions on Circuits & Systems, 2019,\nVol.66(1): 1-19.\n[S37] Kittlaus, Eric A.CAa,Eliyahu,et al. A low-noise photonic heterodyne synthesizer and its\napplication to millimeter-wave radar[J]. Nature Communications, 2021, Vol.12(1): 4397.\n[S38] Alouini, M., Benazet,et al. Offset phase locking of Er,Yb:glass laser eigenstates for RF\nphotonics applications[J]. Photonics Technology Letters, IEEE, 2001, Vol. 13(4): 367-369.\n[S39] L. Goldberg,R.D. Esman,K.J. Williams. Generation and control of microwave signals by\noptical techniques[J]. IEE Proceedings. Part J: Optoelectronics, 1992, Vol. 139(4): 288-295.\n[S40] Eliyahu, Danny,Seidel,et al. Phase noise of a high performance OEO and an ultra low noise\nfloor cross-correlation microwave photonic homodyne system[J]. 2008 IEEE International Frequency\nControl Symposium, FCS, 2008, 811-814.\n[S41] Tang H, Yu Y, Zhang X. Widely tunable optoelectronic oscillator based on selective parity-\ntime-symmetry breaking[J]. Optica, 2019, 6(8): 944-950.\n[S42] G. K. M. Hasanuzzaman, Stavros Iezekiel, Atsushi Kanno. W-Band Optoelectronic\nOscillator[J]. IEEE Photonics Technology Letters, 2020, Vol. 32(13): 771-774.\nComment. 4: Since the optical to electrical conversion occurs during the\nduration of the pulse, how do you characterize the ~1MW output power – is the\npulse duration and repetition rate considered? How does the system function with\na CW optical signal? Can you modify the design to accommodate CW light?\nResponse： We thank the reviewer for the careful attention to power\ncharacterization. We have explicitly distinguished between peak power and intra-\npulse average power and have clarified the adaptation scheme for continuous-\nwave (CW) operation.\nRevisions related to power characterization appear in Section 3.4:\nFigure 5a presents the time-domain output waveforms of the OEMS. Under a\nbias voltage of 22 kV and a trigger energy of 30 mJ (Supplementary Note 11), the\nmicrowave pulse at 1 GHz exhibits a peak power of 1.36 MW and an intra-pulse\naverage power of 0.68 MW (Supplementary Note 12). The pulse width is 30 ns,\nwith a repetition rate of 100 Hz.\nAdditional details provided in Supplementary Note 12:\nFig. S18. Test link and actual test scene photo.\nPrior to testing, both the coaxial–waveguide directional coupler and the\nbroadband attenuator were calibrated to determine the total voltage attenuation\nof the measurement chain k . Based on the calibrated attenuation, the actual peak-\nv\nto-peak output voltage of the PCSD was obtained using Eq. (40), and the\ncorresponding peak mic𝑽𝑽ro𝐩𝐩w−𝐩𝐩ave power —defined as the “peak power’’ in this\nwork—was calculated using Eq. (41)𝑷𝑷 [𝐩𝐩1𝐩𝐩7𝐥𝐥𝐩𝐩]. Considering the root-mean-square\nvalue of the pulse, the intra-pulse average power was derived from Eq.\n(42). 𝑷𝑷𝐦𝐦𝐒𝐒𝐜𝐜𝐦𝐦𝐥𝐥𝐦𝐦𝐥𝐥𝐦𝐦𝐩𝐩\nV\np−p\n=V\ntest\n×k\nv\n（40）\nP = (V / 2)2 / R\npeak P−P load\n（41）\nP = P /2 （42）\nmicrowave peak\nThe nominal and calibrated parameters of the test link are summarized in Table\nS5, yielding a total attenuation of 82.68 dB. The oscilloscope measured a peak\nvoltage of 605 mV (1.21 V peak-to-peak at 1 GHz). Because all components in the\nchain have an input impedance of 50 Ω, R =50 Ω. Substituting these values into\nload\nEqs. (40)–(42) gives P =1.36 MW@1 GHz，P =0.68 MW@1 GHz。The\npeak microwave\npulse width was 30 ns with a pulse interval of 10 ms (repetition rate 100 Hz), as\nshown in Fig. S19.\nTable. S5 Nominal and calibrated parameters of components in the measurement chain\nDevice Model Nominal Nominal Measured Input\nFrequency Attenuation Attenuation Impedance\n(GHz) (dB) (dB) (Ω)\nDirectional DTO-\n0.3-2.4 40±1.8 40.77@1GHz 50\nCoupler 300/2400-40H\nAttenuator PDTS100-40-\nDC-4 40±1 40.34@1GHz 50\n-- -- -- 1.57 50\nConnectors\nOscilloscope Lecroy\nWaverunner DC-4 -- -- 50\n9404M\nTotal -- -- -- 82.68 --\nFig. S19 Measurement of pulse repetition rate (screenshot of the oscilloscope display).\nThe definitions of and do not incorporate the pulse duration or\nrepetition rate, as th\n𝑷𝑷\ne 𝐩𝐩i𝐩𝐩n𝐥𝐥t𝐩𝐩ent h\n𝑷𝑷\ner𝐦𝐦e𝐒𝐒 𝐜𝐜i𝐦𝐦s𝐥𝐥 𝐦𝐦to𝐥𝐥 𝐦𝐦c𝐩𝐩haracterize the maximum instantaneous\noutput capability of the system. Nevertheless, pulse width and repetition frequency\nremain key performance parameters. Although the OEMS offers some degree of\ntunability (e.g., via the AOM), further optimization is required to achieve higher\nrepetition rates and broader pulse widths—an important direction for future\ndevelopment.\nCW operation is described as a potential extension of the OEMS, as clarified in\nSection 3.4 of the revised manuscript.\nThe system presented here is designed to demonstrate its maximum\ninstantaneous output capability and therefore operates in pulsed mode.\nAdaptation to continuous-wave (CW) operation can be achieved by reconfiguring\nthe optical source. By replacing the pulsed LD with a CW laser, the MOPA-based\narchitecture is able to generate stable continuous microwave output\n(Supplementary Note 19). Although the maximum power in CW mode is lower\nthan that in pulsed operation, power scaling can be realized through multi-channel\nsynthesis, enabling broader application potential.\nFurther technical details are provided in Supplementary Note 19:\nThe photoconductive conversion process is governed by a linear mapping\nprinciple; therefore, replacing the pulsed laser with a continuous-wave (CW)\nsource enables continuous microwave generation. The MOPA (master oscillator\npower amplifier) configuration used in this work (pulse width: 10–100 ns, peak\npower: MW level) is readily adaptable. To verify pulse-width tunability, we\nmeasured the output waveform and spectrum under a 90-ns optical trigger pulse\n(Fig. S36a,b). By adjusting the AOM pulse width and the pumping parameters of\neach amplification stage, the optical pulse width can be extended by orders of\nmagnitude. For example, in our previous work, we demonstrated a 1-GHz, 1.15-\nμs MOPA laser output (Fig. S36c,d), where the peak power decreased to 300 kW\n[39].\nFig. S36 (a)Output signal waveform and (b) spectrum at a 90-ns optical pulse width. (c)\nOptical waveform and (d) spectrum of a 1-GHz, 1.15-μs MOPA laser output [39].\nThe specific modification scheme for CW operation is as follows: replace the\npulsed LD with a CW laser source, and re-optimize the pump parameters of each\nstage to maintain sufficient gain. The control architecture can be simplified by\nremoving the AOM, as CW operation no longer requires envelope modulation.\nAlthough the maximum CW power is lower than in pulsed mode, it can be\nincreased through multi-stage amplification and beam combining.\nReference：\n[17] B. James, S. Edl, S. J. Coty, S. J. A., and Z. Peng, Eds., High Power Microwaves. New\nYork: Taylor & Francis Group, 2024.\n[39] Yanran Gu,Xinyue Niu,Fuyin Liu, et.al., High-power microsecond ultraviolet burst-\nmode pulse laser with a rectangular envelope and GHz-adjustable intra-burst pulses[J]. High\nPower Laser Science and Engineering,2025,13(2): 89-97.\nComment. 5: Results are shown for amplification of single tone RF waveforms.\nIs the output affected if the RF signal to be amplified has a nonzero bandwidth,\nfor ex: 500MHz center frequency and 500MHZ bandwidth signals.\nResponse：The system is not significantly affected. The key reason is that the\noptoelectronic conversion relies on a linear photoconductive semiconductor\nmechanism, analogous to a standard photodetector, where the output RF\nwaveform faithfully reproduces the input optical waveform within the device\nbandwidth. The upper frequency limit is jointly determined by the material\nresponse (e.g., carrier lifetime) and the circuit bandwidth (e.g., parasitic elements).\nWithin the measured 3-dB bandwidth of 0.2–1.5 GHz, the system supports\nwaveform and spectrum customization, enabling broadband signal generation.\nTo verify this behavior intuitively, we provide an example of the combined\noutput under dual-channel optical triggering. The output signals exhibit center\nfrequencies of 168.8, 190.0, 225.0, 275.0, and 525.0 MHz, with corresponding 3-dB\nbandwidths of 237.5, 286.8, 339.9, 455.8, and 958.2 MHz. The results show that\neven for signals with a center frequency of 500 MHz and a bandwidth of 900 MHz,\nthe measured spectrum remains highly consistent with the simulated target\nspectrum. In future work, we will further expand the system bandwidth to support\neven wider-band excitation.\nFig. R1 (a) Waveform and (b) spectrum of the ultra-wideband signal generated through push–\npull combining.\nComment. 6: How do you characterize and control nonlinear affects especially\nat such high RF powers?\nResponse： At MW-level output power, nonlinear effects indeed require careful\ncharacterization and suppression, and we appreciate the reviewer’s emphasis on\nthis point. We performed a systematic analysis of the nonlinear mechanisms\narising from both the optoelectronic conversion stage and the laser amplification\nstage, identifying five contributing factors—voltage-division nonlinearity, carrier-\nlifetime effects, optical/electrical saturation, parasitic circuit parameters, and\nlaser-source nonlinearities—and we propose corresponding mitigation strategies.\nRevisions related to power characterization appear in Section 3.4:\nAt megawatt output levels, potential sources of harmonic or nonlinear\ncontributions include the voltage-division network, carrier dynamics in the\nmaterial, parasitic circuit elements, and optical/electrical saturation effects.\nAmong these, series load division is currently the most probable origin of\nharmonic generation. Material doping and device-level parasitics may introduce\nfrequency-dependent nonlinearities in the output voltage. Additionally, when the\nincident optical energy exceeds 12 mJ within a 10 ns pulse and the bias field\nsurpasses 30 kV/mm, nonlinear phenomena such as optical saturation and carrier\nvelocity saturation are expected to become prominent. In the current OEMS\nsystem, however, both the optical power and electric field strength operate within\nthe linear regime. Detailed saturation thresholds are provided in Supplementary\nNote 14.\nSupplementary Note 14:\n(1) Nonlinearity introduced by the series voltage-division circuit\nAfter optical excitation, the photogenerated carrier concentration\nconsists of a unipolar sinusoidal component superimposed on a DC offset\n𝒏𝒏\n(𝒔𝒔F\n(\nt\ng\n)\n.\nS22a), indicating that the photoconductive conversion process itself does not\nintroduce nonlinearities. However, second-order harmonics appear in the output\nafter passing through the series load (Fig. S22b), demonstrating that high-order\nspectral components arise primarily from the voltage-division process rather than\nfrom the material's photoelectric response.\n1\n∝n ∝ P (43)\nR e optic\nSiC\nV =U ⋅R /(R +R ) (44)\nout bias load load SiC\nFig. S22 Frequency spectra of the carrier concentration and the OEMS output.\nAs shown in Fig. S23a, further reducing the on-state resistance below 5 Ω yields\nnegligible improvement in output power, revealing a strong nonlinear dependence\nbetween and the output voltage. This nonlinearity threshold can be reduced by\nlowering\n𝑹𝑹\nth𝐥𝐥𝐨𝐨e load resistance. Fig. S23b compares the spectral amplitude at the\nfundamental frequency with the peak-to-peak output voltage, showing close\nagreement and confirming that harmonic components contribute minimally to the\npower at the target frequency.\nFig. S23 (a) Relationship between minimum on-state resistance and maximum output\nvoltage. (b) Effect of load resistance on the spectral amplitude at the target frequency.\n（2）Influence of carrier lifetime (doping ratio)\nFor a 30 ns pulse width and a 1 GHz modulation frequency, the output voltage\nexhibits nonlinear growth with increasing N/V doping ratio under weak optical\nexcitation and low bias. A ratio of 0.4 was selected to maximize the output voltage\nacross the 0–2 GHz operating band.\nFig. S24 Effect of doping ratio on the peak-to-peak output voltage and spectral content.\n（3）Effects of optical saturation and high-field velocity saturation\nUnder strong optical excitation or high bias, the SiC resistance becomes a\nnonlinear function of both incident optical power and electric field strength. These\nnonlinearities are examined in this section.\nAs shown in Fig. S25a, when the incident optical energy exceeds ~100 mJ/10 ns,\nthe carrier concentration enters a nonlinear regime and gradually saturates. The\noutput voltage exhibits even earlier nonlinearity: deviations begin at ~12 mJ/10 ns\nand saturate above 15 mJ/10 ns (Fig. S25b,d). Spectral analysis (Fig. S25c) reveals\na significant increase in third-order harmonics above 20 mJ/10 ns, explaining the\ndivergence between peak-to-peak voltage and the amplitude of the fundamental\nspectral component in the saturation regime. In this work, a 30 mJ/30 ns optical\npulse is used, ensuring that the carrier response remains in the linear region.\nFig. S25 Effects of trigger-light intensity on (a) carrier concentration, (b) output waveform,\n(c) output spectrum, and (d) normalized fundamental-frequency amplitude vs. peak-to-peak\nvoltage.\nElectron mobility determines the material conductivity and decreases under\nstrong electric fields, approaching velocity saturation at fields above 20 kV/mm\n(Fig. S26a). During device conduction, the internal field is small and mobility\nremains high, supporting large conduction currents. In the off-state, a high\ninternal field suppresses leakage current due to reduced mobility. Increasing the\nfield strength thus improves RF electrical efficiency (output voltage normalized by\nbias voltage), as shown in Fig. S26b,c. Above 20 kV/mm, both carrier velocity and\noutput voltage become nonlinear; therefore, the optimal operating field should\nremain below 30 kV/mm.\nFig. S26 Effects of bias field on (a) electron mobility and velocity, (b) normalized output\nvoltage, and (c) output waveform.\n（4）Influence of parasitic parameters\nAn increased interstage capacitance reduces output amplitude, while the circuit\ninductance exhibits an optimal value that maximizes the output (Fig. S27). For the\n1.5-mm-thick SiC substrate used in this study, the measured interstage\ncapacitance is 1.5 pF and the fitted parasitic inductance is 10 nH. Further\noptimization of the RF structure is expected to reduce parasitic effects and\npreserve linearity at higher frequencies.\nFig. S27 Effects of interstage capacitance on (a) output waveform and (b) spectrum, and effects\nof circuit inductance on (c) waveform and (d) spectrum.\n（5）Nonlinearities from the laser source: pulse energy and envelope distortion\nThe cascaded fiber–solid-state laser amplifier exhibits nonlinear behaviors in\npulsed operation, including stimulated Raman scattering (SRS), stimulated\nBrillouin scattering (SBS), and gain-induced envelope distortion.\n1）SRS nonlinearity\nOnce the output power exceeds the SRS threshold, energy transfers from the\nsignal to Raman Stokes components, limiting further power scaling. SRS has\nminimal impact on temporal waveform quality but reduces usable energy.\nExperimentally, SRS was observed near 1120 nm; its threshold increases with\nlarger fiber core diameters and shorter fiber lengths. For a 30 µm core and 2.8 m\nfiber length, the SRS threshold reaches ~120 kW. A 2 nm bandpass filter is inserted\nin the system to suppress SRS components.\n2）SBS nonlinearity\nSBS is the primary limitation for further power scaling of the pulse-cluster laser.\nStep-wise optimization of fiber core diameter and length was used to mitigate SBS\nwhile maintaining increasing pulse energy. The modified SBS threshold model\n[S44] indicates that larger cores and shorter fibers increase the threshold. For\nfixed fiber length, decreasing pulse width and repetition rate also increases the\nSBS threshold.\n3）Gain saturation and envelope distortion\nGain saturation distorts the temporal envelope, which directly affects the\nexpected modulation spectrum (Fig. S28).\nFig. S28 (a) Optical waveforms with different envelopes under the same optical power. (b)\nExample of a carrier-modulated optical waveform. (c) Optical signal spectrum. (d) Magnified\nview of the optical spectrum.\nThe leading edge of the pulse depletes the population inversion most strongly,\nreceiving higher gain and causing asymmetry. In gain fibers, the extractable stored\nenergy is typically ~10× the saturation energy [S45], and the total extractable\nenergy is determined by the stored energy minus the signal gain threshold .\nFor fib\n𝑬𝑬\ner𝐩𝐩s𝐞𝐞 𝐞𝐞with 20/125, 25/250, and 30/250 µm core/cladding diameters,\n𝑬𝑬\nth𝐞𝐞𝐭𝐭e\nextractable energies are 1.65, 2.57, and 3.71 mJ, respectively.\nEnvelope pre-compensation can suppress distortion and restore a near-square\noptical waveform. Using an AOM in the seed-laser stage, a pre-shaped envelope is\ngenerated via a stochastic parallel gradient descent (SPGD) algorithm.\nRepresentative waveforms before and after pre-compensation, as well as the\ncorresponding amplified output, are shown in Fig. S29. Higher-power operation\nwill require more accurate gain-saturation modeling or additional AOM stages.\nFig. S29 (a) Distorted amplifier output, (b) computed transfer function , (c) pre-\ncompensated seed waveform, and (d) compensated amplified output [S1]. 𝑮𝑮(𝒕𝒕)\nReference：\n[S43] Ranaud C C, Offerhaus H L, Alvarez-Chavez J A, et al. Characteristics of Q-switched\ncladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs[J].\nIEEE Journal of Quantum Electronics, 2001, 37(2): 199-206.\n[S44] Long Huang, Lei Li, Pengfei Ma, Xiaolin Wang, and Pu Zhou, 434 W all-fiber\nlinear-polarization dual-frequency Yb-doped fiber laser carrying low-noise radio frequency\nsignal[J]. Opt. Express 24, 26722-26731 (2016)\n[S45] Wang Y, and Po H. Dynamic Characteristics of Double-Clad Fiber Amplifiers for\nHigh-Power Pulse Amplification [J]. Journal of Lightwave Technology, 2003, 21(10): 2262–\n2269.\n[S1] Xuan He, Bin Zhang, Shuailin Liu, Linyong Yang, Jinmei Yao, Qilin Wu, Yuxin Zhao,\nTao Xun, Jing Hou, High-power linear-polarization burst-mode all-fibre laser and\ngeneration of frequency-adjustable microwave signal[J]. High Power Laser Sci. Eng. 9,\n02000e13 (2021)"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have substantially revised the manuscript, to my satisfaction. While I think that the draft remains a bit to dense, it is now much more complete and readable.\nI now recommend publication.", "reviewer_2": "The authors have very clearly addressed my comments. The changes they've implemented to the main manuscript and supplemental information enhance the clarity and broaden the scope of their work. For these reasons I believe this manuscript is well suited for publication in its current form."}, "author_response": ""}]

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