Monolithic lithium niobate photonic chip for efficient terahertz-optic modulation and terahertz generation

Domain: physics
Published: 2025-11-24
Editorial outcome: major_revision

Abstract
The terahertz (THz) range, bridging microwave and infrared frequencies, enables advanced imaging, sensing, communications, and spectroscopy. Analogous to microwave photonics, terahertz photonics offers a promising optical solution to critical THz challenges-THz-optical interfacing, including THz-optic modulation and optical generation of THz waves. We address these with a monolithic integrated photonic chip enabling efficient THz-optical bidirectional interaction. Leveraging strong second-order optical nonlinearity and optical/THz confinement in thin-film lithium niobate on quartz, the chip supports efficient THz-optic modulation and continuous THz generation up to 500 GHz. The measured continuous wave THz generation efficiency of 4.8×10−6/W at 500 GHz also marks a tenfold improvement over existing lithium niobate-based tunable THz generation devices. We further leverage the coherent nature of the optical THz generation process and on-chip modulators to realize 65 GHz high-speed electro-THz modulation. The chip-scale THz-photonic platform enables more compact, efficient, and cost-effective THz systems for communications, sensing, and spectroscopy.

Introduction
Terahertz (THz) wave, spanning 0.1–10 THz in the electromagnetic spectrum, is increasingly recognized for its potential applications across diverse fields, including high-speed wireless (6G) communications1, medical imaging2, chemical identification3, THz radar4, and THz time-domain spectroscopy5. However, current THz technology still faces critical challenges, including the lack of efficient THz emitters and detectors, excessive loss in cables and electronic devices at high frequencies, and difficulties in achieving more compact and integrated THz devices and systems6. THz photonics, drawing inspiration from microwave photonics, could potentially provide a compelling solution to these challenges by generating, transmitting, and processing THz signals in the optical domain7. This is because photonic systems typically feature low transmission loss, no inherent gain-bandwidth limitations, and convenience for large-scale integration8. Central to such THz photonics systems are THz-optic modulators that coherently convert THz signals into the optical domain and optical generation of THz waves for conversion back to THz frequencies. Importantly, such coherent and bidirectional conversion processes allow the use of low-cost and versatile optical techniques and instruments like lasers, modulators, and fibers for the currently challenging tasks of control, manipulation, and transmission of THz signals.

On the THz-optic modulation front, traditional electro-optic modulator platforms, such as silicon (Si)9, indium phosphide (InP)10, and bulk lithium niobate (LiNbO3, LN), face significant challenges in achieving modulation frequencies beyond 100 GHz. Recently, modulators based on electro-optic polymers have reported bandwidths significantly exceeding 100 GHz with the assistance of plasmonic11 or silicon-slot12 waveguides. They also feature reduced footprints due to enhanced light-matter interaction. However, these modulators usually exhibit significant optical losses (0.4-0.5 dB/µm in plasmonic and 40 dB/cm in slot structures) and limited power handling capabilities11–13. Intrinsically, LN is an excellent material for THz-optic modulation due to its large and almost instantaneous electro-optic response (r33 = 30.8 pm/V), high optical damage threshold, and low optical losses14. However, traditional bulk LN modulators are typically limited to bandwidths around 35 GHz due to their long device lengths, leading to exacerbated RF loss at increased frequencies15. The thin-film LN (TFLN) platform has recently emerged as a promising candidate to achieve ultrabroad-band modulators thanks to the dramatically improved electro-optic efficiencies in high-confinement waveguides and much reduced RF loss. Further combining electro-optic modulators with other high-performance functional devices on the same TFLN platform, including high-quality (Q) resonators16,17 and frequency combs18 as well as low-loss delay lines19, has led to the realization of ultrahigh-speed and low-power microwave photonics20. Such TFLN microwave photonics systems could be readily extended to the THz range if efficient THz-optic modulation could be achieved. Currently, many state-of-the-art TFLN modulators can support 3 dB bandwidths beyond 100 GHz21–28, in particular those with advanced capacitively loaded electrodes26,27 for more flexible control of RF velocity and loss. Yet very few of them have experimentally validated performances deep into the THz bands due to difficulties associated with measurements at ultrahigh frequencies23. Our previous work has demonstrated an RF Vπ of 7.3 V at 250 GHz, which, however deteriorates quickly beyond this frequency and would have extrapolated to around 28 V at 500 GHz, mainly due to substantial transmission line losses and residual velocity mismatch at ultrahigh frequencies29. In short, challenges persist in achieving efficient modulation and low RF Vπ in the THz band, especially above 300 GHz.

On the THz generation front, various optical methods have been proposed and demonstrated. The difference frequency generation (DFG) method, which involves mixing two optical signals separated by the desired THz frequency via a second-order (χ(2)) nonlinearity, is particularly interesting for THz photonics since it allows a seamless and coherent conversion between optics and THz. Among various χ(2) nonlinear material platforms, such as LN30–37, gallium phosphide (GaP)38, gallium arsenide (GaAs)39, zinc telluride (ZnTe)40, gallium selenide (GaSe)41, and zinc germanium phosphide (ZGP)42, LN stands out with its large χ(2) coefficients, relatively high optical damage threshold, and ultra-low optical absorption in the near-infrared spectral range. Most of these devices make use of pulsed optical input to increase the instantaneous pump power and produce pulsed THz radiation31–34, which is ideal for ultrafast imaging and time-domain spectroscopy. However, many other applications, such as 6G wireless communication and biomedical imaging, necessitate continuous THz wave sources for uninterrupted radiation and non-destructive testing43. Although there have been successful attempts at continuous THz wave generation35–37, these methods often require high optical input power often of watts or more due to the weak nonlinear interactions in bulk crystals. This leads to considerable power consumption and relatively low conversion efficiency (approximately 10−7/W36,37). Additionally, these devices feature large footprints and require complex and extensive experimental conditions. While TFLN waveguides provide much tighter optical confinement and, in principle, stronger nonlinear interactions44, current exploration of THz generation in the TFLN platform has been limited to pulsed operation with relatively low conversion efficiency if normalized by continuous-wave pump power45,46. In short, there is still an unmet demand for systems capable of generating continuous THz waves in a compact, tunable fashion at room temperature.

In this study, we address the above challenges by demonstrating a monolithic integrated TFLN platform simultaneously capable of efficient THz-optic modulation and continuous THz wave generation at frequencies up to 500 GHz. The strong bidirectional interaction results from an optimized THz-optic co-design on a TFLN-on-quartz platform, which simultaneously features velocity- and impedance-matching, large overlap between THz and optical waves, and low THz transmission loss. We first present a THz-optic modulator with a low RF half-wave voltage of 8 V at 500 GHz, as well as ultrahigh 3 dB and 6 dB bandwidths of 145 GHz and 310 GHz, respectively. We then demonstrate a continuous-wave THz generator with conversion efficiencies exceeding 10−6/W across a wide frequency range from 220 to 500 GHz, using only milliwatt-level pump power. This performance surpasses all previous tunable optical THz wave generation devices by at least tenfold when normalized to continuous-wave efficiencies36,37. We further take advantage of the coherent nature of optical THz generation to demonstrate high-speed electro-THz modulation, i.e., encoding radio-frequency signals onto the generated THz carrier, at up to 65 GHz, by modulating one of the optical pump lasers using another on-chip TFLN modulator. The successful integration of an efficient THz-optic modulator and THz generator on the same chip-scale platform paves the way for compact and multifunctional THz photonic systems.

Results
Working principle and device design
Figure 1 presents a schematic representation of the dual-functional monolithic integrated LN photonic platform, which supports strong and velocity-matched interaction between optical and THz waves. We use a metallic coplanar waveguide transmission line with a slow-wave electrode design, as depicted in Fig. 1a. Although this choice involves higher THz transmission loss compared to dielectric waveguides47, it allows deep sub-wavelength THz field confinement within the metallic electrode gap and significantly increases the nonlinear overlap between THz and optical modes. Figure 1b, c depict the simulated THz (500 GHz) and optical (200 THz) mode profiles (Ez), featuring strong field confinement at both frequencies and polarization both along the z-crystal direction, which allows the exploitation of the largest χ(2) tensor component (r33 and d33) in LN. During the THz-optic modulation process, the incident transverse-electric (TE0) light from the left side is split into two branches of a Mach-Zehnder interferometer (MZI) and co-propagates with a THz wave confined in a ground-signal-ground (GSG) transmission line. Phase modulation accumulates along the two arms in a push-pull configuration, driven by the Pockels effect, and is finally converted into amplitude modulation when the two arms recombine. Figure 1d shows the frequency-domain schematic of the modulation process, which produces first-order sidebands separated from the carrier wave by the THz signal frequency. On the other hand, THz generation makes use of a similar device configuration but without an MZI structure, where two input light sources of closely spaced frequencies (ω1 and ω2) and identical polarization (TE0) are combined and introduced into the optical waveguide from the same port. The strong nonlinear overlap between the two optical waves and the THz wave leads to frequency mixing and generation of the THz signal at the frequency separation ω1 – ω2, as illustrated in Fig. 1e. The generated THz wave collinearly propagates and continuously accumulates inside the transmission line before finally being extracted from the output end by a GSG THz probe. In both processes, the rib LN waveguide (1.2 µm wide and 250 nm tall) facilitates effective optical confinement with low loss below 0.1 dB/cm. We use an optimized electrode gap of 5.5 µm to balance optic loss and electro-optic interaction strength.

The key to an efficient and continuous build-up of THz-optic interaction in these devices is to achieve low THz propagation loss while maintaining velocity- and impedance-matching conditions. In our previous TFLN-on-Si modulation devices, the coplanar transmission line sees substantial propagation loss at THz frequencies (2 dB/mm at 500 GHz) due to significantly increased conductor (ohmic) loss in the narrow signal line (20 µm) and field leakage into the Si substrate29. In contrast, our design incorporates a 50 µm signal width and utilizes a quartz substrate to reduce the conductor loss and substrate leakage, respectively (see SI Note 2 for detailed comparison). To compensate for the relatively high velocity of THz waves on the quartz substrate, we implement a slow-wave structure with periodically loaded electrodes to achieve matched THz phase velocity with optical group velocity. This ensures a coherent energy transfer between the optical and THz waves along the entire device length. By carefully engineering the T-shaped capacitive loading structures, we also achieve a near 50 Ω transmission line impedance to align with our external THz driving and detection circuits. Compared with previous reports26,27, our design utilizes a much shorter capacitive loading period of 20 µm such that each loaded element still effectively operates as a lumped capacitor even at an extremely high frequency of 500 GHz (wavelength = 600 µm). The more detailed engineering parameters are listed in Table S1. Figure 1f, g show the top-view scanning-electron microscope (SEM) image and cross-sectional schematic of our fabricated device, respectively.

We first perform a detailed characterization of the basic electro-optic and electrical properties of our devices. The 8 mm long MZI electro-optic modulator shows a measured low-frequency Vπ of 3.04 V under triangular voltage sweeps, corresponding to a voltage-length product VπL of 2.43 V·cm, as shown in Fig. 2a. This value is consistent with previous results in TFLN platforms and represents a good electro-optic overlap in our device14,26. We then evaluate the electrical performance, i.e., effective refractive index and propagation loss, of the fabricated slow-wave transmission line at THz frequencies using a vector network analyzer (VNA) and a frequency-extension module. Figure 2b displays the simulated and measured THz dispersion curves from 220 to 320 GHz, showing a THz phase index of ~2.26 (blue dots) matched with the optical group index (blue dashed line) for H=2 µm. Our simulation results using the finite element method (FEM, Ansys HFSS) suggest a larger H value corresponds to a higher RF effective index and a slower velocity of THz wave [solid lines in Fig. 2b], consistent with our experimental results.

From the measured scattering parameters (S-parameters), we also extract the electrical loss coefficient (αRF) of the transmission line at THz frequencies, as displayed in Fig. 2c. The electrical loss stems from three primary sources: conductor loss (αc), dielectric loss (αd) and radiation loss (αr). According to coplanar waveguide theory48 and our simulation results, the conductor loss αc typically scales with the square root of the frequency, the dielectric loss αd increases linearly with frequency, while the radiation loss αr is negligible in the current quartz-substrate design (SI Note 2 and Fig. S1). As a result, we model and fit the measured electrical loss (black dots) using the following equation (shown as blue dashed line in Fig. 2c):

S21 = (αc√f + αd f)L + A (1)

where L is the electrode length, and intercept A represents the RF loss at low frequency due to residual impedance mismatch. Our achieved low-frequency RF loss of 0.4 dB is significantly lower than the 2.6 dB value reported in our previous work thanks to the capacitively loaded electrode design with improved impedance matching29. The measured result translates into a characteristic impedance (Zc) of the transmission line being approximately 46 Ω, closely matching the target 50 Ω impedance. Based on the fitting results, we estimate αc = 0.264 dB cm−1 GHz−1/2 and αd = 0.028 dB cm−1 GHz−1, both of which show good agreement with the previous work on quartz substrate26. Our TFLN-on-quartz device achieves a significantly lower overall THz propagation loss (14 dB/cm at 300 GHz) compared to our previous design on silicon (22 dB/cm) thanks to the wider signal line and the reduced substrate leakage (see SI Note 2 for more details)29. Our measurement extrapolates to a propagation loss of approximately 2 dB/mm at 500 GHz, which is sufficient to support a total device length of 5–8 mm without excessive THz wave attenuation. The relatively low loss levels are crucial for facilitating a coherent accumulation of nonlinear interactions in both THz-optic modulation and THz wave generation processes.

According to these results, our design meets all requirements for effective THz-optic interactions, including optimal nonlinear overlap, precise velocity matching between THz and optical waves, minimal THz propagation loss, and impedance matching. Next, we make use of these devices to demonstrate efficient THz-optic modulation, optical THz generation, and electro-THz modulation functions.

On-chip THz-optic modulation
We demonstrate low-voltage THz-optic modulation at frequencies up to 500 GHz using the testing setups shown in Fig. 3a, b following our previously established methodologies (see Methods and SI Note 3 for more details)29. In an ideal scenario, increasing the length of the modulator always lowers the modulation voltage, which however comes at the cost of reduced tolerance to velocity mismatch, particularly at high frequencies. Here, we use an 8 mm long device to balance this trade-off. At high frequencies (10–500 GHz), the RF Vπ values are determined by analyzing the power ratios between the first-order sidebands and the carrier across different frequencies captured by an optical spectrum analyzer (OSA), as shown in Fig. 3a. The raw measured data (blue circles) and the smoothed data for clearer visualization (purple line) in Fig. 3c show good alignment with the theoretical predictions (red dashed line) derived from the measured electrical S-parameters. The electro-optic S21 parameters are obtained by comparing the measured RF Vπ values with low-frequency Vπ following our theoretical model29, which aligns well with direct S21 measurements from a VNA at the lower-frequency band [10 MHz−67 GHz, orange triangles in Fig. 3d]. This agreement validates the reliability and robustness of our measurement approach at THz frequencies.

Notably, our THz-optic modulator maintains low RF Vπ throughout the entire measured frequency range, i.e., 6 V at 300 GHz and 8 V at 500 GHz. In comparison, our previous TFLN device on a silicon substrate with a longer length of 10.8 mm exhibited an extrapolated RF Vπ of 28 V at 500 GHz29. Since electrical power consumption scales quadratically with voltage, this 3.5 times decrease in RF Vπ leads to a modulation power reduction of more than an order of magnitude, which is of great significance for practical application scenarios. Furthermore, our device achieves ultrahigh 3-dB and 6-dB bandwidths of 145 GHz and 310 GHz, respectively, significantly surpassing all measured bandwidths in previous LN-based modulators (see Table. S2 for a detailed comparison). The 3-dB bandwidth of our design can be readily extended to ~290 GHz using a shorter (5 mm) device, at the cost of slightly increased RF Vπ (SI Note 4). Detailed comparisons with state-of-the-art results from prior works are provided in SI Note 5. Combining the ultrabroad electro-optic bandwidths and low driving voltage, our THz-optic modulators could become a highly promising solution for 6G communications and advanced THz photonics applications.

On-chip continuous THz wave generation
We then demonstrate efficient, continuous-wave, and highly tunable THz generation across a broad frequency range from 220 GHz to 500 GHz (Fig. 4). Here a straight optical waveguide runs through one dielectric gap of the GSG transmission line instead of the MZI structure used earlier. This is primarily because symmetrically pumping the two optical waveguides would generate nonlinear polarizations PNL ~ E(ω1) E(ω2)* with the same phase in the two coplanar waveguide gaps, which features zero overall nonlinear overlap with our target differential THz mode. Although finite overlap with the symmetric (common) THz mode exists, the generation efficiency would be low due to substantial velocity mismatch. The MZI structure could be used by adding an optical delay line in one arm to introduce a π phase in the nonlinear polarization, however the splitting of input optical power would lead to reduced optical intensity in each arm and ultimately the same overall conversion efficiency as the straight-waveguide design used here. Figure 4a shows the continuous THz wave generation setup.

Figure 4b shows the measured THz signal spectra extracted at the output end of the transmission line at a wide range of frequencies, which can be simply controlled by adjusting the frequency difference between the two laser sources. The generated continuous THz wave power across the measured frequency range is consistently at the level of −65 dBm at a total on-chip optical pump power of 8 dBm, as illustrated in Fig. 4c. Our THz generator does not see a significant efficiency drop even at the 500 GHz upper measurement limit imposed by our current probes and characterization equipment. Further integrating THz antennas directly on chip could circumvent the limitations imposed by probes and other peripheral electronics, enabling THz generation at frequencies well beyond the current accessible range49. By placing the output probe at different locations of the transmission line, we can measure the generated THz power for different device lengths, i.e., 5 mm, 8 mm, and 10 mm (neglecting the effect from the remaining unused section). Figure 4d shows the simulated and measured conversion efficiencies for different lengths and at various frequencies. The highest measured THz generation efficiencies are 2.90×10−6/W at 300 GHz (black squares), 4.13×10−6/W at 400 GHz (red circles), and 4.86×10−6/W at 500 GHz (blue triangles) for a device length of 10 mm. Theoretical analysis of the simulated conversion efficiency could be found in our earlier work44 and in SI Note 6. Briefly, the normalized THz generation efficiency Γ in a lossless system can be defined and calculated using the following equation50:

Γ = PTHz / (Popt1 Popt2) = (2ωTHz^2 d33^2) / (nopt^2 nTHz ε0 c^3 A) * L^2 * sinc^2(ΔkL/2) (2)

where Popt1,2 are the optical powers of input lasers at ω1 and ω2, PTHz is the output THz power at ωTHz, Δk is the wave vector mismatch between optical and THz waves, L is the waveguide length, ε0 and c are the permittivity and speed of light in vacuum, nopt and nTHz are the effective refractive indices of the optical and THz modes, A is the effective spot area dictated by the nonlinear overlap between the three waves51,52:

A = (∫all |Eopt|2 dxdy * ∫all |ETHz|2 dxdy) / |∫LN Eopt,z* ETHz,z* dxdy|^2 (3)

where ∫LN and ∫all denote cross-section integration over the LN region only and all space, respectively. Eopt and ETHz are the electric fields of the optical and THz modes and Eopt,z and ETHz,z are their corresponding z components that utilize the largest nonlinear coefficient d33. As Eq. (2) shows, the THz generation efficiency inherently increases quadratically with device length when the THz transmission loss is not significant. Remarkably, our device shows a strong upward trend in THz conversion efficiency even at a 10 mm length, which also matches well with our full theoretical model [dashed lines in Fig. 4d] that takes into account the measured THz loss [Fig. 2c]. This trend suggests that there is potential for further efficiency gain with the use of longer electrodes53. The small discrepancies between simulated and experimental efficiencies may be attributed to larger-than-expected on-chip and facet optical losses and fabrication-induced deviation of structural parameters (e.g., metal gap). Despite this, our measured efficiencies are more than ten times higher than those of current LN-based tunable THz generators when normalized to continuous-wave values36,37 (see Table. S3 in SI Note 8 for detailed comparison). We further evaluate the input-output power relationship by concurrently increasing the input power of the two lasers from 12.5 mW to 25.5 mW (11 dBm to 14 dBm) at THz frequencies of 280, 360, and 400 GHz, as shown in Fig. 4e. Here, the power levels correspond to total on-chip optical powers and the two lasers are kept at 1:1 power ratio. The output THz powers exhibit good quadratic relationships with input optical powers among these three frequencies, as evidenced by the linear fitting curves in the double logarithmic plot in Fig. 4e with slopes of approximately 2. Currently, the generated THz signals see relatively large linewidths since the two pump lasers are not frequency locked, as detailed in SI Note 7, which could be substantially improved by locking the two lasers via electro-optic or Kerr frequency combs54,55. Compared to other technologies requiring up to dozens of watts of peak pump power35–37, our system could achieve microwatt-level outputs using sub-watt input power, significantly reducing power consumption while maintaining excellent frequency tunability.

The THz wave generation efficiency could, in principle, be further enhanced by embedding the system in a racetrack optical resonator44, as schematically shown in the inset of Fig. 4f. Thanks to the non-resonant nature of the THz mode, no additional phase and velocity matching conditions are required as long as the optical pump frequencies are matched to the cavity resonances. This resonator configuration dramatically increases effective pump powers by the cavity finesse. Here, we assume that a racetrack resonator with a bending radius of 80 µm, a straight section length of 5 mm, and a free-spectral range (FSR) of ~12 GHz is critically coupled with loaded Q factors ranging from 0.5×10^6 to 5×10^6, which have well been achieved in many recent reports in the TFLN platform56,57. The effective pump power experiences an amplification from 10 to 96 times inside the resonator compared to the power in the bus waveguide, leading to an overall conversion efficiency enhancement of approximately 10,000 times at a Q factor of 5×10^6. This corresponds to a remarkable theoretical THz generation efficiency of 1.85%/W at 500 GHz. The detailed calculation method is shown in SI Note 9. Although this resonant system allows THz emission only at discrete frequencies (with spacing of FSR~12 GHz), the ability to generate continuous-wave THz signals at a wide range of stepped frequencies (e.g., 200–500 GHz) could still offer significant potential for many applications including communications and imaging.

High-speed electro-THz modulation
Finally, we showcased the versatility of our optical THz wave generation scheme by demonstrating high-speed modulation of the generated THz waves via mature and cost-effective optical modulation techniques. Figure 5a illustrates the experimental setup for electro-THz modulation, where one of the optical pump signals is first modulated by either a standard commercial electro-optic modulator, or an in-house fabricated on-chip modulator based on the same TFLN-on-quartz substrate, before mixing with the other pump laser with a center frequency difference of 420 GHz. Figure 5b−d illustrate the measured electrical spectra of the modulated THz wave at various frequencies up to 65 GHz, whereas Fig. 5e–g show the corresponding modulated input optical spectra. The power ratios between the carrier and sidebands are highly consistent between the optical and electrical spectra, e.g., 7.96 dB optically and 8.08 dB electrically at 35 GHz [Fig. 5c, f]. The highest electro-THz modulation frequency of 65 GHz is currently limited by the bandwidths of the probes and the mixer. Achieving THz wave modulation at such frequencies is typically non-trivial and necessitates costly THz mixers. The experimental results based on TFLN modulators not only verify the electro-THz modulation capability at ultrahigh frequencies deep into the millimeter-wave band, but also demonstrate the potential of achieving fully integrated THz generation and modulation systems on a single TFLN chip.

Methods
Device design and simulation
The propagation properties of the THz wave along the transmission line were analyzed using the finite element method (FEM) in Ansys HFSS. We simulated performance parameters such as the THz wave’s refractive index and the characteristic impedance over an electrode length of 1000 µm, then scaled these parameters up to match the actual required electrode length. Detailed parameters of our device design can be found in SI Note 1. In the simulation, we considered the dielectric losses of all materials, including LN58, quartz substrate59, and the deposited cladding60. The THz mode profile in Fig. 1b was computed through an FEM in Comsol Multiphysics, whereas the optical mode profile in Fig. 1c was generated using a commercial Finite Difference Eigenmode (FDE) solver (Lumerical, Mode Solutions). Our design incorporated a slow wave structure within the transmission line to achieve velocity matching between the THz and optical waves, while targeting a characteristic impedance close to 50 Ω. We adopt the same structure and principles as in the previous paper26, while using a smaller capacitive loading period to increase the cut-off frequency. We numerically simulated the slow wave effect by adjusting the height (H) within the metal electrode slot using the finite element method and extracted the THz effective index from the numerically converged propagation constant29. We evaluated the THz generation conversion efficiency by numerically calculating the overlap between the simulated THz and optical mode profiles. This calculation considered both the effects of velocity matching and the experimentally measured THz wave propagation losses within actual devices.

Device fabrication
Devices were fabricated using a commercial x-cut LN wafer from NANOLN. This wafer consists of a 500 nm-thick LN, a 2 µm-thick buried oxide (BOX) layer, and a 500 µm-thick quartz substrate. Waveguide patterns were initially defined using electron-beam lithography (EBL) on hydrogen silsequioxane (HSQ) resist. The patterns were then transferred into the TFLN by dry etching 250 nm of the LN film using an Argon-plasma (Ar+) based reactive ion etching (RIE) process. The fabricated rib waveguides have a height and top width of 250 nm and 1.2 µm, respectively. Subsequently, a layer of SiO2 was deposited over the LN chip as a cladding layer using plasma-enhanced chemical vapor deposition (PECVD). Slow-wave electrodes were constructed through a series of processes, including photolithography, RIE, thermal evaporation, and a lift-off process. The final steps involved dicing and polishing the chip edges to enhance fiber-chip coupling.

Characterization of THz wave transmission line
The S-parameters of the slow wave transmission lines were measured using VNA with frequency extension modules. The measurements spanned from 10 MHz to 50 GHz using the VNA (Keysight E5080B), and from 220 to 320 GHz using another VNA (Agilent N5230C) with millimeter wave VNA Extender (V05VNA2-T/R). GSG probes for respective frequency bands were used for THz signal input and output. To ensure the accuracy of these measurements, the probes were calibrated to the tips using a commercial Short-Open-Load-Through (SOLT) calibration kit, which effectively removed the influence of any unwanted parasitic effects.

Characterization of THz-optic modulation
The electro-optic characterization was performed in the telecom C-band using a tunable-wavelength laser source (Santec TSL-510). A three-paddle polarization controller was used to ensure TE0 mode excitation. Light was coupled into and out from the chip under test using tapered lensed fibers, with a coupling loss of ~5 dB/facet. For the measurement of DC/low-frequency Vπ, a 100 kilohertz electrical sawtooth waveform was generated from an arbitrary-waveform generator (AWG, RIGOL DG4102) and applied to the transmission line of the electro-optic modulator through a GSG probe (GGB industries, 50 GHz). The output optical signal of the electro-optic modulator was detected using a photodetector (New Focus 1811) and recorded on an oscilloscope (RIGOL DS6104). For high-speed THz-optic modulation performance of RF Vπ, measurements were separately conducted in five frequency bands ranging from 9 to 500 GHz using different signal generation methods. For the lowest band (<67 GHz), modulation electrical signals were directly generated from an RF generator (MG3697C, Anritsu). For higher frequencies (>67 GHz), RF signals were up-converted and amplified by frequency multipliers to the respective bands, i.e., 90–140 GHz, 140–220 GHz, 220–320 GHz, 320–500 GHz. The modulator was biased at the quadrature point, generating an output optical signal with two sidebands separated from the carrier by the THz frequency. The RF Vπ was tested by monitoring the power ratio between the sideband and the carrier, using an OSA (Yokogawa AQ6370)29. For direct electro-optic response measurement between 1 and 50 GHz, a small RF signal from VNA (Keysight, E5080B) was input into the modulator electrodes through a GSG probe. The output signals at various frequencies were captured by a high-speed photodetector (50 GHz photodetector, XPDV21x0) and sent to the other port of the VNA. Calibration of the VNA test results involves first measuring the transmission loss of all cables by a two-port VNA test. The loss data of the probes and photodetectors (PDs) at corresponding frequencies were retrieved from the datasheets provided by the manufacturers. These losses were finally subtracted from the measured EO S21 parameter.

To ensure precision measurements in the OSA tests, the entire experimental setup was calibrated using a VDI source module in conjunction with a power meter (Erickson PM5B). The output power of the VDI source across multiple frequency bands was carefully measured. The actual electrical power that was applied to the chip is determined by subtracting the measured source power by the probe loss values from GGB datasheet. The detailed connection for measurement is shown in Fig. S6a. The RF Vπ values quoted in this paper all correspond to on-chip voltages after calibration.

Characterization of THz wave generation
THz wave generation process was characterized by using two continuous wave laser sources with certain frequency differences. The tunable telecom lasers (Santec TSL-510 and Santec TSL-710) were individually polarized into the TE0 mode using three-paddle fiber polarization controllers. The signals were then combined through a 50/50 coupler, amplified using an erbium-doped fiber amplifier (EDFA, Amonics, AEDFA-L-30-B-FA), which also served as a regulator of the on-chip optical power. Tapered lensed fibers were used to couple light into and out from the waveguide facets of the LN chip. The generated THz signals were collected by a high-speed GSG probe and underwent frequency down-conversion via spectrum analyzer extension modules (SAX, VDI, WR3.4 SAX-M & WR2.2 SAX-M). The down-converted signal was then sent to the local oscillator of an electrical spectrum analyzer (ESA) for precise measurement of the THz signal frequency and power. In this process, the intermediate frequency (IF) is determined by heterodyne mixing of the on-chip THz signal with the local oscillator within the SAX module. We calibrated and deducted losses incurred from various components of the entire testing system, including the probe, waveguide, cable, and SAX, as shown in SI Note 10 Fig. S6b. The measured THz power values and the associated conversion efficiencies quoted in this paper all correspond to on-chip power after calibration.

For the measurement of the electro-THz modulation process, we first utilized a commercial electro-optic modulator (EOSPACE, AX-0MVS-40) with RF and DC inputs to modulate one input laser at frequencies up to 35 GHz. We applied different RF input power, frequency, and DC voltage to adjust the modulation state. The continuous wave THz signal generated through optical methods can transfer the modulation information carried by the optical signal to the THz frequency band. The modulated THz signal was down-converted using the SAX and monitored using an ESA. For higher-speed measurements up to 65 GHz, we replaced the commercial modulator with an in-house fabricated broadband integrated LN modulator based on quartz substrate. The modulator is optically packaged and electrically interfaced using a high frequency probe (GGB, 67 GHz).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Authors demonstrated terahertz electro-optic modulator, terahertz-wave generator, and electro-terahertz modulator based on thin film lithium niobate platform. In the first part, by leveraging the fast electro-optic response of lithium niobate, authors pushed the 3-dB modulation bandwidth to millimeter-wave regime. Secondly, authors generated millimeter wave and terahertz wave via the difference frequency generation processing in an integrated lithium niobate phase modulator. Thirdly, authors generated modulated terahertz signal via the mixing of a modulated optical wave and an unmodulated optical wave. These works are interesting to the integrated lithium niobate photonics community as well as terahertz community. Moreover, authors wrote this manuscript in smooth analytical English with most representative previous work cited. Hence, Reviewer recommends accepting this manuscript if authors can successfully address following comments:\n1. Authors claimed that the first electro-optic modulator can modulate optical wave by terahertz wave. However, the 3-dB bandwidth of this modulator is only 145 GHz, which is comparable to several state-of-the-art integrated lithium niobate modulators with 3-dB bandwidth over 110 GHz [1-4]. To reach the quality and impact of Nature Communications, reviewer strongly recommends authors to improve the 3-dB bandwidth of the presented electro-optic modulator to outperform the state of the arts. For example, a 3-dB bandwidth two-fold higher than that of the state of the art will be very favorable (over ~220 GHz).\n2. For the terahertz generator, reviewer can clearly observe the mode mismatching between the near-infrared mode at 200 THz (fig. 1c) and the terahertz mode at 500 GHz (fig. 1b). This mismatching will drastically limit the conversion efficiency of the difference frequency generation processing from near infrared to terahertz. Hence, reviewer strongly recommends that authors design special structure for improving the mode mismatching between near-infrared mode and terahertz mode. With this design, authors will able to significantly increase the conversion efficiency and the generated terahertz power.\n3. In the third work, authors used a commercial electro-optic modulator to achieve a modulated optical signal, limiting the bandwidth to 40 GHz. To improve this bandwidth, reviewer would suggest authors to modulate the optical signal using an integrated lithium niobate modulator. In this way, authors will able to achieve modulated terahertz signals with millimeter-wave or even terahertz sidebands. This is will be very interesting to applications such as terahertz communications.\nIn summary, this work bridges integrated lithium niobate photonics and terahertz, leading to three promising devices. To reach the quality and impact of Nature Communications, authors still have to improve the performance of these three devices. Based on authors’ strong expertise in integrated lithium niobate photonics and terahertz, reviewer truly believes that authors can successfully achieve these improvements.\n[1] F. Yang et al., \"Monolithic thin film lithium niobate electro-optic modulator with over 110 GHz bandwidth,\" Chin. Opt. Lett., vol. 20, no. 2, p. 022502, 2022/02/10 2022. [Online]. Available: http://opg.optica.org/col/abstract.cfm?URI=col-20-2-022502.\n[2] M. Xu et al., \"Dual-polarization thin-film lithium niobate in-phase quadrature modulators for terabit-per-second transmission,\" Optica, vol. 9, no. 1, pp. 61-62, 2022/01/20 2022, doi: 10.1364/OPTICA.449691.\n[3] X. Liu et al., \"Capacitively-loaded thin-film lithium niobate modulator with ultra-flat frequency response,\" IEEE Photonics Technology Letters, vol. 34, no. 16, pp. 854-857, 2022.\n[4] F. Valdez, V. Mere, and S. Mookherjea, \"100 GHz bandwidth, 1 volt integrated electro-optic Mach–Zehnder modulator at near-IR wavelengths,\" Optica, vol. 10, no. 5, pp. 578-584, 2023.", "reviewer_2": "Review of paper NCOMMS-24-36318\nThe paper of Zhang et al. reports on three different experiments, all performed on TFLN:\n1. demonstration of continuous wave terahertz emission,\n2. modulation of this CW emission by an in-line, fiber-based EO modulator, and\n3. using a slow wave electrode design similar to the one proposed in Ref. 25.\nI must say I enjoyed reading this work very much, and consider it to be a timely addition to the young field of integrated terahertz photonics. Although only few conceptual changes are being made at the design level compared to ref. 25, the authors are pushing the figures of merits for these devices, as well as demonstrating terahertz generation from a very similar design. Further modulating the generated terahertz with an in-line EO modulator (fiber) demonstrates the capabilities of this approach.\nThat being said, my evaluation is that the paper still lacks quite substantial discussion and clarity, and my questions and comments below are intended to improve on clarity, especially when comparing to existing literature:\n1. Most important of all is that the authors provide extensive details on how they calibrate all of their experiments to extract the figures of merit that they emphasise in their paper: V_pi, losses, generation efficiency of THz on-chip. This calibration is extremely important as it impacts the exact value of all figures of merit they estimate and with the current information in the paper it is impossible to assess if this calibration is done correctly. In more details:\na. For equation (1) they mention A is the “low-frequency insertion loss” – what does that mean, and why is it correct to assume that the insertion loss is not frequency dependent. The authors must explain this, and give the number for A. why is A not dependent on f.\nb. Wouldn’t it be a much better way to measure losses from different modulator lengths to extract A(f)?\nc. Also in equation (1) they split their losses into dielectric loss and metallic loss, assuming they scale like ~f and ~sqrt(f), respectively. This is too hand-wavy in my view, and the authors should back up this assumption with simulations that compare the radiative loss to the dielectric loss and the metallic loss.\nd. Related to the above, the authors mention they replace the high resistivity silicon substrate with quartz because the latter has lower “transmission line loss”. The authors should provide comparative loss curves showing alpha_HR-Si vs alpha_quartz in the frequency range of interest. Also here, by looking at established literature e.g. Grischkowsky et al. J. Opt. Soc 7, 10 (1990), we find that the loss curves of crystalline quartz shown there neither scale like ~f nor linearly! Please provide data to support this assumption.\ne. What about the losses of lithium niobate, won’t those be dominant? Authors must discuss this in detail.\nf. For Fig. 2a please mention the frequency at which the measurement is taken.\ng. For Fig. 3c please provide all as measured data of sideband ratios in the supplementary material (i.e. without any filtering or amplification after the chip) and full derivation of extracting V_pi from how much is the applied THz power from the instrument, how much power is efficiently injected into the chip, and how much are the losses from attenuation in the cables used to bring the terahertz to the chip. Is the V_pi they mention as-applied, taking into account the whole system, or the one on-chip? This must be clearly mentioned.\nh. Since at the end the performance of the entire system counts, the authors should discuss how the entire scheme compares to using antennas directly, as discussed in: https://ieeexplore.ieee.org/abstract/document/10298946 precisely on thin film lithium niobate. Plus about further increasing the frequency. The data presented in this paper showcases that even higher frequencies are supported by the LN platform (extends well into 1 THz).\ni. For Fig. 3d, please explain in detail how you compute the EO S21 response, again considering the calibration of frequency-dependent transmission through cables and importantly RF probes. How do you compute the red dashed line “from measured S-parameters”. Again, if this is from the VNA measurement in the range 140-220 GHz as mentioned in the methods, how do you calibrate the rest of the frequency band up to 500 GHz to measure only the chip? Please provide exact formulas wherever possible. Please provide exact sketch of experiment in the supplementary and label with corresponding THz powers.\nj. For Fig. 3d please provide in the supplementary material the systems’ S21, that is including losses of cables and probes in and out. + RF power applied.\nk. For Fig. 4c please provide details on how exactly you do the power calibration. How much terahertz power do you have at the various positions of the coax cables (i.e. just before the output RF probe, just after the RF probe, just before the mixer)? Please provide exact sketch of experiment in the supplementary and label with corresponding THz powers.\nl. Is the power you mention in fig. 4c and e, and correspondingly used to compute the conversion efficiency in d, on-chip or at the end of your coax cables – i.e. out of chip, there where it would be used e.g. to drive an EO modulator as they show in their first experiment of Fig. 3? These details are extremely important and need careful mentioning.\nm. My previous point l is very important because the authors mention ref. 44 noting the “low efficiency” in their introduction, which was the first demonstration of thz generation in circuits from TFLN. It may be just a timing issue, but they don’t mention the more recent work where the generation efficiency is significantly higher, see recent arxiv terahertz generation: https://arxiv.org/abs/2406.15651 which was recently shown all the way to 3.5 THz. In fact, in that paper, the as-measured power efficiency in the farfield (hence out of chip) is power_THz_in_the_farfield/power_optical = 4.5*10^-9 for 72 pJ pulse energies (without any corrections). Instead, if accounting for coupling efficiency out of chip and all other losses, on-chip the conversion efficiency of ~10^-5. Note that here conversion efficiency is defined as THz power out over optical power in. This number would be significantly larger than what the current paper presents and needs to be presented as such. If I see this right, compared to the current paper where the efficiency is 4.86*10^-6 /W and where the authors demonstrate up to 20 mW (~14 dBm) optical power on-chip, this would yield a conversion efficiency of power THz/power optical = 4.86*10^-6 /W*20 mW (13 dBm) ~10^-7, that is a factor of about 20 in the as-measured efficiency and 1/20 in the on-chip efficiency compared to the arxiv paper above. In fact, from fundamental principles, it would only make sense that the pulsed emission is more efficient because of the higher peak powers, so the authors need to correct their statements in the introduction/motivation of their work. Already CW is very interesting.\nn. Similarly, they mention several times in their paper the conversion efficiency of pulsed generation schemes “when normalized to continuous wave efficiencies” (e.g. in the last paragraph before results section) but they don’t provide the exact formulas how they do this “normalization”. What does that mean? Please provide full math in complementary note 5.\no. Similarly, if I understand this well, they compute the conversion efficiency of their device when measured with the ESA settings shown in S1 fig. 1a? is this correct, given that at smaller scans and lower BW we see a clear drop in the amplitude, e.g. in S1 fig. 1d? The authors need to explain why this is correct.\n2. I very much enjoyed their idea and data of Fig. 5, but once again I don’t fully understand what “relative power” is that they plot in their panels b-d. Relative to what exactly? Please give absolute units in dBm, and else explain through formulas what you report. What are the small sidebands that are visible around the tone at 1561.5 nm of panel 5f and in the inset?\n3. In their introduction, the authors mention a few aspects which they need to explain:\na. They mention plasmonic modulators and their loss, and LN as being a good alternative. But there is an entire bulk of work that uses silicon slot waveguides which are far less lossy e.g. from the group of Christian Koos -the authors need to mention that work specifically. In addition, those structures have demonstrated record field enhancement and hence low V_pi – please correctly reference those works.\nb. Compared to 28 V at 500 GHz of ref. 22, the current 8 V is summarized as “an order of magnitude better in power consumption” in the abstract, but I don’t find the exact computation of the power consumption in their paper or supplementary material. I understand that it scales quadratically but please add that for clarity.\nc. They say that bulk systems “limiting their reliability and practicality” – this is arguable in my view. Please explain.\n4. Below fig. 1 they mention the use of quartz “to reduce substrate leakage” – please explain and give numbers how much the leakage is reduced?\n5. Can you please explain how about the birefringence of quartz in the THz? How is the quartz aligned with respect to the LN crystal and what impact does that have?\n6. In the “On-chip THz-optic modulation” they mention they use “test setups using previously established methodologies” – but please also refer to methods.\n7. In the “on-chip continuous-wave terahertz generation” part of their paper, the authors comment that a GSG type of contact could work with an optical delay line that would introduce a pi shift in their nonlinear polarization. Can the authors please explain how they would to this in practice? Is it really correct to say that “results in zero nonlinear overlap if the signals running in the two gaps have the same phase ”? or is it rather that one would generate a symmetric GSG mode?\n8. Could the authors point to where they get their formula (2) and (3) of the supplementary material, else give the entire derivation that that is the correct definition of the effective spot area from the nonlinear wave equation?\n9. The authors provide in Fig. 4f the “computed efficiency when inside a ring resonator” – how do they compute this? Please add a few notes. I’m guessing you’re simply scaling for intra-cavity power but this needs to be clarified in the text, especially since more modes will get coupled to each other.\nIn conclusion, very interesting paper with exciting results but it needs to be substantially revised to improve clarity and transparency before publication. Also, please add line numbering for the next review round.", "reviewer_3": "This paper presents a monolithically integrated thin-film lithium niobate (TFLN) photonic chip capable of both receiving (RX) via modulation and transmitting (TX) via difference frequency generation (DFG) THz signals for high-speed communications, with motivating applications including 6G wireless communications, medical imaging, THz radar and spectroscopy. The paper presents significant improvement over previously published results, with a ~10x reduction in V  for the modulator (RX) and roughly a 10x increase in generated continuous wave THz signals for TX. Both were demonstrated continuously up to 500 GHz.\nThe paper then shows up-converted modulation sidebands up to 35 GHz, on the generated THz carrier, along with a 5 GHz amplitude modulation (AM) signal. Higher level modulation schemes, e.g., quadrature-amplitude-modulation (QAM) are not possible given the large linewidth of the generated THz signals, as a consequence of not phase locking the two off-set lasers for DFG.\nWhile the improve of 10x for both RX and TX modes of operation are significant, the relevance of the presented work to a communications journal is not clear, especially when the highest demonstrated information modulation was only a 5 GHz AM signal.\nThis being said, while the presented results, along with the paper being very well written and well referenced, are clearly publishable it does not meet the originality threshold of a Nature Communications nor Nature Photonics paper, as it is largely improvement over previously published results. Perhaps with higher level QAM and the demonstration of a significantly higher data rate, this paper may meet that threshold but in its current form is not deemed sufficient for publication in this journal."}, "author_response": "Response:\n1. Authors claimed that the first electro-optic modulator can modulate optical wave by terahertz wave. However, the 3-dB bandwidth of this modulator is only 145 GHz, which is comparable to several state-of-the-art integrated lithium niobate modulators with 3-dB bandwidth over 110 GHz [1-4]. To reach the quality and impact of Nature Communications, reviewer strongly recommends authors to improve the 3-dB bandwidth of the presented electro-optic modulator to outperform the state of the arts. For example, a 3-dB bandwidth two-fold higher than that of the state of the art will be very favorable (over ~220 GHz).\nResponse: We sincerely appreciate the reviewer’s valuable comments and suggestions. In our work, we have mainly focused on optimizing the modulation voltage (absolute modulation efficiency) at very high frequencies, which would be important for future terahertz photonic applications. As a result, we have chosen a relatively long modulator length of 8mm to achieve a high overall electro-optic conversion efficiency. We do acknowledge that the relative modulation efficiency (often characterized by the 3-dB bandwidth) could also be important in certain applications, especially digital optical communications where a flat electro-optic response is desired. The 3-dB bandwidth of these modulators can be substantially improved by simply using a shorter device length, without changing the design parameters experimentally verified in this work, at the cost of reduced absolute modulation efficiency. This dependence is also experimentally verified in our earlier work1, where we demonstrated a 3-dB bandwidth of 170 GHz using a 5.8-mm device, although the absolute conversion efficiency there was substantially worse than our current demonstration (~10.2 V vs ~7.0 V in this work at 300 GHz).\nTo provide readers in the broader optics community with more insights into the relative modulation performance of our proposed design, we have now performed additional modeling of the 3-dB and 6-dB bandwidth performance of 5-mm and 10-mm devices based on the current modulator design and the electrical test results established in this work, as shown in the new Fig. S4. (also copied below). To ensure the accuracy and reliability of modeling, we use the fitted electrical properties from high-frequency electrical measurement data, including an extracted impedance of 46 Ω, and 1 an electrical-optical index mismatch of 0.02. The simulation results in Fig. S4(a) suggests that a 5-mm device can support a 3-dB bandwidth of 290 GHz and features only 5 dB roll-off at 500 GHz, while the V at 500 GHz can be maintained to a reasonably low value of 9.2 V, as shown in Fig. π S4(b). Meanwhile, the 10-mm modulator has a bandwidth of 127 GHz at 3 dB and 299 GHz at 6-dB. Compared with previous research results or similar devices2-5, our modulator has achieved a significant improvement in bandwidth performance.\nFig. S4 The calculated electro-optic S (a) and RF V (b) of different lengths (5mm and 10mm) 21 π based on the fitting electrical loss.\nWe have added the above new simulation results in the Supplementary Information to discuss the modulator performance for different lengths. The new text reads “Based on the equations presented in SI Note 3 and the measured parameters (RF loss, impedance and velocity mismatch), we obtained the calculated the bandwidth and driving voltage for modulators of different lengths with same structure, as shown in Fig. S4. Notably, the 5-mm device exhibits a remarkable calculated 3-dB bandwidth of 290 GHz. Even at 500 GHz, it demonstrates only a 5-dB roll-off. As shown in Fig. S4(b), its RF V at 500 GHz can be maintained at a relatively low value of 9.2 V. In addition, the 10-mm modulator has a 3-dB bandwidth of 127 GHz and a 6-dB bandwidth of 299 GHz.”\n2. For the terahertz generator, reviewer can clearly observe the mode mismatching between the near-infrared mode at 200 THz (fig. 1c) and the terahertz mode at 500 GHz (fig. 1b). This mismatching will drastically limit the conversion efficiency of the difference frequency generation processing from near infrared to terahertz. Hence, reviewer strongly recommends that authors design special structure for improving the mode mismatching between near-infrared mode and terahertz mode. With this design, authors will able to significantly increase the conversion efficiency and the generated terahertz power.\nResponse: We thank the reviewer for the insightful comments. We agree that the mismatching between optical mode and the terahertz mode at 500 GHz is a main limiting factor for the 2 achievable conversion efficiency of the THz generation process. It is, however, equally important to have small mode areas for both optical and THz waves, as well as low propagation loss for both modes, in order to achieve an efficient and coherently accumulating generation process, as outlined in the theoretical study in our earlier paper6. We believe the design reported in the current manuscript achieves a good balance between these three factors, leading to an optimal THz generation efficiency at frequencies between 200-500 GHz. The relatively high conversion efficiency is mainly enabled by the excellent THz wave confinement in coplanar waveguides, with mode areas in deep sub-wavelength regimes, while the metallic loss is still manageable. As a result of these optimization, the achieved THz generation efficiency of 4.8×10-6/W is substantially larger than those achieved in earlier works7-9.\n3. In the third work, authors used a commercial electro-optic modulator to achieve a modulated optical signal, limiting the bandwidth to 40 GHz. To improve this bandwidth, reviewer would suggest authors to modulate the optical signal using an integrated lithium niobate modulator. In this way, authors will able to achieve modulated terahertz signals with millimeter-wave or even terahertz sidebands. This is will be very interesting to applications such as terahertz communications.\nResponse: We thank the reviewer for the valuable suggestions. We agree that using an integrated lithium niobate (LN) modulator to modulate the optical signal is a promising approach to increase the electro-THz modulation bandwidth beyond 40 GHz. To validate this, we have conducted additional experiments by replacing the commercial modulator with an in-house fabricated broadband integrated LN modulator also based on quartz substrate. As the measured electrical spectrum and optical spectrum in the revised Fig. 5(d) and 5(g) show (also copied below), we have successfully achieved ultra-broadband electro-THz modulation at a frequency of 65 GHz, currently only limited by the bandwidths of the electrical probes and sources. This result not only validates the effectiveness of our electro-THz modulation approach at high frequency, but further demonstrates the potential of achieving fully functional THz-photonic systems on a single TFLN chip.\nWe have modified the statement and Fig. 5 on Page 10 to add the content for modulating the optical signal using an integrated LN modulator. The new test reads “Figures 5(b-d) illustrate the measured electrical spectra of the modulated THz wave at various frequencies up to 65 GHz, whereas Figs. 5(e-g) show the corresponding modulated input optical spectra.”\nAlso, we added the test method on Page 13. The new test reads “For higher-speed measurements up to 65 GHz, we replaced the commercial modulator with an in-house fabricated broadband integrated LN modulator based on quartz substrate. The modulator is optically packaged and electrically interfaced using a high frequency probe (GGB, 67 GHz).”\nIn summary, this work bridges integrated lithium niobate photonics and terahertz, leading to three promising devices. To reach the quality and impact of Nature Communications, authors still have to improve the performance of these three devices. Based on authors’ strong expertise in integrated lithium niobate photonics and terahertz, reviewer truly believes that authors can successfully achieve these improvements.\nResponse: We thank the reviewer’s recognition of our work’s significance in bridging integrated LN photonics and THz, as well as the constructive suggestions. With the additional experimental results and theoretical studies, we believe the revised manuscript has been significantly improved to meet the high standards of Nature Communications.\n[1] F. Yang et al., \"Monolithic thin film lithium niobate electro-optic modulator with over 110 GHz bandwidth,\" Chin. Opt. Lett., vol. 20, no. 2, p. 022502, 2022/02/10 2022. [Online]. Available: http://opg.optica.org/col/abstract.cfm?URI=col-20-2-022502.\n4\n[2] M. Xu et al., \"Dual-polarization thin-film lithium niobate in-phase quadrature modulators for terabit-per-second transmission,\" Optica, vol. 9, no. 1, pp. 61-62, 2022/01/20 2022, doi: 10.1364/OPTICA.449691.\n[3] X. Liu et al., \"Capacitively-loaded thin-film lithium niobate modulator with ultra-flat frequency response,\" IEEE Photonics Technology Letters, vol. 34, no. 16, pp. 854-857, 2022.\n[4] F. Valdez, V. Mere, and S. Mookherjea, \"100 GHz bandwidth, 1 volt integrated electro-optic Mach–Zehnder modulator at near-IR wavelengths,\" Optica, vol. 10, no. 5, pp. 578-584, 2023.\nReview of paper NCOMMS-24-36318\nThe paper of Zhang et al. reports on three different experiments, all performed on TFLN:\n1. demonstration of continuous wave terahertz emission,\n2. modulation of this CW emission by an in-line, fiber-based EO modulator, and\n3. using a slow wave electrode design similar to the one proposed in Ref. 25.\nI must say I enjoyed reading this work very much, and consider it to be a timely addition to the young field of integrated terahertz photonics. Although only few conceptual changes are being made at the design level compared to ref. 25, the authors are pushing the figures of merits for these devices, as well as demonstrating terahertz generation from a very similar design. Further modulating the generated terahertz with an in-line EO modulator (fiber) demonstrates the capabilities of this approach.\nResponse: We appreciate the reviewer for the positive comments and highlighting the significance of exploring integrated terahertz photonics.\nThat being said, my evaluation is that the paper still lacks quite substantial discussion and clarity, and my questions and comments below are intended to improve on clarity, especially when comparing to existing literature:\n1. Most important of all is that the authors provide extensive details on how they calibrate all of their experiments to extract the figures of merit that they emphasise in their paper: V_pi, losses, generation efficiency of THz on-chip. This calibration is extremely important as it impacts the exact value of all figures of merit they estimate and with the current information in the paper it is impossible to assess if this calibration is done correctly. In more details:\na. For equation (1) they mention A is the “low-frequency insertion loss” – what does that mean, and why is it correct to assume that the insertion loss is not frequency dependent. The authors must explain this, and give the number for A. why is A not dependent on f.\nResponse: We thank the reviewer for raising this question and apologize for the confusion caused by the wording used. A represents the RF loss at low frequency, which is primarily attributed to the impedance mismatch between the transmission line and external measurement equipment, as well as any inherent imperfections in the connections and components. This value is therefore not frequency dependent, and in our measurements is experimentally obtained by extrapolating the fitted line of measured RF loss down to zero frequency, which yields a value of 0.4 dB (Fig. 2c). To avoid confusion, we have modified the statement in Page 5. The new text reads “intercept A represents the RF loss at low frequency”.\n6\nb. Wouldn’t it be a much better way to measure losses from different modulator lengths to extract A(f)?\nResponse: We thank the reviewer for the suggestion. As we have discussed above, A corresponds to the RF loss at low frequency and is not related to frequency, which is extracted by the measured RF loss as a function of frequency. We have modified the relevant words to avoid confusion.\nc. Also in equation (1) they split their losses into dielectric loss and metallic loss, assuming they scale like ~f and ~sqrt(f), respectively. This is too hand-wavy in my view, and the authors should back up this assumption with simulations that compare the radiative loss to the dielectric loss and the metallic loss.\nResponse: We thank the reviewer for the comment. The overall loss α of a transmission line typically consists of three components, α = α + α +α , where α accounts for the conductor loss tot c d r c from the metallic parts (also including additional loss due to metal surface roughness), α accounts d for the dielectric loss from all remaining dielectrics, including the substrate and air, α is the r radiation loss due to power radiated from the fundamental mode of the transmission line into the substrate or air10. This approach of modeling coplanar waveguide transmission loss is a commonly adopted approach1,11,12, also described in the textbook [Microstrip Lines and Slotlines]13. To further verify this, we have now performed additional numerical simulations to investigate the contributions and frequency dependence of the three loss components, as shown in Fig. S2. It can be seen that in our current device design the radiation loss α is significantly smaller compared to r the other two loss origins, and therefore are neglected in the loss modeling. We do note that the radiation loss would be much more substantial if a silicon substrate is used, which will be discussed in more details in our response to the next question (and also shown in the new Fig. S1). The simulation results confirm that the dielectric loss scales linearly with frequency, while the metallic loss scales linearly with sqrt(f). In addition, our simulation results show a f 3 dependence for the radiation loss, consistent with the results in [Terahertz attenuation and dispersion characteristics of coplanar transmission lines]14, though the absolute value is small (below 0.5 dB/cm up to 300 GHz) as we discussed above.\nHere, we have added the Fig. S2 and comments on Supplementary Note 2.\nThe new text reads “Figure S2 illustrates the simulation results of the transmission lines, including conductor loss, dielectric loss, and radiation loss. Notably, all three loss components exhibit frequency dependence. In comparison to the other two loss mechanisms, radiation loss is significantly less pronounced. Specifically, dielectric loss increases linearly with frequency, whereas metallic loss demonstrates a linear relationship with the square root of frequency.”\nd. Related to the above, the authors mention they replace the high resistivity silicon substrate with quartz because the latter has lower “transmission line loss”. The authors should provide comparative loss curves showing alphorn-Si vs alpha_quartz in the frequency range of interest. Also here, by looking at established literature e.g. Grischkowsky et al. J. Opt. Soc 7, 10 (1990), we find that the loss curves of crystalline quartz shown there neither scale like ~f nor linearly! Please provide data to support this assumption.\nResponse: We thank the reviewer for the comment and apologize for not making this clear enough in the previous manuscript. Indeed, the dielectric loss of quartz is similar to HR-Si, according to the results in [Grischkowsky et al. J. Opt. Soc 7, 10 (1990)]15. The main benefit of using quartz substrate is due to the suppression of radiation loss into the substrate. We have now performed additional simulation [new Fig. S1(a) and (b)] to present the simulated near-field distribution of the transmission line on quartz and silicon substrates at 500 GHz, respectively. For the silicon substrate, there is a significant amount of leakage into the substrate side of the transmission line. This phenomenon occurs because the wave velocity along the transmission line exceeds that in the silicon substrate. Similar phenomenon is also observed in terahertz coplanar waveguide on GaAs 8 substrate16. In contrast, in the case of the quartz substrate, the fields are tightly confined along the transmission line, with negligible energy leakage into the substrate. New Fig. S1(c) illustrates the simulated radiation loss for both scenarios as a function of waveguide length. The fitted radiation losses for the quartz and silicon substrates are 9.3 dB/mm and 0.081 dB/mm, respectively. These values confirm the significant radiation loss associated with the silicon substrate. Thus, here, we utilize a quartz substrate instead of a silicon substrate to circumvent the undesired leakage loss.\nRegarding the dielectric loss modeling, in our simulations we have assumed a constant loss tangent for quartz. The measured loss curves of quartz in the literature cited15 indicate that the power absorption of quartz scales approximately linearly with frequency below 500 GHz, leading to a constant material loss tangent, consistent with the assumption used in our numerical model. More specifically, the loss tangent can be calculated based on the equation:\n9\nta n 2 c fn    = (c is optical velocity in the vacuum, f is the frequency, n is the refractive index, α is the power absorption). The measurement result in this literature also shows that variation in linear refractive index is < 0.002 within the frequency range below 0.5 THz. Therefore, a constant loss tangent leads to linear frequency scaling of the power absorption α in the concerned frequency range of our current work. However, we do note that when frequency exceeds 1 THz, the absorption coefficient exhibits an increasing trend in the frequency, and should be taken into account more rigorously at these frequencies. In our study, the measured frequency range is limited to below 500 GHz. Therefore, it is reasonable to assume a linear frequency dependence for dielectric loss in our current devices.\nFig. S1 The simulated electric field distribution on the quartz (a) and silicon (b) substrate. (c) Simulated RF loss versus length on quartz and silicon substrate.\nHere, we have added the comments on Page 4 and Supplementary Note 2.\nThe new text reads “In contrast, our design incorporates a 50 µm signal width and utilizes a quartz substrate to reduce the conductor loss and substrate leakage, respectively (see SI Note 2 for detailed comparison).”\nAnd “Supplementary Note 2: Comparison of mode leakage between quartz and silicon substrates\nFigure S1(a) and (b) present the simulated near-field distribution of the transmission line on quartz and silicon substrates at 500 GHz, respectively. For the silicon substrate, there is a significant amount of leakage occurring into the substrate side1. This phenomenon occurs because the wave velocity along the transmission line exceeds that in the silicon substrate. In contrast, in the case of the quartz substrate, the fields are tightly confined along the transmission line, with negligible energy leakage into the substrate. Figure S1(c) illustrates the simulated radiation loss for both scenarios as a function of waveguide length. The fitted radiation losses for the quartz and silicon substrates are 9.3 dB/mm and 0.081 dB/mm, respectively. These values confirm the significant radiation loss associated with the silicon substrate.”\ne. What about the losses of lithium niobate, won’t those be dominant? Authors must discuss this in detail.\nResponse: We thank the reviewer for the valuable comments. LN is indeed a key material in our device. In our simulation, we have comprehensively taken into account the losses associated with LN, quartz, and also the silicon dioxide cladding layer. The dielectric loss tangent of LN is 0.02517 at THz bands. Our simulation results suggest that the loss from LN film contributes to ~ 70 % of the total dielectric loss at 300 GHz, which does play a dominant role in the overall loss in the system.\nHere, we added the detailed description of simulation part on Page 11. The new text reads “In the simulation, we considered the losses of all materials, including LN57, quartz substrate58 and the deposited cladding59.”\nf. For Fig. 2a please mention the frequency at which the measurement is taken.\nResponse: We thank the reviewer for the suggestion. The DC V was measured using a 100 π kilohertz electrical sawtooth waveform sweep, which was injected into the modulator and monitored by an oscilloscope.\nWe have added the content on Page 12 to emphasize the measurement. The text reads “For the measurement of DC/low-frequency Vπ, a 100 kilohertz electrical sawtooth waveform was generated from an arbitrary-waveform generator (AWG, RIGOL DG4102) and applied to the transmission line of the electro-optic modulator through a GSG probe (GGB industries, 50 GHz).”\ng. For Fig. 3c please provide all as measured data of sideband ratios in the supplementary material (i.e. without any filtering or amplification after the chip) and full derivation of extracting V_pi from how much is the applied THz power from the instrument, how much power is efficiently 10 injected into the chip, and how much are the losses from attenuation in the cables used to bring the terahertz to the chip. Is the V_pi they mention as-applied, taking into account the whole system, or the one on-chip? This must be clearly mentioned.\nResponse: We thank the reviewer for detailed comments regarding Fig. 3c. During the measurement process for Fig. 3c, we have carefully calibrated the power and loss in each stage of the measurement setup, including the probe, cable, and waveguides. To ensure the accuracy of our measurements, the output power of the VDI source across different frequency bands, specifically 10-67 GHz, 90-140 GHz, 140-220 GHz, 220-320 GHz and 320-500 GHz, was measured with a VDI Erickson PM5B power meter. We have now deposited the raw measurement data at: https://doi.org/10.5281/zenodo.15448061. The V quoted in our manuscript all correspond to on- π chip voltages after calibration.\nWe have modified the context and provided the raw data in the revised manuscript.\nThe new text reads on Page 6 “We demonstrate low-voltage THz-optic modulation at frequencies up to 500 GHz using the testing setups shown in Figs. 3(a) and 3(b) following our previously established methodologies (see Methods for more details)29.”\nAnd on Page 12 “Calibration of the VNA test results involves first measuring the transmission loss of all cables by a two-port VNA test. The loss data of the probes and photodetectors (PDs) at corresponding frequencies were retrieved from the datasheets provided by the manufacturers. These losses were finally subtracted from the measured EO S21 parameter. To ensure precision measurements in the OSA tests, the entire experimental setup was calibrated using a VDI source module in conjunction with a power meter (Erickson PM5B). The output power of the VDI source across multiple frequency bands was carefully measured. The actual electrical power that was applied to the chips is determined by subtracting the measured source power by the probe loss values from GGB datasheet. The detailed connection for measurement is shown in Fig. S6(a). The RF Vπ values quoted in this paper all correspond to on-chip voltages after calibration.”\nh. Since at the end the performance of the entire system counts, the authors should discuss how the entire scheme compares to using antennas directly, as discussed in: https://ieeexplore.ieee.org/abstract/document/10298946 precisely on thin film lithium niobate. Plus about further increasing the frequency. The data presented in this paper showcases that even higher frequencies are supported by the LN platform (extends well into 1 THz).\nResponse: We thank the reviewer’s suggestion. The cited reference18 and our current work focus on different wavelength ranges and thus different applications. In sensing applications that require broad frequency range but are less sensitive to system conversion efficiency, integrating antenna with the modulator makes the system compact. Nevertheless, a major drawback of antenna integration is the substantial conversion loss that occurs during the transition from free space to waveguide, especially when a broadband antenna is used. In Ref. 48, the converted signals are relatively low and only quoted in arbitrary units. Although the use of a high gain antenna can 11 mitigate this issue to some degree, it inevitably restricts the system's bandwidth due to inherent gain-bandwidth limitations in antennas. In contrast, our device focuses on THz-optic conversion from coplanar waveguides, which can be either directly driven by waveguide-based feed lines or combined with high-gain off-chip antennas for free-space applications. This approach presents higher conversion efficiencies and supports more versatile application scenarios including radar and communications.\nWith that said, we do acknowledge the compactness and potentially higher-frequency operations offered by further integrating antennas with our current demonstration of ultrabroad-band modulators, and have added the reference to the revised manuscript in the THz generation part on Page 8 to further discuss this prospect. The new text reads “Further integrating THz antennas directly on chip could circumvent the limitations imposed by probes and other peripheral electronics, enabling THz generation at frequencies well beyond the current accessible range48.”\ni. For Fig. 3d, please explain in detail how you compute the EO S21 response, again considering the calibration of frequency-dependent transmission through cables and importantly RF probes. How do you compute the red dashed line “from measured S-parameters”. Again, if this is from the VNA measurement in the range 140-220 GHz as mentioned in the methods, how do you calibrate the rest of the frequency band up to 500 GHz to measure only the chip? Please provide exact formulas wherever possible. Please provide an exact sketch of experiment in the supplementary and label with corresponding THz powers.\nResponse: We thank the reviewer for this important comment. We have computed the electro-optic (EO) S21 response following the analysis framework introduced in our previous work1. The red dashed curve in Fig. 3d is calculated from the electrical S-parameters measured by a VNA and relevant extension modules. Specifically, the refractive index n and characteristic impedance values can be extracted from the S-parameter as shown in Figs. 2(b) and 2(c). Meanwhile, combining the S-parameter test results in the 100KHz – 50GHz and 220-320 GHz frequency bands, the electrical loss of the transmission line across the 0-500 GHz band is fitted using a theoretical model (Fig. 2c), which was discussed in the manuscript and in more details in our response above.\nThe detailed calculation process is as follows. We first use the formula 𝑍 = 𝑍 √ (1+𝑆11 )2−𝑆 2 2 1 to 𝑖𝑛 𝐶 (1−𝑆11 )2−𝑆 2 2 1 calculate the characteristic impedance of the transmission line, 𝑍 . Here Z refers to the 𝑖𝑛 C impedance of the driving circuit. To calculate the effective refractive index, we first calculate the propagation constant  from the measured S parameters, and then, obtain n based on 𝑛 = 𝛽𝜆0, 2𝜋 where 12 0  is the wavelength in free space. With these derived parameters, we calculate the EO S21 following:\n S 2−2S cos ( μ L ) +1 EO S =10log(1−H)2 21 21 opt  (S1), 21  (ln S )2 + ( μ L )2   21 opt \n (S2),\nμ = (n −n ) opt c m o\nwhere S is the electrical forward transmission coefficient in linear scale, representing the 21 contribution from RF loss; βµ is the wavevector (velocity) mismatch term as defined in Eq. (S2); opt Η characterizes the mmWave reflection due to mismatch between the input impedance of the transmission line, Z and that of the driving circuit, Z , as defined in Eq. (S3).\nin C\nThe absolute RF V values can be derived from the EO S21 parameter and the low-frequency V π π value using the following formula:\nV π , R F = V π , L F  1 0 − E O S 21 2 0 (S4).\nWe have added a schematic illustration of the experimental setup (now Fig. S3, also copied below) and detailed explanation for the calculation part in the Supplementary Note 3.\nFig. S3. Schematic illustration of the S-parameter measurement setup. The frequency extender module (FEM) extends the working frequency of the vector network analyzer (VNA) to 220–325 GHz. Transmission parameters are obtained using ground-signal-ground (GSG) probes. (a) Measurement in the 0–50 GHz band; (b) Measurement in the 220–325 GHz band.\nj. For Fig. 3d please provide in the supplementary material the systems’ S21, that is including losses of cables and probes in and out. + RF power applied.\nResponse: We thank the reviewer for the suggestion. Here, we employed two methods to measure the EO S21 parameter. The first method utilized a VNA. Prior to the experiment, all cables were interconnected, and calibration values were set to zero under the assumption of a lossless connection system. After calibration, measurements were performed to acquire the EO S21. Subsequently, to obtain a more accurate actual EO S21 parameter, frequency-dependent self-loss data for the probes and photodetectors (PDs) were extracted from the manufacturers’ datasheets. These losses were then subtracted from the measured EO S21 parameter. Through this process, the EO S21 parameter accurately representing the modulator’s intrinsic performance was ultimately obtained.\nAnother method employs an optical spectrum analyzer (OSA) to characterize the EO S21. Here, the RF V measured at each frequency was converted into the EO S21. All derivation details and π calibration procedures for this calculation are provided in our response to Question i.\nWe have provided all measured raw data at https://doi.org/10.5281/zenodo.15448061. which includes the probe losses and PD loss, the measured EO S21 values and the real EO S21 values at different frequencies.\nWe have also added the text in the revised manuscript to describe the calibration process on Page 12. Moreover, we have listed the tested data and calibration data for every point in the data links.\nThe new text reads “Calibration of the VNA test results involves first measuring the transmission loss of all cables by a two-port VNA test. The loss data of the probes and photodetectors (PDs) at corresponding frequencies were retrieved from the datasheets provided by the manufacturers. These losses were finally subtracted from the measured EO S21 parameter. To ensure precision measurements in the OSA tests, the entire experimental setup was calibrated using a VDI source module in conjunction with a power meter (Erickson PM5B). The output power of the VDI source across multiple frequency bands was carefully measured. The actual electrical power that was applied to the chips is determined by subtracting the measured source power by the probe loss values from GGB datasheet. The detailed connection for measurement is shown in Fig. S6(a). The RF Vπ values quoted in this paper all correspond to on-chip voltages after calibration.”\nk. For Fig. 4c please provide details on how exactly you do the power calibration. How much terahertz power do you have at the various positions of the coax cables (i.e. just before the output RF probe, just after the RF probe, just before the mixer)? Please provide exact sketch of experiment in the supplementary and label with corresponding THz powers.\nResponse: We thank the reviewer’s suggestion. Figure. S6(b) depicts the generation position of the THz signal and enumerates all sources of loss, such as those from the probes, THz waveguide, signal analyzer extension module (SAX), and cables. We have now deposited all the data for different positions during measurement, including probes loss, mixer losses, cable loss and others.\nThe link is shown here: https://doi.org/10.5281/zenodo.15448061.\nWe have added the sketch of experiment in the supplementary Note 10 and labeled the THz powers generated position. And we also added the exact data to the links.\nThe new text reads on Page 12 “The detailed connection for measurement is shown in Fig. S6(a).” and also add an exact sketch in the Supplementary Note 10 to clearly describe the measurement.\n“Supplementary Note 10: Detailed THz-optical modulation and THz generation setups\nl. Is the power you mention in fig. 4c and e, and correspondingly used to compute the conversion efficiency in d, – i.e. out of chip, there where it would be used e.g. to drive an EO modulator as they show in their first experiment of Fig. 3? These details are extremely important and need careful mentioning.\nResponse: We thank the reviewer for this suggestion. The conversion efficiencies in this work all correspond to on-chip values. The data of on-chip THz power shown and used for efficiency calculations in Figs. 4(c–e) are derived from electrical spectrum analyzer (ESA), with systematically de-embedded losses from cables, probes, and mixers.\nWe have added a new sketch figure on SI and added the content on Page 13, to explain the data come from. The new text reads “We calibrated and deducted losses incurred from various components of the entire testing system, including the probe, waveguide, cable and SAX, as shown in SI Fig. 6(b). The measured THz power values and the associated conversion efficiencies quoted in this paper all correspond to on-chip power after calibration.”\nm. My previous point l is very important because the authors mention ref. 44 noting the “low efficiency” in their introduction, which was the first demonstration of thz generation in circuits from TFLN. It may be just a timing issue, but they don’t mention the more recent work where the generation efficiency is significantly higher, see recent arxiv terahertz generation: https://arxiv.org/abs/2406.15651 which was recently shown all the way to 3.5 THz. In fact, in that paper, the as-measured power efficiency in the farfield (hence out of chip) is power_THz_in_the_farfield/power_optical = 4.5*10^-9 for 72 pJ pulse energies (without any corrections). Instead, if accounting for coupling efficiency out of chip and all other losses, on-chip the conversion efficiency of ~10^-5. Note that here conversion efficiency is defined as THz power out over optical power in. This number would be significantly larger than what the current paper 15 presents and needs to be presented as such. If I see this right, compared to the current paper where the efficiency is 4.86*10^-6 /W and where the authors demonstrate up to 20 mW (~14 dBm) optical power on-chip, this would yield a conversion efficiency of power THz/power optical = 4.86*10^-6 /W*20 mW (13 dBm) ~10^-7, that is a factor of about 20 in the as-measured efficiency and 1/20 in the on-chip efficiency compared to the arxiv paper above. In fact, from fundamental principles, it would only make sense that the pulsed emission is more efficient because of the higher peak powers, so the authors need to correct their statements in the introduction/motivation of their work. Already CW is very interesting.\nResponse: We thank the reviewer for bringing up this important issue regarding pulsed operation. The reviewer is correct that the main reason for achieving a higher conversion efficiency in the referenced paper is due to the much higher peak power in a pulsed operation, which is also the operation regime that most past literatures of LN-based THz generators have adopted due to the relatively weak nonlinear interactions. As a result, in our manuscript we have converted all conversion efficiencies in past literatures to an equivalent-CW efficiency based on peak powers, for a fair comparison with the CW efficiency achieved in our work. Specifically in the recent paper (now cited as Ref. 47) the conversion efficiency of 2.3×10⁻⁵/W is achieved with short pulses of 0.06 ps with a repetition rate of 100 MHz, translating to a CW conversion efficiency of 1.38×10-8/W if normalized by its peak optical power, which is still more than two orders of magnitude smaller than that achieved in our work. In our response to the next question, we have detailed the methodology for converting pulsed-wave efficiency to CW efficiency.\nWe also echo strongly with the reviewer’s comment that acknowledges the importance of achieving CW operation by itself, which is important for many applications including imaging and communications.\nWe have modified the text and added the mentioned reference paper [46] on Page 3 to better discuss the comparison with THz generation with pulse light. The new text reads “While TFLN waveguides provide much tighter optical confinement and in principle stronger nonlinear interactions44, current exploration of THz generation in the TFLN platform has been limited to pulsed operation with relatively low conversion efficiency if normalized by continuous-wave pump power45,46.”\nWe also added the mentioned references [20] in the Table. S3 for comparison and detailed context in SI note 8. The new text reads “Recent effort based on the TFLN platform has achieved THz generation and antenna emission on the same chip20, yet the continuous-wave-normalized conversion efficiency is still limited to 1.3810-8/W. ”\nn. Similarly, they mention several times in their paper the conversion efficiency of pulsed generation schemes “when normalized to continuous wave efficiencies” (e.g. in the last paragraph 16 before results section) but they don’t provide the exact formulas how they do this “normalization”. What does that mean? Please provide full math in complementary note 5.\nResponse: We thank the reviewer for pointing this out. To convert pulse efficiency to CW efficiency, we use the pulse width, repetition rate, and average pump power to estimate the peak power of the laser pulses, which is subsequently used to convert the pulsed conversion efficiency into an equivalent CW efficiency.\nMore specifically, we first calculate the duty cycle by 17 D u ty C y c le f  =  (τ is pulse width, f is repetition rate), which reflects the proportion of effective lasing time within the working cycle. The average pump power is calculated as P =E f , where E P is the pulse energy. The instantaneous peak avg p power can therefore be calculated by 𝑃 𝑖𝑛𝑠 =𝑃 𝑎𝑣𝑔 / 𝐷𝑢𝑡𝑦 𝑐𝑦𝑐𝑙𝑒 , leading to the continuous wave normalized conversion efficiency of  = /P , where η p is the absolute pulsed conversion CW p ins efficiency.\nWe have added the detailed calculation process in the Supplementary note 8. The new txt reads “The conversion from pulsed to continuous-wave THz efficiency is performed by estimating the peak optical power of the pulsed source. More specifically, we first calculate the duty cycle Duty Cycle=τf (τ is pulse width, f is repetition rate), which reflects the proportion of effective lasing time within the working cycle. The average pump power is calculated as P =E f, where E is avg p P the pulse energy. The instantaneous peak power can therefore be calculated by P =P /Duty cycle, ins avg leading to the continuous wave normalized conversion efficiency of η =η /P , where η is the CW p ins p absolute pulsed conversion efficiency. ”\no. Similarly, if I understand this well, they compute the conversion efficiency of their device when measured with the ESA settings shown in S1 fig. 1a? is this correct, given that at smaller scans and lower BW we see a clear drop in the amplitude, e.g. in S1 fig. 1d? The authors need to explain why this is correct.\nResponse: We thank the reviewer for the comments. In the paper, we showed the measured electrical spectra of the generated THz signals using different resolution bandwidth settings in the ESA. It should be noted that since the lasers are not locked in the experiments, the THz signal sees significant frequency fluctuations on the order of 10s of kHz. As a result, when the resolution bandwidth of the ESA is set to be finer than this scale, as shown in Fig. S5(b-d) (originally Fig. S1), the frequency-scanned data points are not guaranteed to genuinely capture the amplitude of the THz signal, and thus do not provide meaningful information about the signal amplitude (but they do provide information on the spectral characteristics). In contrast, a large enough measurement bandwidth (as that shown in Fig. S5a) ensures that all THz signal power can be captured during a single scan, and is used for the calculation of conversion efficiency.\nWe added several new sentences in Supplementary Note 7 to explain the reason for drop in THz signal amplitude in measurements with lower BW. The new text reads “Due to the frequency drift during high-resolution scan, the measured amplitudes in Fig. S5(b-d) do not represent the actual THz signal power. The THz power levels reported in this paper and the associated conversion efficiencies all correspond to measurements with a large enough resolution bandwidth [as in Fig. S5(a)] to genuinely capture the total generated THz power within the frequency fluctuation range. ”\n2. I very much enjoyed their idea and data of Fig. 5, but once again I don’t fully understand what “relative power” is that they plot in their panels b-d. Relative to what exactly? Please give absolute units in dBm, and else explain through formulas what you report. What are the small sidebands that are visible around the tone at 1561.5 nm of panel 5f and in the inset?\nResponse: We thank reviewer for the comment. Here, we define the noise as the baseline and the relative power is the comparison between the noise floor for easier display. In order to present the results more clearly, we have modified the data with real power in Fig. 5 on Page 10.\nThe generation of small sidebands are at 1561.276 nm and 1561.848 nm. Both signals are generated through four-wave mixing (FWM) in a nonlinear medium, where the signal light (1561.564 nm) interacts with the pump (1564.98 nm) and its first-order sidebands (1564.696 nm/1565.268 nm). The FWM process is relatively strong at elevated optical power levels, yet the overall powers of these parasitic peaks are insignificant.\n3. In their introduction, the authors mention a few aspects which they need to explain:\na. They mention plasmonic modulators and their loss, and LN as being a good alternative. But there is an entire bulk of work that uses silicon slot waveguides which are far less lossy e.g. from the group of Christian Koos -the authors need to mention that work specifically. In addition, those structures have demonstrated record field enhancement and hence low V_pi – please correctly reference those works.\nResponse: We thank the reviewer for this suggestion. We have now added new references [11-13] and modified the relevant descriptions to incorporate the discussions on silicon-organic hybrid (SOH) devices in the introduction part on Page 2. Although the propagation loss per unit length of SOH devices in Ref. [12] is significantly lower (~40 dB/cm) than those of plasmonic devices (0.4-0.5 dB/um), they also feature substantially weaker electro-optic interaction strength and require significantly longer device to achieve a reasonable modulation efficiency, which ultimately leads to substantial overall device loss. In the particular case of Ref. [12], the overall loss of a 0.5 mm long modulation is 2 dB, with a modulation Vpi of 22 V. This highlights the critical trade-off between reduced per-unit-length loss and voltage-length produce (Vpi-L) in modulation design, which is also a crucial advantage for TFLN modulators.\nTo make this point clearer, we have added new references and modified the relevant part on Page 2. The new sentences read “Recently, modulators based on electro-optic polymers have reported bandwidths significantly exceeding 100 GHz with the assistance of plasmonic11 or silicon-slot12 waveguides. They also feature reduced footprints due to enhanced light-matter interaction. 18 However, these modulators usually exhibit significant optical losses (0.4-0.5 dB/µm in plasmonic and 40 dB/cm in slot structures) and limited power handling capabilities11-13. ”\nb. Compared to 28 V at 500 GHz of ref. 22, the current 8 V is summarized as “an order of magnitude better in power consumption” in the abstract, but I don’t find the exact computation of the power consumption in their paper or supplementary material. I understand that it scales quadratically but please add that for clarity.\nResponse: We thank the reviewer for the detailed suggestion. The electrical power consumption in a properly loaded transmission line is P = V2/R, where V is the drive voltage and R is the load resistance. Therefore a 3.5 times reduction in drive voltage gives approximately an order of magnitude reduction in power consumption.\nWe have modified the relevant descriptions in the manuscript on Page 6 to make this clearer. The new text reads “Since power scales quadratically with voltage, this 3.5 times reduction in RF V π leads to a significant decrease in modulation power consumption by more than an order of magnitude, which is of great significance for practical application scenarios.”\nc. They say that bulk systems “limiting their reliability and practicality” – this is arguable in my view. Please explain.\nResponse: We thank the reviewer for the comment. We agree with the suggestion and have deleted this comment in the manuscript.\n4. Below fig. 1 they mention the use of quartz “to reduce substrate leakage” – please explain and give numbers how much the leakage is reduced?\nResponse: We thank the reviewer for this question. As we have discussed in our response to the reviewer’s Question 1d, our additional simulation results in Fig. S1(a) and (b) present the simulated near-field distribution of the transmission line on quartz and silicon substrates at 500 GHz, respectively. For the silicon substrate, clear and substantial leakage into the substrate side of the transmission line is evident. This phenomenon occurs because the wave velocity along the CPW transmission line exceeds that in the silicon substrate. In contrast, in the case of quartz substrate, the fields are tightly confined along the transmission line, with negligible energy leakage into the substrate16. Fig. S1(c) illustrates the simulated radiation loss for both scenarios as a function of waveguide length. The fitted radiation losses for the quartz and silicon substrates are 9.3 dB/mm and 0.081 dB/mm, respectively. These values confirm the significant radiation loss associated with the silicon substrate. Thus, in this paper, we utilize a quartz substrate instead of a silicon substrate to circumvent the undesired leakage loss.\nHere, we have added the comments on Page 4 and supplementary note 2 on SI part.\nAnd “Supplementary Note 2: Comparison of mode leakage between quartz and silicon substrates\nFigure S1(a) and (b) present the simulated near-field distributions of the transmission lines on quartz and silicon substrates at 500 GHz, respectively. For the silicon substrate, there is a significant amount of leakage into the substrate side1. This phenomenon occurs because the wave velocity along the transmission line exceeds that in the silicon substrate. In contrast, in the case of the quartz substrate, the fields are tightly confined along the transmission line, with negligible energy leakage into the substrate. Figure S1(c) illustrates the simulated radiation loss for both scenarios as a function of waveguide length. The fitted radiation losses for the quartz and silicon substrates are 9.3 dB/mm and 0.081 dB/mm, respectively. These values confirm the significant radiation loss associated with the silicon substrate.”\nFig. S1 Simulated electric field distribution at 500 GHz on quartz (a) and silicon (b) substrates. (c) Simulated radiation loss versus length for the two substrates.\n5. Can you please explain how about the birefringence of quartz in the THz? How is the quartz aligned with respect to the LN crystal and what impact does that have?\nResponse: We thank the reviewer for raising this point. The birefringence of quartz within 0.2-2.2 THz is ~0.05, with refractive indices for ordinary and extraordinary light of about 2.11 and 2.16, respectively19. For the LN wafer we purchased, the quartz substrate is also x-cut, and notably, the x-direction of the quartz is aligned with that of the LN wafer, ensuring a high degree of orientation consistency between the two materials. According to our simulation results, the effective index of the THz mode will increase by ~0.04 if the z-axis of quartz crystal is perpendicular to that of LN. In this case, a slight modification to the design of the transmission line will be needed to re-align the velocities between optics and THz.\n6. In the “On-chip THz-optic modulation” they mention they use “test setups using previously established methodologies” – but please also refer to methods.\nWe also added more detailed measurements in methods on Page 12. The new sentences read “To ensure precision measurements in the OSA tests, the entire experimental setup was calibrated using a VDI source module in conjunction with a power meter (Erickson PM5B). The output power of the VDI source across multiple frequency bands was carefully measured. The actual electrical power that was applied to the chips is determined by subtracting the measured source power by the probe loss values from GGB datasheet. The detailed connection for measurement is shown in SI Fig. 5(a). The RF Vπ values quoted in this paper all correspond to on-chip voltages after calibration.”\n7. In the “on-chip continuous-wave terahertz generation” part of their paper, the authors comment that a GSG type of contact could work with an optical delay line that would introduce a pi shift in their nonlinear polarization. Can the authors please explain how they would to this in practice? Is it really correct to say that “results in zero nonlinear overlap if the signals running in the two gaps have the same phase ”? or is it rather that one would generate a symmetric GSG mode?\nResponse: We thank the reviewer for this valuable comment.\nThe generated THz wave arises from a second-order nonlinear polarization term (P(2)), which is proportional to the product of the two optical pump fields, expressed as:\n𝑃(2) ∝ 𝐸 𝐸∗ = 𝑒−𝑖(𝜔1𝑡+𝜙1 )𝑒𝑖(𝜔2𝑡+𝜙2 ) = 𝑒−𝑖(𝜔1𝑡+𝜙1 )𝑒𝑖[(𝜔1−𝜔𝑇𝐻𝑧 )𝑡+𝜙2 ] = 𝑒−𝑖𝜔𝑇𝐻𝑧𝑡𝑒𝑖(𝜙2−𝜙1 ) 1 2\nSince the two optical frequency components go through the same optical waveguide, their relatively phase difference 𝜙 −𝜙 cannot be changed by a common optical phase shifter. As a 2 1 result, the phase of the generated THz wave mainly depends on the time delay of the waveguide.\nIn a coplanar waveguide configuration, such as a GSG transmission line, the generated THz electric field should exhibit an anti-symmetric (180-degree phase difference) spatial distribution across the two gaps to properly excite the fundamental CPW mode. To achieve this spatially anti-symmetric THz field distribution, the nonlinear polarization terms generated in the two separate waveguide arms of the MZI should differ by a π phase. This can be achieved by incorporating an 𝜋 optical delay line in one of the two arms, with a delay time of 𝑡 = ⁄𝜔 . 𝑇𝐻𝑧\nRegarding the second question, we agree that stating \"zero nonlinear overlap if the signals running in the two gaps have the same phase\" is not rigorous enough. In the case of an equal-arm Mach-Zehnder Interferometer (MZI), the generated nonlinear polarizations in the two arms will feature 21 same phase, with finite overlap with the symmetric mode of the CPW. To investigate this in more detail, we conducted COMSOL simulations for the symmetric and anti-symmetric modes, as shown in Fig. R1. The simulated symmetric mode (right panel) has an effective index of n =1.1548−0.0156i, indicating a large velocity mismatch with the optical mode. As a result, the eff,2 THz generation into symmetric mode is rather inefficient in the current device setting. In addition, the symmetric mode exhibits a significantly faster phase velocity compared to the differential mode, leading to potentially stronger electromagnetic leakage20 and is more prone to electromagnetic interference. As a result, symmetric mode is typically not preferred for high-speed signal transmission21. In summary, the balanced-arm configuration in our current devices would lead to theoretically zero nonlinear overlap with the fundamental symmetric CPW mode and finite overlap with the anti-symmetric mode, which however is highly inefficient due to significant velocity mismatch.\nFig. R1 The simulated electric field distribution for anti-symmetric mode (a) and symmetric mode(b).\nTo make this discussion more rigorous and clearer, we have added some of the above discussions to comment on potential interaction with symmetric mode on Page 7. The new text reads “This is primarily because symmetrically pumping the two optical waveguides would generate nonlinear polarizations PNL ~ E(ω ) E(ω )* with the same phase in the two coplanar waveguide gaps, which 1 2 features zero overall nonlinear overlap with our target differential THz mode. Although finite overlap with the symmetric (common) THz mode exist, the generation efficiency would be low due to substantial velocity mismatch.”\n8. Could the authors point to where they get their formula (2) and (3) of the supplementary material, else give the entire derivation that that is the correct definition of the effective spot area from the nonlinear wave equation?\nResponse: We appreciate the reviewer’s insightful comment. To clarify the origin and derivation of formulas (2) and (3) and the definition of the effective spot area, we have carefully addressed each point as follows:\nFormulas (2) and (3) presented in our paper are derived based on established nonlinear optics theory as described and defined in the “Nonlinear Optics” textbook by Robert W. Boyd22. Specifically, Boyd’s Chapter 2.2 and Chapter 2.8 outline the derivation of coupled-wave equations 22 governing second-order nonlinear processes, including difference frequency generation (DFG) and sum frequency generation (SFG). The main distinction between the equations for DFG (used in our work) and those for SFG (such as second-harmonic generation, SHG) lies primarily in the sign of the wavevector term.\nTo further include the effect of optical loss in our analysis, we refer to Ref. [50] (Bringuier et al., Phys. Rev. B, 1994)23 that provided the nonlinear wave equations in lossy nonlinear media and their solutions. Although its derivation focuses on SHG, the mathematical formalism for coupled-amplitude equations is directly analogous to our DFG equations. We have incorporated this reference in our revised manuscript to strengthen the theoretical background and clearly articulate the derivation steps.\nThe main difference between our analysis and the textbooks is the use of optical waveguides, making the optical intensity varying over spatial dimensions. As a result, effective spot areas are used to capture the spot sizes of different optical modes:\nTo address the origin of the formula for the effective spot area (A), we have added relevant references24,25 in our revised manuscript. These references, [50] and [51], comprehensively cover the definition and theoretical background of the effective spot area in the context of our work. They provide detailed descriptions of how the effective spot area is derived and defined in the framework of the nonlinear wave equation, which directly answers the reviewer's question.\nWe believe these clarifications will significantly enhance the reader’s understanding of the theoretical basis and clearly justify our selection and derivation of the equations employed.\nHere, we have added the references [50] and [51] on Page 8.\n9. The authors provide in Fig. 4f the “computed efficiency when inside a ring resonator” – how do they compute this? Please add a few notes. I’m guessing you’re simply scaling for intra-cavity power but this needs to be clarified in the text, especially since more modes will get coupled to each other.\nResponse: We thank the reviewer for raising this important point.\nAs mentioned in the paper, we assume that a racetrack resonator with a bending radius of 80 µm, a straight section length of 5 mm, so the resonator circumference length L = 10.5 mm, corresponding to an estimated free-spectral range (FSR) ~12 GHz.\nFSR = c / nL\nWhen the racetrack is critically coupled with a loaded Q factor of e.g. 5×106, the corresponding full width at half maximum (FWHM) linewidth is 40MHz.\nFWHM = f / Q 0 , where f is the center frequency. This leads to a finesse of 300 since: 0\nFinesse = FSR/FWHM\nThus the average round-trip number of approximately 48 (Finesse/2π) will see a 96-times amplification of the effective pump power, as optical energy dissipation in a critically coupled resonator is contributed half from the coupling waveguide.\nThe 96 times effective pump power amplification inside the resonator corresponds to an overall conversion efficiency enhancement of approximately 10,000 times at a Q factor of 5×106. This corresponds to a remarkable theoretical THz generation efficiency of 1.85%/W at 500 GHz. Although this resonant system allows THz emission only at discrete frequencies (with spacing of FSR ~ 12 GHz), the ability to generate continuous-wave THz signals at a wide range of stepped frequencies (e.g., 200 – 500 GHz) could still offer significant potential for many applications including communications and imaging.\nWe have added the detailed calculation process in the Supplementary Note 8.\nThe new text reads\n“Supplementary Note 9: Method for calculating THz generation efficiency in a ring resonator\nConsider a racetrack resonator with a bending radius R=80 µm, a straight section length L = 5 str mm, leading to a resonator circumference length L = 2πR+2L =10.5 mm, corresponding to an str estimated free-spectral range (FSR= c/nL) ~12 GHz. For a critically coupled resonator with a loaded quality factor Q of 5×106, the corresponding full width at half maximum (FWHM= f / Q) 0 linewidth is 40 MHz, where f is the center frequency. The resonator Finesse (Finesse = 0 FSR/FWHM) is therefore 300, leading to an average round-trip number of 48 (Finesse/2π). This corresponds to a 96-times amplification of the effective pump power, as optical energy dissipation in a critically coupled resonator is contributed half from the coupling waveguide, resulting in an overall conversion efficiency enhancement of approximately 10,000 times and a theoretical THz generation efficiency of 1.85%/W at 500 GHz.”\nIn conclusion, very interesting paper with exciting results but it needs to be substantially revised to improve clarity and transparency before publication. Also, please add line numbering for the next review round.\nResponse: Thanks for comments. We have added the line numbers and page numbers in the new version.\nThis paper presents a monolithically integrated thin-film lithium niobate (TFLN) photonic chip capable of both receiving (RX) via modulation and transmitting (TX) via difference frequency generation (DFG) THz signals for high-speed communications, with motivating applications including 6G wireless communications, medical imaging, THz radar and spectroscopy. The paper presents significant improvement over previously published results, with a ~10x reduction in Vπ for the modulator (RX) and roughly a 10x increase in generated continuous wave THz signals for TX. Both were demonstrated continuously up to 500 GHz.\nThe paper then shows up-converted modulation sidebands up to 35 GHz, on the generated THz carrier, along with a 5 GHz amplitude modulation (AM) signal. Higher level modulation schemes, e.g., quadrature-amplitude-modulation (QAM) are not possible given the large linewidth of the generated THz signals, as a consequence of not phase locking the two off-set lasers for DFG.\nWhile the improve of 10x for both RX and TX modes of operation are significant, the relevance of the presented work to a communications journal is not clear, especially when the highest demonstrated information modulation was only a 5 GHz AM signal.\nThis being said, while the presented results, along with the paper being very well written and well referenced, are clearly publishable it does not meet the originality threshold of a Nature Communications nor Nature Photonics paper, as it is largely improvement over previously published results. Perhaps with higher level QAM and the demonstration of a significantly higher data rate, this paper may meet that threshold but in its current form is not deemed sufficient for publication in this journal.\nResponse: We thank the reviewer for recognition of the significant improvements we have made in both the THz-optic modulation and THz generation performances, as well as the quality of our writing and referencing. We strongly believe that our results, in particular after incorporating additional experimental and simulation results, represent a major milestone and deliver key performance breakthroughs in both THz-optic modulation and THz generation. The THz photonic technologies provide high-performance and low-cost solutions to bridge the “THz gap” between microwave and infrared frequencies, with vast applications in next-generation wireless communications, medical imaging, chemical sensing, and beyond.\nFor THz-optic modulation, we achieve record-high measured electro-optic bandwidths along with a remarkably low RF half-wave voltage of 8 V at 500 GHz. This represents more than an order of magnitude reduction in modulation power consumption compared with past work, opening up the avenue towards practically relevant THz-photonic signal manipulation and processing systems. On the THz generation front, our device surpasses the efficiencies of all previous lithium niobate- based tunable THz generators by at least tenfold, achieving continuous-wave THz emission in a broad range of 220-500 GHz using milliwatt-level pump power. The high conversion efficiency, broad frequency tunability, and compact design of this system significantly enhance the versatility 25 and integration level for future THz applications. Most importantly, the coherent nature of our optical THz generation approach readily enables high-speed electro-THz modulation, a long- standing challenge in THz technology, using mature and low-cost optical modulation techniques.\nWe do agree with the reviewer that our previous demonstration of electro-THz modulation has not fully illustrated the performance advantage and platform scalability of our proposed TFLN system, mainly limited by the bandwidth of the commercial electro-optic modulator used. To address this concern, we have conducted additional experiments to realize high-speed electro-THz modulation at up to 65 GHz using an integrated on-chip LN modulator fabricated on the same LN-on-quartz platform, as shown in Fig 5 (also copied below). This new result not only validates the effectiveness of our electro-THz modulation approach at high frequency, but further demonstrates the potential of achieving fully functional THz-photonic systems on a single TFLN chip.\nIn conclusion, our research represents a significant milestone in the realm of THz photonics, accomplishing breakthroughs in crucial performance metrics, including modulation voltage, bandwidth, and THz generation efficiency. We believe, with the additional experimental results, it has made substantial contributions to the field and meets the originality and significance requirements of Nature Communications.\nFig. 5 High-speed electro-THz modulation. (a) Schematic diagram of the experimental setup. (b- d) Measured electrical spectra of the modulated THz waves under various modulation frequencies and formats (a commercial modulator or an on-chip LN modulator). (e-g) Corresponding optical spectra of the modulated pump signal. A commercial modulator is utilized for amplitude modulation at 5 GHz (shown in (b) and (e)) and 35 GHz (presented in (c) and (f)). An integrated lithium niobate modulator is employed when the modulation frequency reaches 65 GHz (as depicted in (d) and (g)).\\\n26"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors carefully addressed the reviewer's comments and made the corresponding revisions. Hence, the reviewer would recommend accepting this manuscript as it.", "reviewer_2": "Review of “Monolithic lithium niobate photonic 1 chip for efficient terahertz-optic modulation and terahertz generation “ by Yiwen Zhang et al\nI carefully read the revised version of the manuscript and the authors addressed most of my comments. I really like the concept the authors provide, believe it is a great addition to the field and deserves being published in Nature Comm after addressing some important shortcomings which aim at making it easier to compare with future chips. There are a few places in the paper which are not described with sufficient level of detail that would allow others in the community to estimate the performance of the device with respect to certain metrics. I am detailing below:\n1. My most important point is related to the generation: in their Figure 1 the authors show a GS-type coplanar transmission line (not GSG) for generation. However in lines 245-246 I seem to read that they use still a GSG with a single waveguide passing through one of the arms. Can the authors explain their choice and also how this single-arm pumping of the transmission line impacts the THz mode generated inside and its reflection at the GSG probe? They do mention “Although finite overlap with the symmetric (common) THz mode exists, the generation efficiency would be low due to substantial velocity mismatch” but in my view the biggest problem is at the coupling and read-out further in the chain all the way to their ESA. Can the authors comment?\n2. Fig 4b is missing units of the y axis and doesn’t have any scale. Impossible to quantify. Please add dBm levels. Are these the spectra at the ESA? If so I think it would be important to make two axes (the ESA (IF) freq and the THz freq). My interpretation is that these are the ESA measurements and it would be important that the authors clarify.\n3. How much RF power do you detect at the ESA for -65 dBm on-chip THz power and at which IF frequency? please state total losses of the entire chain (from on-chip) to ESA.\n4. It’s not easy to understand why the capacitive loading would impact losses. I suggest the authors spend 1-2 lines to explain this in line 185\n5. In lines 191 the authors say “Our measurement extrapolates to a propagation loss of approximately 2 dB/mm at 500 GHz, which is sufficient to support a total device length of 5-10 mm without excessive THz wave attenuation”. This doesn’t make much sense as then after 10 mm you have 20 dB attenuation which is definitely significant. The effective length is probably somewhere around 3-4 mm or so after which adding more mm will help the eo modulation only very little.\n6. I suggest writing formula S4 without the power of 10 since the EO S21 is itself a logarithm it makes it all very confusing.\n7. In figure S6 it would be nice to differentiate colors what is THz and what is RF (before the extender module) as now everything is orange and thus can be confusing.\n8. where are the spectra 5e-g measured? after the EDFA? what are side-bands appearing around the first laser line in Fig. 5f?\nThere are a few points that are cofusing and the authors need to address:\n1. Lines 90-91the authors talk about “limited to pulsed operation with relatively low conversion efficiency if normalized by continuous-wave pump power” the comment about normalization is impossible to understand in that short paragraph so I would suggest simply dropping that.\n2. Similarly line 103 “This performance surpasses all previous tunable optical THz wave generation devices by at least tenfold when normalized to continuous-wave efficiencies ”. maybe the authors can find a better phrasing to explain what they mean?\n3. Lines 104-105 they talk about electro-THz modulation but it’s not clear what this means when reading the paragraph.\n4. Cite works on dielectric waveguides in line 114.\n5. Fig. S2 (a) says Simulated conductor loss versus square root frequency but it’s not plotted against squareroot frequency. It’s not clear for which sample (quartz or silicon) this graph is. Please correct."}, "author_response": "Response: We thank the reviewer for recognition of the significant improvements we have made.\n1. My most important point is related to the generation: in their Figure 1 the authors show a GS-type coplanar transmission line (not GSG) for generation. However in lines 245-246 I seem to read that they use still a GSG with a single waveguide passing through one of the arms. Can the authors explain their choice and also how this single-arm pumping of the transmission line impacts the THz mode generated inside and its reflection at the GSG probe? They do mention “Although finite overlap with the symmetric (common) THz mode exists, the generation efficiency would be low due to substantial velocity mismatch” but in my view the biggest problem is at the coupling and read-out further in the chain all the way to their ESA. Can the authors comment?\nResponse: We thank the reviewer for the valuable questions. We apologize for the confusion caused by the visualization in Figure 1(a). To clarify, the actual transmission line structure adopted in our THz generation design is also a GSG configuration, where optical waveguide only goes through one ground-signal gap of this GSG line. To avoid confusion, we have redrawn the figure to present the structure more accurately and intuitively, and added labels of “G” and “S” for better visualization. The revised figure is also shown below.\nIn our scheme, when pumping optical signals in one of the two ground-signal gaps of the GSG transmission line, the resulting nonlinear polarization (distributed THz source) has finite nonlinear overlap with both the symmetric and anti-symmetric THz modes. However, as our simulation results in the previous response letter indicate, the symmetric mode fails to achieve velocity matching with the optical wave, leading to inefficient generation of THz signals into this mode. As a result, the generated THz signal, although pumped in an asymmetric manner, almost entirely emits into the anti-symmetric eigenmode of the GSG transmission line. This ensures that the THz signal can be effectively extracted at the output end using standard GSG probes without significant loss or reflection during the measurement process.\nThe revised figure 1 is shown here:\nFig. 1: Schematic of the dual-functional TFLN chip for THz-optic modulation and THz wave generation. (a) Schematic illustration of the device with strong optical confinement in the waveguides (blue) and THz confinement in the coplanar transmission lines (yellow), fostering a strong and velocity-matched interaction between the two modes. In THz-optic modulation, THz signals are fed into the transmission line via a probe and modulated onto the optical carrier. In THz-wave generation, two laser signals are input into the optical waveguide, resulting in frequency mixing and generation of THz wave, which is extracted via another probe. (b-c) Numerically simulated electric field distributions of the THz mode at 500 GHz (b) and the optical mode at 200 THz (c). (d-e) Frequency-domain illustrations of the THz-optic modulation (d) and THz wave generation (e) processes. (f) Scanning electron microscope image of the fabricated device. (g) Cross-sectional schematic of the device. The corresponding design parameters are shown in SI Note 1.\n2. Fig 4b is missing units of the y axis and doesn’t have any scale. Impossible to quantify. Please add dBm levels. Are these the spectra at the ESA? If so I think it would be important to make two axes (the ESA (IF) freq and the THz freq). My interpretation is that these are the ESA measurements and it would be important that the authors clarify.\nResponse: We thank the reviewer for the suggestion regarding the power units and the frequency-axis presentation (ESA IF frequency and THz frequency). Here, we have added a label of 5 dB/div. to the y axis, and rescaled all plots with fixed measurement power range of -100 dBm to -80 dBm, which together provide quantitative information about the generated THz signals across the measured frequency range. More detailed analysis on the absolute powers and conversion efficiencies are provided in panel (c-e) in this figure. We also appreciate the comment regarding IF frequencies directly measured from ESA. We agree that adding this data could enhance the interpretability of the figure. However, since our measurements here cover two distinct THz bands (220-320 GHz and 320-500 GHz) with different system parameters (e.g. IF bandwidth), the relationship between THz frequency and ESA IF frequency also varies slightly across bands, combining the data into a single dual-axis plot would risk obscuring these differences. After careful consideration, we have decided to stick with presenting the THz frequency in the main text to avoid confusion to general readers, and to provide details of the measurement equipment used in the Methods section and Supplementary information. Specifically, we have included the settings of the ESA and down-conversion equipment, in Characterization of THz wave generation part.\nThe new text reads\n“In this process, the intermediate frequency (IF) is determined by heterodyne mixing of the on-chip THz signal with the local oscillator within the SAX module.”\nThe revised figure is shown here.\nFig. 4: THz wave generation performance. (a) Setup for THz wave generation measurement. Inset shows a microscope image of the full device. FPC, fiber polarization controller; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer. (b) Measured THz wave spectra at different frequencies ranging from 250 to 490 GHz. The y-axes (power) span from -100dBm to -80dBm in all plots. (c) Generated THz wave power at various frequencies for a fixed total on-chip pump power of 8 dBm. (d) Conversion efficiency versus transmission line length at various frequencies. Black squares, red circles, and blue triangles represent 300, 400, and 500 GHz measurements. Dashed curves show the simulated results at corresponding frequencies. (e) THz wave generation power as a function of the input light power at different frequencies in double logarithmic scales, together with linear fitting lines with slopes ~ 2 verifying the quadratic power dependence. (f) Simulated conversion efficiency versus quality factor (Finesse) at 500 GHz in a resonant structure. The inset shows the device schematic.\n3.How much RF power do you detect at the ESA for -65 dBm on-chip THz power and at which IF frequency? please state total losses of the entire chain (from on-chip) to ESA.\nResponse: We appreciate the reviewer’s insightful comment. The actual electrical power that arrives at the electronic spectrum analyzer (ESA) equals to the generated THz power on chip subtracting the total chain loss of the entire measurement system. In our specific experiments, the total chain loss of the mixer, cable, and probe is ~ 20 dB, leading to around -85 dBm power detected at the ESA. The actual numbers vary across different frequency points, and can be found in the raw data provided at https://doi.org/10.5281/zenodo.15448061\nThe IF frequency is determined by the heterodyne mixing of the on-chip THz signal with a local oscillator in the detection module. We have added the description to make the statement more clearly. The detailed information, including IF frequency, raw power measured at ESA, and the entire chain loss, including mixer, probe, cable and THz waveguide, are listed at https://doi.org/10.5281/zenodo.15448061.\nThe new text reads “In this process, the intermediate frequency (IF) is determined by heterodyne mixing of the on-chip THz signal with the local oscillator within the SAX module.”\n4.It’s not easy to understand why the capacitive loading would impact losses. I suggest the authors spend 1-2 lines to explain this in line 185\nResponse: We thank the reviewer for raising this important point. The use of capacitive loading electrode design improves the transmission line impedance, which leads to the significantly lowered low-frequency RF loss. We have modified sentences to explain the advantage of capacitive loading structure.\nThe new text reads “Our achieved low-frequency RF loss of 0.4 dB is significantly lower than the 2.6 dB value reported in our previous work thanks to the capacitively loaded electrode design with improved impedance matching29.”\n5. In lines 191 the authors say “Our measurement extrapolates to a propagation loss of approximately 2 dB/mm at 500 GHz, which is sufficient to support a total device length of 5-10 mm without excessive THz wave attenuation”. This doesn’t make much sense as then after 10 mm you have 20 dB attenuation which is definitely significant. The effective length is probably somewhere around 3-4 mm or so after which adding more mm will help the eo modulation only very little.\nResponse: We thank the reviewer for the suggestion. We agree that a 10-mm device length would indeed induce significant attenuation at 500 GHz. For an electro-optic modulator though, the frequency where total RF attenuation reaches ~ 14 dB corresponds to a relatively moderate EO S21 roll-off at ~ -6 dB in an ideal scenario, which is still quite relevant for practical applications. This is also the regime where our THz-optic modulator operates, with a device length of 8 mm. The loss is also less significant in other measured THz frequencies below 500 GHz. We have modified the description to “5-8 mm” to make the statement more reasonable. The new text reads “Our measurement extrapolates to a propagation loss of approximately 2 dB/mm at 500 GHz, which is sufficient to support a total device length of 5-8 mm without excessive THz wave attenuation.”.\n6. I suggest writing formula S4 without the power of 10 since the EO S21 is itself a logarithm it makes it all very confusing.\nResponse: We thank the reviewer for the suggestion. We have modified the equation accordingly.\nThe new equation reads “EO 𝑆 =−20×log ( 𝑉π, RF)”. 21 𝑉π, LF\n7. In figure S6 it would be nice to differentiate colors what is THz and what is RF (before the extender module) as now everything is orange and thus can be confusing.\nResponse: We thank the reviewer for the advice, and have modified the figures with different color to distinguish the THz, RF and optical signals, with labels in the revised figure as well.\nThe new figure is shown here.\nFig. S6. (a) Schematic diagram of the THz modulation setup. The signal originates from an RF generator, passes through the signal generation extension module (SGX), waveguide, and probe, enters the chip, and is finally analyzed by an optical spectrum analyzer (OSA). (b) Schematic diagram of the THz generation setup. The THz signal generated by the chip is transmitted through the probe, waveguide, signal analyzer extension modules (SAX), and cable, and finally analyzed by the electrical spectrum analyzer (ESA).\n8.where are the spectra 5e-g measured? after the EDFA? what are side-bands appearing around the first laser line in Fig. 5f?\nResponse: We thank reviewer for the question. The optical spectra are measured after the EDFA. The small sidebands seen near the carrier signal at 1561.5 nm in Fig. 5f match the modulation frequency of the other beam (i.e. 35 GHz), and is caused by four wave mixing that occurs when the two beams are combined and amplified. Nevertheless, the sideband powers are significantly lower (50 dB) than signal power and do not impact the key results in this experiment.\nThere are a few points that are cofusing and the authors need to address:\n1. Lines 90-91the authors talk about “limited to pulsed operation with relatively low conversion efficiency if normalized by continuous-wave pump power” the comment about normalization is impossible to understand in that short paragraph so I would suggest simply dropping that.\nResponse: We thank the reviewer for the advice. We believe it is important to keep the statement since it provides an accurate summary of the performances of past literatures, where the absolute conversion efficiency could be relatively high based on pulsed pumping with much higher instantaneous power but the actual efficiency is rather limited if normalized to a continuous-wave scenario. The detailed definition and quantitative analysis of this normalization is provided in Supplementary Note 8 for readers interested in the details of this statement.\n2.Similarly line 103 “This performance surpasses all previous tunable optical THz wave generation devices by at least tenfold when normalized to continuous-wave efficiencies ”. maybe the authors can find a better phrasing to explain what they mean?\nResponse: We thank the reviewer for the suggestion. As we discussed above, we believe this sentence is necessary to accurately compare the efficiencies among past works and our current work. The detailed definition and quantitative analysis of this normalization is provided in Supplementary Note 8 for readers interested in the details of this statement.\n3. Lines 104-105 they talk about electro-THz modulation but it’s not clear what this means when reading the paragraph.\nResponse: We thank the reviewer for raising this point. We have modified the sentences to for easier reading. The new text reads “We further take advantage of the coherent nature of optical THz generation to demonstrate high-speed electro-THz modulation, i.e. encoding radio-frequency signals onto the generated THz carrier, at up to 65 GHz, by modulating one of the optical pump lasers using another on-chip TFLN modulator.”\n4.Cite works on dielectric waveguides in line 114.\nResponse: We thank the reviewer for the suggestion. We have incorporated a relevant reference [47] on dielectric waveguides to enhance the context.\n5.Fig. S2 (a) says Simulated conductor loss versus square root frequency but it’s not plotted against square root frequency. It’s not clear for which sample (quartz or silicon) this graph is. Please correct.\nResponse: We thank the reviewer for pointing out the issues with Fig. S2(a). We have modified the figure accordingly and added the substrate information (TFLN on quartz) in the figure caption, as follows:\nFig. S2 Simulated (a) conductor loss versus square root frequency, (b) dielectric loss versus frequency, and (c) radiation loss versus frequency, for TFLN on a quartz substrate."}, {"round": 3, "reviewer_comments": {"reviewer_2": "This paper is a very nice addition to the field and I suggest accepting it for publication in its current form."}, "author_response": ""}]

Decision letter