Accurately revealing the spectral information of optical devices and systems is of the utmost importance for comprehending performance characteristics, understanding the underlying physics, and discovering potential applications.1 Optical vector analysis (OVA), analogous to electrical vector analysis, is a powerful tool to perform such characterizations by capturing both amplitude and phase information.2^–16 Traditional OVA approaches primarily rely on optical interferometry2 or optical channel estimation techniques.3^,4 The necessity of laser wavelength scanning in these methods often leads to inadequate measurement resolutions on the megahertz level, posing challenges in keeping pace with the fine spectral features in emerging optical devices (down to the kilohertz level). Recently, OVAs based on the concept of microwave photonics (MWP)17^,18 have been proposed and demonstrated5^–15 by performing optical frequency scanning and signal measurement in the electrical domain through electro-optic (EO) modulation and photodetection. Benefiting from the ultrahigh resolution frequency sweeping and accurate vector measurement ability in the electrical domain, MWP-based OVA technology is endowed with hyperfine resolution down to the theoretically hertz level and the capability to extract both amplitude and phase information.8 Nevertheless, all existing MWP-based OVA systems have been demonstrated using either all-discrete optical devices5^–13 or by combining silicon signal processing chips with traditional off-the-shelf modulators.14^,15 These approaches inevitably lead to increased system cost, bulkiness, and complexity, prohibiting the deployment in scenarios involving mobile and remote devices, such as drones, autopilot vehicles, and satellites. In addition, all aforementioned demonstrations are ex situ measurements, where the test equipment and devices under test (DUTs) are physically separated, which is prone to environmental fluctuations and de-embedding errors from the link components between the test instrument and DUTs. This is particularly problematic for measuring the spectral responses of on-chip photonic devices, which are often overwhelmed by substantial fiber–chip coupling losses. Moreover, the presence of undesired Fabry–Perot interference caused by coupling facet reflection often introduces additional undesired amplitude and phase features, resulting in substantial uncertainties in the measurement results.

The recently emerged thin-film lithium niobate (LN) MWP platform19 exhibits tremendous potential for resolving the aforementioned challenges and realizing integrated OVA systems with dramatically reduced size, weight, and power consumption (SWaP), owing to its unique EO properties and low optical loss characteristics.20^,21 To date, many key MWP building blocks have been demonstrated on the LN platform, including linear and broadband EO modulators,22^–26 low-loss functional elements with various spectral responses,27^–30 EO/Kerr comb sources,31^,32 and on-chip stimulated Brillouin scattering (SBS) devices.33^,34 The excellent performances demonstrated in these building blocks could significantly enhance the MWP system metrics, including bandwidth, noise figure, reconfigurability, and spectral resolution.17 Endeavors to further integrate these elements into chip-scale systems have led to integrated LN MWP systems with unparalleled performance, including ultrahigh speed, low-power analog signal processors,19 and broadband multifunction photonic millimeter-wave radars.35

Here, we demonstrate an integrated OVA system based on an LN photonic integrated circuit capable of directly probing the amplitude and phase responses of various optical devices. The integrated OVA system builds on an SSB modulator, which consists of a broadband phase modulator and a reconfigurable flat-top filter, for high-fidelity EO conversion. Fabricated from a 4-in. wafer-scale process, the device is capable of sweeping the modulated optical probe signal with a 20-dB sideband suppression ratio (SSR) and 50-kHz frequency resolution. The total measurement bandwidth could be extended up to tens of terahertz by shifting and stitching different measurement channels. We further leverage the excellent scalability of the LN platform to demonstrate in situ OVA by integrating various photonic DUTs with the SSB modulators on the same chip, enabling unambiguous characterization of the coupling states and lifetimes of single and coupled microring resonators with suppressed background Fabry–Perot fringes. Further performing in situ OVA of an actively modulated microresonator enables, for the first time, direct probing of the collective phase dynamics of the Bloch modes in a synthetic frequency crystal.

Figure 1 shows the schematic illustration and working principle of our proposed OVA system. A continuous-wave optical carrier [fc, (i)] is modulated by high-resolution scanning RF probe signals [f1–f2, (ii)] using an on-chip EO phase modulator, which generates typical double-sideband (DSB) signals with scanning optical frequencies in both sidebands (iii). The DSB signals are subsequently reshaped by an optical flat-top bandpass filter [blue curve in (iv)] that preserves only the carrier and one sideband, leading to SSB modulation (iv). Afterward, the scanning SSB signals capture the frequency-dependent amplitude and phase response of the DUTs and mix with the optical carrier at the photodetector, rendering high-resolution electrical signals that preserve both amplitude and phase information of the different DUTs (vi) thanks to the coherent nature of the entire process (more details on the OVA theories can be found in Appendix C). Apart from directly using this SSB modulator as a miniaturized OVA instrument in a similar manner to that in earlier reports,5^–13 our integrated OVA system also enables in situ measurement by integrating various on-chip DUTs next to the SSB modulators. In the in situ measurement mode, the remaining SSB signals are divided into two branches, wherein one is directed toward the on-chip DUT [using double microring resonators as an example, (v)], and the other goes through a bare optical waveguide with the same path length as a reference arm for calibrating the OVA system. The amplitude and phase response of on-chip DUTs will be obtained through the same process as described above.

The integrated LN OVA is fabricated on a 4-in. wafer-scale manufacturing platform using an ultraviolet (UV) stepper lithography system (more details are provided in Appendix A). Figure 2(a) shows the false-color optical image of the LN SSB modulator, consisting of a high-performance phase modulator (EO bandwidth >50GHz, Vπ∼6V) with advanced slotted-electrodes26 and a tunable flat-top optical filter based on a ring-assisted Mach–Zehnder interferometer (RAMZI) configuration.36^–38 The left inset in Fig. 2(a) shows a photograph of a fabricated chip clamped by tweezers. Middle and right insets highlight details of the slotted electrodes and thermo-optic (TO) phase shifter through scanning electron microscope (SEM) images. The operation principle of the RAMZI flat-top filter is shown in Fig. 2(b), where the top and middle panels plot the optical transmission and phase response, respectively, of a microring resonator (light blue) and a Mach–Zehnder interferometer (MZI, dark blue), as functions of wavelength detuning [normalized by the free spectral range (FSR) of MZI]. To build a flat-top bandpass filter,37 the FSR of the microring resonator should equal half the FSR of the MZI, such that the extra phase induced by microring resonances always applies on the slope (i.e., quadrature point) of the sinusoidal transfer function of the MZI. By carefully engineering the coupling coefficient between the microring resonator and the bus waveguide to be κ=0.94 using a multimode interferometer (MMI), an ideal phase relationship between the microring and the MZI could be achieved, leading to a sharp transition from on to off states (or vice versa) near the quadrature points (more details are provided in Appendix B). As a result, the transmission spectrum is strongly modified from the typical sinusoidal curve of an asymmetric MZI to a “box-like” response with near-flat and periodically occurring pass- and stopbands [bottom panel of Fig. 2(b)]. In actual experiments, non-ideal coupling coefficients κ could lead to an undesirable phase relationship at the off-resonance points [dashed lines in top panel of Fig. 2(c)], resulting in ripples in the pass/stopbands [bottom panel of Fig. 2(c)] and compromised extinction ratios.

To take full advantage of the broad modulation bandwidths of LN modulators, we design FSRs of the microring resonator and the asymmetric MZI to be 120 and 60 GHz, respectively, resulting in a flat passband of ∼50GHz. The resonant wavelength of the microring resonator is aligned to the quadrature point of the MZI by TO phase shifters fabricated in the vicinity of both the microring resonator and one arm of the MZI [Fig. 2(a)]. The measured spectral response of the RAMZI filter in a representative channel is shown in Fig. 2(d) (gray), with a 210dB/nm roll-off slope and a 20-dB extinction ratio. By locating the optical carrier at the edge of the pass band, SSB modulation could be achieved within a wide RF frequency range between 10 and 50 GHz, with measured optical SSR consistently at ∼20dB [Fig. 2(d)]. Moreover, the passband of our RAMZI filter could be flexibly shifted without affecting the flat-top nature by simultaneously tuning the TO phase shifters on the microring and the MZI. Figure 2(e) shows a series of measured flat-top bandpass profiles when the TO phase shifters are adjusted to set the relative phases of MZI at 0, π/2, π, and 3π/2 (from top to bottom), with TO tuning efficiencies of 12pm/mW for the microring resonator and 5pm/mW for the MZI, respectively. The ability to shift the passband over a full period unlocks the possibility of achieving an ultrawide measurement bandwidth by separately performing OVA within individual bands and subsequently shifting and stitching the channels.

To implement the in situ measurement of integrated photonic devices, we fabricate various DUTs next to the SSB modulators on the same LN chip and perform OVA using the experimental setup shown in Fig. 3(a). High-resolution sweeping RF signals (10 to 50 GHz) from an electrical vector network analyzer (EVNA) are used to drive the SSB modulator and probe the optical properties of DUT following the working principle introduced above. The signals are converted back into the electrical domain using a high-speed photodetector and analyzed at the other port of the EVNA (more details are provided in Appendix D). We use RF power of 5 dBm to avoid the impact from higher-order sidebands and noise, staying in the small-signal modulation regime (more details are provided in Appendix G).13 The fabricated passive on-chip devices for the in situ OVA include a single-ring resonator, a double-ring coupled-resonator system, and coupled-resonator optical waveguides (CROWs). These devices are fundamental building blocks for a variety of applications in integrated photonics, such as electromagnetically induced transparency (EIT) models,39 non-Hermitian photonics,40 and optical filters.41

Figure 3(b) depicts the measured and fitted amplitude and phase responses of a single microring resonator, showing two optical modes (a fundamental and a high-order mode) simultaneously present in the measurement window with resonant frequencies separated by 6.2 GHz. The amplitude responses of the two resonances indicate notch depths of 4 and 11 dB, and full width at half-maximum linewidths (in linear scale) of 500 and 378 MHz, respectively. The measured amplitude responses are in good agreement with those obtained using the traditional laser scanning method (yellow dashed lines), but with substantially suppressed background Fabry–Perot fringes thanks to the in situ measurement mode (see Note II in the Supplemental Material). Importantly, the vector analysis adopted in our experiments allows us to directly probe the phase responses of these resonances and infer their coupling states (under/critical/over), which is typically not possible in an amplitude-only transmission spectrum measurement. In this particular case, we measure resonant phase jumps of 30 deg and 76 deg for the two resonances, both of which correspond to undercoupling states. Further fitting the experimental results with the theoretical model (dashed black curves) provides unambiguous and quantitative analysis on the coupling coefficients of these two modes at κ1=0.092 (high-order mode) and κ2=0.093 (fundamental mode); as well as the intrinsic quality factors of 3.86×105 and 9.03×105, respectively. To validate the high resolution of our OVA system, the right panel of Fig. 3(b) shows the fine measurement results near one resonance notch, which comprises 40,001 data points over a span of 2 GHz, resulting in a resolution of 50 kHz, currently limited by the linewidth of our tunable laser. The implementation of a narrow linewidth laser could in principle enable hyperfine resolution down to the hertz-level.8^,13

For more complicated photonic systems, such as the double-ring resonator shown in Fig. 3(c), our in situ OVA system could also reliably capture the resonant phase jumps for both split modes, i.e., 40 deg and 78 deg in this case. The fitting results reveal an initial resonance frequency difference (Δf) of 0.457 GHz between the two ring resonators due to fabrication nonuniformity, a ring-bus coupling coefficient of κ1=0.16, and a coupling coefficient between the two ring resonators of κ2=0.03. We further conduct an in situ vector analysis of a triple-ring CROW system at the through port, as shown in Fig. 3(d). Assuming the two ring–ring couplers (κr) and the two ring-bus couplers (κb) are identical, our measurement and fitting results again lead to reliable estimation of the coupling coefficients, i.e., κr=0.26 and κb=0.03. Such information could be highly valuable in inferring the actual operating states of complex photonic systems and providing instruction for achieving the design targets. For example, if the objective is to design a Butterworth filter, we could straightforwardly conclude that both coupling coefficients need to be slightly increased (ideally: κr=0.33 and κb=0.04).

Building upon the broadband reconfigurability of our flat-top filter, we demonstrate ultrawide measurement bandwidth up to tens of terahertz by stitching a series of 40-GHz measurement channels, as the schematic diagrams in Fig. 3(e) illustrate. Within each 120-GHz spectral period of the flat-top filter, e.g., between fci and fc(i+1), we strategically perform four measurements by biasing the filter at relative MZI phases of 0, π/2, π, and 3π/2, leading to a frequency offset of 30 GHz between adjacent measurement channels. Considering each measurement could yield a reliable measurement bandwidth of 40 GHz (between fc+10GHz and fc+50GHz) with a near-flat spectral response and high SSR; this provides an effective overlapping region of 10 GHz between adjacent channels that could be used to stitch amplitude and phase information of the DUT over a wide frequency range (see Note III in the Supplemental Material). Figure 3(f) shows the measured spectral responses of a single microring resonator from 1500 to 1630 nm (16.2 THz), exhibiting a total of 84 resonance notches with an FSR of 219 GHz. The inset shows a zoom-in view between 1626 and 1629 nm with two adjacent resonance notches of the same optical mode. Through an analysis similar to the above, we conclude this resonator is at an overcoupling state with a coupling coefficient of 0.11. It should be noted that currently the absolute frequencies of measurement channels are not accurately referenced, since they are only stitched together numerically. Further calibrating the optical carriers in each channel using a phase-stable fiber cavity or interferometer could enable applications that require broadband absolute wavelength accuracy, such as extraction of high-order dispersion information.16

We further demonstrate that our integrated OVA system facilitates the direct characterization of both amplitude and phase evolutions of an actively modulated microring resonator, providing additional probing degrees of freedom for complex physical systems, such as a synthetic frequency crystal. The concept of frequency synthetic dimension utilizes different optical frequency modes to form a lattice and induce coupling between lattice points through optical nonlinearities.42^,43 Leveraging the large bandwidth, good reconfigurability, and tunable gain/loss of photonic systems, frequency synthetic dimension is well suited to explore complicated systems that are difficult to implement or control in solid states, such as non-Hermitian,44 high-dimensional,45 and topological systems.46 Here, we implement and perform in situ vector analysis of a synthetic frequency crystal on thin-film LN, which offers the desired low dissipation rate and strong nonlinear interaction via EO effect.45^,47^,48 An LN racetrack resonator is employed to generate a set of frequency modes, separated by the FSR of the resonator (24.8 GHz). Efficient modulation, matching the FSR, is achieved through two pairs of electrodes with reversed polarity along the straight sections of the racetrack [Fig. 4(a)]. This creates strong EO coupling between adjacent frequency modes that emulates a tight-binding model45 (more details are provided in Appendix F), where optical photons can hop between different lattice points with a large hopping rate proportional to the microwave driving voltage, which is also known as a resonant EO comb generator.31 In the steady state of such an actively modulated resonator, input laser signals with different detuning effectively excite different Bloch states whose frequencies match the detuning [Fig. 4(b) (i) and (ii)]. Traditionally, probing only the optical transmission spectrum reveals the density-of-states of the frequency crystal.45 Here, leveraging the in situ OVA system, we directly capture both the amplitude and phase responses of the Bloch states within the crystal. This direct measurement unveils the collective phase dynamics of the Bloch states [Fig. 4(b) (iii) and (iv)]. Specifically, for a given laser detuning, a coherent summation [Fig. 4(b) (iii) and (iv)] of the phase responses of the excited Bloch states [Fig. 4(b) (i)] is obtained. The reversed phase response between adjacent Bloch states inside the energy band leads to coherent cancellation [Fig. 4(b) (iii)] on the detected phase dynamics (except for the energy band edges), resulting in a near-flat in-band phase response curve with two sharp phase changes at the top and bottom of the band [Fig. 4(b) (iv)]. Our experimental results under varying microwave signal powers (0, 15, 18, and 20 dBm) agree well with the theory, as shown in Fig. 4(c). By slightly detuning the RF frequency from the resonator FSR (detuning ∼85MHz), we further transition the frequency crystal dynamics into a triple resonance state where only three neighboring modes are strongly coupled [Fig. 4(d)], illustrating the reconfigurability of the amplitude and phase dynamics of the crystal. Our in situ OVA system represents a stable and compact technology for directly probing active systems with ultrafast modulation, offering extra degrees of freedom for investigating various complex physical systems using frequency synthetic dimensions.

In summary, we propose and experimentally implement a miniaturized and flexible OVA system for integrated photonic devices featuring 50 kHz measurement resolution and 16.2 THz measurement bandwidth on the LN platform. The ability to place various DUTs on the same chip as the SSB-based OVA enables in situ measurements of the amplitude and phase responses, leading to unambiguous and accurate characterization of the intrinsic loss and coupling states of photonic devices. Moreover, we demonstrate the direct probing of full amplitude and phase dynamics of an actively modulated microresonator that emulates the Bloch states in the synthetic frequency dimension. This offers important extra degrees of freedom for understanding and investigating complex physical models like non-Hermitian, high-dimensional, and topological systems.

We envisage that the in situ OVA could become an important building block in future large-scale photonic networks that provide accurate and real-time monitoring and feedback control of on-chip elements. This could be achieved by combining the OVA with an electronic field programmable gate array (FPGA) chip, which can be trained to process the comprehensive spectral information extracted from the OVA and adjust the operation states of critical network components accordingly (see Note I in the Supplemental Material). The LN in situ OVA system could potentially also probe devices in other material platforms like Si or InP through hybrid packaging or heterogeneous integration. Moreover, our demonstrated system is highly compatible with other high-performance photonic components available on the integrated LN platform, such as frequency comb sources,31^,32^,49 which could dramatically expedite the processing speed by parallel channelized measurement; and polarization-manipulation components,50^,51 which could be adopted to enable the retrieval of polarization dependent loss and polarization group delay. In addition, leveraging the wide transparency window of LN (from visible to mid-infrared),20 the OVA system could be readily configured to function across a broad range of wavelengths that are of interest to not only optical communications and information technologies, but also biosensing, gas/nanoparticle detection, and atomic physics.

Devices are fabricated from a commercially available x-cut LNOI wafer (NANOLN), with a 500-nm LN thin film, a 4.7-μm buried SiO2 layer, and a 500-μm silicon substrate. First, SiO2 is deposited on the surface of a 4-in. LNOI wafer as an etching hard mask using plasma-enhanced chemical vapor deposition. Various functional devices are patterned on the entire wafer using an ASML UV Stepper lithography system (NFF, HKUST) die-by-die (1.5cm×1.5cm) with a resolution of 500 nm. Next, the exposed resist patterns are transferred first to the SiO2 layer using a standard fluorine-based dry etching process, and then to the LN device layer using an optimized Ar+ based inductively coupled plasma reactive-ion etching process. The LN etch depth is ∼250nm, leaving a 250-nm-thick slab. After removal of the residual SiO2 mask and redeposition, an annealing process is carried out. Afterward, second, third, and fourth lithography and lift-off processes are used to fabricate the microwave electrodes, heater, and wires/pads, respectively. Finally, chips are carefully cleaved for end-fire optical coupling with a total insertion loss of ∼15dB [including 10 dB coupling loss (5dB/facet) and 4 dB on-chip loss (3 dB from the filter and 1 dB from the phase modulator)], and wire-bonded with a printed circuit board to realize multiport control of the TO phase shifters.

The 2×2 MMI is designed through full 3D finite-difference time-domain simulations (Ansys Lumerical) to serve as the resonator coupling region, providing the suitable imparted phase shift. The core MMI region has a size of 31.4μm×4.8μm. The widths of the input waveguides are first tapered from 1.2 to 2.15μm over a taper length of 15μm before entering the MMI region to minimize scattering loss. The output waveguides are tapered in a similar but reversed manner.

More details are presented here for the construction of the RAMZI filter. To achieve a “box-like” transfer function instead of the sinusoidal curve of a typical asymmetric MZI structure, the side-coupled ring resonator serves as a periodic phase shifter to adjust the transfer function. The FSR of the microring resonator determines the periodicity of these phase shifts, so the length relationship between the perimeter of the ring resonator and the length imbalance of MZI arms should satisfy ΔLmzi=ΔLring/2, where ΔLmzi is the length difference of the two MZI arms, and ΔLring is the perimeter of the ring resonator. When the propagation loss is negligible, the optical field of the RAMZI filter can be expressed as Eramzi=12[Eringe−j(ϕ1+ϕring)+1·e−jϕ2],(1)where Ering is the electric field amplitude of the ring resonator, ϕring is the phase response of the ring resonator, and ϕ1 and ϕ2 are the phases induced in the two arms of the MZI. The output transfer function of the RAMZI filter can be written as Tramzi=|Eramzi|2=14[|Ering|2+1+2|Ering|·cos(ϕring−ϕmzi)],(2)where ϕmzi=ϕ2−ϕ1=βΔLmzi, β is the propagation constant, and ϕring can be calculated as ϕring=arctan(1−κ2)αsin(θ)(1+α2)κ−α(1+κ2)cos(θ),(3)where κ is the optical field coupling coefficient of the ring resonator, α is the amplitude attenuation coefficient of the ring resonator, and θ is the round-trip phase shift. In addition, the RAMZI configuration requires an external phase shift ∼π/2 between two branches of RAMZI to align the resonance notches with the quadrature point of the MZI. Therefore, the phase relation is expressed as βΔLmzi=βΔLmzi2±π2, and the following relation needs to be satisfied at the off-resonance points [θ=(2n+1)·π,n=1,2,3…]: dϕringdθ=dϕmzidθ.(4)

The calculated coupling coefficient of the ring resonator should be κ=2√23≈0.94. In this case, the phase response characteristics allow the RAMZI filter to flatten its bandpass region and sharpen the roll-off part.

More details are presented here for the principle of the SSB-based OVA system. In the analysis of the operation for the SSB-based OVA system, the optical carrier is considered as ejw0t, where ω0 denotes the carrier frequency. The input RF signal is represented as cosωmt, where ωm is the scanning modulation frequency. The input electric field can be written as Ein=ejw0tejβcosωmt≈jJ1(β)ej(ω0−ωm)t+J0(β)ejω0t+jJ1(β)ej(ω0+ωm)t,(5)where β is the modulation index and Jn(β) (n=0, 1) is the Bessel function of the first kind. Considering small-signal modulation, the higher-order sidebands are ignored. After the Fourier transform, the input electric field can be written in the frequency domain as Ein(ω)=2πjJ1(β)δ(ω−ω0+ωm)+2πJ0(β)δ(ω−ω0)+2πjJ1(β)δ(ω−ω0−ωm).(6)

When the signal passes through the flat-top bandpass filter, the optical carrier and one of the sidebands are preserved, resulting in SSB modulation. We assume the first term on the right-hand side of Eq. (6) is suppressed. When the remaining SSB signal is transmitted through the DUT, the output optical signal can be written as $$\begin{gathered} Eout(ω)=Ein(ω)Hsys(ω)HDUT(ω) \\ =2πJ0(β)δ(ω−ω0)Hsys(ω0)HDUT(ω0)+2πjJ1(β)δ(ω−ω0−ωm)Hsys(ω0+ωm)HDUT(ω0+ωm), \end{gathered}$$(7)where Hsys(ω) and HDUT(ω) are the transfer functions of the reference arm (used as OVA calibration background) and the DUT, respectively. After sending the signal to an AC-coupled PD, ignoring the DC and high-frequency terms, the output PD current could then be written as i(ωm)∝4π2jRJ0(β)J1(β)Hsys*(ω0)HDUT*(ω0)Hsys(ω0+ωm)·HDUT(ω0+ωm),(8)where R is the responsivity of the PD. The calibration process is performed by measuring the reference arm using the OVA system (without DUT). In this case, it is equivalent to HDUT(ω)=1, and the output current of the PD could then be written as isys(ωm)=4π2jRJ0(β)J1(β)Hsys*(ω0)Hsys(ω0+ωm).(9)

Based on Eqs. (8) and (9), the spectral transfer function of the DUT can be obtained as H(ωm)=HDUT(ω0+ωm)=i(ωm)isys(ωm)HDUT*(ω0).(10)

In this equation, HDUT*(ω0) is the spectral response of the DUT at the optical carrier frequency, which can be considered as a complex constant. It is noted that Eq. (10) is only applicable in the absence of high-order sidebands, which could induce additional measurement errors at elevated input RF power levels (see Appendix G for more details).

In our OVA experiment, the optical carrier from the tunable laser (Santec TSL-510) is sent to the LN chip using a lensed fiber after a polarization controller to ensure transverse electric (TE) polarization. The high-resolution scanning RF signals (10 to 50 GHz) are generated from a vector network analyzer (VNA, E5080B, 50 GHz) and loaded into the modulation electrodes via a high-speed probe (GGB Industries, 50 GHz). The output optical signals, which contain the full information of DUTs, are amplified using an EDFA (Amonics), detected by a high-speed photodetector (Finisar XPDV21X0RA, 50 GHz), and analyzed at another port of VNA. For ultrawide measurement experiments, two DC sources are utilized to shift the bandpass positions of filters to stitch different measurement channels.

In the fitting process for different on-chip devices, initial values and appropriate bounds are set for the parameters to be fitted, and the trust region algorithm is adopted to determine their optimal solution for the theory models. Specifically, for the single microring resonator, the key parameters, such as the coupling coefficient (κ), the resonator round-trip amplitude attenuation factor (a), and the perimeter of ring (L), are obtained. For the double ring system, building on the directional coupling theory,53 the coupling coefficients of both rings (κ1,κ2), resonator round-trip amplitude attenuation factors (a1,a2), and the initial resonance frequency difference (Δf) between two rings can be obtained. For the CROW system, the time-domain coupling model54 is adopted to fit the curve with the assumption of the identical coupling coefficient κr in the two ring–ring couplers, identical coupling coefficient κb in the two ring–bus couplers, as well as identical loss rates of the three rings. Then, the coupling coefficients (κr,κb), the resonator round-trip amplitude attenuation factor (a), and the perimeter (L) are retrieved.

The Hamiltonian of the actively modulated microring resonator can be described as45^,47H=∑j=−NNωjaj†aj+Ωcosωmt(aj†aj+1+h.c.),(11)where ωj is the frequency of each frequency mode, Ω is the coupling rate due to modulation, and ωm is the frequency of the RF signal. The total number of frequency modes that are coupled is labeled by number −N to N. Using the Heisenberg–Langevin equation, we obtain a set of equations of motion: aj˙=(−iωj−κ2)aj−iΩcosωmt(aj+1+aj−1)−κeαine−iωLtδj,0.(12)

Switching the system into the rotating frame by aj→aje−iωLte−ijωmt gives aj˙=(iΔ+ilδ−κ2)aj−iΩ2(aj+1eiϕ+aj−1e−iϕ)−κeαinδj,0.(13)

We perform a transformation: cq=1Nt∑jaje−iqj and aj=1Nt∑qcqeiqj with Nt=2N+1. In the case that δ=0 (note that, for the case of δ≠0, it effectively couples fewer modes; therefore the phenomena can be simulated by reducing the N), we have cq˙=(iΔ−κ2)cq−iΩcos(q+ϕ)cq−Ntκeαin.(14)

In the steady state, we can derive the expression of cq=κeNtαin1iΔ−κ2−iΩcos(q+ϕ). The final output signal from the device can be written as aout=(αin+κe∑jaje−ijωmt)=(αin+κeNtcq=ωt). The amplitude and phase responses can be extracted as |aout|2 and Arg(aout). The photodetector averages the aout within a certain time; therefore the measured phase response is a collective sum of aout over the excited modes cq.

Error analysis in this work is performed by calculating the mean absolute error (MAE) between the simulation results and the ideal frequency responses (using a single microring resonator as an example) due to noise and higher-order sidebands, at different input RF power levels. As shown in Fig. 5, low measurement errors of <1% (dash line) could be maintained within the input RF powers of −10 to 15 dBm. The error on the low RF power side is mainly due to decreased signal-to-noise ratios (as shown in the left inset), whereas on the high RF power side is restricted by the existence of high-order sidebands (as shown in the right inset). During our real experiments, the input RF power is around 5 dBm (blue star in Fig. 5), where the noise and the high-order sidebands would not severely influence the results.

If the high input RF power is needed, this undesired error could also be effectively suppressed by conducting two consecutive measurements, i.e., one with the optical carrier and another without the optical carrier to obtain the subtracting results with higher accuracy.52

Table 1 lists a detailed performance comparison among various previously demonstrated OVA schemes, including MWP-based (SSB and DSB), interferometry-based, optical channel estimation-based, and laser-chirping-based methods. The performance metrics include the integration level, in situ measurement ability, resolution, measurement range, and dynamic range. As can be seen, our work has demonstrated the first integrated OVA system with good overall performance and functionality. More specifically, OVA technologies based on MWP approaches (whether SSB or DSB) generally feature better resolutions than optical scanning schemes (interferometry or optical channel estimation). This is because MWP technology shifts the scanning frequency from the optical domain to the more precise RF domain, enabling theoretical resolutions as low as hertz level. Our current resolution is mainly limited by the linewidth of the laser (around 50 kHz), which can be further improved by adopting an ultranarrow linewidth laser.13 In addition, our measurement range surpasses all reported SSB-based methods owing to the employment of a spectrum-stitching scheme. Although the measurement dynamic range is currently limited by the extinction ratio of the flat-top filter, this could potentially be improved by further optimizing the fabrication process and/or adoption of new filter configurations. We note that previous demonstrations based on DSB13 and laser chirping16 schemes show impressive and all-round performance metrics. Yet these systems are substantially more complicated, bulky, and costly (e.g., three modulators used in Ref. 13 and three lasers in Ref. 16) compared to our system.

Hanke Feng received his PhD from City University of Hong Kong in 2024. He is currently a postdoctoral researcher at City University of Hong Kong. His research interests focus on integrated lithium niobate photonic circuits and system-level applications in microwave photonics and optical communications. He was recognized as a Rising Star of Microwave Photonics, China, in 2024.

Tong Ge is an undergraduate student at City University of Hong Kong. His research interests focus on integrated photonics, microwave photonics, and nonlinear optics. He is the recipient of the IET Prize 2022.

Yaowen Hu is an assistant professor at Peking University. He received his BS degree from Tsinghua University in 2018 and his PhD from Harvard University in 2023. His research focuses on quantum optics, nonlinear optics, photonic neuromorphic computing, and optical frequency combs. He was recognized in the MIT Technology Review 35 Innovators Under 35 (China) in 2023.

Zhenzheng Wang is a PhD student at City University of Hong Kong. He received his MS degree from Huazhong University of Science and Technology (2017). His research focuses on optical microcavities and packaging of lithium niobate photonics.

Yiwen Zhang is a PhD candidate at City University of Hong Kong. She received her BS degree from Shandong University in 2016 and her MS degree from Zhejiang University in 2019. Her research is focused on terahertz technologies on lithium niobate and their applications.

Zhaoxi Chen received his BS and MS degrees from Tianjin University and his PhD from City University of Hong Kong. He is currently a postdoctoral researcher in City University of Hong Kong. His recent research includes integrated lithium niobate photonics, especially in optical frequency comb.

Ke Zhang is a postdoctoral researcher at City University of Hong Kong and the CEO of Kokoxili Photonics Limited. He received his BS and MS degrees from the University of Science and Technology Beijing in 2014 and 2017, respectively, and his PhD from City University of Hong Kong in 2023. His work focuses on developing power-efficient chips in integrated lithium niobate platform.

Wenzhao Sun is an assistant professor at City University of Hong Kong (Dongguan). He received his BS, MS, and PhD degrees from Harbin Institute of Technology. His research focuses on micro & nanophotonics, microcavity, perovskite lasers, and integrated devices.

Cheng Wang is an associate professor at City University of Hong Kong. He received his BS degree from Tsinghua University in 2012 and his PhD from Harvard University in 2017. His research interests focus on integrated lithium niobate photonic and their applications in the fields of optical communication, microwave photonics, and nonlinear optics. He received the NSFC Excellent Young Scientist Fund in 2019 and the Croucher Innovation Award in 2020, and was recognized in the MIT Technology Review 35 Innovators Under 35 (China) in 2021.