Microwave photonics (MWP) [1,2] combines microwave engineering with photonics to process and transmit high-frequency microwave signals, involving the use of optical components, such as lasers, modulators, and optical fibers, to generate, manipulate, transport, and detect microwave signals, widely applied in communication, radar, sensing, and computing systems. Linearity [3] is one of the essential characteristics in MWP links, typically evaluated by the spurious-free dynamic range (SFDR) parameter, to show the capability of the system to distinguish between the desired signal and unwanted spurious distortions or harmonics. Nonlinearity in optical modulators is one of the primary sources contributing to overall system nonlinearity, which can be attributed to two main factors: the intrinsic properties of the material and the transfer function of the structural design.

Lithium niobate (LN) has long been favored for high-speed electro-optic (EO) modulation due to its linear, fast response and wide transparent window [4]. However, traditional LN modulators, which rely on weakly confined titanium-diffused or proton-exchanged optical waveguides, face limitations in modulation efficiency, bandwidth, and size. With advancements in micro-nano fabrication technologies, the thin-film lithium niobate (TFLN) platform has emerged and attracted significant attention [5], which not only retains the superior properties of bulk LN but also offers enhanced optical confinement, leading to substantial improvements in modulation efficiency and bandwidth while significantly reducing device footprint. Recent reports indicate that TFLN modulators can achieve bandwidths exceeding 100 GHz with low drive voltages (∼1V) and low on-chip losses (<2dB) [6,7]. Despite these advancements, TFLN modulators have mostly been designed as conventional Mach–Zehnder modulators (CMZMs) with a typical cosine transfer function [8,9] and demonstrated primarily for digital communication applications, while research on the linearity performance remains limited. The reported high-bandwidth (>40GHz) integrated LN modulator achieved an SFDR of only 99.6dB·Hz2/3 at 1 GHz [8], whereas an ultra-linear integrated LN ring-assisted Mach–Zehnder interferometer (RAMZI) modulator [10], with an SFDR of 120.04dB·Hz4/5 at 1 GHz, has been experimentally verified only up to 5 GHz.

To address the nonlinearity resulting from the structural design of the CMZMs, various linearization strategies, as illustrated in Fig. 1, have been proposed and implemented using either discrete bulky setups or integrated platforms. These methods can be broadly categorized into four types. (i) Mixed-polarization MZMs [11–13]: this method utilizes the anisotropy of the LN crystal, wherein there is an inherent ratio of γ=1/3 between EO coefficients for the fundamental transverse electric (TE) and transverse magnetic (TM) modes. By simultaneously inputting mixed-polarization (both TE0 and TM0 modes) light at an optimal optical power ratio, bulk modulators supporting mixed-polarization transmission and modulation can theoretically achieve improved linearity. (ii) Dual-polarization power-combined MZMs [14–18]: unlike method (i), this approach employs two modulators with single-mode (typically TE0 mode) modulation. The two modulators are driven by two paths of radio-frequency (RF) signals with specific power ratios and relative phases, and their outputs are power-combined optically to enhance linearity. (iii) X-assisted MZMs (where X represents a new structure, such as a ring or a racetrack [10,19–21]): the key idea is to modify the cosine transfer function of CMZMs by incorporating the response of new structures. For example, by carefully designing micro-ring structures with specific transmission, coupling, and loss coefficients, it is possible to suppress nonlinear terms, thereby improving overall linearity. (iv) Parallel or cascaded MZMs [22–26]: this strategy involves paralleling or cascading two or more MZMs to achieve linearization by adjusting RF power ratios, RF relative phases, optical power ratios, and optical bias points of the individual MZMs. However, these linearization approaches face several challenges: being incompatible with integration, involving multiple RF inputs with complex power and phase management, requiring tight fabrication tolerances, and suffering from bandwidth limitations due to resonant structures. To sum, these linearization strategies are hindered by significant issues related to volume, cost, complexity, and bandwidth.

Here we present a novel, linear, and integrated TFLN modulator configured with ground-signal-ground (GSG) traveling-wave electrodes (TWEs) and dual-optical-mode co-modulated MZMs with 3-dB EO bandwidths of over 50 GHz, achieving a record-high SFDR of 121.7dB·Hz4/5 at 1 GHz, with an optical power (OP) of 5.5 dBm into the photodetector (PD). Additionally, a 1-dB increase in OP leads to an approximately 1.6-dB improvement in SFDR. Compared to CMZMs, our LMZM demonstrates an SFDR improvement of over 10.6 dB across an OP range of −8 to 10 dBm. The LMZM also features a compact footprint of 15mm×1.5mm, incorporating 10-mm-long TWEs. The wide operational bandwidth is experimentally verified, showing SFDR improvements of 12.10 dB, 7.94 dB, 8.24 dB, 8.53 dB, and 6.07 dB at frequencies of 1 GHz, 5 GHz, 10 GHz, 15 GHz, and 20 GHz, respectively. The tolerances to optical splitting ratio variations and heating power fluctuations at the dual-optical-mode bias points are also analyzed experimentally. Our LMZM not only exploits the advantages of TFLN materials with linear and fast EO response, but also innovatively breaks the typical transfer function of CMZMs by utilizing the orthogonality of the two on-chip optical modes (TE0 and TE1), effectively suppressing third-order intermodulation distortion (IMD3) terms with only one path of TWEs and a single RF input. Overall, our approach addresses the issues of low linearity, bulkiness, complexity, and bandwidth limitations associated with conventional schemes, offering a compact and efficient solution for achieving highly linear modulation in MWP links.

As illustrated in Fig. 2, the design of our LMZM employs a dual-optical-mode co-modulated architecture. The on-chip optical processing involves five main steps: coupling in, power splitting, mode conversion and dual-optical-mode modulation, mode conversion and combination, and coupling out. Step I and Step II: light is coupled into the chip at the left-side facet via an edge coupler, and enters an adjustable optical power splitter, which consists of a phase shifter (labeled as DC1) and a Mach–Zehnder interferometer (MZI). The light is then distributed into the upper and lower branches after the 2×2 multimode interference (MMI) coupler. Step III: in the upper branch, the light can be regarded as going through a TE1-mode Mach–Zehnder modulator (TE1-MZM) as shown in Fig. 2(a). The process can be explained as follows. Initially, the light is split by a 2×2 MMI into two waveguides. The light in the lower waveguide is mode-converted from TE0 mode to TE1 mode by a mode converter (MC), modulated via TWEs when RF signals are input, and then reconverted to TE0 mode. The light in the upper waveguide undergoes the same mode conversion without modulation. A phase shifter (labeled as DC3) is placed on the upper waveguide to control the phase difference between the two waveguides. The light from both waveguides is eventually combined in TE0 mode via a 2×2 MMI. In the lower branch, the light can be regarded as passing through a TE0-mode Mach–Zehnder modulator (TE0-MZM), wherein it remains in TE0 mode and is modulated in push-pull mode. A phase shifter (labeled as DC2) is placed on the lower waveguide to control the optical bias, similar to the one (labeled as DC3) in the TE1-MZM. Note that a pair of grating couplers connected to TE0-MZM or TE1-MZM facilitates pretesting and monitoring the optical bias. Step IV: the outputs from the TE1-MZM (upper branch) and TE1-MZM (lower branch) are combined using a polarization rotator combiner (PRC). In this step, the light from the upper branch is converted from TE0 mode to TM0 mode, while the light from the lower branch remains in TE0 mode. Step V: finally, the light is coupled out via a polarization-insensitive edge coupler at the right-side facet and transmitted into an optical fiber.

In this configuration, the conventional cosine-type transfer function of a single-mode CMZM is replaced by a novel transfer function, derived in the following. As known, the transfer function of an ideal CMZM operating in push-pull mode can be expressed as TCMZM=12[1+cos(2αRF+θbias)],(1)where αRF represents the phase change induced by the RF signal, and θbias is the phase difference between the two arms of the modulator. For the proposed LMZM, the characteristics of the TE0-MZM and TE1-MZM, including loss, the voltage inducing π-phase shift in one arm, EO bandwidth, etc., are assumed to be identical. Under these ideal conditions, the transfer function of the LMZM can be written as TLMZM=R2[1+cos(2αRF+θbias1)]+1−R2[1+cos(αRF+θbias2)],(2)where R is the optical power splitting ratio, θbias1 represents the phase difference between the two arms of TE0-MZM modulated in push-pull mode, and θbias2 is the phase difference between the two arms of the TE1-MZM with only one arm modulated. The modulation mode of the two MZMs can be interchanged as long as satisfying Eq. (2). When R takes a value of 0 or 1, the structure simplifies to a single-mode CMZM.

To theoretically determine the optimal R, θbias1, and θbias2, we consider the RF signals applied on the TWEs, which consist of two tones, f1 and f2, with identical amplitudes V0. The input RF signals can be expressed as VRF=V0[cos(w1t)+cos(w2t)]=V0[cos(2πf1t)+cos(2πf2t)],(3)where wi (i=1,2) represents the angular frequency, and fi denotes the corresponding frequency in units of GHz. Assuming that the voltages required to induce a π-phase shift in one arm of the CMZM, TE1-MZM, and TE0-MZM are identical and denoted as Vπ0, we define m as follows: m=V0Vπ0π,(4)αRF=m[cos(w1t)+cos(w2t)].(5)

By substituting αRF into the transfer functions of the CMZM and the LMZM in Eqs. (1) and (2), and performing a Bessel expansion along with a small signal approximation [18], the signal term and the IMD3 term of the CMZM can be expressed as follows: TCMZM−Signal=12sinθbiasJ1(2m)J0(2m)≈12msinθbias,(6)TCMZM−IMD3=12sinθbiasJ1(2m)J2(2m)≈14m3sinθbias.(7)

It can be seen when θbias=π/2, both the signal term and the IMD3 term reach their maximum values. Since the signal and IMD3 terms both contain sinθbias, it is not possible to eliminate the IMD3 while maintaining the signal term. Previous studies have tried to suppress the IMD3 by low-biasing techniques [27], shifting the bias point away from the quadrature point towards the null point, albeit at the cost of reduced signal power.

Similarly, the signal term and the IMD3 term of the proposed LMZM can be written as TLMZM−Signal=R2sinθbias1J1(2m)J0(2m)+1−R2sinθbias2J1(m)J0(m),(8)TLMZM−IMD3=R2sinθbias1J1(2m)J2(2m)+1−R2sinθbias2J1(m)J2(m),(9)which can be simplified by retaining only the first term of the Bessel expansion: TLMZM−Signal≈R2msinθbias1+1−R4msinθbias2,(10)TLMZM−IMD3≈R4m3sinθbias1+1−R32m3sinθbias2.(11)

It can be observed that three adjustable parameters influence the values of the signal and IMD3 terms. There are various combinations of these parameters where the IMD3 term can be minimized to zero. Among these combinations, the signal term reaches its maximum value when R=1/9 and −sinθbias1=sinθbias2=1. Figures 3(a)–3(d) present the simulated results for the LMZM and the reference CMZM at four different OPs. Compared with the SFDR values achieved for the CMZM (denoted by dotted lines with double arrows) of 112.16dB·Hz2/3, 105.50dB·Hz2/3, 98.84dB·Hz2/3, and 92.16dB·Hz2/3 at OPs of 10 dBm, 5 dBm, 0 dBm, and −5dBm, respectively, the corresponding SFDR values are 128.49dB·Hz4/5, 120.50dB·Hz4/5, 112.50dB·Hz4/5, and 104.47dB·Hz4/5 for the proposed LMZM (denoted by solid lines with double arrows), demonstrating improvements in SFDR of 16.33 dB, 15.00 dB, 13.66 dB, and 12.31 dB in 1-Hz bandwidth. Figure 3(e) compares the normalized transmission curves of the LMZM and CMZM under the same value of half-wave voltage (Vπ), where the improvement in linearity can be intuitively observed. Figure 3(f) illustrates the normalized transmission curves of the proposed structure for different values of the parameter R, varying from zero to one in steps of 1/18, according to Eq. (2). The half-wave voltage for the TE0-MZM (R=1) is half that of the TE1-MZM (R=0), while the half-wave voltage of the LMZM (R=1/9) is theoretically approximately 1.144 times that of the TE1-MZM.

The device has a compact footprint of 15mm×1.5mm, including 10-mm-long TWEs. The LMZMs were fabricated on commercially available 360-nm-thick x-cut TFLN (from NanoLN). Passive components, including optical waveguides, grating couplers, mode converters, and others, were defined via electron-beam lithography (EBL) and subsequently transferred into the LN layer using argon plasma-based reactive ion etching (RIE). The etch depth of the waveguides was 180 nm, leaving a 180-nm-thick TFLN slab. The top width of the optical waveguides in the modulation region was designed to be 2.2 μm to support both the fundamental TE0 mode and the higher-order TE1 mode. After resist removal, the devices were cladded with a 1-μm-thick SiO2 layer using plasma-enhanced chemical vapor deposition (PECVD). Gold electrodes and gold contact pads were formed through aligned photolithography, electron-beam evaporation, and lift-off processes. The main ground (G) and signal (S) electrodes have a gap of 24 μm, while the T-rails of the G and S electrodes have a gap of 2.6 μm, ensuring strong EO coupling with manageable metal-induced optical losses. The final device, as shown in Fig. 4(a), was cleaved for end-fire coupling, with both the input and output ports located on the same side for testing.

At the operating point (R=1/9, −sinθbias1=sinθbias2=1), the total insertion loss of the LMZM was measured to be approximately 12.5 dB, including a 3-dB loss for optical biasing, a 5-dB propagation loss, and a 4.5-dB fiber-to-chip coupling loss, which can be optimized in the future design and fabrication process. The normalized small-signal EO responses S21 of the TE0-MZM and TE1-MZM, measured using the pairs of grating couplers, indicate 3-dB EO bandwidths both exceed 50 GHz, as shown in Fig. 4(b). The measured half-wave voltage Vπ was 2.6 V for the TE0-MZM and 5.6 V for the single-arm modulated TE1-MZM. In push-pull mode, the half-wave voltage Vπ was derived as 2.8 V for the TE1-MZM, approximately 1.08 times that of the TE0-MZM. In Fig. 4(c), the measured Vπ of the LMZM was 6.37 V, about 1.14 times that of the TE1-MZM, which is consistent with the simulation result. The transmission curve also shows good agreement with the theoretical one, as shown in Fig. 4(d). As depicted in Fig. 2, there are three thermo-optic phase shifters, labeled DC1, DC2, and DC3, with resistances of 833Ω, 824Ω, and 824Ω, respectively. In Figs. 4(e) and 4(f), the normalized transmission versus voltage characteristics for both the TE0-MZM and TE1-MZM are presented. The bias voltages applied to DC2 and DC3 were determined to be 6.5 V and 3.7 V for the TE0-MZM and TE1-MZM, corresponding to power dissipation of 51.3 mW and 16.6 mW, respectively. Figure 4(g) shows the optical power splitting ratio R as a function of the voltage and heating power applied to DC1. Optimal linearity was achieved at approximately 2.2 V, 3.3 V, 7.5 V, and 7.9 V, corresponding to R=1/9. The half-wave power Pπ for all phase shifters is around 30 mW, as shown in Fig. 4(g).

A schematic of the setup for linearity measurement is depicted in Fig. 5(a), while the experimental setup is shown in Figs. 5(b) and 5(c). A continuous-wave laser (Santec TSL570, max 13 dBm) at 1550 nm was coupled into the device under test (DUT) via a lensed fiber after a polarization controller (PC) to ensure TE polarization. An erbium-doped fiber amplifier (EDFA, Amonics AEDFA-33-B-FA) was employed when the input power requirements exceeded 13 dBm. The optical biasing voltages for DC2 and DC3 were provided by the power supply (Keithley 2230-30-3), while the voltage on DC1 for the optical splitting was adjusted using a programmable device (Keithley 2280S-32-6). The output optical signal was collected with a lensed fiber and subsequently directed to a 50-GHz photodetector (PD, Finisar XPDV2320R). For RF signal generation, two sinusoidal signals with a 10-MHz separation were generated using two RF sources (Keysight E8257D), combined by a high-isolation 12-GHz electrical power combiner (EPC, Marki PBR-0012), and injected into the TWEs via a high-speed GSG probe (Ceyear). The fundamental signal and IMD3 were subsequently measured using an electrical spectrum analyzer (ESA, Agilent PXA N9030A). Figures 5(d)–5(f) present the measured output RF powers of the signal and IMD3 as functions of input RF power at input frequencies of 1 GHz and 1.01 GHz, corresponding to OPs of about 5.5 dBm, 0 dBm, and −4.7dBm into the PD, respectively. Specifically, Fig. 5(d) demonstrates an ultra-high SFDR value reaching up to 121.7dB·Hz4/5 in our LMZM at the OP of 5.5 dBm. The noise floor (NF) of the ESA was −165dBm/Hz at 1 GHz. As shown in Figs. 5(d)–5(f), a decline of about 16 dB in SFDR values can be calculated as the OP decreases by about 10 dB. The output RF power versus input power of IMD3 in our LMZM displays a slope of 5, indicating the cubic terms of IMD3 are significantly suppressed [Eq. (11)], with the fifth-order terms now dominating. These fifth-order terms can be evident when the second terms of the Bessel functions are included according to Eq. (9). Consequently, the SFDR is expressed in units of dB·Hz4/5 when normalized to the 1-Hz resolution bandwidth (RBW). This behavior aligns with the findings reported in Ref. [10], benefiting from the TFLN platform that combines an intrinsically linear response with optimized structural design.

Figures 6(a)–6(c) show the output RF powers of the signal and IMD3 as a function of input RF power for the LMZM, TE0-MZM, and TE1-MZM with OPs of 0.1 dBm, 0 dBm, and 0.65 dBm, respectively. The calculated SFDR values were 112.7dB·Hz4/5, 100.7dB·Hz2/3, and 100.6dB·Hz2/3, respectively. Notably, the IMD3 in the TE1-MZM exhibits a slope of 3 on the log-log scale, consistent with the behavior of conventional TE0-MZM. Consequently, the SFDRs take a unit of dB·Hz2/3 for CMZMs (TE0-MZM and TE1-MZM) while dB·Hz4/5 for the LMZM. For clearer comparison, a quantitative relationship between SFDR values and OPs was established. The extracted slopes for the LMZM, TE0-MZM, and TE1-MZM were 1.6673, 1.3819, and 1.4362, respectively, closely matching the simulation results shown in Figs. 6(d)–6(f). The results for the TE0-MZM (TE1-MZM) were obtained using the same device as in our LMZM, with the TE0-MZM (TE1-MZM) branch turned on and the TE1-MZM (TE0-MZM) branch off. The LMZM exhibits a predicted SFDR of over 128.5dB·Hz4/5 in both simulation and experimental linear fitting results when the OP reaches the saturation level (10 dBm) of the PD. In the experiment, the maximum OP coupled into the device was 19 dBm, corresponding to an OP of 5.5 dBm into the PD, accounting for a 12.5-dB device loss and an additional 1-dB external link loss. The OP coupled into the chip was not further amplified to avoid exceeding the chip’s handling capability. The losses can be reduced by optimizing the device design and fabrication process further. Figure 6(g) shows the simulation and experimental results of SFDR improvement as a function of OP, indicating an improvement of 11.5–16.3 dB compared to the CMZM (TE0-MZM or TE1-MZM) in OP range of −8 to 10 dBm in the simulation and an enhancement of 10.7–16.1 dB in the experiment. Note that since SFDR values can be expressed in different units, comparisons are valid only at a certain RBW. For consistency, a normalization to 1-Hz bandwidth is employed for comparison here.

To verify the operational bandwidth, we measured the signal and IMD3 components using various frequency pairs at F and F+0.01GHz (F=1, 5, 10, 15, 20 GHz), as shown in Figs. 7(a)–7(e). The OP into the PD was maintained at approximately 0 dBm. The calculated SFDRs in a 1-Hz bandwidth for the LMZM at these five pairs of frequencies were 112.68 dB, 105.87 dB, 107.26 dB, 107.94 dB, and 103.33 dB, while for the CMZM were 100.58 dB, 97.92 dB, 99.02 dB, 99.41 dB, and 97.26 dB, showing improvements of 12.10 dB, 7.94 dB, 8.24 dB, 8.53 dB, and 6.07 dB, as presented in Fig. 7(f), respectively. Even at 20 GHz, our device still exhibits a 6.07-dB improvement over the reference CMZM. Note that the observed degradation in SFDR can be attributed to two primary factors: first, the deterioration in RF power combiner’s isolation, which increases from <−40dB at 1 GHz to over −30dB above 12 GHz; second, differences in higher-frequency characteristics between the TE0-MZM and TE1-MZM become more pronounced, such as increasing disparity in the half-wave voltage Vπ0 at higher frequencies. Further optimizations are necessary to improve the broadband performance consistency between the TE0-MZM and TE1-MZM.

Furthermore, the relationship between the SFDR and the optical ratio R was both simulated and experimentally analyzed. The simulation results shown in Fig. 8(a) indicate that our device can achieve superior SFDR performance compared to single-mode CMZMs (R=0) when R is within the range of 0 to 0.1333, across six different OPs. Besides, an improvement of more than 3 dB in SFDR can be realized when R is between 0.097 and 0.119. In our device, R was controlled by adjusting the voltage applied to the phase shifter DC1 experimentally, as shown in Fig. 4(g). Consequently, the SFDR as a function of voltage on DC1 can be derived, as shown in Fig. 8(b). The corresponding voltages for maximum SFDR were 2.16 and 3.33 V. Within the voltage ranges of 2.16–3.33 V and 7.51–7.89 V, the SFDR values of our device could outperform those of CMZMs, owing to the optical ratio R being within the range of 0–0.111. Figures 8(c) and 8(d) present the measured SFDR when the voltage applied to the phase shifter was adjusted from 2 to 3.3 V in 0.1 V increments, which closely aligns with the simulated results. To further investigate the tolerance to heating power fluctuations of the phase shifters DC2 and DC3 [labeled in Fig. 2(b)], which were used for biasing at the 3-dB quadrature points of the TE0-MZM and TE1-MZM (−sinθbias1=sinθbias2=1), we measured the fundamental signal and IMD3 components under several detuning voltages. As shown in Figs. 8(e) and 8(f), the results indicate that the SFDR remains superior to that of the CMZM, demonstrating an improvement of more than 5 dB within ±1.5mW (±2mW) for the TE0-MZM (TE1-MZM).

In this work, we have experimentally verified the fundamental characteristics of the proposed LMZM, including its insertion loss, half-wave voltage, EO bandwidth, voltage, and power for optical splitting and biasing. The relationships between SFDR and various key factors, such as device architecture, OP into the PD, operational bandwidth, optical splitting ratio, and heating power fluctuation, were thoroughly analyzed through both simulations and experiments.

To our knowledge, as summarized in Table 1, our LMZM device demonstrates outstanding overall performance, featuring high integration, excellent linearity, wide bandwidth, and structural simplicity. Leveraging the intrinsically linear EO response of TFLN and a single-RF dual-optical-mode co-modulated scheme, we achieved a record-high SFDR of 121.7dB·Hz4/5, the highest ever reported on integrated platforms. Even higher SFDR values, potentially exceeding 128.5dB·Hz4/5, could be achieved in the future by reducing on-chip losses and increasing the power into the PD. Moreover, our LMZM has a broad EO bandwidth exceeding 50 GHz, ensuring excellent linearity across a wide frequency range, which has been experimentally validated, with an observed SFDR improvement of 6.07 dB even at 20 GHz using an optical power of 0 dBm. Additionally, our ultra-linear modulator is highly compact, with a footprint of only 15mm×1.5mm, compatible with other high-performance photonic components on the platform for the development of future large-scale, high-performance, chip-scale microwave photonic systems, such as tunable lasers, frequency combs, and reconfigurable filters. With this proof-of-concept demonstration, our work opens new avenues for the development of linear, wide-band, integrated modulators, holding significant potential for future commercial applications.Table 1.

Comparison of Various Linearization Strategies in Optical Domain