A wide-spectrum mid-infrared electro-optic intensity modulator employing a two-point coupled lithium niobate racetrack resonator

The mid-infrared (mid-IR) spectral region holds considerable significance for various applications, including bond-selective chemical sensing and free-space communications through atmospheric windows.^1–4 Integrated photonics presents the most promising approach to achieve these unique functions at low cost, with high yield, and in a miniaturized form factor.^5–11 In parallel with the ongoing efforts to implement essential building blocks of mid-IR photonics on a chip, optical intensity modulators (OIMs), indispensable for information encoding and sensitivity enhancement via synchronous detection, have been demonstrated using various material platforms, mainly relying on the electroabsorption effect.^12–15 However, their performance remains significantly lagged behind that of near-IR modulators.¹⁶ 

Lithium niobate (LN), known for its pronounced second-order nonlinearity, is an ideal candidate for high-performance OIMs due to its high electro-optic (EO) coefficient and broad transparency range, spanning from the ultraviolet to the mid-IR.¹⁷ The hybrid integration of silicon photonics with bonded LN bulk crystals has demonstrated the potential of LN for mid-IR modulators.^18,19 Moreover, recent advances in thin-film lithium niobate (TFLN) fabrication techniques have enabled tight optical confinement within an LN waveguide, resulting in OIMs that operate with sub-volt voltages in the visible and near-infrared spectrum.^20–24 Although TFLN-based OIMs for the mid-IR are promising, they have yet to be demonstrated.

In addition to the conventional performance metrics of OIMs, a wide operational spectrum, particularly in the mid-IR, is highly desirable. This capability allows for system reconfiguration with a limited number of modulators to cover different carrier frequencies for communications or to access various molecular absorption bands for sensing. However, superior material properties alone are insufficient to support wide spectral operation. The internal characteristics of conventional devices, such as the beam splitting ratio for Mach–Zehnder interferometers (MZIs), do not maintain their optimal values (50:50 for MZI) and vary with wavelength. Therefore, effective active control mechanisms need to be integrated into LN OIMs to compensate for the chromatic variations in internal properties and maintain them at optimum values, ensuring wide spectral operation in a single modulator.^25,26

In this study, we demonstrate an on-chip LN optical modulator based on a microresonator that operates over a wide wavelength range in the mid-IR spectrum. By actively adjusting its coupling strength using a two-point coupling method (TPCM), a critical coupling that ensures a high extinction ratio of the modulation can be maintained across the entire operating wavelength range. The design rules for the coupling structure, significantly relaxed by the TPCM, have been quantitatively described by a simple analytic form, which we coined the relaxed critical coupling conditions (RCCCs). The developed modulator fully leverages the broad transparency window and the strong EO coefficient of LN, exhibiting high extinction ratios of over 20 dB and modulation efficiencies of 7.7 V cm over the wavelength range of 3.3–3.8 μm, which falls within the first atmospheric transmission window.

We refer to this constraint as the relaxed critical coupling condition (RCCC). Previous studies on TPCM have described a sinusoidal modulation of the effective coupling strength, assuming a small coupling strength at one coupler.^25,31 However, we note that the RCCC derived in this work provides a more generalized description of the coupling properties. Compared to OPCM, TPCM significantly relaxes the practical requirements to achieve critical coupling, allowing for intensity modulation with a high extinction ratio [both the black and gray lines in Fig. 1(d)] over a wide spectral range. Notably, the wavelength range satisfying the RCCC broadens as α² increases.

To verify the validity of the RCCC, we numerically simulated the transmission spectrum of the TPCM platform in the mid-infrared wavelength range. Here, we chose a structure with a length of 1.5 mm for the modulated straight segment and a radius of 250 μm for the curved part of the resonator in Fig. 1(b). To confirm the existence of a critical coupling state, the transmission spectrum for the different applied voltages was obtained, reflecting the EO modulation efficiency with a value of 15 V⁻¹ cm⁻¹. Initially, Fig. 2(a) shows the transmission spectrum for three different values of $τ2$ (0.9, 0.5, 0.2) with α² fixed at 0.45, corresponding to Q_int = 1 × 10⁴. Since the RCCCs specify that $0.275<τ2<0.725$ according to Eq. (3), the case of $τ2=0.5$ supports critical coupling but the other two cases do not. Increasing α² to 0.85 (Q_int = 5 × 10⁴) extends the RCCC range to $0.075<τ2<0.925$⁠, and the transmission spectrum shows that critical coupling is attained for all three values of $τ2$⁠, as shown in Fig. 2(b). This simulation result confirms that the RCCC is a reliable criterion for determining the coupler design parameters needed to achieve critical coupling, which are significantly relaxed by the TPCM, especially with high-Q resonators.

To satisfy the RCCC across a wide wavelength range from 3 to 4 μm, maintaining sufficiently low optical loss is crucial. We tailored the cross-sectional design of the TFLN [Fig. 3(a)] to reduce optical absorption loss from the SiO₂ bottom cladding, which is a dominant source of loss in on-chip mid-IR photonics.¹⁸ A waveguide geometry with a top air cladding was employed, and the loss from the bottom cladding was mitigated by engineering the thickness of the TFLN.³⁵ The observed trend of increasing propagation loss with wavelength is attributed to a greater overlap of the evanescent field with the SiO₂ film, whose absorption coefficient increases with wavelength in this region.³⁶ For an LN thickness of 900 nm and an etching depth of 350 nm [orange solid line in Fig. 3(a)], we theoretically expect a low propagation loss of less than 1.1 dB/cm (Q ∼ 1.9 × 10⁵) over the target wavelength range, considering the material absorption.

We also optimized the electro-optic modulator (EOM) configuration to reduce the optical losses caused by the circuit design while maintaining sufficient EO modulation efficiency. The length and radius of the resonator are the same as those of the simulated structure in Sec. II. To ensure consistent EO efficiency throughout the device, the waveguide width of the modulated segment was fixed at 3 μm for both the bus waveguide and the resonator. The spacing between electrodes was optimized to 14 μm, which balances minimizing electrode-induced losses and maximizing EO modulation efficiency, as shown in Fig. 3(c). In addition, to explore designs satisfying the RCCC over a wide spectral range, samples were fabricated with different gap sizes of the point-coupler, which support various transmission coefficients.

The on-chip LN device was fabricated using electron beam lithography (EBL) to pattern the FOX-16 resist and Ar-based inductively coupled plasma-reactive ion etching (ICP-RIE) to transfer the pattern onto the TFLN. The 900 nm thick, x-cut LN film was etched to a depth (Hetch) of 350 nm, followed by Ar–O₂ mixture plasma exposure. Subsequently, the LN devices were thermally annealed at 530 °C for 12 h to restore optical transparency in the mid-IR wavelengths (details in Method B), after which the electrodes (100 nm Au/30 nm Ti) were formed [Fig. 3(b)].³⁷ 

We experimentally demonstrated full modulation of the coupling state, ranging from the under-coupling and critical to over-coupling regimes, across the wavelength spectrum from 3.3 to 3.8 μm within a single device. In Fig. 4, the measured DC responses of the four EOMs with different gap distances of the point coupler (denoted as Gap) are characterized. The representative resonant modes at each wavelength are successfully modulated depending on the applied DC bias through the push–pull electrodes.

For the EOMs with Gap values of 1700 and 1500 nm, the longer the wavelength, the greater the transmission depth [Figs. 4(a) and 4(b)]. This is because the evanescent coupling between the bus waveguide and the resonator increases with the wavelength, allowing resonant modes at longer wavelengths to be tunable to the critical coupling state. Similarly, reducing the gap size increases the coupling coefficient κ due to the larger evanescent field overlap at the point coupler and enables the achievement of the critical coupling state over a wider spectral range. Remarkably, as shown in Fig. 4(d), the device with an 800 nm Gap reaches the critical coupling state over the entire wavelength range under investigation. Furthermore, it exhibits the EO modulation with a negligible resonant frequency change for the resonant modes at the wavelengths of 3500 and 3600 nm, which will be investigated in detail later.

By analyzing the DC response, we proved that the wide-spectrum operation of the developed device is attributed to the achievement of the RCCC. Initially, $κQc$ and $αQint$ were extracted by fitting the numerical simulation with the experimental results, which showed good correspondence for all four devices with different gap distances. The simulation and experimental results of the transmission spectra for the devices with a gap distance of 1700 and 800 nm are plotted in Figs. 5(a) and 5(b), respectively. The Nelder–Mead simplex optimization algorithm was used for the fitting process (Method C).

Figure 5(c) shows the coupling and intrinsic Q factors, Q_c and Q_int, depending on the wavelength and the gap distance. For all the devices, an inverse relationship between the wavelength and Q_c was consistently observed, which originates from the wavelength-dependent evanescent field overlap at the point coupler. On the other hand, Q_int increases with wavelength, reaching a peak value of 5.2 × 10⁴ (∼4.02 dB/cm) at the wavelength of 3800 nm. This trend indicates that the optical losses by the bottom SiO₂ layer and electrode, which increase with wavelength, were masked by the dominant losses such as those by hydrocarbon molecules exhibiting strong absorption around a wavelength of 3.4 μm.¹⁸ In this study, these additional losses were introduced during the electrode patterning process, as evidenced by a reference sample that underwent the same fabrication steps as the EO modulator device but without the electrode formation, which exhibited significantly higher and more uniform Q-factors across the measured wavelength range (Method B).

Figure 5(d) confirms that the capture of the RCCC enables the full coupling modulation observed experimentally. τ and α were evaluated from Q_c and Q_int. The upper and lower bounds of the RCCC are given as $τth2=κth2±α2$⁠, $τthlow2=κth2−α2$⁠, and $τthup2=κth2+α2$ [dashed lines in Fig. 5(d)]. The full modulation of the resonant mode traversing from under-, critical, to over-coupling, observed in Fig. 4 and highlighted in Fig. 5(d) with a light red box, occurs when the condition of the RCCC, $τthlow2<τ2<τthup2$⁠, is satisfied. Notably, under the push–pull configuration of the electrode, $τ2$ tuned to 0.5 [indicated by the red blank star in Fig. 5(d)] results in no shift in the center frequency, as confirmed by the EO modulation of the transmission spectrum [the case of λ = 3500 nm in Fig. 4(d)].^21,30 We expect that this specific condition, termed “pure coupling control” can be exploited for ultra-fast modulation exceeding 100 GHz as envisioned in the near-IR.²¹ 

We note that the observed working bandwidth of the EOM with Gap of 800 nm ranging from 3.3 to 3.8 μm was limited by the operational wavelength range of the employed optical parametric oscillator (OPO) laser. We expect the actual working bandwidth to surpass the measurement. Furthermore, pulley couplers, which exhibit a more chromatically uniform coupling strength, could be a promising alternative to the point couplers used in this experiment for further expanding the operational bandwidth.^38,39

Previous studies on mid-infrared OIMs have typically demonstrated operation at a single fixed wavelength or over a narrow wavelength band. However, for the first time to the best of our knowledge, we report intensity modulation with a high extinction ratio across a wide spectral range using a single modulator. Initially, the full modulation voltage (V_full), defined as the swinging voltage required for maximal change in the transmission depth, was characterized by utilizing the critical-to-under coupling transition in the optimized device (Gap = 800 nm). The laser frequency was set to the center of the resonant mode under the critical coupling, and a 50 Hz voltage was applied. The average V_full was 51.3 V, with the lowest value of 46.5 V being achieved at the wavelength of 3600 nm, where Q_int reached its maximum (⁠$Vfull∝λ/Q$⁠. Considering the modulated segment length of 1.5 mm, the EO modulation efficiency was determined to be 7.7 V cm, comparable with other mid-IR platforms utilizing the Pockels effect.^18,19 in addition, the extinction depth across the entire wavelength range exceeded 20 dB. In the final step, full intensity modulation with a square wave was successfully demonstrated across the entire wavelength range under investigation by applying 1 kHz rate square pulses [Fig. 6(b)]. The demonstrated modulation speed was limited by the bandwidth of the employed high-voltage amplifier.

The operating voltage can be further reduced by optimization strategies, which would enable ultrafast modulation of mid-IR light. First, additional improvement of Q factors leads to a narrower linewidth of the resonant mode, thereby reducing V_full. Second, increasing the length of the phase modulator can induce more phase difference between the resonator and the bus waveguide. Finally, the use of advanced deep LN etching techniques can surpass the current etching depth limit of 350 nm, which restricts the electrode gap spacing to 15 μm.^40–44 We expect that etching depths beyond 600 nm would reduce the gap spacing between the electrodes due to the increased confinement of the optical mode, thereby enhancing the EO efficiency.

In this study, we demonstrated a TFLN micro-resonator-based OIM that operates across a broad mid-IR wavelength range, which is crucial for detecting and manipulating molecular vibrational dynamics. By employing a two-point coupling geometry, the device design requirements for achieving high modulation extinction were significantly relaxed, which was quantitatively described by a simple, general analytic form called the RCCC. To the best of our knowledge, this study is the first to achieve mid-IR intensity modulation across a wide spectral range within a single modulator despite challenges associated with the chromatic dispersive nature of the coupling coefficient and the intrinsic Q factor, which are particularly pronounced in the mid-IR wavelength. The developed modulator exhibited high extinction ratios of over 20 dB and modulation efficiencies of 7.7 V cm in the wavelength range from 3.3 to 3.8 μm. Our methods hold promise for further expansion into the deeper mid-IR spectrum by integrating with material platforms that provide high optical transmission, such as chalcogenide glass.

We assume that the passes through each half of the resonator and the bus waveguide exhibit the same attenuation since their length difference is about 400 μm, which results in only a 3% imbalance. The phase shifts for the paths passing through the bus waveguide and both the top and bottom parts of the resonator are given by $ϕ=k0neffLWG+ΔnL$⁠, $θ1=k0neffLRes/2−ΔnL$⁠, and $θ2=k0neffLRes/2$⁠, respectively. Here, L_Res, L_WG, and L are the circumference of the racetrack resonator, the total length of the bus waveguide, and the length of the electrode, respectively. The refractive index change by the Pockels effect is given as $Δn=∂k∂VΔVk0,$⁠, where $∂k∂V$ and k₀ are the modulation efficiency and wavenumber in the free space, respectively. In the numerical simulation shown in Fig. 2, the value of 15 V cm⁻¹ was used for $∂k∂V$⁠, which was extracted from our device.

We demonstrated that thermal annealing successfully reduces the propagation loss in TFLN waveguides and micro-resonators. We fabricated a 300 μm radius LN microring resonator using the same fabrication processes as those used for the EOMs. As shown in Fig. 8, we monitored the transmission spectrum and Q factor of the LN microring resonator for each of the following stages: (1) initial, as-is condition, (2) after 2 h of thermal annealing at 530 °C, (3) after additional 4 h of thermal annealing at 530 °C, and (4) following the electrode patterning process. Figure 8(b) shows the intrinsic quality factor (Q_int) extracted from the loaded quality factor and transmission depth measurements. Remarkably, the thermal annealing process significantly improved Q_int, reaching up to 2 × 10⁵. As shown in Fig. 8(c), the resonances over the wide wavelength range get narrower and deeper as applying an additional annealing process. In the final step, the reference microring resonator sample undergoes the same electrode lift-off process as the main EOM sample, resulting in a decrease in Q factors, which is attributed to chemical loss. It is emphasized that the thermal annealing process should be conducted as the very last step in the whole fabrication process, or the appropriate passivation layer is essential to prevent post-fabrication contamination.

Once the initial values of α and κ and the geometrical information of the TPCM are given, the iterative fitting begins. The Nelder–Mead simplex algorithm was employed to update the parameters iteratively toward the minimum of σ_err and resulted in a good agreement of the simulated results with the experimental data, as shown in Fig. 5. We note that the initial parameter set was sparsely scanned to avoid local minima problems in the optimization process.

We have established an experimental setup for precise characterization of transmission spectra spanning from 3 to 4 μm using an OPO laser [Fig. 10(a)]. To accurately measure the linewidth and relative frequency shift of the resonant modes, the OPO laser is partially divided into a free-space interferometer with a bandwidth of 75.25 MHz, and the resulting signal is used as a reference for correcting the relative frequency [Fig. 10(b)]. The coupling of light into and out of the on-chip integrated photonic device has been achieved using two identical single-mode InF₃ fibers (Thorlabs) with a mean field diameter of 11 μm. To increase the fiber-to-chip coupling efficiency, we gradually adjusted the waveguide’s width from 2 to 5 μm at the device’s end facets. The measured coupling loss averaged over the employed spectral range was 31.2 dB. The out-coupled light signals were detected using a HgCdTe photodetector (VIGO Photonics). To examine the behavior of the target high-Q resonant mode in response to the applied voltage, we finely tuned the OPO laser source employing a servo-controller. For the characterization of the DC response of the resonant mode, the transmission spectrum was measured at a 10 Hz repetition rate, while the induced voltage was simultaneously modulated at a frequency of 1 Hz [Fig. 10(c)], which enabled effective measurements at ten different applied voltages.

M.-K.S. and H.L acknowledge the support from the KAIST Cross-Generation Collaborative Lab project, the Institute for Information, Communication Technology Promotion of Korea (Grant Nos. 2020-0-00890 and 2021-0-00552), the National Research Foundation of Korea (Grant Nos. RS-2024-00350185 and RS-2024-00408271), the National Research Council of Science and Technology (Grant No. 21031-200), and the Samsung Research Funding & Incubation Center of Samsung Electronics (Grant No. SRFC-IT1801-03).

The authors have no conflicts to disclose.

Hyeon Hwang: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Kiyoung Ko: Data curation (equal); Resources (equal); Writing – review & editing (equal). Mohamad Reza Nurrahman: Data curation (equal); Formal analysis (equal); Writing – review & editing (equal). Kiwon Moon: Investigation (supporting); Resources (supporting). Jung Jin Ju: Investigation (equal); Resources (equal). Sang-Wook Han: Investigation (equal); Resources (equal). Hojoong Jung: Investigation (equal); Resources (equal). Min-Kyo Seo: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Hansuek Lee: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.