The interaction between light and matter establishes the first basis for essential components that enable on-chip photon manipulation technologies¹. Conventional silicon-based photonic crystal nanobeam cavities (PCNBCs) strongly confine light with both high-quality (Q) factors and small mode volumes, dramatically enhancing these interactions². Additionally, these cavities can further synergize with the thermo-optic (TO)³ or free-carrier dispersion (FCD) effect⁴, enabling a broad spectrum of applications across multiple disciplines. Notable examples include high-efficiency optical modulators and switches^5,6, ultra-compact filters⁷, and advanced nonlinear optics⁸. However, the modulation speed of silicon photonics is primarily constrained by its inherent absorptive and nonlinear characteristics, which has led to a plateau in its development, making it challenging to satisfy the exponentially increasing demand for large-capacity interconnects and communications⁹. On the other hand, lithium niobate (LiNbO₃, LN), although an “old” and extensively studied material, has played a crucial role in advancing photonics and acoustics for several decades¹⁰. From enabling high-speed optical communications¹¹ to the development of acoustic filters used in mobile terminals¹², LN has proven its versatility and reliability. Specifically, in photonics, its extraordinarily strong and highly linear electro-optic (Pockels) properties have propelled LN optical modulators into the Terabit era¹³.

Inheriting the exceptional optical properties of LN, thin-film lithium niobate on insulator (LNOI) has recently been recognized as a cutting-edge platform that is leading another revolution in integrated photonics on chip¹⁴⁻¹⁶. Contrasting with the CMOS-compatible process of silicon photonics, LNOI photonics encounters a significant barrier in manufacturing low-loss waveguides and nanoscale optical components¹⁰. The principal challenge is the high-quality etching of LN. While precise methods like ion beam etching¹⁷ and focused ion beam (FIB) milling¹⁸ are accurate, they can damage the crystal lattice and introduce ion contamination. An alternative technique, the femtosecond laser photolithography assisted chemo-mechanical etching (PLACE) technique¹⁹⁻²¹, overcomes these issues and ensures an ultra-smooth surface but lacks sufficient etching selectivity for fabricating sophisticated structures such as PCNBC. Moreover, methods such as reactive ion etching (RIE) and inductively coupled plasma etching (ICP-RIE), while compatible with batch fabrication, suffer from significant redeposition issues¹⁰. These challenges collectively hinder the enhancement of optical performance in LN-based devices.

Recently, a novel route has been proposed that involves spinning and patterning a low-refractive-index polymer (~1.5) on top of the LNOI substrate²². This approach allows for the creation of a polymer-loaded rib-waveguide capable of accommodating both transverse electric (TE) and transverse magnetic (TM) modes. Nonetheless, most research efforts have primarily focused on TM-polarized modes produced by photonic bound states in the continuum (BIC)²³. On this etchless platform, various intriguing physical phenomena^24,25 and high-performance key optical components have been demonstrated²⁶⁻²⁸. In addition, many other novel applications have also been unlocked in the metasurfaces based on the BIC regime^29,30. However, there are challenges when it comes to manufacturing high-Q resonator cavity devices due to the highly sensitive radiation losses of the TM mode associated with the polymer stripe widths. In comparison, the TE modes represent standard bound modes that propagate without radiation losses for any width within their supported range³¹. Therefore, the design strategy for the polymer/LN hybrid structure still has room to be developed.

In this paper, we present an experimental demonstration highlighting the significant potential of TE-polarized polymer-loaded waveguides as a feasible pathway for the realization of highly efficient and productive nanocavities. To the best of our knowledge, the achieved Q factor is over one order of magnitude higher than any previously reported etchless LN PCNBCs (~0.1×10⁵)^26,32. This remarkable enhancement in Q inspire a series of strong light-matter interaction phenomena, including highly efficient thermo-optic (TO) tuning, exceptionally strong optical bistability, and facile generation of Fano resonances. Our successful demonstration of high-Q LNOI photonic cavities represent a significant milestone towards the development of LN nanophotonics, merging the unique material properties of LN with versatile nanophotonic device design and fabrication methods. This breakthrough holds tremendous promise for a wide range of applications, including nonlinear photonics, electro-optic (EO) or acousto-optic (AO) tunable devices, optical logic devices, and quantum photonics.

Figure 1(a) depicts the cross-section view of the polymer-loaded waveguide, which is placed on a y-cut LNOI substrate. The loaded polymer has a thickness of 0.4 μm and a width of w. To obtain the optimal w, the finite element method (FEM) is employed to model the propagation loss of this waveguide. In our simulations, the refractive index of the polymer is set to 1.53, and the refractive index of ordinary (n_o) and extraordinary (n_e) for LN are 2.21 and 2.14, respectively. Figure 1(b) illustrates the relationship between the propagation loss and waveguide width w for different modes at the wavelength of 1550 nm. It is observed that TM modes exhibit minimal losses at certain specific waveguide widths. This behavior can be explained from the perspective of the photon potential²³, as shown in the inset of Fig. 1(b). The energy of the TM mode can couple into the TE continuum through the edges of the waveguide due to the potential well of the TM mode being located within the TE continuum. By adjusting w, it is possible to eliminate coupling loss through destructive interference between the coupling channels. In this mechanism, the TM mode exhibits lower loss at w of 2.1 μm compared to 3.0 μm, due to stronger confinement within the potential well. By contrast, for TE modes, the potential well has the lowest energy and is not coupled with TE continuum in the LN substrate (not shown). Therefore, the propagation loss of TE modes is low and stable, decreasing as w increases. Consequently, TE modes are robust compared to TM modes, a characteristic of critical importance given that fabrication tolerances have a lesser impact on device performance.

To reveal the light propagation mechanism within the waveguide, an analysis of optical modes with electric field profiles was performed. Figure 1(c) displays the electric field profiles of |E_y| for both TM₀₀ and TM₀₁ modes, revealing energy concentrated in the upper and lower cladding layers. Correspondingly, Fig. 1(d) illustrates electric field profiles of |E_z| for both TE₀₀ and TE₀₁ modes, confirming the predominant localization within the LN layer, which facilitates the effective utilization of the outstanding material properties. Compared to the TM modes, the TE modes exhibit relatively weaker confinement in the z-direction, potentially resulting in larger losses in designs involving curved waveguides. Nevertheless, the transmission characteristics of the TE modes are instrumental in avoiding the disruption of BIC condition caused by the anisotropy of LN. This feature is very important for the design of high-Q PCNBC.

Based on the discussion of waveguide modes and optical losses above, we further investigate the losses inside the nanocavity. As illustrated in Fig. 2(a), the proposed PCNBC is constructed by a series of dielectric blocks in two regions, including taper and mirror, which are symmetrical with the red dashed line. The width of the polymer waveguide is 2 μm, and the fixed lattice constant of a = 0.43 μm enables phase matching for each unit cell. In the taper region, pulling the confined mode with a Gaussian-shaped field profile away from the light line effectively minimizes radiation loss³³. It is realized by establishing a parabolic distribution of the filling factor³⁴, which is utilized to define the dimension of the dielectric block. Here, the filling factor f is defined as the ratio of the air area to that of the unit cell. The relationship of the filling factor from the center of PCNBC (f_c) to the end of the taper region (f_e) is

fi=fc−(fc−fe)i2/Nt2,(1)

where N_t represents the number of dielectric blocks in the taper region, and i is an integer increasing from 0 to N_t. f_c and f_e are determined by mirror strength γ, which is determined by³⁴

γ=(ω0−ω1)2/(ω0+ω1)2−(ωres−ω2)2/ω22,(2)

where ω_res is the target resonance frequency of the fundamental mode, and ω₀, ω₁, ω₂ are the air band edge, dielectric band edge, and midgap frequency of each segment. Figure 2(b) shows the band diagram of the TE₀₀ mode. The filling factors of 0.3 and 0.42 are chosen, which correspond to the maximum mirror strength and the minimum mirror strength (see Fig. 2(c)). As shown in Fig. 2(b), a photonic band gap (PBG) is obtained at f = 0.3 (blue curves). When f is 0.42 (red curves), the dielectric band is pulled into the PBG. It means that the fundamental mode becomes a discrete mode. As a result, f_c is set to 0.42 and f_e to 0.3. The filling factor is gradually changing from f = 0.3 to f = 0.42 according to Eq. (1). At the mirror region, the filling factor remains the same (i.e., f_e = 0.3).

Next, we investigate the optical mode field profile of the PCNBC based on the above parameters. To better confine optical mode, the transition from f_e to f_c should be smoother. Thus, the numbers of N_t and N_m are set to N_t = 120 and N_m = 100, respectively. Figure 2(d) illustrates the simulation results for the profile of Gaussian-shaped electric field energy for the fundamental and second-order modes. It indicates that the PCNBC we designed has the capability to support other high-order resonant modes. Furthermore, as depicted in Fig. 2(e), the electric field distribution of the fundamental mode is parallel to the z-axis of the LN crystal. Thus, it confirms the optical mode of the PCNBC is based on TE₀₀ mode. The relationship between w, N_t, N_m, and Q will be discussed in detail in the next section.

Devices were fabricated on a custom-made y-cut LNOI substrate with a 0.3 μm LN layer (NanoLN Corp.). The substrate is cleaned sequentially in N-methyl-2-pyrrolidone (90 °C), isopropyl alcohol (ultrasonic), deionized water (ultrasonic), and piranha solution (90 °C) for 10 minutes, respectively. Then a 0.4 μm polymer (ARP-6200.13) was spin-coated on the substrate and prebaked on a hot plate at 180 °C for 10 minutes. The pattern was transferred to the polymer by e-beam lithography (NanoBeam, nB5). Finally, the residual polymer was removed with the developer. Figure 3(a) shows the scanning electron microscope (SEM) image of the sample. The polymer waveguide is well-defined, which guarantees its process stability.

To characterize the proposed device, the light from the tunable semiconductor laser (Santec, TSL-550) is pumped into the grating coupler through a polarization controller, which is used to adjust the polarization of the pump light. The transmitted light of PCNBC is collected by the optical power meter (Thorlabs, PM100D) from the other grating coupler. Throughout the testing process, the chip is placed on a high-accuracy thermoelectric cooler (TEC) with a stabilized temperature of 21.5 °C. As shown in Fig. 3(b), there exist several peaks. The fundamental mode is located at 1528.320 nm, which is close to the simulated result of 1530.612 nm (the fundamental mode resonance wavelength in Fig. 2(d)). The slight deviation can be attributed to the influence of the fabrication. Other high-order modes appear at larger wavelengths. Compared with the high-order modes, the fundamental mode has a higher Q factor of 0.47×10⁵ (see the inset in Fig. 3(b)) and a lower transmission of 52.4%. Since only the fundamental mode is optimized, the high-order modes suffer a larger radiation loss. Moreover, the coupling loss quality factor (Q_c) from the PCNBC to the bus waveguide and the radiation loss quality factor (Q_r) can be used to determine transmission (T)³⁵

T=Qr2/(Qc+Qr)2.(3)

For radiation-Q-limited PCNBC, Q_c is much larger than Q_r. According to Eq. (3), the high-order modes exhibit larger transmissions due to their smaller values of Q_c. Figure. 3(c) describes the relationship between the Q factor of the fundamental mode and w (N_t = 120, N_m = 100, f_c = 0.42, and f_e = 0.3). The Q factor becomes larger along with w because a larger w results in a smaller propagation loss (see Fig. 1(b)).

Here, we discuss the influence of the dielectric block on the Q factor. Figure 3(d) presents the transmission spectrum at different N_t, revealing that as N_t increases, the Q factor correspondingly rises, while the transmission gradually diminishes. A similar behavior is observed in Fig. 3(e) for varying values of N_m. These results can be attributed to three mechanisms. First, an increased number of dielectric blocks in the taper region leads to a more gradual parabolic distribution of the filling factor, ranging from 0.3 to 0.42. This design facilitates a more uniform confinement of the optical Gaussian-shaped field profile along the x-direction, thereby minimizing the scattering of optical energy into radiation modes. Second, a higher value of N_m enhances the mirror reflectivity, which significantly strengthens the confinement of the Gaussian-shaped field profile within the PCNBC. Third, an increase in both N_t and N_m can reduce the coupling losses, which result in reduced transmission, as illustrated in Eq. (3). Combining these mechanisms, the increasing Q factors with the number of dielectric blocks can be attributed to a tighter Gaussian-shaped field profile, resulting in reduced cavity losses and coupling losses. Thereby, the properly optimal N_m and N_t parameters are crucial for achieving high-Q and high-transmission PCNBCs that are much more desirable for high-efficient optical modulators. Despite a decrease in transmission, the Q increases to above 1.87×10⁵ when N_m is set to 200, as shown in the inset of Fig. 3(e). Table 1 presents a comparison of the reported LN-based PCNBCs. Noted that, our PCNBCs exceed the most similar cavities on LN substrate, featuring a much simpler fabrication process³⁶.

The high Q factor of PCNBCs enhance the light-matter interactions, enabling the exploration of intriguing novel optical phenomena. In this section, the potential functions of the Q-induced phenomen based on our LN PCNBCs are examined and studied.

TO tuning is one of the most efficient methods to manipulate photons, providing a significant refractive index change almost without optical loss^40,41. This mechanism plays a crucial role in photonic integrated circuits (PICs), where TO switches and modulators are indispensable components^42,43. For example, optical devices like microring resonators and PCNBCs, are highly sensitive to fabrication errors leading to resonance wavelength shifts. This problem can be solved by integrating a heater near the waveguide. The optical material with a large TO coefficient is critical for achieving highly energy-efficient TO tuning. Nevertheless, in the proposed LNOI platform, the maximum TO coefficient of the LN is dne/dT≈3.3×10−5K−1, which is smaller than that of the polymer material as reported⁴⁴. For our PCNBCs, polymer serves not only as the structural element but also facilitates TO tuning compared to monolithic LN, since part of the optical mode is distributed within the polymer layer. The TO tuning capability of polymers has been demonstrated in various types of PCNBCs^45,46. Generally, to evaluate the modulation efficiency of the TO modulator, the π-phase shift temperature ΔT_π is calculated by⁴⁷

ΔTπ=πδλ0(Δλ/ΔT)−1,(4)

where δλ₀ is the linewidth, corresponding to the full width at half maximum (FWHM) of the transmission spectrum, and Δλ/ΔT is the sensitivity of temperature, which is determined by the material properties. To improve modulation efficiency, it often involves complex structures and fabrication processes, such as suspended device structures and p-n junction waveguides^48,49. High modulation efficiency and a simple fabrication process are desirable for TO tuning, especially in LN photonics with a weak TO coefficient.

To study the thermal tuning characteristics of our PCNBCs, the chip is heated from 20 °C to 30 °C at a step of 2 °C. The transmission spectra for a PCNBC operating in the fundamental mode are presented in Fig. 4(a). The resonance peak redshifts obviously as the temperature rises and ΔT_π of 2.36 °C is obtained. Therefore, the device possesses TO tuning capability. In general, an increase in the Q tends to reduce the ΔT_π of the TO modulator, as shown in Eq. (4), indicating a lower power consumption. For this purpose, devices with different Q factors are measured under the same condition. The corresponding ΔT_π and Δλ/ΔT are shown in Fig. 4(b). With the increase in the Q factor, the ΔT_π reduces. It is due to a larger optical energy density that enhances light-matter interactions. A device with a larger Q is suitable for temperature-sensitivity applications. The sensitivity of temperature remains around 26 pm/°C as the Q increases, which reveals the Δλ/ΔT of this platform. ΔT_π reaches its minimum value of 1.05 °C when the Q reaches 1.87×10⁵, surpassing the performance of a device employing TO tuning with an integrated metal heater^7,45. Through the measured data and the results from FEM calculations, the TO coefficient of the polymer is extracted as 0.8×10⁻⁴ K⁻¹. Most importantly, the demonstration of thermal tuning indicates that the proposed high-Q PCNBCs provide a novel solution to the TO tuning issues experienced by LN photonics while also allowing for easy fabrication processes.

Optical bistability is a phenomenon observed in high-Q silicon photonics, predominantly attributed to complex nonlinear effects such as two-photon absorption (TPA), the TO effect, FCD, and the Kerr effect⁵⁰. This bistability is critical for the development of next-generation all-optical applications, including high-speed modulation and optical logic circuits^51,52. LN, despite its widespread use in photonic applications, has a poor TO coefficient and lacks a mechanism for TPA at 1550 nm due to its wide bandgap of 3.78 eV⁵³. Therefore, it is nontrivial to excite optical bistability even in microcavities, limiting its potential for all-optical modulation. In contrast, the polymer introduces inherent defect absorption and has a large TO coefficient as previously discussed in TO tuning. Moreover, the high-Q PCNBC may facilitate this process due to the small mode volume and strong confinement of the Gaussian-shaped field profile. Taking into account the above-mentioned analysis, it is a feasible solution to facilitate the application of LN photonics in all-optical information processing. Consequently, we investigate optically-induced bistability in the proposed high-Q PCNBCs.

First, we set the tunable semiconductor laser with wavelength increment steps of 1 pm, and the required sample time is 0.37 seconds for each point. Second, we measure the transmission spectrum for the fundamental mode at different input power levels. At this state, the power-dependent transmission spectra for one of the PCNBCs are shown in Fig. 5(a). As the power injected into the cavity increases from 72.4 μW to 738.9 μW, there are two significant changes are observed. The resonance peak exhibits a pronounced redshift, which is induced by the positive TO coefficient of LN and polymer. Additionally, the measured line shapes gradually change from a Lorentzian type to a bistability feature induced by the TO effect. The optical bistability comes into being when the shift (Δλ) of the transmission spectrum satisfies the Eq. (5)⁵⁴. Meanwhile, Eq. (5) indicates that a PCNBC with a large Q factor (small linewidth) will benefit under the identical condition, which requires lower optical power to induce bistability. The corresponding injected power is defined as the threshold power P_t. For this device, P_t is 160 μW.

Δλ⩾3δλ0/2.(5)

Figure 5(b) illustrates the threshold power of optical bistability for different devices with varying Q factors and transmissions. Initially, the threshold power gradually decreases as the Q increases, which agrees with our prediction. The underlying mechanism is mainly due to the dramatically enhanced optical energy density in PCNBC. When the Q exceeds 1.63×10⁵, the threshold power begins to increase. It is caused by the decline in transmission intensity with increasing Q. Therefore, achieving high-efficient optical bistability depends on the careful design of PCNBCs with both high Q factors and optimal transmission characteristics. This experiment validates the feasibility of LN photonics devices with optical response, potentially paving the way for the development of LN all-optical logic chips.

Fano resonance, characterized by its sharp and asymmetric line shape, opens up extensive prospects for the advancement of the field of photonics, especially proving immensely attractive in the realms of switching and sensing^55,56. Numerous efforts have been put to demonstrate high-performance Fano resonance^57,58. However, these devices often suffer from a larger footprint and complex tunability. Recently, the tunable Fano line shapes have been demonstrated in the silicon-based 1D PCNBC by adjusting the position of the input and output fibers⁵⁹. This efficient Fano tunability benefits from two aspects. First, the high-index-contrast silicon waveguide ensures strong confinement of light within the waveguide. Second, the rectangular photonic crystal grating couplers provide heightened light sensitivity. All these factors enhance the dependency of the grating on the position of the fiber. However, achieving highly efficient Fano tunability on this etchless LNOI platform remains challenging due to the wake interaction between discrete state (cavity resonance mode) and continuum state (waveguide propagating mode). Therefore, the high-Q PCNBCs provide a good platform for studying the high-efficiency generation of Fano resonance.

When the pump laser is near the resonance wavelength of the PCNBC, part of the energy is converted into the high-order leak TE mode, which serves as a continuous state and can propagate through the PCNBC^59,60. Then, it interferes with the discrete fundamental mode. The transmission spectrum produced by the interaction is described as follows⁶¹

|T(ω)|2=T0+k[q+2(ω−w0)/Γ]21+[2(ω−w0)/Γ]2,(6)

q=cotφ,(7)

where T₀ and k are the constant factors of offset and scaling factor. And q, φ, w₀, and Γ are the Fano asymmetry factor, the phase difference between the continuum state and discrete state, the resonance frequency of the cavity mode, and the resonance linewidth, respectively.

To introduce the interference, the positions of the input fiber (left red dot) and output fiber (right red dot), located at the top of the grating couplers, are gradually altered, as illustrated in Fig. 6(a). When two fibers perfectly coincide with the center of the grating couplers, the phase difference φ between the continuum state and the discrete fundamental mode is zero, and the measured transmission spectrum has a Lorentzian line shape. However, the phase difference φ is not zero when the fibers are off-center from the grating couplers, the two modes start to interfere with each other, and the measured transmission spectrum has an asymmetric Fano line shape. In this approach, the transmission spectrum will experience a π phase shift change in theory. That is, the transmission spectrum will go through Lorentzian, Fano, quasi-Lorentzian, inverted Fano, and Lorentzian line shapes⁶².

The measured transmission spectra are displayed in Fig. 6(b). For simplification and effective monitoring of the interference, the output fiber is fixed at y_o = 3 μm. To change the phase, the input fiber is moved from y_i = 2 μm to y_i = 6 μm in the direction of y_i at a step of 2 μm. During this process, the measured transmission spectra show a significant change. With the increase in y_i, the extinction ratio (ER) reaches 15.14 dB, 19.03 dB, and 25.43 dB for the φ values of 0.24 rad, 0.43 rad, and 0.58 rad. When the input fiber goes along −y_i with the same displacement, the inverted Fano line shapes are obtained. The corresponding ER is 25.83 dB, 16.38 dB, and 12.89 dB, with φ being −0.09 rad, −0.19 rad, and −0.22 rad. In sharp Fano line shapes, a large ER enables low-power operation. The effect of the Q factor on Δφ is also investigated in Fig. 6(c). Here, Δφ is defined as the sum of the absolute phase difference between two antisymmetric Fano line shapes (y_i = |−y_i|), corresponding to the variation degree of the line shape. The Δφ tends to increase with Q at y_i/|−y_i| = 4 μm. A larger Q factor means less displacement shift of the input fiber to attain the same Δφ. Although there is much room for improvement in Fano tuning, the impact of the Q factor on the phase tunability of the Fano line shapes is demonstrated for the first time on the LNOI platform. This discovery introduces a new avenue of research for ultra-compact Fano resonance tunability photonic devices.

In this paper, we theoretically proposed and experimentally demonstrated a method for achieving high-Q PCNBCs based on LNOI platform. The design principle of a radiation-limited cavity enabled the successful fabrication of nanocavities with Q factors exceeding 10⁵ and high transmittance. To the best of our knowledge, the achieved Q is over one order of magnitude higher than the previous reports on etchless LN PCNBCs. Moreover, we explore the application potential of high Q microcavities in the interaction between light and external fields, demonstrating efficient modulation effects in TO tuning, optically-induced bistability, and Fano line shapes generation. These results hold tremendous promise for providing a versatile platform technique to develop high performance EO or AO modulator, optical logic devices, and quantum photonics, demonstrating significant potential in the field of photonic integration.