Introduction

High-Q optical resonators are essential components in nanophotonics, enabling narrowband filtering1, enhanced nonlinearity2,3, cavity quantum electrodynamics4,5, sensing6, precision spectroscopy7,8, laser stabilization9, and more. Quality factors in these resonators are fundamentally limited by optical losses from material absorption and surface scattering, and can be as high as 107 for microring resonators in the thin-film lithium niobate platform studied here10,11. Higher quality factors would have a direct impact for enabling functionality on a chip that is currently only possible in macroscopic systems, which is vital for making scalable, robust, and deployable devices. For instance, the most stringent sensing and spectroscopic applications require Q-factors that are far out of reach for nanophotonics and only possible in macroscopic cavities (Q ≳ 1011,9,12) and atomic systems (Q ≳ 1015,13,14,15). Higher Q factors would also enable new functionalities for building scalable quantum networks such as integrating ultra-narrowband photon generation and efficient quantum memory on-chip. Continued materials and fabrication improvements will likely lead to continued incremental improvements in Q, but here we pursue a pathway that gets around the materials and fabrication limits by engineering a slow group velocity for light propagating in the cavity. This approach uses the fact that optical losses are propagation losses, and therefore depend on the propagation length, while Q depends on the rate of optical loss in time. Thus, a reduction in the group velocity of light leads directly to an increase in the Q by the same factor. High optical depth atomic ensembles enable group velocity reduction of many orders of magnitude via electromagnetically induced transparency16,17 and other schemes18,19, however, incorporating such ensembles with nanophotonics is challenging. Previous work on resonance narrowing via slow light has primarily focused on two regimes: very slow group velocities in macroscopic cavities20,21,22 and modest group velocity reduction via band engineering in nanophotonic cavities23,24.

We use a unique platform, erbium-doped thin-film lithium niobate (Er:TFLN)25,26, in which a high optical depth ensemble of coherent Er emitters is directly coupled to low-loss nanophotonic structures fabricated in TFLN. We employ spectral hole-burning (SHB), a powerful technique for absorption and dispersion engineering in rare-earth ensembles27,28 and other media29,30. A narrowband laser selectively depopulates or shelves a spectrally narrow subset of emitters from a large inhomogeneously broadened ensemble, thereby creating a narrow transparency window (and a corresponding sharp slope in the index of refraction) that can persist for ms or longer depending on the medium. The group velocity of light propagating through this spectral hole vg = c/(n(ω) + ω∂n/∂ω) ≈ Δhole/α where Δhole/(2π) is the width of the spectral hole and α is the absorption coefficient outside the spectral hole20,29,30. This can be dramatically reduced from c for typical rare-earth spectral holes with Δhole/(2π) ≳ MHz and α ≳ cm−1. In this work, we show a nearly three order of magnitude decrease in the group velocity, and a corresponding Q-factor greater than 108, beyond the state of the art for TFLN to date. Such narrow resonances on chip enable new functionality for tunable spectral filtering31, photon storage32, laser stabilization33, and more34,35.

We also work out a theoretical model for the unique regime we are able to study in the Er:TFLN platform. We show that the narrowing can be understood as an interference of resonances, which leads to tunable Fano lineshapes, which we demonstrate by electro-optic (EO) tuning of our narrowed Fano feature. We further model the spectral hole width and show that the large circulating intensity in the resonator during the hole-burning phase decouples the Er emitters from the surrounding spin bath and dramatically reduces the excess dephasing. This results in much narrower features than expected based on a naive Bloch equation treatment. We showcase the necessary modification to the Bloch equations and show good agreement with our data, a vital step for accurately modeling and understanding spectral hole-burned features in rare-earth emitters coupled to resonators.

Results

Slow light-induced linewidth narrowing

The maximum achievable Q-factor (Q = ωc/κ) of resonators is primarily constrained by intrinsic loss mechanisms (κ > κi), which includes both the material absorption rate and imperfect mode confinement, resulting in coupling to undesired radiation modes. We overcome this limitation by adding a highly dispersive medium within the resonator, which leads to a significant reduction in the group velocity of light (vg). When introduced into a microcavity, this reduction increases the round-trip time of circulating light, effectively extending the cavity lifetime and enhancing the Q-factor. One might initially guess that such a slowdown would actually increase the coupling to lossy modes, as photons would interact with the absorptive medium and radiative decay channels for a longer time. However, Soljačić et al.36, demonstrated that dispersion not only reduces the group velocity but also slows down the coupling rates to lossy modes, thereby increasing the Q-factor, which scales as \(Q=\frac{c}{n{v}_{g}}(\frac{{\omega }_{c}}{\kappa })\), where n is the group index without a tranperancy window, and ωc is the cavity center in angular frequency.

In our system, we first investigate the bare cavity resonance of the microring resonators away from the Er absorption band (≈1534.5 nm). Two bus waveguides are used to evanescently couple light in and out of the ring cavity (Fig. 1a, b) with a rate of κext = 2π × 324 MHz each (Supplementary Note 2E), while the intrinsic loss rate was extracted to be κi = 2π × 471 MHz, resulting in the total κ = 2π × 1.12 GHz or a Q-factor of 1.8 × 105 (Fig. 1d). We further measured similar κi for identically fabricated devices with no Er, validating that the loss rates are mainly limited by the sidewall roughness of waveguides (Supplementary Note 2E). The 300 μm diameter of our resonators means we are guaranteed at least 2 resonances within the  ~158 GHz wide Er absorption band on the I15/2 − I13/2 transition centered at 1531.6 nm. The large inhomogeneous linewidth is due to charge compensation and disorder created when Er substitutes for lithium, as well as the intrinsic disorder in congruent lithium niobate. We use devices with heavy erbium doping (0.5%) to achieve high optical depth. The resulting Er absorption introduces an additional loss rate of κEr = 2π × 16 GHz (Supplementary Note 2E), which dominates both intrinsic and coupling losses, leading to significantly broadened and undercoupled resonances within the erbium absorption bandwidth. We next perform SHB at the center of the cavity resonance by optically pumping a spectrally narrow subset Er ions (see Supplementary Fig. 1 for experimental setup details).

Fig. 1: Slow light induced linewidth narrowing.
Fig. 1: Slow light induced linewidth narrowing.
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a Schematic of an Er:TFLN ring resonator cavity coupled to through and drop ports with electro-optic tuning. Inset: schematic cross-sectional view of the waveguide. b Optical image of the fabricated microring resonator, which was loaded onto a stage at a temperature of  ~2 K and with an estimated magnetic field B = 0.1–0.2 T aligned along the c-axis of the TFLN. The gold colored regions show the electrodes utilized in the EO tuning. Light was coupled in and out using grating couplers and an additional drop port at the top is used for the slow light measurements. c Schematics of a bare cavity mode with no absorption (left) and ultra high-Q resonator mode (right) formed in a narrow transparency window in a region of high absorption that creates a highly dispersive medium with ultra-low group velocity. d Measured transmission through a resonance tuned away from the Er absorption (left) and a narrowed resonance (right) showing narrowing by nearly three orders of magnitude due to preparing a spectral hole in a region of high absorption.

This results in a narrow transparent window, or spectral hole, in the absorption profile at the frequency of the burn pulse. The width of the spectral hole is fundamentally limited to be larger than twice the measured homogeneous linewidth, Δhole/2π ≥ 490 kHz (Supplementary Note 2C). However, due to power broadening the holes are much broader, estimated to be between 30 and 100 MHz for the range of optical powers used here (Supplementary Note 2F), which is still much narrower than the resonator κ even away from the Er absorption. The narrow transparency window is accompanied by strong dispersion, resulting in a dramatically reduced group velocity and a longer time for the photons to finish each round trip, described by the expression nvg/c = Δhole/κEr. Consequently, this results in a narrowed resonance mode at the frequency of the spectral hole. Since the decay rate of the spectral hole is slow compared to all other frequency scales (<10 kHz), we can ignore any hole dynamics beyond the approximately flat spontaneous emission background we observe during our measurements. We note that moving to lower temperatures and/or higher magnetic fields would extend the lifetime of our spectral holes beyond the Er optical lifetime37,38 and enable operation without this spontaneous emission background. We measure the transmission as a function of detuning by sending a weak probe pulse 4 μs after the burn pulse and detecting at the through port of the device. We observe a sharp Lorentzian dip at the burn frequency with a width of 1.9 MHz, corresponding to a Q-factor of 1.1 × 108 (Fig. 2a). Furthermore, we measured the output at the drop port and observed a corresponding peak, consistent with the microring resonator model.

Fig. 2: Extending cavity lifetime.
Fig. 2: Extending cavity lifetime.
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a The narrowed resonance measured at the through port (brown) and the drop port (red). b The extended ring down time of the cavity measured through the drop port (blue), showcasing a significantly longer time when compared with the bare cavity mode (red) measured at a resonance off the absorption. Inset: delay of a narrowband Gaussian pulse measured through the drop port.

To verify that the Q-factor extends the cavity lifetime, we perform time-domain measurements to measure the ringdown time. Specifically, we send an optical square pulse and measure the decaying tail at the falling edge at the drop port (“Methods”). Our measurements reveal that the narrowed cavity mode exhibits a lifetime of 82 ns, whereas the bare cavity (in the absence of absorption) has an expected lifetime of 0.14 ns, below the resolution of our detection scheme (Fig. 2b). This significant increase further validates the formation of a high-Q resonance mode and confirms the extended cavity lifetime.

To further investigate the slow light effect, we measure the resonant group delay experienced by a Gaussian pulse. We send a narrowband, 1.5 μs Gaussian pulse through the resonance and observe a 200 ns delay compared to the bare cavity mode case (Fig. 2b inset). This corresponds to a group velocity reduced to nearly 2 × 105 m/s in the ring waveguide,  ~700× slower than the speed of light in the LN waveguide. This result aligns closely with our theoretical estimates (Eq. S41) as well as the scaling of the Q-factor compared to the bare cavity Q. The delay could be further extended by employing a coupled resonator optical waveguide architecture, which can provide a linear scaling of pulse delay with the number of coupled rings39. The current delays represent some of the longest optical pulse delays achievable on an integrated chip, offering promising opportunities for scalable quantum memory and quantum information applications.

Electro-optic tuning

We can think of our slow-light resonances as arising from the interference of a spectrally narrow resonant mode (the spectral hole) and a broader continuum (the damped resonator mode). Such a system is described by a Fano profile40, which is apparent from the rigorous theoretical description of our system in the Supplementary Note 1C. A Fano profile will shift and become asymmetric as the detuning increases between the narrow and broad resonances. In our case, we can identify the Fano asymmetry parameter as a function of the detuning between the burn laser frequency (ωl) and the bare cavity mode (ωc):

$$q=\frac{{\omega }_{c}-{\omega }_{l}}{\frac{\kappa }{2}+\frac{{\kappa }_{{{\rm{Er}}}}}{2}}.$$
(1)

In Fig. 3a we see a clear shift of the experimentally measured resonance as we detune the burn laser from the center of the bare cavity mode. The center of the slow light mode matches our theory predictions, though the shape deviates due to the uncertainties in the extracted parameters and the effects of residual absorption in the bus waveguide. We see clear Fano shapes when the optical depth is lower and this residual absorption is smaller (see Supplementary Note 2H).

Fig. 3: Fano lineshape and EO tuning.
Fig. 3: Fano lineshape and EO tuning.
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a Experimental data and theoretical model showing the slow-light resonance at different burn laser detunings with respect to the bare cavity resonance. b The bare cavity resonance is tuned electro-optically while keeping the burn frequency constant, demonstrating dynamic spectral tunability of the narrow resonance.

In addition to tuning the burn laser frequency, we can alternatively manipulate the bare cavity mode itself to shift the resonance. The high χ(2) nonlinearity of lithium niobate (LN) provides an effective mechanism for this control. By applying a DC voltage across the resonator, we electro-optically shift the bare cavity resonance frequency by a rate of 0.12 GHz V−1 (Supplementary Note 2G), thereby tuning the slow-light mode. As shown in Fig. 3b, we observe a voltage-induced tuning range of  ≈15 MHz, limited by our electro-optic setup. We also note that the system exhibits a broader spectral response at higher applied voltages, a characteristic feature of the Fano lineshape under increased detuning.

These high-Q resonator modes exhibit some of the narrowest filter responses demonstrated in an integrated photonic platform. Combined with the fast electro-optic tunability of LN (>GHz), this approach enables a wide range of applications in dynamically reconfigurable filtering, high-speed photonic switching, and adaptive on-chip laser stabilization.

Modified Bloch equation model

We next examine the dependence of resonance linewidth on input pump power (Pin), as illustrated in Fig. 4. To provide deeper insight, our model diverges from heuristic group velocity approach used earlier and instead considers a more fundamental approach of analyzing a cavity coupled to an atomic ensemble (Supplementary Note 1)41. One might expect the standard optical Bloch equations, incorporating experimentally extracted system parameters including the spontaneous decay rate (γs), decoherence rate (γ), cavity loss rates (κi, κext, κEr), and the single-photon coupling rate (g) to explain the resonance width (see Supplementary Note 2A for details). In this model the slow light induced narrowed resonance loss rate (κSL) would be expected to follow the form:

$${\kappa }_{{{\rm{SL}}}}=\left(\frac{{\Delta }_{{{\rm{hole}}}}}{{\kappa }_{{{\rm{Er}}}}}\right)\kappa$$
(2)

where the spectral hole can be expressed as \({\Delta }_{{{\rm{hole}}}}=2\Omega \sqrt{\frac{\gamma }{{\gamma }_{s}}}\), including the Rabi frequency given by \(\Omega=\frac{2g\sqrt{{\kappa }_{{{\rm{ext}}}}}}{\kappa /2}\sqrt{\frac{{P}_{{{\rm{in}}}}}{\hslash {\omega }_{c}}}\). Since, the group velocity can be expressed as nvg/c = Δhole/κEr, the theory naturally reveals the scaling of the cavity linewidth (κ) with the group velocity.

Fig. 4: Modified Bloch Equation model.
Fig. 4: Modified Bloch Equation model.
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The power (Pin)-dependent linewidth of the resonator at zero detuning from the bare cavity resonance. The data (blue points) showcases a stark deviation from the standard Bloch theory (red line). The modified Bloch theory (gray line) matches the data much better, indicating a lower decoherence rate at higher power. Error bars represent the standard errors associated with the fits. The inset illustrates the physical mechanism behind the approach, where the emitter is decoupled from the spin bath due to the large Rabi frequencies in the cavity.

The simple Bloch model exhibits a striking discrepancy with the experimentally observed linewidths (Fig. 4), which are up to two orders of magnitude narrower than the theoretical prediction. This deviation cannot be attributed solely to experimental uncertainties in parameter extraction (see Supplementary Note 2A) and, furthermore, the observed linewidths do not follow the square root dependence on optical power predicted by the Bloch model.

The failure of the conventional Bloch equations stems from the underlying assumption that the Lindbladian describing the dephasing and decoherence is independent of the optical field strength. However, prior investigations of rare-earth-doped solids such as Pr3+: LaF3 have demonstrated that the dephasing induced by a dynamic bath is effectively suppressed when the Rabi oscillation frequency at high intensity exceeds the correlation time τc of the bath42.

In our system, the erbium ions couple to a dense nuclear spin bath composed of lithium and niobium nuclear spins as well electron spins of other erbium ions, a phonon bath, and an electronic bath consisting of charge traps and charged two level systems. Irrespective of the microscopic details of the bath, it can modeled as stochastic process with a correlation time τc. The bath and, consequently, the corresponding stochastic process, can be assumed to be Markovian when the condition \(\sqrt{\gamma {\tau }_{c}} < 1\) is satisfied. At an intuitive level, fast Rabi flopping results in time averaging of the dephasing, similar to continuous dynamical decoupling.

Reaching the requisite Rabi frequencies to observe this effect in bulk rare-earth-doped materials is difficult, as the optical intensity required is typically out of reach. However, in a nanophotonic waveguide with sub-micron mode area (Amode = 0.78 μm2), the local intensity is greatly enhanced. Additionally, in a ring resonator configuration, the circulating optical power is further amplified. For instance, an input power Pin = 21 μW in the bus waveguide leads to a Rabi Frequency Ω = 2π × 106 MHz in the ring resonator. To account for this phenomenon, we introduce a dephasing rate described by the modified Bloch equation formalism (γm)43,44,45, given by:

$${\gamma }_{{{\rm{m}}}}=\frac{\gamma }{1+{(\Omega {\tau }_{c})}^{2}}+\frac{{\gamma }_{s}}{2}$$
(3)

At sufficiently high optical power (Ω ≫ 1/τc) the dephasing rate asymptotically approaches the spontaneous emission limit (γm → γs/2), thereby eliminating spin-bath-induced broadening. By incorporating γm and fitting the experimental data, we extract a correlation time of τc ≈ 1 μs. This value lies well within the range of typical correlation times previously observed in Er:LN systems37 and satisfies the Markovianity condition \(\sqrt{\gamma {\tau }_{c}} < 1\). With this correction, the theoretical prediction aligns closely with the experimental data, effectively resolving the discrepancy encountered with the conventional model. It is also important to note that the experimental data also aligns qualitatively with the trend predicted by the modified theory, deviating from the standard saturable absorber power broadening \({\kappa }_{SL}\propto \sqrt{{P}_{{{\rm{in}}}}}\) dependence expected from the Bloch model. The modification accounts for the significant decoherence narrowing at higher input power, suppressing the linewidth increase from the power-broadening term. This finding is consistent with prior studies42,44 demonstrating that optical linewidths in impurity-ion solids can exhibit a field-dependent narrowing due to suppression of local environmental fluctuations, but goes beyond past demonstrations that could not reach such high Rabi rates. This modified model is vital for understanding the limits on (and possibilities for) atomic frequency comb storage in nanophotonic devices, as it dramatically changes the optical power required to prepare a high-resolution comb in the presence of a dephasing spin bath.

Discussion

The slow-light narrowing we demonstrate here can be combined with narrower initial resonators to reach even higher Q factors, and can be used for a variety of classical and quantum photonic devices. It can also be extended to other rare-earth dopants with transitions in other frequency bands throughout the visible and near-infrared46. The commonly cited upper bound of 108 in LN arises from material limits under the assumption of negligible scattering and no slow-light effects. With state-of-the-art TFLN fabrication (Q = 2 × 10710), slow-light resonances could surpass this bound, reaching effective Q factors approaching 1010, corresponding to a cavity linewidth as small as κ < 10 kHz and a ringdown time as long as τ > 10 μs. Our system can be used in a long list of potential operations on chip that are otherwise possible only with bulky, macroscopic systems, if at all. First, our system is a tunable spectral filter with dramatically narrower resolution than any other on-chip system1. Such a device is vital for quantum applications to collect photons from spin qubits or other highly coherent sources47. Combined with the ability to generate entangled photon pairs in lithium niobate, our narrowband features likely could be used to generate photons with sufficiently narrow linewidths to interface with narrowband spin qubits in a way that is otherwise not possible on-chip. The details of such a scheme would have to be worked out, as this represents a substantially different configuration than other cavity-enhanced photon pair schemes. Another challenge, particularly for quantum information, is integrating highly stable lasers with chip-based atom and ion traps. This requires a sub-MHz reference for laser stabilization that is currently out of reach in an integrated platform, but should be easily attainable with our system48. Finally, we can consider combining the high-bandwidth electo-optic tunability of lithium niobate with the long cavity lifetime to investigate novel pulse shaping application at dramatically higher resolution than is otherwise possible.

Importantly, the system presented here has two major differences from a resonator with similarly high Q achieved without reducing the group velocity. One is the spontaneous emission noise that prevents operation at the single photon level (see Supplementary Note 2I). This can be eliminated by preparing persistent spectral holes, which has been demonstrated in erbium-doped lithium niobate37,38 but is not possible in our apparatus due to restrictions on temperature and magnetic field. The other difference is more fundamental, the circulating electric field in the resonator does not increase between the bare resonance with no absorption and the slow light narrowed resonance. Slowing light via coupling to an atomic medium comes with a reduction in electric field that exactly matches the increase in the time spent in the medium. Thus, there is no increase in the Purcell factor, the cooperativity, or the effective χ(2) nonlinearity in the lithium niobate. The proposed scheme is fundamentally limited by the fixed absorption frequencies and inhomogeneous broadening of rare-earth ions, with potential extension to other discrete wavelengths through co-doping or alternative materials with larger inhomogeneous broadening like Er-doped silica49.

In conclusion, we have demonstrated ultra-high-Q resonator modes in erbium-doped thin-film lithium niobate by engineering a low-loss slow light medium in fabricated microring cavities. We show agreement with theoretical models that account for the interference of resonator modes and the role of spin-bath-induced dephasing. This platform has potential for a wide variety of quantum and classical photonic applications, particularly for overcoming the typical bandwidth mismatch between photonic and atomic systems.

Methods

Device design and fabrication

We use grating couplers to couple light from angle-cut optical fiber into our waveguides. The grating couplers are designed such that they couple in and out only the transverse electric (TE) mode. The bus waveguide width is 800 nm, which allows us to effectively couple light into the 1200 nm width and 300 μm diameter ring resonator. The through and drop waveguides are positioned symmetrically on opposite sides of the ring resonator, each separated by a 800 nm gap from the ring. Electrodes were placed 5 μm away from the in-plane ring waveguides.

We use a wafer with 600 nm of 0.5% erbium-doped lithium niobate on insulator. We fabricate the devices using a two step electron-beam (e-beam) lithography process. First, we pattern the waveguides, rings, and grating couplers using ZEP e-beam resist. We then etch 300 nm using Argon-based inductively coupled plasma reactive ion etching. The device is next cleaned of the remaining resist and redeposition of LN with a standard RCA clean. We anneal the sample in an O2 environment at 500 °C for 2 h. To fabricate the electrodes, we perform the second e-beam step using PMGI SF6 resist. We use electron beam deposition to deposit 15 nm of Cr and 285 nm of Au. We then clean and lift-off the deposited metals using a PG remover bath in a sonicated bath at 70 °C.

Experimental setup

The devices were characterized in a 1.7 K closed cycle cryostat (Montana Instruments). The laser utilized is a Velocity 1628 tunable telecom laser whose polarization was controlled using a fiber polarization controller. A single acousto-optical modulator (AOM) (Aerodiode) is used to pulse the light and tune the frequency for probe scans. By switching between two RF drives for the AOM, we were able to interchange between the pump and probe fields. We used angle-cut fiber array v-grooves (OZ Optics) to couple light in and out of the grating couplers from the through port and the drop port (see Supplementary Fig. 1). The sample is mounted on a 3-axis nanopositioner (AttoCube) to allow precise alignment of the fiber array with the grating couplers. A Samarium-cobalt magnet was used to provide a static magnetic field of 0.1–0.2 T. The light collected from the device passes through another AOM, polarizer, and attenuator before being detected by a superconducting nanowire single photon detector (SNSPD) (PhotonSpot). The second AOM is used to shutter the SNSPD while high-intensity input pulses are used in burning or photoluminescence.

Linewidth narrowing using spectral hole burning

Spectral hole burning was performed by applying a 50 μs burn pulse at a fixed frequency, followed by measuring the transmission of a probe pulse at the drop or through port. The probe pulse, with a duration of 5 μs and a weaker power of Pprobe = 40 nW, was introduced 4 μs after the burn pulse. This process was repeated while maintaining a fixed burn laser frequency and sweeping the probe detuning from −20 MHz to 20 MHz. By recording the probe transmission at various detunings relative to the pump, we extracted the transmission of the narrowed resonance. The input power into the device was varied by changing the rf power supplied to the input AOM. It is important to note that the linewidth data used for analyzing power dependence and Fano resonance characteristics were acquired using a 5 ms burn pulse. This extended burn time ensured that the system reached a steady state, a critical assumption in our theoretical framework for deriving analytical solutions. In contrast, the 50 μs burn pulse resulted in an even narrower resonance feature, which was challenging to model due to the transient nature of the atomic population dynamics.

Ring-down time and slow light measurement

The ring-down measurement was done by sending a square wave optical pulse of 1 μs at a frequency where the narrowed resonance was burned. The pulse width was chosen to allow the the square pulse to fit spectrally within the narrowed resonance bandwidth. The trailing edge was fit with an exponential function Ae−τt where τ is the ring-down time. The slow light measurement was done similarly by sending a Gaussian optical pulse of 1.5 μs at the burn frequency. The pulse was fit with a Gaussian and the center was compared with center of a reference pulse to give us τg. In both these experiments, the reference was measured at a frequency of the bare cavity mode, which is a resonance away from the Er absorption.

Electro-optic tuning of Fano shape

The electro-optic tuning was done by depositing gold electrodes around the ring resonator as described earlier. The two electrodes were wire-bonded to two ports of a printed circuit board (see Supplementary Fig. 6). The details of device architecture used in Fig. 3b are given in the Supplementary Note 2G. A DC voltage was applied to produce a strong DC electric field across the waveguide, which changed the effective refractive index (neff) of the LN via its χ(2) nonlinearity. Consequently, the resonance wavelength of the bare cavity shifts, as does the Fano q parameter.