Silicon Nitride Dual-Pol Micro-Fabry-Perot Resonator

• Silicon nitride dual-polarization micro-Fabry-Perot resonators are integrated standing-wave cavities that support both TE and TM modes with high Q factors and thermal tunability.
• They utilize polarization-insensitive Sagnac loop reflectors and multimode cavity designs to minimize scattering and polarization-dependent loss.
• Reconfigurable architectures enable switching between Fabry-Perot, Möbius-like, and microring states, offering versatile performance for sensing and nonlinear photonics.

Silicon nitride dual-polarization micro-Fabry-Perot resonators are integrated standing-wave cavities in a Si$_3$N$_4$/SiO$_2$ photonic platform that support both fundamental transverse electric and fundamental transverse magnetic modes with useful quality factor, thermal tunability, and low polarization-dependent loss. In recent work, the concept appears in two closely related forms: as a standalone integrated micro-Fabry-Perot resonator using polarization-insensitive Sagnac loop reflectors and multimode cavity waveguides, and as the Fabry-Perot operating phase of a reconfigurable binary-star Si$_3$N$_4$ microresonator whose topology is selected by a single thermo-optic control parameter $\Delta \phi$ (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

1. Resonator concept and standing-wave physics

A micro-Fabry-Perot resonator confines light between two on-chip mirrors and supports a standing-wave field with discrete resonances when the round-trip phase is an integer multiple of $2\pi$. For the integrated Si$_3$N$_4$ implementations discussed here, the defining resonance relation is

$m\lambda = 2 n_{\mathrm{eff}} L,$

with free spectral range

$_4$0

This standing-wave condition distinguishes micro-Fabry-Perot resonators from whispering-gallery or ring resonators, whose traveling-wave resonances scale as $_4$1 for the same optical path length (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

In the reconfigurable Si$_4$2N$_4$3 device, the Fabry-Perot state is obtained when counterpropagating clockwise and counterclockwise waves are strongly coupled by tunable retroreflection, producing standing-wave supermodes. In the Temporal Coupled Mode Theory description,

$_4$4

$_4$5

with eigenfrequencies

$_4$6

When $_4$7, the cavity remains in a traveling-wave regime; when $_4$8, the modes hybridize into even and odd standing waves, and the effective path before constructive interference doubles, halving the FSR relative to the traveling-wave states (Lin et al., 16 Sep 2025).

For symmetric Fabry-Perot transmission, the intensity response is written as

$_4$9

where

$_2$0

The associated finesse and quality factor relations are

$_2$1

For an ideal Fabry-Perot with mirror power reflectivity $_2$2 and negligible intrinsic loss,

$_2$3

These formulas are used explicitly in the recent Si$_2$4N$_2$5 micro-Fabry-Perot analyses (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

2. Integrated silicon nitride architectures

One integrated implementation uses two identical polarization-insensitive Sagnac loop reflectors as the Fabry-Perot mirrors, with the cavity formed directly in the in-line transmission path between input and output inverse-taper couplers. The platform is a $_2$6 Si$_2$7N$_2$8 film on SiO$_2$9, specifically LIGENTEC MPW-AN800-35. Near-square single-mode access waveguides of approximately $_3$0 minimize birefringence, while a $_3$1-wide multimode cavity section reduces scattering from sidewall roughness. Two $_3$2 linear tapers connect the single-mode and multimode regions. The routed cavity includes a multimode straight length of $_3$3 implemented in a Bézier bend-assisted spiral, and each Sagnac loop reflector uses two S-bends with $_3$4 radius and one circular bend of $_3$5 radius. The directional coupler in each loop reflector uses a $_3$6 gap and $_3$7 coupling length, chosen for near-3-dB splitting for both TE$_3$8 and TM$_3$9 modes (Xiong et al., 5 Sep 2025).

A second implementation embeds the Fabry-Perot state within a reconfigurable “binary-star orbital architecture.” Here the resonant loop is realized by port-to-port interconnection of two identical Sagnac-loop retroreflectors, forming a closed drop-like perimeter. The core element is a balanced Mach-Zehnder interferometer whose outputs are looped back through S-bends and circular bends. In this geometry, the MZI drop perimeter is $_4$0, each interconnecting S-bend is $_4$1, the MMI body length is $_4$2, and four $_4$3 circular bends of $_4$4 radius interconnect the elements. The total optical path length used in resonance calculations is

$_4$5

This layout creates two counterpropagating pathways that can be strongly or weakly coupled by the central balanced MZI, which acts as a tunable interferometric coupler and retroreflector (Lin et al., 16 Sep 2025).

These two architectures represent distinct design philosophies. The first is a dedicated compact micro-Fabry-Perot optimized for loaded $_4$6, low insertion loss, and broadband thermal tuning. The second treats the Fabry-Perot response as one topology among several cavity states, allowing continuous morphing between standing-wave and traveling-wave behavior with a single electrical actuator. This suggests that, within Si$_4$7N$_4$8 photonic integrated circuits, the micro-Fabry-Perot need not be a fixed cavity class but can also be a reconfigurable operating point.

3. Dual-polarization engineering in Si$_4$9N$\Delta \phi$0

Dual-polarization operation means that the same device supports useful resonances for both TE and TM fundamental modes. In integrated silicon nitride, this is technically difficult because reflected and transmitted amplitudes of many chip-scale mirrors and couplers depend strongly on polarization, which introduces polarization-dependent loss. In the standalone micro-Fabry-Perot, this issue is addressed with polarization-insensitive Sagnac loop reflectors, large low-loss bends, a near-square access-waveguide cross-section, and a wide multimode cavity section that reduces sidewall-scattering sensitivity. Simulations show near-unity TM$\Delta \phi$1 reflectance around $\Delta \phi$2, with TE$\Delta \phi$3 somewhat lower due to residual coupler imbalance and birefringence, which matches the measured $\Delta \phi$4 asymmetry (Xiong et al., 5 Sep 2025).

In the reconfigurable binary-star device, dual-polarization support is achieved on a commercial Si$\Delta \phi$5N$\Delta \phi$6-on-insulator platform with a single-mode waveguide cross-section of $\Delta \phi$7 and nearly vertical sidewalls of $\Delta \phi$8. Operation is demonstrated around $\Delta \phi$9 for both TE and TM polarizations. The Si$2\pi$0N$2\pi$1 stack and geometry are engineered for low birefringence, with group indices $2\pi$2 and $2\pi$3, a difference of only approximately $2\pi$4. The polarization-insensitive $2\pi$5 MMIs provide about $2\pi$6 per port for TE and about $2\pi$7 per port for TM at $2\pi$8, the latter reflecting minor MMI insertion loss for TM (Lin et al., 16 Sep 2025).

The Sagnac retroreflector in the reconfigurable device provides a direct measure of remaining TE/TM asymmetry. For TE, reflection approaches unity near $2\pi$9; for TM, peak reflection is about $_3$0 near the same phase because of higher MMI loss. Despite this difference, the measured TE and TM spectra follow similar reconfiguration trajectories, and the loaded $_3$1 for TM is experimentally observed to be higher than for TE, attributed to lower TM propagation loss (Lin et al., 16 Sep 2025).

A common misconception is that dual-polarization operation implies nearly identical performance for both polarizations. The reported devices do not support that simplification. The million-$_3$2 micro-Fabry-Perot exhibits loaded $_3$3 and $_3$4, while the reconfigurable device reports near-unity TE retroreflection but higher TM loaded $_3$5. The technical target is therefore not exact TE/TM symmetry, but simultaneous support of both polarizations with controlled loss, useful tunability, and predictable spectral evolution (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

4. Reconfigurable Fabry-Perot operation and coupled-mode behavior

In the reconfigurable Si$_3$6N$_3$7 microresonator, a single integrated microheater located approximately $_3$8 above the waveguides imposes a relative phase $_3$9 between the arms of the balanced MZI. This single control knob reconfigures the cavity among three topologies: a Möbius-like microcavity, a Fabry-Perot resonator, and a microring resonator. The MZI transfer matrix is written as

$_4$0

with ideal lossless $_4$1 coupler

$_4$2

and arm phase matrix

$_4$3

The effective Sagnac reflection and transmission follow

$_4$4

with static phases and loop losses absorbed into $_4$5 and $_4$6 (Lin et al., 16 Sep 2025).

When the MZI is in the cross state near $_4$7, counterpropagating coupling is minimized, $_4$8, and the device supports a traveling-wave Möbius-like cavity. The measured FSRs are $_4$9 and $m\lambda = 2 n_{\mathrm{eff}} L,$0. At maximal retroreflection near $m\lambda = 2 n_{\mathrm{eff}} L,$1, the router acts like a bidirectional mirror pair, $m\lambda = 2 n_{\mathrm{eff}} L,$2, and the cavity becomes Fabry-Perot-like, with measured $m\lambda = 2 n_{\mathrm{eff}} L,$3 and $m\lambda = 2 n_{\mathrm{eff}} L,$4. When the MZI is in the bar state near $m\lambda = 2 n_{\mathrm{eff}} L,$5, the device forms a microring-type traveling-wave resonance with $m\lambda = 2 n_{\mathrm{eff}} L,$6 and $m\lambda = 2 n_{\mathrm{eff}} L,$7. The Fabry-Perot state therefore exhibits the expected FSR multiplication factor

$m\lambda = 2 n_{\mathrm{eff}} L,$8

through the standing-wave path-doubling mechanism (Lin et al., 16 Sep 2025).

The same device also demonstrates controllable mode splitting and the photonic pinning effect. In the TCMT picture, the standing-wave regime produces a frequency splitting $m\lambda = 2 n_{\mathrm{eff}} L,$9; the maximal measured splitting is $_4$00 for TE and $_4$01 for TM. Unlike gap-tuned couplers, the interferometric coupler introduces a compensatory phase term that can pin one supermode’s frequency while the other shifts, creating a phase-compensated avoided crossing. Experimentally, one branch remains nearly stationary while the other moves with $_4$02, with a small linear tilt produced by thermal crosstalk (Lin et al., 16 Sep 2025).

This reconfigurable behavior is significant because it places the micro-Fabry-Perot state inside a continuously tunable family of cavity topologies rather than treating it as a fixed terminal design. The Fabry-Perot resonator becomes a dynamically addressable standing-wave phase within a broader polarization-diverse circuit.

5. Performance metrics, thermal tuning, and loss mechanisms

The dedicated Si$_4$03N$_4$04 dual-polarization micro-Fabry-Perot reports loaded quality factors of $_4$05 for TM$_4$06 and $_4$07 for TE$_4$08. The TM$_4$09 resonance is measured near $_4$10 with extinction ratio up to about $_4$11 and linewidth $_4$12, while the TE$_4$13 resonance at $_4$14 has extinction ratio about $_4$15 and $_4$16. The measured FSRs are approximately $_4$17 for TM$_4$18 and $_4$19 for TE$_4$20. Through transmission insertion loss is about $_4$21 for TM$_4$22 and about $_4$23 for TE$_4$24 (Xiong et al., 5 Sep 2025).

Thermal tuning in that device is implemented with a Pt microheater placed approximately $_4$25 above the Si$_4$26N$_4$27 layer over the multimode section so that the cavity phase changes with minimal perturbation of the reflectors. The measured tuning efficiencies are about $_4$28 for TM$_4$29 and about $_4$30 for TE$_4$31, obtained from linear least-squares fits with $_4$32. Example traces show about $_4$33 shift at $_4$34, and the device is tuned gaplessly across one full FSR for both polarizations. Using $_4$35, the power required to traverse one FSR is about $_4$36 for TM$_4$37 and about $_4$38 for TE$_4$39, consistent with the statement that full-FSR tuning requires under about $_4$40 for a $_4$41 phase shift (Xiong et al., 5 Sep 2025).

In the reconfigurable microresonator, heater powers across the spectral evolution range from $_4$42 in TM State I to $_4$43 in TM State IX, and from $_4$44 in TE State I to $_4$45 in TE State IX. Thermal crosstalk introduces a common red shift with slopes $_4$46 for TE and $_4$47 for TM, confirming polarization-insensitive thermal response. Absolute linewidths and absolute $_4$48 values are not explicitly reported in that work, although TM loaded $_4$49 is stated to be higher than TE (Lin et al., 16 Sep 2025).

The principal loss mechanisms are also explicit. In the million-$_4$50 micro-Fabry-Perot, the lower TE$_4$51 performance is attributed to lower Sagnac-loop-reflector reflectivity caused by residual coupler imbalance from non-perfectly square cross-sections and 3-dB bandwidth limits of straight directional couplers. In the reconfigurable device, MMI imbalance and TM insertion loss limit peak reflectivity and extinction. Both works therefore identify polarization-dependent coupler behavior, rather than cavity length or thermo-optic tuning range, as the dominant constraint on fully symmetric TE/TM performance (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

6. Related phenomena, applications, and design constraints

The recent Si$_4$52N$_4$53 literature places dual-polarization micro-Fabry-Perot resonators at the intersection of standing-wave cavity engineering, dual-mode metrology, and polarization-multiplexed nonlinear photonics. The dedicated micro-Fabry-Perot work emphasizes optical sensors, nonlinear photonics, and integrated quantum photonics, noting that the standing-wave architecture provides intrinsic reflection at resonance and can be useful for self-injection locking. The reconfigurable device extends the application space to reconstructive spectrometers and on-chip synthetic dimensions, where phase-tunable coupling, FSR multiplication, and photonic pinning provide programmable spectral structure (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).

Dual-polarization thermometry gives a second application axis. In a Si$_4$54N$_4$55 waveguide resonator, dual-mode TE/TM thermometry was demonstrated with temperature responsivity $_4$56, temperature sensitivity $_4$57, and feedforward laser-drift improvement from $_4$58 uncompensated to $_4$59 compensated; the same work states that the thermometry and stabilization principles translate directly to a silicon nitride micro-Fabry-Perot designed with dual-polarization TE/TM modes (Zhao et al., 2021). This suggests that a dual-polarization micro-Fabry-Perot can function not only as a resonant filter or feedback element but also as a self-referenced thermometric discriminator.

A second adjacent direction is polarization-multiplexed Kerr-comb dynamics. In an on-chip Si$_4$60N$_4$61 traveling-wave microresonator, TE$_4$62 and TM$_4$63 dissipative Kerr solitons were individually generated and controlled with measured mean FSRs $_4$64 and $_4$65, respectively, producing $_4$66. The same source explicitly maps these results to micro-Fabry-Perot resonators, stating that the core findings translate directly provided both polarizations have anomalous GVD, sufficiently high $_4$67, controlled coupling, and minimized TE-TM mixing at the reflectors (Geng et al., 2022). For the micro-Fabry-Perot platform, this places reflector design and polarization purity at the center of any nonlinear extension.

A further design constraint comes from microscopic Fabry-Perot cavity theory. In cavities with elliptical mirrors, the degeneracy of the polarization eigenmodes is lifted by geometry-induced vector boundary corrections. For one elliptical mirror,

$_4$68

with

$_4$69

With two elliptical mirrors, the round-trip phase depends on the relative rotation angle $_4$70 as

$_4$71

Although that analysis was performed for CO$_4$72-machined microscopic Fabry-Perot cavities rather than integrated Si$_4$73N$_4$74 loop-reflector devices, it shows that polarization splitting can arise from cavity geometry itself and that cancellation can be achieved when the differential phase shifts are matched and the mirrors are rotated by $_4$75 (Uphoff et al., 2014). In integrated silicon nitride, the analogous concern is not mirror eccentricity in the same literal form but geometry-induced polarization asymmetry in reflectors, couplers, and bends.

The present design trade-offs are therefore well defined. High dual-polarization performance requires polarization-insensitive reflectors, low-scattering multimode or weakly birefringent waveguides, and thermal actuators that shift cavity phase without adding optical loss. The current limitations are also explicit: residual coupler imbalance, TE/TM insertion-loss asymmetry, thermal crosstalk, and incomplete reporting of intrinsic $_4$76 or linewidth in some reconfigurable demonstrations. The broader implication is not that dual-polarization micro-Fabry-Perot operation is intrinsically symmetric, but that silicon nitride now supports compact standing-wave resonators in which TE and TM modes can both be engineered as practical resources rather than as parasitic alternatives (Xiong et al., 5 Sep 2025, Lin et al., 16 Sep 2025).