Meandered Thermal Phase Shifters

• Meandered thermal phase shifters are thermo-optic tuning elements that use folded, serpentine, or spiral designs to increase the heated optical interaction length and reduce required temperature rise.
• They balance phase efficiency, thermal uniformity, and fabrication constraints across diverse platforms including femtosecond-laser-written glass, silicon, and silicon nitride.
• Design trade-offs involve optimizing heater resistance, thermal confinement, and crosstalk mitigation, while maintaining compact footprints in photonic integrated circuits.

Searching arXiv for recent and foundational papers on meandered thermal phase shifters. Meandered thermal phase shifters are thermo-optic tuning elements in photonic integrated circuits in which either the resistive heater, the optical path, or both are folded into a serpentine, spiral, or multi-pass geometry to increase the effective interaction length within a constrained footprint. Their operating principle is the local conversion of electrical power into heat, followed by a refractive-index perturbation through the thermo-optic effect, which induces an optical phase shift. Across femtosecond-laser-written glass, silicon, silicon nitride, and silicon-rich silicon nitride platforms, meandered layouts are used to trade among phase efficiency, current density, thermal uniformity, crosstalk, speed, and fabrication complexity. The resulting design space spans buried waveguides heated from surface metal films in glass (Ceccarelli et al., 2020), suspended cryogenic glass bridges with straight heaters but directly relevant thermal-confinement principles (Ceccarelli et al., 2024), compact spiral thermo-optic arrays in silicon (Gurses et al., 2022), multi-pass visible SiN shifters in which the optical path meanders beneath a straight heater (Yong et al., 2021), and rectangular-spiral SRN devices heated by serpentine microheaters (Nejadriahi et al., 2021).

1. Thermo-optic basis and phase-shift scaling

The phase shift in a thermal phase shifter follows the standard thermo-optic relation

$$\Delta \phi = \frac{2\pi}{\lambda}\,\Delta n_{\mathrm{eff}}\,L,$$

with

$$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$

in femtosecond-laser-written glass circuits, so that

$$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$

For a $\pi$ shift,

$$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$

These relations are explicitly used in glass FLW-PICs and establish the central benefit of meandered designs: increasing the heated optical length $L$ reduces the temperature rise needed for a target phase shift (Ceccarelli et al., 2020).

The same scaling appears in silicon thermo-optic arrays, where

$$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$

and therefore

$$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$

In this formulation, meandering improves efficiency primarily by enlarging $L$ without proportionally enlarging footprint (Gurses et al., 2022). The visible-wavelength SiN devices use the same logic, but implement it by folding the optical path multiple times under a localized hot zone rather than by meandering the metal heater itself; there the heated waveguide length $L_{\mathrm{wg}}$ reaches 1.5 mm in a 3-pass device and 6.9 mm in a 7-pass device (Yong et al., 2021).

This common mathematical structure clarifies an important distinction. “Meandered thermal phase shifter” can refer to at least three different geometries: a meandered heater over a nominally straight optical arm, a straight heater over a meandered optical path, or a co-designed meander of both. The literature surveyed here contains all three conceptual variants, even when individual demonstrations emphasize one more than the others.

2. Geometric forms of meandering

In femtosecond-laser-written alumino-borosilicate glass, the baseline device is a straight Cr/Au heater on the chip surface above one arm of a Mach–Zehnder interferometer, with buried waveguides at depth $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$0 and arm pitch $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$1 (Ceccarelli et al., 2020). The explicit extension to meandered or serpentine layouts is geometric rather than purely phenomenological: the heater resistance obeys

$$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$2

so increasing the total path length $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$3 through meandering raises resistance at fixed footprint. This reduces the current required for a given dissipated power $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$4 and thereby mitigates electromigration (Ceccarelli et al., 2020).

In silicon photonics, the meander is built into the optical waveguide itself. A compact spiral thermo-optic phase shifter routes a $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$5 strip waveguide as a spiral or meander to obtain a heated optical length $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$6 within a heater footprint of about $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$7, with doped silicon serving as the heater around the spiral waveguide (Gurses et al., 2022). This topology is specifically intended for dense row-column addressed arrays.

In visible-light SiN, the multi-pass structure is even more explicit. The PS1 device has 3 passes through the suspended hot zone with total heated SiN length $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$8, while PS3 has 7 passes and $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$9. The heater remains straight TiN, but the optical path is folded beneath it. The suspended region footprints are approximately $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$0 for PS1 and $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$1 for PS3 (Yong et al., 2021).

In silicon-rich silicon nitride, both the optical and thermal layouts are compact and explicitly serpentine. A 1.2 mm active waveguide is folded into a $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$2 rectangular spiral comprising twenty-seven $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$3 bends and two $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$4 bends, while the heater is a serpentine 300 nm Ni:Cr microheater with six parallel filaments, each $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$5 wide and separated by $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$6 (Nejadriahi et al., 2021). This is one of the clearest examples of a meandered thermal phase shifter in the narrow sense.

A concise comparison of the reported meander-related implementations is useful.

Platform	Meandered element	Representative dimensions
FLW glass	Heater path can be meandered; baseline devices straight	$$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$7–$$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$8, $$\Delta \phi = \frac{2\pi}{\lambda}\,\Gamma\left(\frac{dn}{dT}\right)L\Delta T.$$9, $\pi$0 (Ceccarelli et al., 2020)
Silicon SOI	Spiral/meandered optical path with surrounding doped heater	$\pi$1, heater area $\pi$2 (Gurses et al., 2022)
Visible SiN	Multi-pass meandered optical path under straight heater	PS1: $\pi$3; PS3: $\pi$4 (Yong et al., 2021)
SRN	Rectangular-spiral optical path plus serpentine heater	$\pi$5 in $\pi$6 (Nejadriahi et al., 2021)

This diversity suggests that “meandered” is best understood as a layout strategy for extending interaction length and engineering thermal impedance, rather than as a single canonical mask pattern.

3. Geometry-driven efficiency and thermal confinement

A central issue in meandered thermal phase shifters is the distinction between longitudinal heating uniformity and lateral thermal selectivity. In FLW glass, the paper extends a cylindrical-wire model to finite-width heaters and defines a geometry efficiency factor $\pi$7, where $\pi$8 captures heating of the targeted arm and $\pi$9 the parasitic heating of the adjacent arm (Ceccarelli et al., 2020). The empirically confirmed design rule is that when $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$0, $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$1 approaches the cylindrical-wire limit and the power required per phase shift is minimized. As $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$2 grows so that $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$3 becomes comparable to $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$4, both interferometer arms are heated more equally and the phase shift decreases. For a meandered layout, the paper interprets $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$5 as the lateral envelope of the serpentine above the heated arm and advises that its half-width remain much smaller than $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$6 (Ceccarelli et al., 2020).

This principle is platform independent. A meander that lengthens the resistive path but becomes laterally too wide can improve electrical resistance while degrading thermo-optic efficiency. The same trade-off appears in the visible SiN suspended devices, although formulated differently: seven folded waveguide passes improve phase efficiency, but the wider suspended region in PS3 leads to incomplete undercut between anchors and reduced thermal isolation, limiting the improvement (Yong et al., 2021). Likewise, the cryogenic FLW work emphasizes that thermal confinement is dominated by 3D undercuts and suspended bridges, with temperature decaying to baseline within “a few tens of microns” outside the bridge (Ceccarelli et al., 2024). Although those heaters are straight rather than meandered, the results show that geometry-defined thermal resistance can dominate phase-shifter performance more strongly than heater routing alone.

The suspended-bridge cryogenic devices offer a useful limiting case. The bridge cross section is $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$7 by $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$8, with heater width $$\Delta T_\pi = \frac{\lambda}{2\,\Gamma\left(\frac{dn}{dT}\right)L}.$$9 and bridge lengths $L$0 (Ceccarelli et al., 2024). Longer bridges achieve lower $L$1 because they improve insulation and reduce heat leakage to the substrate, even though reinforcement pillars introduce local thermal sinks. This suggests that in meandered architectures, increasing optical length is most effective when accompanied by confinement features that preserve the corresponding thermal resistance.

In SRN, thermal uniformity across adjacent folded segments was directly simulated: at 8 mW input, waveguides between heater filaments reach about 97% of the temperature of those directly under the filaments (Nejadriahi et al., 2021). This is a particularly relevant result for serpentine heaters, because meander-induced nonuniformity is often presumed to be severe. Here, the multi-filament heater improves lateral averaging rather than harming it.

4. Materials stacks, fabrication, and process limits

Meandered thermal phase shifters are strongly constrained by the deposition, patterning, and thermal-stabilization methods available in each platform. In FLW glass, the heater metal is Cr/Au with 2 nm Cr and 100 nm Au, magnetron sputtered on Corning EAGLE XG glass. The same femtosecond laser used for waveguide writing, operating at 1030 nm, 300 fs, 1 MHz, and 200 nJ pulses, ablates isolation gaps; five scans produce about $L$2 wide ablation lines for clean electrical isolation. A post-deposition anneal at $L$3 with 10 $L$4/min ramp, 30 min soak, and $L$5 h cooldown stabilizes the grain structure and reduces sheet resistance from approximately $L$6 to approximately $L$7 (Ceccarelli et al., 2020). For meanders, the minimum $L$8 isolation gap sets the achievable serpentine pitch and limits how densely turns can be packed before metal density and lateral heat spreading degrade performance (Ceccarelli et al., 2020).

The cryogenic FLW work uses a Cr/Au bilayer of 5 nm / 100 nm deposited by thermal evaporation, followed by a $L$9, 1 h anneal. The measured sheet resistance after anneal is approximately $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$0 (Ceccarelli et al., 2024). The difference from the room-temperature FLW work reflects differing deposition conditions and film properties; it also indicates that resistance targets for meandered heaters are platform and process specific rather than universal.

Visible SiN devices are fabricated on 200-mm silicon wafers with deep ultraviolet lithography, PECVD films, RIE, CMP, and metallization. The heater is TiN with design sheet resistance around $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$1, sitting atop a suspended SiO$$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$2 bridge with heater–waveguide vertical separation around $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$3 (Yong et al., 2021). The multi-pass layout is enabled not by metal routing complexity but by dense waveguide folding with nominal gaps of $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$4 and dissimilar waveguide widths to suppress inter-waveguide optical coupling (Yong et al., 2021).

In SRN, the heater is a 300 nm Ni:Cr film above a 1 $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$5m SiO$$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$6 top cladding, with Cr/Au pads for contacts (Nejadriahi et al., 2021). The compact rectangular spiral depends critically on the high index of SRN, $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$7 at $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$8, and on modified Euler bends with effective radii of 4.1–4.4 $$\Delta \Phi = \frac{2\pi L}{\lambda_0}\gamma \Delta T,\qquad \Delta T_{\pi} = \frac{\lambda_0}{2L\gamma},$$9m and simulated per-bend losses around 0.025–0.026 dB (Nejadriahi et al., 2021). This is a reminder that meandering the optical path is only useful if the bend technology is sufficiently low loss.

Across these platforms, annealing emerges as a common reliability step. In FLW glass, it minimizes drift and lowers sheet resistance (Ceccarelli et al., 2020); in cryogenic FLW, it stabilizes resistance and suppresses long-term drift at high temperature (Ceccarelli et al., 2024). A plausible implication is that for meandered heaters, which often rely on narrow lines and long total path lengths, resistance stabilization is especially consequential because small per-square variations integrate over many turns.

5. Electrical drive, calibration, and crosstalk

The electrical behavior of meandered thermal phase shifters is governed by the same Joule-heating relations as straight devices,

$$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$0

but meandered layouts alter the resistance and therefore the preferred drive regime. In FLW glass, increasing $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$1 by meandering raises resistance via $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$2, so a target power can be reached at lower current, which is beneficial for electromigration and routing (Ceccarelli et al., 2020). The same paper distinguishes three power definitions: the actual dissipated power $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$3, the voltage-based estimate $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$4, and the current-based estimate $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$5. Because the gold heater has temperature coefficient of resistance about $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$6, $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$7 overestimates and $$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$8 underestimates the true dissipated power as the heater warms (Ceccarelli et al., 2020).

That distinction matters for calibration. In the same FLW platform, phase is linear in actual dissipated power,

$$P_{\pi} = A k \frac{\lambda_0}{2L\gamma}, \qquad \tau = \frac{C}{Ak} = \frac{C}{G}.$$9

whereas voltage-controlled calibration requires a quadratic correction,

$L$0

Moreover, voltage control in shared-ground arrays creates nonlinear electrical crosstalk through a ground resistance $L$1, while constant-current drive removes this electrical crosstalk and yields overlapping calibration curves irrespective of neighboring heater bias (Ceccarelli et al., 2020). This is directly relevant to meandered heaters because higher resistance makes constant-current sources easier to implement at modest voltage.

The silicon spiral-array work treats drive and crosstalk at the system level. A 32 × 9 row-column addressed array of 288 elements is driven with PAM or PWM, and the average power per element is controlled through duty cycle and amplitude (Gurses et al., 2022). The array uses an influence matrix

$L$2

to correct thermal crosstalk. First-neighbor crosstalk in a test structure corresponds to $L$3 and $L$4, while in-array fitting uses approximately $L$5 (Gurses et al., 2022). The correction algorithm compensates both phase bias and extinction-ratio degradation by modifying the power vector and, in one demonstration, raising PAM frequency from 200 kHz to 367 kHz (Gurses et al., 2022).

This system-level result addresses a common misconception: meandered phase shifters do not become scalable merely because their footprint is compact. Compactness can intensify thermal coupling, so scalable deployment generally requires explicit crosstalk modeling and compensation. The silicon array study makes this point quantitatively, while the FLW glass study shows a complementary route in which thermal crosstalk is kept negligible by spacing and electrical crosstalk is removed by constant-current drive (Ceccarelli et al., 2020, Gurses et al., 2022).

6. Reported performance across platforms

The performance of meandered and meander-compatible thermal phase shifters varies by several orders of magnitude because the dominant thermal path differs sharply across platforms.

In FLW glass without isolation trenches, the most compact straight heater with $L$6, $L$7, $L$8, and $L$9 achieves a measured $L_{\mathrm{wg}}$0 at 785 nm using actual dissipated power, corresponding to $L_{\mathrm{wg}}$1 (Ceccarelli et al., 2020). The inferred heater temperature rise at $L_{\mathrm{wg}}$2 is about $L_{\mathrm{wg}}$3, giving thermal efficiency $L_{\mathrm{wg}}$4 (Ceccarelli et al., 2020). These numbers define the operating scale for buried-waveguide glass circuits without aggressive structural isolation.

By contrast, in cryogenic-compatible FLW PICs with suspended bridges and vacuum operation, the reported full-fringe powers at 606 nm are dramatically lower: at room temperature, $L_{\mathrm{wg}}$5 for $L_{\mathrm{wg}}$6, $L_{\mathrm{wg}}$7 for $L_{\mathrm{wg}}$8, and $L_{\mathrm{wg}}$9 for $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$00; at cryogenic temperature, the corresponding values are $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$01, $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$02, and $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$03 (Ceccarelli et al., 2024). The increase at cryo is attributed primarily to the reduction in $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$04, and the phase–power relation becomes strongly nonlinear at low power (Ceccarelli et al., 2024). Although these are straight heaters, they show what structural thermal confinement can achieve and thus provide a useful benchmark for future meandered cryogenic designs.

Visible SiN suspended meandered-waveguide devices report sub-milliwatt to low-milliwatt $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$05 powers. For the 3-pass PS1 device, the measured power consumption to achieve a $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$06 phase shift, averaged over multiple devices, is 0.78, 0.93, 1.09, and 1.20 mW at wavelengths of 445, 488, 532, and 561 nm, respectively (Yong et al., 2021). The 7-pass PS3 reduces $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$07 further to approximately 0.65–0.93 mW across the same wavelength range, at the expense of increased insertion loss and less complete thermal isolation (Yong et al., 2021). The measured 10–90% rise and fall times are about 570 and 590 $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$08s (Yong et al., 2021).

The SRN rectangular-spiral device occupies a different point in the trade space: $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$09 and 3 dB switching bandwidth is about 15 kHz (Nejadriahi et al., 2021). The extracted thermal time constant is about $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$10, and the serpentine heater lowers $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$11 by about 30% relative to a simple rectangular heater, which requires approximately 11.5 mW (Nejadriahi et al., 2021). This is a much faster device than the suspended visible SiN shifters, but at higher power.

The silicon spiral TOPS array provides yet another benchmark: individual devices show $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$12–14.3 mW, insertion loss below 0.2 dB, and thermal time constants around 18.6–23.1 $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$13s, with a reported “bandwidth” example of 56.8 kHz in a test extraction (Gurses et al., 2022).

These values underscore that “meandered” does not imply a single efficiency regime. Instead, performance is set by the combined product of interaction length, thermal resistance, heat capacity, and material thermo-optic coefficient.

7. Design trade-offs, misconceptions, and outlook

Several recurring trade-offs define the field.

First, increasing electrical path length is not identical to increasing optical interaction length. In FLW glass, a serpentine heater increases resistance and can improve longitudinal heat distribution, but if its lateral envelope approaches the interferometer arm spacing, the geometry factor $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$14 drops and thermo-optic efficiency worsens (Ceccarelli et al., 2020). In visible SiN, by contrast, the heater stays simple while the optical path meanders, so efficiency gains arise primarily from increased $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$15 rather than from altered electrical resistance (Yong et al., 2021). These are distinct optimization problems.

Second, better efficiency often implies slower response. The suspended SiN PS1 achieves sub-milliwatt $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$16 power but has rise and fall times around 570/590 $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$17s, whereas the non-suspended PS2 is much faster, about 34.5/33.5 $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$18s, but requires approximately 15.9, 18.4, 22.2, and 23.0 mW at 445, 488, 532, and 561 nm (Yong et al., 2021). The same general trade appears between suspended cryogenic glass bridges optimized for low power and silicon or SRN devices optimized for higher bandwidth (Ceccarelli et al., 2024, Nejadriahi et al., 2021).

Third, compactness does not eliminate crosstalk. The silicon array work demonstrates that dense spiral TOPS require a thermal crosstalk correction algorithm based on an influence matrix, and that drive-scheme choice matters: PAM yields better extinction ratio than PWM under bandwidth-limited conditions, while PWM requires more stringent voltage swing for small phases (Gurses et al., 2022). In FLW multiheater arrays, constant-current drive is identified as the key method for eliminating electrical crosstalk associated with shared grounds (Ceccarelli et al., 2020).

Fourth, narrow and thermally isolated structures create fabrication sensitivities. In FLW meanders, the achievable pitch is limited by fs-laser ablation gaps of about $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$19 (Ceccarelli et al., 2020). In PS3 visible SiN devices, incomplete undercut in the wider suspended region leaves residual Si posts that reduce isolation and partially offset the advantage of increased number of passes (Yong et al., 2021). In long cryogenic bridges, reinforcement pillars preserve mechanical robustness but create temperature waviness and local thermal sinks (Ceccarelli et al., 2024).

A plausible implication of these results is that future meandered thermal phase shifters will increasingly rely on co-optimization rather than on geometric folding alone: the heater resistance, optical pass arrangement, thermal isolation topology, and control electronics must be designed as a coupled system. The surveyed literature already points toward this synthesis. FLW glass establishes geometry rules for narrow-envelope serpentine heaters and constant-current operation (Ceccarelli et al., 2020); cryogenic FLW demonstrates the leverage of suspended bridges and localized heating in vacuum (Ceccarelli et al., 2024); silicon arrays contribute multiplexed control and crosstalk inversion for hundreds of elements (Gurses et al., 2022); visible SiN shows that multi-pass meandered optical paths can deliver sub-milliwatt operation (Yong et al., 2021); and SRN illustrates how a high-index platform plus a serpentine microheater can compress millimeter-scale active length into a $$\Delta n_{\mathrm{eff}} \approx \Gamma \left(\frac{dn}{dT}\right)\Delta T$$20 footprint while retaining useful bandwidth (Nejadriahi et al., 2021).

In that sense, meandered thermal phase shifters are not a single device class but a family of thermo-optic architectures that use folding, spiraling, or serpentine routing to increase phase accumulation per unit area while managing the competing constraints of electrical drive, thermal localization, optical loss, and scalable control.