Electrically Reconfigurable Beam Splitter

• Electrically reconfigurable beam splitter is a device that uses electrical signals to dynamically modify the distribution of power between output channels via changes in phase, coupling, or modal conversion.
• They include varied implementations such as phase-change directional couplers, electro-optic interferometers, and electro-mechanical devices, each offering distinct trade-offs in speed, loss, and footprint.
• Recent experiments demonstrate precise multi-level control, rapid switching, and nonvolatile behavior, enabling applications in adaptive optical networks, quantum information processing, and electron optics.

An electrically reconfigurable beam splitter is a device whose output power division is changed by an electrical control signal that modifies phase, coupling, modal conversion, or scattering between output channels. In integrated photonics, this functionality has been implemented with phase-change directional couplers, electro-optic Mach–Zehnder interferometers, electro-mechanical directional couplers, and electro-optic frequency converters; in adjacent electron-optics literature, analogous devices redistribute electron current between terminals by gate control, bias control, or microwave pseudopotentials (Li et al., 19 Sep 2025, Ma et al., 2011, Hu et al., 2020).

1. Operational concept and mathematical description

Two formalisms recur across electrically reconfigurable beam splitters. In directional couplers, the splitting ratio is set by the coupling coefficient over a finite interaction length. For the Sb$_2$Se$_3$-on-Si hybrid coupler, the power exchange is governed by

$$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$

and, for a uniform coupler of length $L_c$,

$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$

Electrical programming changes the local refractive index and therefore tunes $\kappa$ (Li et al., 19 Sep 2025).

In interferometric splitters, electrical control imposes a relative phase between two paths. In the tunable beam splitter of Ma et al., the reflectivity and transmissivity are

$$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$

so the splitting ratio is set by the electrically induced interferometric phase $\phi$ (Ma et al., 2011). A closely related transfer-matrix form was used for a fiber-based 2$\times$2 Mach–Zehnder interferometer with a LiNbO$_3$ electro-optic phase modulator, yielding

$_3$0

with $_3$1 V in the reported device (Švarc et al., 2019).

A third formulation appears in frequency-domain beam splitters. In coupled lithium-niobate resonators, electrical microwave drive coherently couples two frequency modes, and the converted-power fraction is

$_3$2

At $_3$3, the device reaches full frequency conversion; at $_3$4, it acts as a 50:50 frequency-domain beam splitter (Hu et al., 2020).

These frameworks describe the same functional objective: controlled redistribution of power between two output channels. The electrical knob, however, can be non-volatile, volatile, mechanical, or frequency-converting, and the implementation details determine bandwidth, insertion loss, footprint, and static power.

2. Non-volatile phase-change directional couplers

The most explicit recent optical realization of an electrically reconfigurable arbitrary-splitting-ratio beam splitter is the Sb$_3$5Se$_3$6-based hybrid silicon directional coupler reported in "Electrically Reconfigurable Arbitrary Splitting-Ratio Optical Splitter Based on Low-Loss Sb2Se3" (Li et al., 19 Sep 2025). The device consists of two parallel silicon rib waveguides brought into close proximity over a coupling length $_3$7. One waveguide is capped with a 30-nm Sb$_3$8Se$_3$9 film; the other is a plain Si arm of width $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$0 nm, while the hybrid arm has width $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$1 nm. The waveguides are separated by a gap $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$2 nm, and the total coupler footprint is $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$3. The substrate is Si (220 nm) on 2 $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$4m SiO$$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$5, with a rib geometry formed by a 130 nm partial etch leaving a 90 nm slab. A 10–20 nm Al$$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$6O$$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$7 insulator sits beneath Ti/Au micro-heaters spanning the coupling region, with a heater–waveguide gap of $$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$8 (Li et al., 19 Sep 2025).

Its operating principle depends on phase-dependent mode matching. In the amorphous state, phase matching is achieved between the plain Si arm and the hybrid Sb$$\kappa = (\omega/2)\int_A \Delta n(x,y)\,E_1(x,y)\,E_2^*(x,y)\,dA$$9Se$L_c$0-on-Si arm, so light launched into the Input port transfers efficiently to the Cross port. In the crystalline state, the hybrid arm’s effective index rises by $L_c$1, detuning the phase-matching condition and suppressing coupling so that light remains in the original arm and exits the Bar port. The refractive indices at $L_c$2 nm were given as $L_c$3 with $L_c$4, $L_c$5 and $L_c$6 for amorphous Sb$L_c$7Se$L_c$8, and $L_c$9 and $$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$0 for crystalline Sb$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$1Se$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$2 (Li et al., 19 Sep 2025).

Fabrication combined 193-nm DUV lithography and reactive-ion etch for the Si rib waveguides with P$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$3 and N$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$4 implants under each rib region to enable carrier-injection heaters. The Sb$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$5Se$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$6 layer was deposited by electron-beam evaporation to 30 nm and patterned by lift-off, followed by post-deposition anneal in Ar/H$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$7 at $$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$8 to stabilize the amorphous phase. A 10-nm Al$$SR \equiv P_{\mathrm{Cross}}/(P_{\mathrm{Bar}} + P_{\mathrm{Cross}}) = \sin^2(\kappa L_c).$$9O$\kappa$0 layer was then deposited by ALD as electrical insulation, and Ti(10 nm)/Au(100 nm) heaters were patterned via lift-off. A final $\kappa$1 forming-gas bake improved metal–dielectric interfaces (Li et al., 19 Sep 2025).

Electrical programming was demonstrated through crystallization pulses of 20 $\kappa$2s duration with amplitudes swept from 3.5 V to 4.45 V. The typical crystallization current was $\kappa$3 mA with series resistance $\kappa$4 k$\kappa$5, giving $\kappa$6 pJ per pulse plus overhead. Reset to the amorphous state was not explicitly demonstrated in the work. Once crystallized or partially crystallized, the Sb$\kappa$7Se$\kappa$8 remains in its state indefinitely with zero static power until rewritten by another electrical pulse (Li et al., 19 Sep 2025).

Experimentally, the device achieved 8-level power splitting states within the $\kappa$9 footprint. Reported splitting states spanned Bar:Cross $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$0 by stepping the crystallization pulse amplitude from 3.50 V to 4.45 V in $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$1–0.25 V increments. Measured insertion loss was $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$2 dB in the fully amorphous Cross-ON state at 1540 nm and rose to $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$3 dB in intermediate and crystalline states across 1515–1550 nm. The transmission was flat with $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$4 dB ripple from 1500–1580 nm for all eight splitting states, and the extinction ratio was $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$5 dB for both amorphous-to-Cross and crystalline-to-Bar operation. The calibration curve $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$6 was smooth and monotonic from 0 to 1, negligible drift was observed over $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$7 ms after each write pulse, minor hysteresis of $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$8 V was attributed to thermal-inertia effects in the micro-heater, and pulse-amplitude steps as fine as 0.1 V enabled arbitrary splitting ratios with $$R(\phi)=\sin^2(\phi/2),\qquad T(\phi)=\cos^2(\phi/2),$$9 precision (Li et al., 19 Sep 2025).

This implementation establishes a non-volatile beam splitter in which electrical actuation writes a material state rather than continuously maintaining an operating point. A plausible implication is that the main system-level distinction from interferometric electro-optic splitters is not only the absence of static power in the programmed state, but also the replacement of continuous analog biasing by write-and-retain calibration.

3. Electro-optic interferometric beam splitters

A second major class of electrically reconfigurable beam splitters uses electro-optic phase tuning in Mach–Zehnder interferometers. The tunable beam splitter demonstrated for feed-forward photonic quantum information processing employed two bulk electro-optic modulators inside a balanced Mach–Zehnder interferometer formed by two 50:50 beam splitters and two high-reflectivity mirrors (Ma et al., 2011). Each electro-optic modulator used a Rubidium Titanyl Phosphate crystal, chosen because it exhibits no piezo-resonances up to 200 kHz and only rare resonances up to 2.5 MHz. By driving the two EOMs with equal amplitude and opposite polarity, the device imposed a net relative phase and continuously tuned the splitting ratio from fully transmitting to balanced to fully reflecting. With heralded single photons, the reported interference visibilities were $\phi$0 for H input and $\phi$1 for $\phi$2 input, the overall polarization fidelity exceeded 98%, a Hong–Ou–Mandel dip with visibility $\phi$3 was observed at the balanced setting, the switching time was about 5.6 ns, and the maximal repetition rate was 2.5 MHz. The current insertion loss was approximately 70%, mainly from single-mode fiber coupling and uncoated surfaces, while anti-reflection coatings and optimized coupling were projected to reduce the total insertion loss to $\phi$4 (Ma et al., 2011).

A fiber-based 2$\phi$52 photonic coupler extended this interferometric approach to high-bandwidth, low-voltage operation with active phase stabilization (Švarc et al., 2019). Its core was a 2$\phi$62 fiber Mach–Zehnder interferometer using two nominally 50:50 fiber couplers and an integrated LiNbO$\phi$7 waveguide electro-optic phase modulator in one arm. A weak reference beam at $\phi$8 nm co-propagated with an $\phi$9 nm single-photon signal, and real-time dual-wavelength phase locking stabilized the interferometer at the quadrature point. The measured $\times$0 was 2.2 V, the electrical 3 dB bandwidth was 10 GHz, the extinction ratio was 26 dB from fringe visibility 99.55% over $\times$1 nm at 810 nm, the dynamic splitting range covered 0:100 to 100:0 continuously, the measured rise time was 0.7 ns, and after de-embedding detector jitter, control rise, and time-tag resolution, the EOM-limited switching was $\times$2 ps. The optical path of approximately 9 m imposed a propagation delay of approximately 45 ns, reducible below 20 ns by shortening the delay path (Švarc et al., 2019).

An integrated LiNbO$\times$3 Mach–Zehnder beam splitter was used as the central balancing element in a broadband quantum-noise source (Vashukevich et al., 2021). The substrate was an X-cut congruent LiNbO$\times$4 wafer, the waveguides were formed by thermal diffusion of Ti stripes, and push–pull electrodes ran alongside one arm over a length $\times$5–20 mm with electrode gap $\times$6m. The reported operating wavelength range was 1500–1600 nm, tested at $\times$7 nm. The half-wave voltage was on the order of 3–5 V for $\times$8 mm, insertion loss was $\times$9 dB per MZI, static extinction ratio was $_3$0 dB, common-mode suppression in the balanced detector was $_3$1 dB up to 3 GHz, and the measured splitting-control accuracy was better than $_3$2 in output power via a feedback loop. The practical balanced-detector quantum-noise bandwidth exceeded 4 GHz, with a reported excess of quantum noise over classical noise by 12 dB in the frequency band over 4 GHz (Vashukevich et al., 2021).

These electro-optic interferometric splitters illustrate a distinct design regime from phase-change couplers. They supply high-speed, continuously tunable splitting through voltage-controlled phase, often with explicit servo loops or feed-forward logic. This suggests that their main strengths lie in dynamic modulation and synchronous control, while non-volatile retention is not their defining feature.

4. Electro-mechanical and frequency-domain implementations

Electrical reconfiguration need not be purely electro-optic. In a GaAs nanophotonic directional coupler containing a quantum dot single-photon source, the splitting ratio was tuned by electro-mechanical actuation that varied the out-of-plane separation of two suspended nanobeam waveguides (Bishop et al., 2017). The directional coupler was fabricated in a 160 nm-thick GaAs membrane with waveguide width $_3$3 nm and coupling length $_3$4m. The design target for the in-plane gap was 40 nm, while the experimental device had $_3$5 nm. The moving waveguide was attached to a cantilever of length $_3$6m and width $_3$7m above a substrate gap $_3$8 nm. At $_3$9, the experimental splitting ratio was approximately 80:20 (through:drop), and it increased monotonically to approximately 100:0 by $_3$00 V, corresponding to $_3$01 nm. Maximum controllable displacement exceeded 400 nm before pull-in, the simulated TE-mode coupling efficiency was $_3$02 over the full displacement range, the measured propagation loss in individual nanobeams was $_3$03 dB/mm, the full-decoupling contrast was experimentally $_3$04 dB, the 3 dB bandwidth was $_3$05 nm over 880–980 nm, and the fundamental mechanical resonance was approximately 0.5 MHz, implying $_3$06s rise/fall times in cryogenic vacuum (Bishop et al., 2017).

A conceptually different beam splitter is realized in the frequency domain rather than in physical space. In the electro-optic frequency shifter on x-cut LiNbO$_3$07 on insulator, two coupled racetrack or microring resonators were driven by a single microwave tone so that the device could be reconfigured as a tunable frequency-domain beam splitter, with the splitting ratio controlled by microwave power and the splitting frequency controlled by microwave frequency (Hu et al., 2020). The platform used 600 nm LN on 2 $_3$08m SiO$_3$09 on Si, with two-layer gold electrodes optimized for capacitance $_3$10 pF and inductance $_3$11 nH. Loaded $_3$12 was $_3$13, intrinsic $_3$14 was $_3$15, and arbitrary shift frequencies from 11 GHz up to 28.2 GHz were realized by changing the inter-ring gap. Reported performance included 99.1% up-shift efficiency with 1.2 dB insertion loss at 12.5 GHz, 97.7% efficiency at 11.0 GHz and 78.4% at 8 GHz detuning with 3 GHz 3 dB microwave bandwidth, and 98.7% efficiency with 0.45 dB insertion loss at 28.2 GHz. The splitting ratio $_3$16 was tuned smoothly from 0 to 99% by varying microwave power at fixed $_3$17, and the 50:50 frequency-beam-splitter point followed directly from $_3$18 at $_3$19 (Hu et al., 2020).

Taken together, these devices broaden the standard meaning of beam splitting. The GaAs device preserves a spatial directional-coupler geometry but uses electrostatic mechanics, whereas the lithium-niobate resonator device performs beam splitting between frequency channels. A plausible implication is that “beam splitter” in reconfigurable photonics increasingly denotes a tunable two-mode unitary, independent of whether the two modes are spatial ports or spectral bins.

5. Phase-change metasurfaces and the distinction between reconfigurable and electrically demonstrated devices

Phase-change materials also appear in free-space beam-deflection and beam-splitting metasurfaces, but the presence of a reconfigurable material does not by itself imply an electrically demonstrated beam splitter. The reflective meta-array based on Sb$_3$20S$_3$21 nanorods achieved broadband and wide-angle beam deflection in the near-infrared and, in the crystalline state, realized intrinsic beam-splitting through coexistence of the $_3$22 and $_3$23 diffraction orders (Sadzi et al., 20 Oct 2025). The unit-cell period was 1150 nm, the nanorod width was 300 nm, the nanorod height was 200 nm, the SiO$_3$24 buffer thickness was 60 nm, and the Al backplane thickness was 100 nm. In the amorphous state, the device acted as a nearly pure $_3$25st-order deflector with $_3$26 over a 1000 nm passband covering from O-band to U-band; in the crystalline state, $_3$27 decreased to 20–60% over $_3$28 nm around the C-band, while specular reflection remained non-zero, producing power division between the two orders (Sadzi et al., 20 Oct 2025).

The crucial limitation is explicit in the publication record: the paper does not describe an integrated electrode layout, drive voltages or currents, or pulse-duration optimization for electrically triggered switching. Instead, the amorphous-to-crystalline transition is invoked passively by pump-induced heating when the Sb$_3$29S$_3$30 temperature exceeds $_3$31 K. No finite-element thermal simulations or explicit $_3$32 models are provided, and switching speed and energy are not reported in the paper (Sadzi et al., 20 Oct 2025).

This distinction matters because phase-change beam steering and phase-change electrical beam splitting are often conflated. The Sb$_3$33Se$_3$34 directional coupler provides integrated micro-electrodes, pulse parameters, multi-level calibration, and non-volatile retention (Li et al., 19 Sep 2025), whereas the Sb$_3$35S$_3$36 meta-array demonstrates reconfigurable beam-splitting behavior without a monolithic electrical switching implementation (Sadzi et al., 20 Oct 2025). A common misconception is therefore that all phase-change beam splitters are equally “electrically reconfigurable”; the literature shows that this depends on whether the electrical writing architecture is actually demonstrated.

6. Electronic and matter-wave analogues

The terminology of electrically reconfigurable beam splitting extends beyond photonics into electron optics and matter-wave transport. In low-energy electron guiding, a microwave chip-based beam splitter transformed a single-well transverse guiding potential into a double-well, generating two separated output beams with 5 mm lateral spacing (Hammer et al., 2014). The device used a planar electrode structure driven at $_3$37 MHz and $_3$38 V, corresponding to $_3$39, $_3$40 MHz, and trap depth $_3$41 meV. Efficient beam splitting was observed for electron kinetic energies up to 3 eV, and classical trajectory simulations reproduced two spots with $_3$42 mm FWHM each and 80% guided fraction. Reconfiguration via RF amplitude or phase could be effected on nanosecond time scales, limited by amplifier bandwidth and chip capacitance (Hammer et al., 2014).

In crossed armchair graphene nanoribbons, first-principles transport calculations identified a tunable electronic beam splitter at $_3$43 (Brandimarte et al., 2016). For two H-passivated 14-AGNRs separated by $_3$44 Å, zero-bias transmission at $_3$45 gave $_3$46 for $_3$47 eV and $_3$48, so electrons injected from one terminal were split with almost negligible back-reflection. The splitting ratio could be modified by angle, inter-ribbon separation, stacking order, and bias scheme. In a related zigzag-graphene configuration, two crossed nanoribbons rotated by 60 degrees supported a 50/50 electronic beam splitter that could be switched on and off by varying the doping and interlayer potential; representative values were $_3$49, $_3$50, and a 50/50 window of $_3$51–100 meV, with $_3$52 and $_3$53 (Lima et al., 2016).

Bilayer graphene kink-state routers supply a more explicitly gate-defined electron beam splitter (Li et al., 2017). In a four-kink device with alternating gate polarities across quadrants, the valley valve at zero magnetic field reached an on/off ratio of 8, while at finite magnetic field the splitting ratio $_3$54 could be tuned continuously from 0 to 1; by $_3$55 T the full range $_3$56 was reached. Single-channel kink resistance saturated at $_3$57 k$_3$58, implying $_3$59 and mean free path $_3$60m (Li et al., 2017).

These systems are not optical splitters, but they preserve the defining abstraction: an electrically controlled two-output scattering element. This suggests that the subject has become cross-disciplinary, encompassing spatial photonics, spectral photonics, and ballistic electron transport under a shared two-mode control paradigm.

7. Performance landscape, applications, and recurrent misconceptions

The reported literature spans markedly different operating envelopes.

Platform	Electrical mechanism	Selected reported metrics
Sb$_3$61Se$_3$62-on-Si directional coupler	Phase-change programming with integrated micro-electrodes	8-level states; $_3$63m footprint; $_3$64 dB IL in fully amorphous state; $_3$65 dB across 1515–1550 nm; $_3$66 dB ER; $_3$67 pJ per crystallization step (Li et al., 19 Sep 2025)
Bulk RTP Mach–Zehnder tunable beam splitter	Dual EOM phase control	5.6 ns switching time; 2.5 MHz repetition rate; visibilities $_3$68 and $_3$69; HOM visibility $_3$70 (Ma et al., 2011)
Fiber MZI with LiNbO$_3$71 EOM	Single-arm EO phase modulation with phase lock	$_3$72 V; 10 GHz bandwidth; 26 dB extinction ratio; 0.7 ns rise time; EOM-limited switching $_3$73 ps (Švarc et al., 2019)
GaAs nanobeam directional coupler	Electro-mechanical out-of-plane actuation	$_3$74 to $_3$75 by $_3$76 V; $_3$77 dB contrast; $_3$78 nm 3 dB bandwidth; $_3$79 MHz mechanical resonance (Bishop et al., 2017)
LiNbO$_3$80 frequency-domain beam splitter	Microwave-driven EO mode coupling	99.1% at 12.5 GHz with 1.2 dB IL; 98.7% at 28.2 GHz with 0.45 dB IL; $_3$81 tuned 0→99% (Hu et al., 2020)

Several recurrent misconceptions can be separated using these results. First, an electrically reconfigurable beam splitter is not necessarily a 50:50 device: the Sb$_3$82Se$_3$83 coupler demonstrated multi-level and arbitrary splitting-ratio control, and the fiber and resonator devices were reported to tune continuously from 0:100 to 100:0 or from 0 to 99% (Li et al., 19 Sep 2025, Švarc et al., 2019, Hu et al., 2020). Second, electrical control does not imply identical energy semantics: the Sb$_3$84Se$_3$85 device retains its state with zero static power after a write pulse, whereas interferometric electro-optic devices define the ratio through an electrically imposed phase (Li et al., 19 Sep 2025, Ma et al., 2011). Third, beam splitting is not restricted to spatial port division: frequency-bin splitting was explicitly demonstrated in lithium-niobate resonators (Hu et al., 2020). Fourth, a phase-change beam-splitting function is not equivalent to an electrically characterized phase-change beam splitter: the Sb$_3$86S$_3$87 meta-array is reconfigurable in optical function but does not report integrated electrical switching details (Sadzi et al., 20 Oct 2025).

Applications likewise span several layers of system design. The Sb$_3$88Se$_3$89 directional coupler was positioned for adaptive optical networks, photonic computing, optical computing, and intelligent communication systems (Li et al., 19 Sep 2025). Electro-optic Mach–Zehnder splitters were used for feed-forward single- and two-qubit gates, balanced homodyne detection, photon-number-resolving detectors, and active temporal-qudit preparation (Ma et al., 2011, Vashukevich et al., 2021, Švarc et al., 2019). The frequency-domain splitter directly addressed frequency routing, swap operations, and frequency-domain photonic quantum computing (Hu et al., 2020). Electronic analogues were proposed as building blocks for Mach–Zehnder interferometers, Hong–Ou–Mandel experiments, valleytronic routers, and electron quantum optics (Hammer et al., 2014, Li et al., 2017, Lima et al., 2016).

Across these implementations, the central design axis is the same: electrical control is used to select a point on a two-mode transfer manifold. The main differentiators are the physical state variable being actuated—material phase, interferometric phase, mechanical displacement, resonant mode coupling, or ballistic transmission pathway—and the consequent trade-off among footprint, loss, bandwidth, and retention.