Collinear Free-Space Photonic Circuit

• Collinear free-space photonic circuits are architectures where optical modes share a common propagation axis and are manipulated via structured phase masks, metasurfaces, and grating couplers.
• They integrate both passive and active components—such as programmable MZI meshes and liquid-crystal metasurfaces—to achieve mode conversion, beam steering, and efficient free-space projection.
• Key performance metrics like conversion efficiency, crosstalk suppression, and calibration fidelity are critical for advancing applications in quantum communications, beam projection, and adaptive optical systems.

A collinear free-space photonic circuit is an optical-processing architecture in which structured optical modes share a common propagation axis, or a common surface-normal path with respect to a photonic chip, while transformations are executed by phase masks, metasurfaces, grating couplers, free-form reflectors, or programmable photonic meshes. In current usage, the concept includes passive multi-plane light conversion between free-space Laguerre–Gauss modes and waveguide eigenmodes, surface-normal free-space projection from near-zero-index grating couplers, liquid-crystal metagratings acting as tunable beam splitters for transverse-momentum modes, reconfigurable MZI meshes that sample and process incident fields, and hybrid PIC–metasurface systems for ultrawide-angle beam steering (Stranden et al., 2 Dec 2025, Yulaev et al., 2021, Ammendola et al., 8 Jan 2026, Bütow et al., 2022, He et al., 14 Apr 2026).

1. Geometric definition and architectural scope

The defining geometric property is collinearity: optical channels are not routed through spatially separated bulk interferometer arms, but instead co-propagate along a common axis and are distinguished by spatial mode, polarization, transverse momentum, or guided superposition. In the liquid-crystal metagrating platform, “all modes copropagate and are resolved only at the Fourier plane” (Ammendola et al., 8 Jan 2026). In He et al., the free-space beam axis is “strictly normal to the PIC surface (‘collinear’)” because a free-form reflector is mounted directly on the waveguide facet (He et al., 14 Apr 2026). In the amplitude–phase camera, the beam is incident “at normal incidence” on a pixelated grating-coupler array, so that all 16 couplers sample the same free-space wave (Bütow et al., 2022). In the integrated silicon-mesh transmitter/receiver, the authors describe the geometry as “co-axial launch/receive” (Milanizadeh et al., 2021).

This geometric constraint does not imply a single implementation class. The literature spans passive, active, bulk-assisted, and chip-scale realizations. Stranden et al. use a collinear cascade of phase-only planes on a single SLM to map higher-order free-space Laguerre–Gauss modes into the first three TE modes of a multimode silicon waveguide (Stranden et al., 2 Dec 2025). Paneru et al. implement the standard interferometric paradigm directly in a Hilbert space of polarized structured-light modes using liquid-crystal metasurfaces (Paneru et al., 29 May 2026). Milanizadeh et al. and related silicon-photonics work use grating-coupler arrays and reconfigurable MZI meshes to receive, demultiplex, and adaptively reconstruct free-space beams (Milanizadeh et al., 2021, Milanizadeh et al., 2021).

A central consequence of the collinear geometry is the relocation of complexity from path stabilization to mode engineering. In the g-plate interferometer, “no beam-splitter cubes or interferometric alignment are needed” (Ammendola et al., 8 Jan 2026). In the hybrid PIC–metasurface beam-steering system, strict surface-normal propagation “simplif[ies] mechanical alignment to the metasurface” (He et al., 14 Apr 2026). This suggests that collinearity primarily changes the locus of control: patterned phase response, modal basis design, calibration, and loss management become the principal design variables.

2. Interfaces between free-space modes and photonic chips

A major branch of collinear free-space photonic circuits concerns interfaces between free-space beams and guided modes. These interfaces can perform mode conversion, beam projection, or beam expansion before subsequent free-space processing.

Platform	Core mechanism	Representative figures
Stranden et al. MPLC interface	$N=4$ phase-only planes on a single SLM; LG-to-TE conversion	$\eta_j \simeq 0.65$ before chip; overall power-throughput $10$–$15\%$; off-diagonals $< -10$ dB
NZI grating coupler	constrained inverse design; slow-light standing-wave resonance	theoretical and measured $\eta \approx 70\%$; $90\,\mu\mathrm{m}$ FWHM Gaussian; $Q \approx 3000$
He et al. hybrid emitter	free-form reflector plus ultrawide-FOV metasurface	$\eta_c \approx 83\%$; waist $\sim 107\,\mu\mathrm{m}$; FOV $\eta_j \simeq 0.65$0

In Stranden et al., the free-space/chip interface is an MPLC device optimized for a particular mode set, such that

$\eta_j \simeq 0.65$1

The proof-of-principle uses $\eta_j \simeq 0.65$2 phase-only planes implemented by four holograms on a single SLM, each visited in turn by four reflections of the beam. The platform experimentally demonstrates low-crosstalk conversion between various sets of three LG modes and the first three TE modes of a multimode silicon waveguide across the telecom C-band; it is passive, broadband, and adaptable to different spatial mode sets (Stranden et al., 2 Dec 2025).

The surface-normal grating coupler of (Yulaev et al., 2021) addresses a different interface problem: direct projection of an on-chip slab mode into a large-area collimated free-space Gaussian beam. The inverse-designed structure couples the incident slab mode into a spatially extended slow-light near-zero-index region, backed by a Bragg reflector, and forms a spectrally broad standing-wave resonance at the target wavelength. The reported lower-cladding optimization provides $\eta_j \simeq 0.65$3 overall theoretical conversion efficiency, and the experiment validates efficient surface-normal collimated emission of an approximately $\eta_j \simeq 0.65$4 full width at half maximum Gaussian at the thermally tunable operating wavelength of approximately $\eta_j \simeq 0.65$5 nm (Yulaev et al., 2021).

He et al. extend the interface concept by inserting a three-dimensional free-form micro-optical reflector between the waveguide facet and a metasurface. The reflector transforms a near-Gaussian TE waveguide mode of effective mode-field diameter $\eta_j \simeq 0.65$6–$\eta_j \simeq 0.65$7 into a collimated free-space Gaussian beam with waist $\eta_j \simeq 0.65$8, which then illuminates an analytically optimized metasurface for 2D steering. The measured waveguide-to-free-space reflector efficiency is $\eta_j \simeq 0.65$9 $10$0 (He et al., 14 Apr 2026).

3. Elementary operations and unitary descriptions

The circuit primitives of collinear free-space photonic systems are usually phase-only transformations, mode-selective couplers, and mode-dependent phase shifters. In Stranden et al., the MPLC transformation is written as

$10$1

with

$10$2

The phase masks are obtained with the “wavefront matching” iterative algorithm of Hashimoto et al. 2005, maximizing overlaps $10$3. This places MPLC within the broader class of finite-plane unitary approximants acting on spatial channels (Stranden et al., 2 Dec 2025).

Liquid-crystal metagratings provide a different primitive set. In the circular-polarization basis $10$4, a local metasurface element is described by the Jones matrix

$10$5

For the g-plate geometry $10$6, the device couples neighboring transverse-momentum rails with a splitting amplitude $10$7 and $10$8, so that the transmittance and reflectance are $10$9 and $15\%$0. Because $15\%$1 is voltage-tunable, the splitting ratio is tunable according to

$15\%$2

This is the basis for electrically controlled two-photon interference in a collinear geometry (Ammendola et al., 8 Jan 2026).

Paneru et al. recast these ideas as a universal interferometric architecture for polarized structured light. Logical states are encoded in spin–orbit modes

$15\%$3

and patterned liquid-crystal metasurfaces implement both mode beam splitters and mode phase shifters. In the demonstrated four-mode space $15\%$4, cascading four near-field and far-field layers spans the full $15\%$5. Numerical optimization over $15\%$6 Haar-random $15\%$7 targets yields a mean infidelity $15\%$8, which supports the universality claim for the proposed scheme (Paneru et al., 29 May 2026).

4. Reconfigurable photonic meshes for sampling, correction, and reception

Integrated silicon photonic meshes provide a programmable realization of collinear free-space circuits in which a sampled incident field is processed on-chip. In the amplitude–phase camera of (Bütow et al., 2022), the free-space interface consists of $15\%$9 identical surface-grating couplers arranged on two concentric rings of radii $< -10$0 and $< -10$1. A binary-tree mesh implements an arbitrary $< -10$2 unitary in $< -10$3 rows of interferometers. The output intensities obey

$< -10$4

A global nonlinear calibration fit returns $< -10$5, $< -10$6, and phase-shifter offsets determined to $< -10$7 accuracy. Once calibrated, the same chip reconstructs the pixel-by-pixel amplitude and phase of an unknown beam at $< -10$8 nm, even though the grating design wavelength is $< -10$9 nm (Bütow et al., 2022).

In the automated-manipulation architecture of (Milanizadeh et al., 2021), a diagonal MZI mesh drives four optical antennas to generate or receive a free-space beam along the surface normal. The far field is

$\eta \approx 70\%$0

When the outputs are set to equal phase and amplitude, the four radiators form a single collimated beam. The notable feature is closed-loop self-configuration: dithering-based gradient descent maximizes on-axis intensity while CLIPP detectors stabilize internal splitting ratios. The system compensates inserted phase and amplitude distortions, re-establishes a sharply focused spot through an obstacle, and infers an unknown obstacle’s per-port phase profile from the final optimized settings (Milanizadeh et al., 2021).

Milanizadeh et al. demonstrate the same adaptive logic in receiver form with a $\eta \approx 70\%$1 diagonal mesh. Nine grating-coupler antennas sample the incoming field; two rows of tunable MZIs then unitarily transform the 9-dimensional input into two selected output waveguides. The self-configuration algorithm tunes the mesh row by row so that $\eta \approx 70\%$2, thereby demultiplexing orthogonal beams that have mixed in free space. The reported results include $\eta \approx 70\%$3 operation at $\eta \approx 70\%$4 nm, crosstalk suppression of direction-diversity $\eta \approx 70\%$5, HG-mode diversity $\eta \approx 70\%$6, arbitrary mixing $\eta \approx 70\%$7, and optical bandwidth $\eta \approx 70\%$8 nm with $\eta \approx 70\%$9 dB variation in XT (Milanizadeh et al., 2021).

5. Metrics, bandwidth, and beam-quality regimes

The literature uses several recurring figures of merit. For MPLC mode conversion, the single-mode efficiency is defined as

$90\,\mu\mathrm{m}$0

and crosstalk from channel $90\,\mu\mathrm{m}$1 is

$90\,\mu\mathrm{m}$2

Before coupling into the chip, Stranden et al. report $90\,\mu\mathrm{m}$3 for $90\,\mu\mathrm{m}$4; after coupling into the silicon rib waveguide and propagating through $90\,\mu\mathrm{m}$5 mm, the coupling yields $90\,\mu\mathrm{m}$6, $90\,\mu\mathrm{m}$7, and $90\,\mu\mathrm{m}$8. Measured matrices before the chip show diagonal $90\,\mu\mathrm{m}$9 dB and off-diagonals $Q \approx 3000$0 dB, while the 3×3 visibility remains $Q \approx 3000$1 after the chip (Stranden et al., 2 Dec 2025).

For beam-projecting and beam-steering interfaces, efficiency is typically referenced to power transfer and beam quality. The NZI grating coupler defines $Q \approx 3000$2, with theoretical and measured $Q \approx 3000$3, a fundamental resonance at $Q \approx 3000$4 nm with $Q \approx 3000$5, and thermal tuning $Q \approx 3000$6 over approximately $Q \approx 3000$7 nm for $Q \approx 3000$8 K (Yulaev et al., 2021). In He et al., diffraction-limited behavior is assessed by angular divergence versus angle and by $Q \approx 3000$9; measured divergences of $\eta_c \approx 83\%$0 at $\eta_c \approx 83\%$1 and $\eta_c \approx 83\%$2 at $\eta_c \approx 83\%$3 lie on the diffraction-limited curve within error bars, while adjacent-beam crosstalk is $\eta_c \approx 83\%$4 dB (He et al., 14 Apr 2026).

For programmable meshes, figures of merit often emphasize calibration fidelity, insertion loss, and communication performance. The amplitude–phase camera reconstructs amplitudes and phases to within “a few percent and a few degrees” over all 16 pixels, with full calibration requiring $\eta_c \approx 83\%$5 minutes for $\eta_c \approx 83\%$6 points (Bütow et al., 2022). The multibeam receiver reports insertion loss normalized to free-space coupling of $\eta_c \approx 83\%$7 dB additional from the mesh and “no OSNR penalty” in BER curves relative to a single-mode reference (Milanizadeh et al., 2021). The automated transmitter/receiver reports a nearly diffraction-limited central lobe with $\eta_c \approx 83\%$8, first sidelobe $\eta_c \approx 83\%$9 dB for uniform excitation, and beam recovery in approximately $\sim 107\,\mu\mathrm{m}$0 s after phase-mask perturbation (Milanizadeh et al., 2021).

Bandwidth behavior depends strongly on architecture. Stranden et al. optimize the MPLC masks at four equally spaced wavelengths in $\sim 107\,\mu\mathrm{m}$1 nm and obtain nearly wavelength-independent performance over the C-band $\sim 107\,\mu\mathrm{m}$2–$\sim 107\,\mu\mathrm{m}$3 nm), with $\sim 107\,\mu\mathrm{m}$4 fluctuations $\sim 107\,\mu\mathrm{m}$5 and crosstalk visibility $\sim 107\,\mu\mathrm{m}$6 across the $\sim 107\,\mu\mathrm{m}$7 nm span (Stranden et al., 2 Dec 2025). By contrast, the NZI emitter operates around a spectrally selective standing-wave resonance at $\sim 107\,\mu\mathrm{m}$8 nm, although it remains thermally tunable (Yulaev et al., 2021). This contrast illustrates two recurring regimes in collinear free-space photonic circuits: broadband modal conversion and resonant surface-normal emission.

6. Scalability, applications, and interpretive issues

Scalability is addressed in several non-equivalent ways. For MPLC, the supported mode count $\sim 107\,\mu\mathrm{m}$9 scales with the number of planes $\eta_j \simeq 0.65$00, with the empirical relation $\eta_j \simeq 0.65$01 for low crosstalk; increasing to $\eta_j \simeq 0.65$02–$\eta_j \simeq 0.65$03 planes via cascaded metasurfaces or multi-pass SLM folds can address $\eta_j \simeq 0.65$04 modes with $\eta_j \simeq 0.65$05 per-mode efficiency (Stranden et al., 2 Dec 2025). In the g-plate platform, multiple devices with different spatial frequencies $\eta_j \simeq 0.65$06 may be cascaded in the near field to build large 1D and 2D interferometric meshes in free space (Ammendola et al., 8 Jan 2026). In the universal structured-light architecture, Paneru et al. argue that for general $\eta_j \simeq 0.65$07, $\eta_j \simeq 0.65$08 patterned plates suffice and the optical depth still grows linearly in $\eta_j \simeq 0.65$09 (Paneru et al., 29 May 2026). For large-aperture surface-normal emitters, the polynomial parameterization domain can be extended to larger beams, provided that adiabatic variation remains gradual and the standing-wave length covers the desired aperture (Yulaev et al., 2021). He et al. further note that populating the PIC with many emission sites in a 2D array would make a multi-aperture beam projector for parallel steering or holographic wave-front synthesis practical (He et al., 14 Apr 2026).

The application space is correspondingly broad. The MPLC interface is motivated by scalable multi-mode communication networks, increased data capacities, and on-chip signal processing (Stranden et al., 2 Dec 2025). The NZI emitter is positioned for trapping, cooling, and interrogation of atoms, bio- and chemi-sensing, and complex free-space interconnect (Yulaev et al., 2021). The liquid-crystal metagrating platform targets high-dimensional quantum key distribution, mode-multiplexed telecom, free-space boson sampling, quantum simulators, cluster-state measurement, photonic quantum computing, and quantum metrology (Ammendola et al., 8 Jan 2026). Programmable silicon meshes address FSO links, adaptive multibeam reception, imaging through obstacles, obstacle identification, and depth imaging or LIDAR through clutter or turbulence (Milanizadeh et al., 2021, Milanizadeh et al., 2021). Hybrid reflector–metasurface emitters are aimed at inter-satellite optical links, airborne LiDAR, point-to-point optical wireless communications, and collaborative robotic platforms (He et al., 14 Apr 2026).

Two recurrent simplifications are not supported by the present literature. First, collinear operation is not limited to passive optics: the record includes thermo-optic MZI meshes, voltage-tunable liquid-crystal metasurfaces, and thermally tunable NZI resonances (Bütow et al., 2022, Ammendola et al., 8 Jan 2026, Yulaev et al., 2021). Second, collinearity does not imply a single-mode or non-universal device class: existing demonstrations cover low-crosstalk three-mode LG-to-TE conversion, 16-pixel amplitude–phase reconstruction, adaptive two-channel demultiplexing, and representative four-mode gates with numerical support for arbitrary unitary transformations (Stranden et al., 2 Dec 2025, Bütow et al., 2022, Milanizadeh et al., 2021, Paneru et al., 29 May 2026). The main practical constraints instead appear in loss budgets, alignment tolerances, and calibration complexity. He et al. specify relative tilt $\eta_j \simeq 0.65$10 and axial spacing $\eta_j \simeq 0.65$11 for diffraction-limited performance (He et al., 14 Apr 2026); Stranden et al. report overall end-to-end throughput of $\eta_j \simeq 0.65$12–$\eta_j \simeq 0.65$13 in the proof-of-principle MPLC interface (Stranden et al., 2 Dec 2025); the silicon-mesh work explicitly manages thermal crosstalk and off-design-wavelength calibration (Milanizadeh et al., 2021, Bütow et al., 2022). A plausible implication is that future progress will depend less on establishing the viability of collinear free-space photonic circuits than on integrating low-loss mode transforms, scalable actuation, and robust calibration into a common fabrication stack.