---
title: Collinear Free-Space Photonic Circuit
url: https://www.emergentmind.com/topics/collinear-free-space-photonic-circuit
type: topic
---

# Collinear Free-Space Photonic Circuit

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 [2512.02658, 2104.01230, 2601.04947, 2204.09284, 2604.13233].

## 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” [2601.04947]. 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 [2604.13233]. 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 [2204.09284]. In the integrated silicon-mesh transmitter/receiver, the authors describe the geometry as “co-axial launch/receive” [2104.08174].

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 [2512.02658]. Paneru et al. implement the standard interferometric paradigm directly in a Hilbert space of polarized structured-light modes using liquid-crystal metasurfaces [2605.31216]. 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 [2112.13644, 2104.08174].

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” [2601.04947]. In the hybrid PIC–metasurface beam-steering system, strict surface-normal propagation “simplif[ies] mechanical alignment to the metasurface” [2604.13233]. 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 \(161^\circ \times 161^\circ\) |

In Stranden et al., the free-space/chip interface is an MPLC device optimized for a particular mode set, such that
\[
\psi^{\mathrm{out}}_j(x,y)=U[LG_j(x,y)] \simeq \psi^{\mathrm{ideal}}_j(x,y).
\]
The proof-of-principle uses \(N=4\) 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 [2512.02658].

The surface-normal grating coupler of [2104.01230] 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 \(70\%\) overall theoretical conversion efficiency, and the experiment validates efficient surface-normal collimated emission of an approximately \(90\,\mu\mathrm{m}\) full width at half maximum Gaussian at the thermally tunable operating wavelength of approximately \(780\) nm [2104.01230].

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 \(\sim 0.5\)–\(1\,\mu\mathrm{m}\) into a collimated free-space Gaussian beam with waist \(\sim 107\,\mu\mathrm{m}\), which then illuminates an analytically optimized metasurface for 2D steering. The measured waveguide-to-free-space reflector efficiency is \(83\%\) \((-0.8\,\mathrm{dB})\) [2604.13233].

## 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
\[
U = P_N D_N \dots P_2 D_2 P_1 D_1,
\]
with
\[
P_i[\psi(x,y)] = \exp[i\phi_i(x,y)]\psi(x,y),
\qquad
D_i[\psi(x,y)] = \exp\!\left[-i\frac{k}{2R_i}(x^2+y^2)\right]\psi(x,y).
\]
The phase masks are obtained with the “wavefront matching” iterative algorithm of Hashimoto et al. 2005, maximizing overlaps \(C_{ij}=\langle \psi_i^{\mathrm{ideal}}|U LG_j\rangle\). This places MPLC within the broader class of finite-plane unitary approximants acting on spatial channels [2512.02658].

Liquid-crystal metagratings provide a different primitive set. In the circular-polarization basis \(\{|L\rangle, |R\rangle\}\), a local metasurface element is described by the Jones matrix
\[
Q_{(\delta)}(\theta)=
\begin{pmatrix}
\cos(\delta/2) & i\sin(\delta/2)e^{-2i\theta(x,y)} \\
i\sin(\delta/2)e^{+2i\theta(x,y)} & \cos(\delta/2)
\end{pmatrix}.
\]
For the g-plate geometry \(\theta(x)=\pi x/\Lambda+\alpha\), the device couples neighboring transverse-momentum rails with a splitting amplitude \(t=\cos(\delta/2)\) and \(r=\sin(\delta/2)\), so that the transmittance and reflectance are \(T=t^2\) and \(R=r^2\). Because \(\delta\) is voltage-tunable, the splitting ratio is tunable according to
\[
R(V)=\sin^2\!\bigl[\tfrac12\,\delta(V)\bigr].
\]
This is the basis for electrically controlled two-photon interference in a collinear geometry [2601.04947].

Paneru et al. recast these ideas as a universal interferometric architecture for polarized structured light. Logical states are encoded in spin–orbit modes
\[
|m,j\rangle \equiv A(x,y,z)e^{ik_z z}e^{i\,m\,x\,\Delta k_\perp}|j\rangle,
\]
and patterned liquid-crystal metasurfaces implement both mode beam splitters and mode phase shifters. In the demonstrated four-mode space \(\{-1,L;0,R;0,L;1,R\}\), cascading four near-field and far-field layers spans the full \(\mathrm{SU}(4)\). Numerical optimization over \(1000\) Haar-random \(\mathrm{SU}(4)\) targets yields a mean infidelity \(1-F \simeq 3.5\times 10^{-14}\), which supports the universality claim for the proposed scheme [2605.31216].

## 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 [2204.09284], the free-space interface consists of \(N=16\) identical surface-grating couplers arranged on two concentric rings of radii \(200\,\mu\mathrm{m}\) and \(225\,\mu\mathrm{m}\). A binary-tree mesh implements an arbitrary \(N\times N\) unitary in \(\log_2 N = 4\) rows of interferometers. The output intensities obey
\[
I_k=\bigl|\,[M_{\mathrm{mesh}}\mathbf{E}_{\mathrm{in}}]_k\,\bigr|^2.
\]
A global nonlinear calibration fit returns \(r^2=0.27\), \(\gamma_{\mathrm{range}}=1.94\pi\), and phase-shifter offsets determined to \(\sim 0.01\,\mathrm{rad}\) accuracy. Once calibrated, the same chip reconstructs the pixel-by-pixel amplitude and phase of an unknown beam at \(1600\) nm, even though the grating design wavelength is \(1550\) nm [2204.09284].

In the automated-manipulation architecture of [2104.08174], a diagonal MZI mesh drives four optical antennas to generate or receive a free-space beam along the surface normal. The far field is
\[
E(\theta)=A_{\mathrm{elem}}(\theta)\sum_{n=0}^{N-1} a_n e^{j(\phi_n-kx_n\sin\theta)}.
\]
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 [2104.08174].

Milanizadeh et al. demonstrate the same adaptive logic in receiver form with a \(9\times 2\) 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 \(U_{\mathrm{mesh}} \approx U_{\mathrm{mix}}^{-1}\), thereby demultiplexing orthogonal beams that have mixed in free space. The reported results include \(10\,\mathrm{Gbit/s}\) operation at \(1550\) nm, crosstalk suppression of direction-diversity \(\ge 25\,\mathrm{dB}\), HG-mode diversity \(\ge 30\,\mathrm{dB}\), arbitrary mixing \(\ge 28\,\mathrm{dB}\), and optical bandwidth \(>40\) nm with \(<3\) dB variation in XT [2112.13644].

## 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
\[
\eta_j = |\langle \psi_j^{\mathrm{ideal}}|\psi_j^{\mathrm{out}}\rangle|^2,
\]
and crosstalk from channel \(i\to j\) is
\[
\mathrm{Crosstalk}_{i\to j}=10\log_{10}\bigl[|\langle \psi_j^{\mathrm{out}}|\psi_i^{\mathrm{ideal}}\rangle|^2\bigr].
\]
Before coupling into the chip, Stranden et al. report \(\eta_j \simeq 0.65\) for \(j=0,1,2\); after coupling into the silicon rib waveguide and propagating through \(5\) mm, the coupling yields \(\eta_{TE_0}\simeq 0.86\), \(\eta_{TE_1}\simeq 0.65\), and \(\eta_{TE_2}\simeq 0.63\). Measured matrices before the chip show diagonal \(\approx -1.8\) dB and off-diagonals \(< -10\) dB, while the 3×3 visibility remains \(\simeq 75\%\) after the chip [2512.02658].

For beam-projecting and beam-steering interfaces, efficiency is typically referenced to power transfer and beam quality. The NZI grating coupler defines \(\eta=P_{\mathrm{out}}/P_{\mathrm{in}}\), with theoretical and measured \(\eta \approx 70\%\), a fundamental resonance at \(780\) nm with \(Q\approx 3000\), and thermal tuning \(\Delta\lambda/\Delta T \approx 0.012\,\mathrm{nm/K}\) over approximately \(1\) nm for \(\Delta T \approx 80\) K [2104.01230]. In He et al., diffraction-limited behavior is assessed by angular divergence versus angle and by \(M^2\); measured divergences of \(0.27^\circ\) at \(0^\circ\) and \(0.74^\circ\) at \(69^\circ\) lie on the diffraction-limited curve within error bars, while adjacent-beam crosstalk is \(< -20\) dB [2604.13233].

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 \(\sim\) minutes for \(16\times 4\times 25^2=40\,000\) points [2204.09284]. The multibeam receiver reports insertion loss normalized to free-space coupling of \(\lesssim 1\) dB additional from the mesh and “no OSNR penalty” in BER curves relative to a single-mode reference [2112.13644]. The automated transmitter/receiver reports a nearly diffraction-limited central lobe with \(M^2 \approx 1.2\), first sidelobe \(\approx -13\) dB for uniform excitation, and beam recovery in approximately \(1\) s after phase-mask perturbation [2104.08174].

Bandwidth behavior depends strongly on architecture. Stranden et al. optimize the MPLC masks at four equally spaced wavelengths in \([1540,1570]\) nm and obtain nearly wavelength-independent performance over the C-band \((1528\)–\(1568\) nm), with \(\eta_j\) fluctuations \(<5\%\) and crosstalk visibility \(>70\%\) across the \(40\) nm span [2512.02658]. By contrast, the NZI emitter operates around a spectrally selective standing-wave resonance at \(780\) nm, although it remains thermally tunable [2104.01230]. 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 \(M\) scales with the number of planes \(N\), with the empirical relation \(M \approx N/1.3\) for low crosstalk; increasing to \(8\)–\(12\) planes via cascaded metasurfaces or multi-pass SLM folds can address \(\ge 10\) modes with \(>80\%\) per-mode efficiency [2512.02658]. In the g-plate platform, multiple devices with different spatial frequencies \((\Lambda/N)\) may be cascaded in the near field to build large 1D and 2D interferometric meshes in free space [2601.04947]. In the universal structured-light architecture, Paneru et al. argue that for general \(\mathrm{SU}(2n)\), \(2n\) patterned plates suffice and the optical depth still grows linearly in \(n\) [2605.31216]. 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 [2104.01230]. 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 [2604.13233].

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 [2512.02658]. The NZI emitter is positioned for trapping, cooling, and interrogation of atoms, bio- and chemi-sensing, and complex free-space interconnect [2104.01230]. 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 [2601.04947]. Programmable silicon meshes address FSO links, adaptive multibeam reception, imaging through obstacles, obstacle identification, and depth imaging or LIDAR through clutter or turbulence [2104.08174, 2112.13644]. Hybrid reflector–metasurface emitters are aimed at inter-satellite optical links, airborne LiDAR, point-to-point optical wireless communications, and collaborative robotic platforms [2604.13233].

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 [2204.09284, 2601.04947, 2104.01230]. 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 [2512.02658, 2204.09284, 2112.13644, 2605.31216]. The main practical constraints instead appear in loss budgets, alignment tolerances, and calibration complexity. He et al. specify relative tilt \(<0.1^\circ\) and axial spacing \(\pm 10\,\mu\mathrm{m}\) for diffraction-limited performance [2604.13233]; Stranden et al. report overall end-to-end throughput of \(10\)–\(15\%\) in the proof-of-principle MPLC interface [2512.02658]; the silicon-mesh work explicitly manages thermal crosstalk and off-design-wavelength calibration [2104.08174, 2204.09284]. 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.

Source: https://www.emergentmind.com/topics/collinear-free-space-photonic-circuit