ReLOAD: Relayed-Loop Amplified Optical Deflection

• ReLOAD is an optical architecture that multiplies the effective scan angle by repeatedly relaying a laser beam through a tailored cavity.
• It employs afocal relays and mirrors to convert each deflection event into a multiplied output angle, achieving up to 8x amplification.
• Experimental results using a KTN electro-optic deflector demonstrated enhanced performance with increased resolvable spots and high-speed imaging capabilities.

Searching arXiv for recent and foundational papers relevant to ReLOAD. Relayed-Loop Optically Amplified Deflection (ReLOAD) is an optical architecture that multiplies the effective scan angle, and therefore the optical invariant and throughput, of a laser deflector by forcing the same beam to interact with the deflector multiple times inside a carefully designed relay cavity. In the 2025 formulation, ReLOAD is presented as a method for increasing the effective optical invariant beyond $2\times$ by repeated relaying of the deflected beam onto the deflector in an optical loop created within a cavity, with an experimental demonstration of $8\times$ amplification of electro-optical deflection (Jayakumar et al., 22 Sep 2025). The architecture is explicitly non-inertial: the deflector itself does not move faster or over a larger intrinsic angle, but the optical system converts each unit of deflection into $N$ times larger scan at the output (Jayakumar et al., 22 Sep 2025).

1. Optical invariant and the motivation for relayed-loop amplification

In scanning systems, the operative constraint is the optical invariant, also referred to as étendue. For a simple paraxial, rotationally symmetric system with a collimated beam of radius $d/2$ and a maximum scan half-angle $\theta$, a useful scalar optical invariant is

$H \sim n\,d\,\theta ,$

while a more general area–solid-angle form is

$G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$

For single-mode or well-defined Gaussian beams, the simpler product $n d \theta$ captures the relevant constraint: one cannot increase both beam size and scan angle arbitrarily without encountering fundamental limits (Jayakumar et al., 22 Sep 2025).

This constraint directly determines the accessible field of view and the number of resolvable spots. The one-dimensional field of view is approximately

$\mathrm{FOV} \approx 2 f\,\tan \theta ,$

and the diffraction-limited spot diameter along the scan axis is

$$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$

Using a full-width-at-half-maximum criterion,

$8\times$0

which yields

$8\times$1

The number of resolvable spots therefore scales linearly with both beam diameter $8\times$2 and scan angle $8\times$3 for small angles, whereas practical deflector speed is described as inversely related to optical invariant (Jayakumar et al., 22 Sep 2025).

The immediate motivation for ReLOAD is that many fast non-mechanical deflectors, including electro-optic deflectors, offer unparalleled speed but limited optical invariant. The 2025 ReLOAD work states that passive optical systems had previously been developed that can effectively double the optical invariant and maximum throughput of a single deflector, but that ReLOAD extends the effective optical invariant beyond $8\times$4 by repeated relaying inside a cavity (Jayakumar et al., 22 Sep 2025). This places ReLOAD in a lineage of angle-amplification schemes while distinguishing it by repeated reuse of the same deflection event.

2. Cavity architecture and the mechanism of angle multiplication

The core ReLOAD concept is an optical cavity built from afocal relays and mirrors in which the deflector sits at an afocal plane that is conjugate to the cavity’s end mirrors. The beam enters through an inject mirror at a focal plane, is relayed to the deflector, acquires a small angle $8\times$5 in its active scan dimension, is relayed to an end mirror tilted slightly in the orthogonal “loop” dimension, and is then returned for another pass. The tilt in the loop dimension ensures that each return pass samples a different lateral position on the deflector while preserving the deflection-axis contribution, so the output angle after $8\times$6 loops is

$8\times$7

This is the central amplification relation in the ReLOAD formulation (Jayakumar et al., 22 Sep 2025).

A defining feature of the geometry is the separation of the deflection axis from the loop axis. In the deflection axis, the beam’s angular excursion accumulates with each pass. In the orthogonal loop axis, the cavity tilt determines how many passes occur before the beam reaches the eject mirror and exits the cavity (Jayakumar et al., 22 Sep 2025). This separation allows the amplification factor $8\times$8 to be adjusted by cavity geometry rather than by modifying the deflector drive.

For transmissive ReLOAD, the reported implementation uses two $8\times$9-$N$0 relays in series, forming an $N$1-$N$2 cavity. Each $N$3-$N$4 relay comprises two telecentric scan lenses separated by $N$5, with the deflector placed at the common afocal plane. The inject mirror is positioned at one relay’s focal plane near the edge of the scan lens field of view along the loop axis, and a high-aspect-ratio rectangular eject mirror is placed on axis at the same focal plane. End mirrors at conjugate focal planes complete the relay cavity (Jayakumar et al., 22 Sep 2025).

The same underlying principle is stated to be adaptable to reflective mechanical deflectors, including mirror galvanometers, resonant mirrors, polygon mirrors, and MEMS mirrors, by replacing the transmissive deflector with a scan mirror placed at a conjugate plane and preserving the looped relay geometry (Jayakumar et al., 22 Sep 2025). This suggests that ReLOAD is a deflector-agnostic optical architecture rather than a device-specific technique.

3. Governing relations, acceptance limits, and resolvable spots

The 2025 paper derives explicit limits on loop count from acceptance angles in the deflection and loop dimensions. For a given beam diameter $N$6, let $N$7 denote the acceptance angle in the deflection axis and $N$8 the acceptance angle in the loop axis. If $N$9 is the maximum single-pass deflection and $d/2$0 the minimum practical tilt angle of the loop-control mirror, then the maximum amplification factor for the folded $d/2$1-$d/2$2 implementation is

$d/2$3

This relation encodes the requirement that both the cumulative amplified deflection and the cumulative loop-axis excursion remain within the relay acceptance (Jayakumar et al., 22 Sep 2025).

The minimum loop-control mirror tilt is tied to the eject mirror width and the focused spot size. For Gaussian beams, using a $d/2$4 power capture criterion and choosing the eject mirror width equal to the $d/2$5 spot diameter, the main-text expression is

$d/2$6

This relation makes explicit that smaller wavelengths and larger beam diameters reduce the minimum loop-axis tilt required for extraction (Jayakumar et al., 22 Sep 2025).

The ReLOAD scaling of resolvable spots is then expressed as

$d/2$7

In the idealized diffraction-limited limit, this relation is linear in $d/2$8, so repeated relaying directly multiplies the scan-limited addressable space. In the specific electro-optic implementation, the parameters $d/2$9, $\theta$0, $\theta$1, and $\theta$2 yield an ideal prediction of approximately $\theta$3 resolvable spots, compared with $\theta$4 for the raw single-pass deflector in the same configuration (Jayakumar et al., 22 Sep 2025).

This mathematical structure distinguishes ReLOAD from simple $\theta$5 passive multipliers. A plausible implication is that ReLOAD exploits unused angular acceptance in the loop dimension to increase the useful deflection-axis optical invariant until one of the two acceptance bounds becomes active.

4. Electro-optic implementation and reported performance

The reported experimental realization uses a KTN electro-optic deflector in space-charge mode. The single-pass KTN deflection angle is given as

$\theta$6

where $\theta$7 is the refractive index, $\theta$8 the applied voltage, $\theta$9 the quadratic electro-optic coefficient, $H \sim n\,d\,\theta ,$0 the permittivity, $H \sim n\,d\,\theta ,$1 the trapped charge density, $H \sim n\,d\,\theta ,$2 the interaction length, and $H \sim n\,d\,\theta ,$3 the electrode separation (Jayakumar et al., 22 Sep 2025).

The crystal dimensions are reported as $H \sim n\,d\,\theta ,$4, with Ti/Pt/Au electrodes on the $H \sim n\,d\,\theta ,$5 mm faces and light propagating along the $H \sim n\,d\,\theta ,$6-mm thickness. The device is operated in space-charge mode by applying a temporary $H \sim n\,d\,\theta ,$7 V DC bias that injects and traps electrons, producing a cylindrical convex GRIN lens orthogonal to the electrodes. During operation, an AC voltage shifts the GRIN lens center and thereby deflects the beam. Because the KTN GRIN acts as a cylindrical convex lens in the deflection axis, the implementation adds a cylindrical concave lens of $H \sim n\,d\,\theta ,$8 to form a cylindrical Galilean telescope that cancels the GRIN focusing (Jayakumar et al., 22 Sep 2025).

The cavity uses four telecentric scan lenses, dielectric end mirrors, an inject mirror measuring $H \sim n\,d\,\theta ,$9, and a $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$0 rectangular eject mirror. The beam diameter in the cavity is $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$1, and the wavelength range used is $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$2–$G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$3 nm (Jayakumar et al., 22 Sep 2025).

The principal reported results are succinctly summarized in the abstract: ReLOAD is used to accomplish $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$4 amplification of electro-optical deflection, and the system demonstrates $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$5 kHz frame rate imaging, $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$6 MHz line scan rate, and $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$7s step times across an addressable space well beyond the capabilities of typical electro-optical deflectors (Jayakumar et al., 22 Sep 2025). In the detailed experimental report, a single-pass test at $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$8 kHz sinusoidal drive and $G = \iint n^2\,\mathrm{d}A\,\mathrm{d}\Omega .$9 V$n d \theta$0 yielded $n d \theta$1 resolvable spots, whereas the $n d \theta$2 EO-ReLOAD output yielded $n d \theta$3 resolvable spots, corresponding to an effective improvement of about $n d \theta$4 in resolvable spot count (Jayakumar et al., 22 Sep 2025).

A separate diagnostic, based on imaging leakage through an end mirror, showed that the deflection angle increases linearly with loop number, supporting the claim that angle amplification itself is near-ideal and that the shortfall in resolvable spots is caused by spot-size growth rather than failure of angular accumulation (Jayakumar et al., 22 Sep 2025). The step response measured with a $n d \theta$5 V rectangular drive gave a step time of $n d \theta$6 across a distance equivalent to $n d \theta$7 resolvable spots within $n d \theta$8 EO-ReLOAD, with the limitation attributed to drive electronics bandwidth (Jayakumar et al., 22 Sep 2025).

For reflectance imaging, the EO-ReLOAD output was relayed to a mirror galvanometer for orthogonal scanning. With the electro-optic deflector driven at $n d \theta$9 kHz, corresponding to $\mathrm{FOV} \approx 2 f\,\tan \theta ,$0 MHz bidirectional line rate, and the galvanometer at $\mathrm{FOV} \approx 2 f\,\tan \theta ,$1 kHz, corresponding to $\mathrm{FOV} \approx 2 f\,\tan \theta ,$2 kHz bidirectional frame rate, the system achieved $\mathrm{FOV} \approx 2 f\,\tan \theta ,$3 MHz line rate and $\mathrm{FOV} \approx 2 f\,\tan \theta ,$4 kHz frame rate imaging of a metal mask using a standard femtosecond laser at $\mathrm{FOV} \approx 2 f\,\tan \theta ,$5 nm and commercial ScanImage acquisition (Jayakumar et al., 22 Sep 2025).

5. Performance limitations, trade-offs, and implementation constraints

Although angle amplification is reported to be near-ideal, resolvable-spot scaling is limited by cumulative aberrations, vignetting, and cavity loss. In the demonstrated $\mathrm{FOV} \approx 2 f\,\tan \theta ,$6 EO-ReLOAD prototype, the ideal prediction of approximately $\mathrm{FOV} \approx 2 f\,\tan \theta ,$7 resolvable spots contrasts with the measured $\mathrm{FOV} \approx 2 f\,\tan \theta ,$8, and the explanation given is increased spot size due to aberrations rather than reduced angular multiplication (Jayakumar et al., 22 Sep 2025).

Three non-idealities are highlighted. First, cumulative aberrations arise because the beam traverses the relay lenses and the KTN-plus-cylindrical-optics assembly multiple times; misalignment or non-telecentricity of the scan lenses produces beam shifts at the crystal edges and field-dependent aberrations. The reported consequence is that average spot FWHM increases by approximately $\mathrm{FOV} \approx 2 f\,\tan \theta ,$9 with ReLOAD (Jayakumar et al., 22 Sep 2025). Second, unanticipated vignetting at the crystal edges causes spot intensity to decrease by up to $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$0 from the center to the edge of the deflection range, reducing throughput and broadening the effective spot at wide angles (Jayakumar et al., 22 Sep 2025). Third, multi-pass cavity losses accumulate, and the overall measured power throughput for $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$1 EO-ReLOAD is reported as approximately $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$2 (Jayakumar et al., 22 Sep 2025).

The acceptance-angle analysis also constrains scalability. In the electro-optic implementation, the commercial scan lenses provided $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$3 mrad, with $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$4 mrad and $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$5 mrad, so the deflection-axis acceptance limited the ideal maximum loop count to $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$6. The actual choice $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$7 is presented as a compromise that preserves reasonable throughput (Jayakumar et al., 22 Sep 2025).

The design guidance is correspondingly specific. Telecentric scan lenses are described as critical, and custom lenses with tighter telecentric tolerances are suggested as an avenue for improved performance. Precise $$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$8-$$\text{Spot diameter}_{1/e^2} \approx \frac{4}{\pi} \frac{f}{d}\,\lambda .$$9 relay spacing, correct placement of the deflector at the common afocal plane, and accurate cylindrical correction of the KTN GRIN focusing are all stated to be important for avoiding astigmatism, vignetting, and field-dependent blur (Jayakumar et al., 22 Sep 2025). This suggests that ReLOAD trades deflector-limited optical invariant for a more demanding system-level alignment and relay-design problem.

6. Relation to earlier amplified-deflection and looped optical architectures

ReLOAD is not isolated from prior work on optically amplified deflection; rather, it intersects several earlier lines of research. One is weak-value amplification in dispersive media. In a four-level tripod EIT medium with a transverse magnetic-field gradient, the 2013 study of weak-value amplification derives an effective polarization-dependent linear potential and a weak-value-amplified displacement

$8\times$00

with the amplification arising from preselection, weak coupling, and postselection of polarization states (Zhou et al., 2013). That work characterizes the result as an optically amplified deflection mechanism rooted in interference and wavepacket reshaping (Zhou et al., 2013). ReLOAD differs in architecture and operating principle: it multiplies deflection by repeated relaying in a cavity rather than by weak-value postselection. A plausible implication is that both schemes increase observable beam displacement without increasing the primitive single-interaction deflection, but they do so through distinct mechanisms.

A second antecedent is stored-light beam steering. In thermal $8\times$01Rb vapor, non-dispersive deflection is produced by storing a pulse as a spin wave, imprinting a transverse phase gradient during storage, and retrieving the light so that the phase gradient becomes an output angle

$8\times$02

This stored-light deflection is reported to be non-dispersive and to suppress chromatic aberration by ten orders of magnitude relative to propagating slow-light Stern–Gerlach deflection (Karpa et al., 2010). The conceptual connection to ReLOAD is that both rely on repeated or staged optical-state manipulation to convert a small controllable internal action into a larger deflection at readout. The data explicitly state that a ReLOAD-type architecture could be analyzed by chaining such storage–phase–retrieval stages (Karpa et al., 2010).

A third relevant line is recursive integrated photonics. The 2025 integrated recursive electro-optic circuit in thin-film lithium niobate uses a switch-coupled loop in which an optical packet can be kept inside the loop or released, allowing repeated traversal of an embedded processing block. The architecture demonstrates up to $8\times$03 roundtrips, frequency shifts up to $8\times$04 GHz using a $8\times$05 GHz sinusoidal microwave signal, a recursive delay line with $8\times$06 ps/nm group delay over a $8\times$07 nm optical bandwidth, and reconfigurable differentiation up to fifth order (Li et al., 29 Sep 2025). That platform is described as a recursive optical signal processing framework rather than a beam-deflection system, but it provides a concrete integrated realization of looped reuse of a single operation block. This suggests a structural analogy to ReLOAD: repeated traversal through a compact optical element can synthesize an effective interaction much larger than the single-pass primitive.

A fourth comparison is interferometric amplification of minute deflection signals. In the 2024 DeLLight pilot experiment, a Sagnac interferometer transforms a direct geometric shift $8\times$08 into an amplified dark-port displacement

$8\times$09

The measured example gives $8\times$10 nm, $8\times$11 nm, and $8\times$12 (Kraych et al., 2024). DeLLight amplifies the readout of an extremely small nonlinear deflection interferometrically, whereas ReLOAD amplifies the physical scan angle by repeated relaying. The commonality is that both seek increased useful deflection without requiring a proportionally larger primitive deflector response.

Finally, at the quantum-memory level, a 2020 proposal for storing and redirecting light at the photon level shows that a spin-wave wavevector can be modified by a magnetic-field gradient so that retrieved light exits in a new direction determined by the altered phase-matching condition (Korzeczek et al., 2020). The proposal states that efficiencies comparable with forward retrieval can be achieved for arbitrary deflection angles in the plane and that the routing time scale is on the order of few to $8\times$13 microseconds depending on deflection angle (Korzeczek et al., 2020). This is not ReLOAD in the cavity-relay sense, but it shows that repeated storage-and-redirection stages could serve as a relayed optical routing substrate in another physical regime.

7. Applications, scope, and interpretation

The 2025 ReLOAD work presents the architecture as a way to extend high-speed scanning into regimes normally inaccessible to the underlying deflector. The experimental demonstration emphasizes electro-optical deflection because electro-optic deflectors have unparalleled speed but limited optical invariant (Jayakumar et al., 22 Sep 2025). The achieved $8\times$14 kHz frame rate imaging, $8\times$15 MHz line scan rate, and $8\times$16s step times are therefore significant not as evidence of a faster primitive deflector, but as evidence that the same primitive deflector can address a much larger effective space through relay-cavity reuse (Jayakumar et al., 22 Sep 2025).

The paper explicitly identifies applicability to transmissive and reflective deflectors, and it names potential use domains including ultrafast multiphoton microscopy, 3D nanomanufacturing and multiphoton lithography, trapped-ion quantum computing, OCT, LIDAR, and laser scanning cytometry (Jayakumar et al., 22 Sep 2025). In each case, the relevant bottleneck is the trade-off between speed and optical invariant. ReLOAD addresses that bottleneck optically rather than mechanically or electronically.

At the same time, the reported limitations delimit the present scope. The measured improvement in resolvable spots is substantial but not equal to the nominal $8\times$17 angle multiplication because cumulative aberrations and vignetting degrade spot quality (Jayakumar et al., 22 Sep 2025). Throughput is also low in the current prototype, at approximately $8\times$18 for $8\times$19 EO-ReLOAD (Jayakumar et al., 22 Sep 2025). These constraints indicate that ReLOAD is best understood as an architectural method whose practical utility depends on high-quality relay optics, careful telecentricity control, and loss management.

Taken together, the available literature places ReLOAD within a broader category of optically amplified deflection schemes while making its defining principle precise: repeated relaying of the same beam through the same deflector inside a cavity causes the output angle, optical invariant, and scan throughput to scale with loop count $8\times$20, subject to acceptance-angle, aberration, and throughput limits (Jayakumar et al., 22 Sep 2025). This suggests that ReLOAD is less a single device than a general optical strategy for converting unused relay-space degrees of freedom into additional effective deflection.