Topology -enabled highly efficient beam combination Yuhao Jing 17 Yucong Yang 237 Wei Yan 23 Songgang Cai 23 Jiejun Su 23 Weihan Long 4 Nuo Chen 1 Yu Yu 156 Lei Bi23 Yuntian Chen156

2025-05-06 0 0 1.04MB 15 页 10玖币

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Topology-enabled highly efficient beam combination

Yuhao Jing, 1,7 Yucong Yang, 2,3,7 Wei Yan, 2,3 Songgang Cai, 2,3 Jiejun Su, 2,3 Weihan Long, 4

Nuo Chen, 1 Yu Yu, 1,5,6 Lei Bi2,3 & Yuntian Chen1,5,6

Beam combination with high efficiency is desirable to overcome the power limit of single

electromagnetic sources, enabling long-distance optical communication and high-power laser. The

efficiency of coherent beam combination is severely limited by the phase correlation between

different input light beams. Here, we theoretically proposed and experimentally demonstrated a new

mechanism for beam combining, the topology-enabled beam combination (TEBC), from multiple

spatial channels with high efficiency based on a unidirectional topological edge state. We show that

the topologically protected power orthogonal excitation arising from both the unidirectional edge

states and the energy conservation ensures -0.31dB (93%) efficiency experimentally for a multi-

channel combination of coherent microwaves at 9.1-9.3 GHz. Moreover, we demonstrate broadband,

phase insensitive, and high-efficiency beam combination using the TEBC mechanism with one

single topological photonic crystal device, which significantly reduces the device footprint and

design complexity. Our scheme transcends the limits of the required phase correlations in the

scenario of coherent beam combination and the number of combined channels in the scenario of

incoherent beam combination.

1School of Optical and Electronic Information, Huazhong University of Science and Technology,

Wuhan, 430074, China.

2National Engineering Research Centre of Electromagnetic Radiation Control Materials, University

of Electronic Science and Technology of China, Chengdu 610054, China.

3State Key Laboratory of Electronic Thin-Films and Integrated Devices, University of Electronic

Science and Technology of China, Chengdu 610054, China.

4School of Electronic Science and Engineering, University of Electronic Science and Technology

of China, Chengdu 610054, China.

5Wuhan National Laboratory of Optoelectronics, Huazhong University of Science and Technology,

Wuhan, 430074, China.

6Optics Valley Laboratory, Hubei 430074, China.

7These authors contributed equally: Yuhao Jing, Yucong Yang.

Correspondence and requests for materials should be addressed to Y. Y. (email:

yuyu@mail.hust.edu.cn), L. B. (email: bilei@uestc.edu.cn), or to Y. T. C. (email:

yuntian@hust.edu.cn)

Introduction

Power scaling of electromagnetic radiation is a demanding technology for many applications,

including laser particle accelerators1–6, advanced materials processing7–10, and medical treatment11.

In microwave frequency, the high-power systems12 also have high potential applicability in areas

such as directed energy, space-to-earth energy transfer13, and high-power radar. Notably, the power

scaling of the single laser systems has encountered several physical limitations14–16, thus beam

combination of multiple output power of laser systems has been the first measure to boost the power

level. As for continuous waves, beam-combining technology can be categorized into coherent or

incoherent beam combinations. The coherent beam combination essentially relies on the carefully

delayed and locked phase of each combination channel for either tiled aperture or filled aperture

geometries to maintain mutual coherence in both space and time.17–24 Despite significant advances

in recent years25–33, this technology relies on complicated feedback and control systems. For

monochromatic incoherent beam combinations, the passive combiner, such as polarization beam

splitters34, has a very limited number of input channels that maintain power orthogonality. In this

regard, it is important to develop a beam combination strategy that can operate without complicated

feedback and simultaneously admit multiple input channels.

In this work, we report an unprecedented strategy to realize a highly efficient electromagnetic

beam combination enabled by topologically protected scattering-free edge states35–40, namely the

topology-enabled beam combination (TEBC). As sketched in Fig. 1(a), the principle of bulk-edge

correspondence guarantees the existence of the unidirectional edge state, the direction of which

depends on the relative values of topological invariants of the associated bulk materials. As such,

one can pack the topologically different bulk materials in a spiral fashion by cascading down their

Chern numbers, as shown in Fig. 1(b). Highly efficient beam combination can be realized for all the

boundary states, since each input channel is scattering-free and only supports one forward

propagating state. The edge states are robust against the material or structure imperfections as long

as the band gaps are open. Thus, the electromagnetic power flows from N-input channels to a single

output channel due to the absence of backward propagating states. The topologically protected

power orthogonal excitation ensures that the output modes, excited by any input sources, are

pairwisely orthogonal in power basis. We first illustrate our idea using a Y-shaped combiner formed

by three topologically distinct photonic crystals, where the theoretical prediction perfectly agrees

with numerical calculations. Based on the same underlying principle, we design and fabricate a 3×1

combiner containing four topologically distinct photonic crystals, with experimental beam

combination efficiency upper to 93%.

Results

Beam combination model based on spiral-staircase topology. In topology-related physics, a

significant result is the existence of gapless edge states localized at the interface as the topological

invariant of two neighbor bulk materials changes. In two-dimensional (2D) systems, the topological

invariant is usually coined as Chern number and calculated by integrating Berry curvature over the

entire 2D Brillouin zone41,42. Implied by the stability of the topology associated with the Bloch

modes across the entire Brillouin zone, the chiral edge state is robust against small perturbations,

i.e., without closing or opening the bandgap. In the topological scenario, the broken of time-reversal

symmetry at the Dirac point brings a massive Dirac Hamiltonian,  , where

the mass term  flips sign across two topologically different bulk materials38. At the interface,

 has an elegant stationary solution given by , where group velocity 

 and the sign of  determines the chirality of edge states. Although  could

develop a kink, the number of edge states is fully determined by the topological structure of the bulk

states, which has been dictated by the bulk-boundary correspondence. Specifically, the gap Chern

numbers of two neighboring bulk photonic crystals are  and  respectively, the difference and

its sign, i.e.,  , essentially determines the number and propagation direction of edge

states, as shown in Fig. 1(a).

The general principle of our topology-enabled beam combination is sketched in Fig. 1(b),

which shows a spiral staircase distribution of gap Chern number of topologically different bulk

materials. Each stair interface plays the role of one input channel and only supports one chiral edge

state, while the cliff spatial channel acts as the output port, as indicated by the red and blue arrows,

respectively. The total input energy is forced to combine at the output port, as guaranteed by both

the chirality of edge states and the law of energy conservation. More importantly, the topological

property for scattering-free edge states renders the beam combination phase-insensitive. The number

of beam combination channels is determined by the difference in the gap Chern number across the

cliff interface. It shows the advantage against the incoherent beam combination between orthogonal

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Topology-enabledhighlyefficientbeamcombinationYuhaoJing,1,7YucongYang,2,3,7WeiYan,2,3SonggangCai,2,3JiejunSu,2,3WeihanLong,4NuoChen,1YuYu,1,5,6LeiBi2,3&YuntianChen1,5,6Beamcombinationwithhighefficiencyisdesirabletoovercomethepowerlimitofsingleelectromagneticsources,enablinglong-distanceopticalcommun...

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Topology -enabled highly efficient beam combination Yuhao Jing 17 Yucong Yang 237 Wei Yan 23 Songgang Cai 23 Jiejun Su 23 Weihan Long 4 Nuo Chen 1 Yu Yu 156 Lei Bi23 Yuntian Chen156

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