The optomechanical Kerker effect: Controlling light with vibrating nanoparticles

For the Kerker effect to occur, particles need to have electric and magnetic polarizabilities of the same strength. This, however, is very challenging to achieve, as magnetic optical resonances in small particles are relatively weak. Researchers at Ioffe Institute, in St. Petersburg, have recently shown that a similar effect can be attained when small particles are trembling in space.

"Even though the light scattering has been understood for more than a century after the works of Rayleigh, Raman, Landsberg and Mandelstam, it remains both a fundamental and applied challenge to route light scattered at the nanoscale in the direction at will," Alexander Poshakinskiy, one of the researchers who carried out the study, told Phys.org. "The ability to control the direction, frequency and polarization of the scattered light is essential for operation of optical circuits."

Devices that can control the direction of scattered light could have numerous useful applications, particularly for the operation of antennas and routing of light. In the 1980s, researchers theorized that a directional scattering of light can be achieved via the so-called Kerker effect. This effect essentially exploits the interference of electric and magnetic dipole emission patterns, which have different spatial parity, yielding the suppression of forward or backward scattering when they are superposed.

"Realization of the conventional Kerker effect requires the particles to have electric and magnetic polarizabilities of the same strength," Poshakinskiy said. "However, this is challenging because magnetic response at optical frequencies is extremely weak. A possible workaround is to use large submicron-size nanoparticles hosting both electric and magnetic Mie resonances. However, optical Kerker effect for the particles smaller than the wavelength in the medium is still unfeasible. In our work, we show that even small particles, that lack magnetic response when at rest, do acquire it when they start trembling in space, enabling realization of what we call optomechanical Kerker effect."

In the optomechanical Kerker effect, proposed by Poshakinskiy and his colleague Alexander Poddubny, the tunable directional scattering of light is attained for a particle that lacks magnetic resonances as it trembles in space. The trembling motion of the electric dipole in space leads to the appearance of a magnetic dipole, as one could expect from the Lorentz transformation.

"We show that magnetic and electric dipole induced in the trembling particle by incident light counterintuitively are of the same order when inelastic scattering is considered," Poshakinskiy explained. "The phase difference between the electric and magnetic dipoles is governed by the frequency dependence of the particle permittivity. For a resonant particle, this enables control of the scattering direction via the detuning of light frequency from the resonance: The light is scattered preferably forward at resonance and backward away from it. "

The researchers show that in the optomechanical Kerker effect, the figure of merit that quantifies how much of the light is scattered in a particular direction compared to all other directions (i.e. directivity), can be as high as 5.25. This exceeds the directivity of 3 attained in the classical Kerker effect, due to the additional electric quadrupole momentum induced by the mechanical motion.

In their study, Poshakinskiy and Poddubny also introduced a second effect, which they refer to as 'the optomechanical spin-Hall effect.' In this effect, a directional inelastic scattering of light, depending on its circular polarization, is realized for a small trembling particle.

"The optomechanical spin-Hall effect can be achieved when a particle vibrates around a circular trajectory rather that a straight line," Poshakinskiy said. "We show that the angular mechanical momentum of the particle can be transferred to the spin of light. Then the electromagnetic waves scattered by the trembling particle to the left and to the right attain opposite circular polarization."

The findings gathered by Poshakinskiy and Poddubny suggest that the interaction between light and mechanical motion has an intrinsically multipolar nature. This quality could be exploited in a variety of systems, ranging from cold atoms to two-dimensional materials and superconducting qubits.

"We believe that the proposed optomechanical Kerker opens a new multidisciplinary field by uncovering, for the first time, to our knowledge, a highly untrivial link between optomechanics and nanophotonics," Poshakinskiy said. "From a practical point of view, the proposed effects can be used to design non-reciprocal nanoscale optical devices."

Optical non-reciprocity, meaning that light is transmitted forward and backward through an optical circuit differently, is crucial for optical signal processing. Most existing non-reciprocal optomechanical devices are based on optical resonators, which limit their minimal size to sub-microns. The results collected by Poshakinskiy and Poddubny show that tunable optomechanical non-reciprocity can also occur at nanoscale when using small trembling particles with resonant polarizability.

"Optical non-reciprocity is also a key ingredient for the design of photonic topological circuits," Poshakinskiy added. "In an array of trembling particles, one can expect a disorder-robust propagation of light and sound, ensured by the time modulation of optical and mechanical properties."

The study carried out by Poshakinskiy and Poddubny shows how the tunable directional scattering of light can be achieved at nanoscale, introducing the optomechanical Kerker and spin-Hall effects. In the future, their findings could have several interesting applications, for instance, informing the design of non-reciprocal topological circuits. The researchers are now planning to demonstrate the optomechanical Kerker effect in lab experiments.

"The proof of concept would be observation of the directional backscattering by trembling objects, which can be realized even away from material resonances," Poshakinskiy said "We believe that this can be done in a variety of systems e.g., semiconductor quantum dots, transitional metal dichalcogenides or graphene. However, the key feature of the optomechanical Kerker effect is the possibility to switch the direction of scattering between forward and backward. This requires particles with extremely sharp resonances in their electromagnetic response. Our estimations show that such switching can be realized for cold atoms in optical traps or superconducting qubits in radio-frequency circuits."

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