Optical vortex generation by magnons with spin-orbit-coupled light

The gist: This study demonstrates that breaking time and spatial symmetries through magnons and light focusing transforms an input Gaussian beam into a specific optical vortex beam in a nonreciprocal manner

Optical Vortex Generation by Magnons

The researchers report the first experimental realization of the nonreciprocal transformation of an input Gaussian beam into a specific optical vortex beam, achieved through the combined temporal and spatial asymmetries induced by magnons and light focusing This phenomenon is quantitatively explained by integrating the physics of magnon-induced Brillouin light scattering with optical spin-orbit coupling The experiment involved exciting a uniform magnetostatic mode, known as the Kittel mode [37, 38], in a ferromagnetic spherical monocrystal of yttrium iron garnet (YIG) A circularly polarized Gaussian beam was incident onto the ferromagnetic sphere and gently focused using a convex lens Within the sphere, tightly focusing and divergence occur, causing the propagating light to behave as non-paraxial light The results confirm that the total angular momentum between photons and magnons is conserved in all observed phenomena

Mechanism of Optical Vortex Generation

Optical vortex generation arises from transitions between spin-orbit-coupled modes within the sphere, which occur only when OAM is identical and magnons can mediate SAM changes The input-paraxial-light mode is transformed into a superposition of spin-orbit-coupled light (non-paraxial light) modes through refraction at the spherical surface The interaction between uniform-mode magnons possessing only SAM sm = 1 allows transitions between the spin-orbit-coupled modes sharing the same OAM but differing by SAM of 1 For example, scattering from LG0,+1 to LG′+1,+1 in the far field occurs due to a transition from LGSO+1,0 to LG′SO+1,+1 within the YIG sphere The efficiency is described by a combination of quantities related to the optical spin-orbit coupling and the magneto-optic effect

Conservation Laws and Nonreciprocity

The scattering processes that satisfy total angular momentum conservation in Eq. (1) are allowed, where the change in total angular momentum is written as ∆sm + ∆sp + ∆lp = 0 In helicity-conserving scattering, angular momenta exchange only between magnon SAM and photon OAM The nonreciprocal scattering behavior shown in Figs. 3 and 4 results from the breaking of time-reversal symmetry by the external magnetic field When a quantization axis is defined along the light propagation direction, the magnon SAM sm changes its sign [42] depending on whether the light propagation is parallel or antiparallel to the magnetic ordering direction, which itself is aligned with the external magnetic field

Theoretical Framework and Efficiency Calculation

The key to quantitatively understanding observed scattering lies in the optical spin-orbit interaction acting concurrently with the magneto-optic effect The electric field of non-paraxial light focused by a convex lens is expressed in terms of Laguerre-Gauss modes LGlp,sp The efficiency for a specific transition process is calculated by considering the quantization of the classical interaction Hamiltonian [41] and using the boundary condition between scattered photon flux and magnon number The overall scattering efficiency involves two pathways via Brillouin light scattering within the YIG sphere, with one pathway being five orders of magnitude larger than the other

Future Prospects

The optical vortex-generating BLS enables magneto-optical studies utilizing scattering rules for any magnetic materials Magnons with linewidths exceeding megahertz can change the BLS they mediate at equivalent speeds, offering a new approach to addressing the former challenge of high-speed OAM modulation The exploration of the physics governing the BLS induced by magnons in such magnetic vortex modes is an interesting near-term prospect This optical vortex-generating BLS is free from the constraint that helicity-changing BLS required magnetic materials to possess in-plane threefold rotational symmetry The phenomenon opens a new panorama for topological photonics, optomagnonics, and chiral quantum optics

How it works

The input Gaussian beam is transformed into a superposition of spin-orbit-coupled light modes through refraction at the spherical surface Within the sphere, transitions between spin-orbit-coupled light modes generate optical vortices when magnons mediate SAM changes The conservation of total angular momentum encompasses both magnons and photons, indicating that magnons can control both spin and orbital angular momentum of light

How it works

The scattering process is modeled by a three-wave mixing process involving one magnon and two photons, where the change in total angular momentum is written as ∆sm + ∆sp + ∆lp The observed helicity-conserving scattering processes satisfy total angular momentum conservation, meaning angular momenta exchange only between magnon SAM and photon OAM The nonreciprocal nature arises because the magnon SAM changes sign depending on the direction of light propagation relative to the magnetic ordering direction

How it works

The scattering efficiency for a transition process is calculated by considering the product of the energy partitioning ratio between far-field and spin-orbit-coupled light during two refractions at the sphere surface, and the BLS efficiency within the YIG sphere The calculated efficiencies reproduce experimental results, with theoretical values agreeing well with literature values for various scattering processes

How it works

The nonreciprocal scattering behavior is qualitatively explained by the sign reversal of magnon SAM when a quantization axis is defined along the light propagation direction This sign reversal in the context of angular momentum conservation provides a qualitative explanation for the nonreciprocity of observed scattering processes

How it works

The low efficiency observed for certain scattering combinations, such as (∆sm, ∆sp, ∆lp) = (+1, +2, −3), is attributed to its low efficiency rather than a lack of observation The theoretical framework supports the existence of this scattering but estimates its efficiency to be 7.1 × 10−28 This occurs via transitions between spin-orbit-coupled modes indicated by the second term on the right-hand side of Eq. (D4) The lack of observation is due to its low efficiency

How it works

The phenomenon enables dynamic modulation of the OAM of propagating light using magnons, offering a new approach to addressing the challenge of high-speed OAM modulation Magnons with linewidths exceeding megahertz can change the BLS they mediate at equivalent speeds This suggests that magnon-based optical vortex generation could be controlled with response speeds exceeding megahertz

How it works

The scattering efficiencies are reproduced entirely by the theoretical framework outlined, and polarization-dependent efficiency differences agree well with theoretical values derived from literature and known values The theory also reproduces the absolute values of efficiencies, confirming its validity across all observed scatterings

How it works

The nonreciprocal scattering behavior is shown in Figs. 3 and 4 by reversing the direction of the external magnetic field, which reverses the sign of ∆sm associated with Stokes or anti-Stokes scattering Comparison between Figs. 3 and 4 confirms the nonreciprocal nature of this phenomenon The order of magnitude of allowed scattering processes in Figs. 4 is the reverse of the result in Figs. 3

How it works

The overall scattering efficiency for vortex-Stokes scattering is calculated by summing two pathways, and the leading 1/2 in both terms reflects that the excited magnons contribute to this process The combination of probabilities for transitions between spin-orbit-coupled modes superimposes to give the overall scattering efficiency

How it works

The conservation laws of energy and SAM between light and magnons during BLS are implied by the Hamiltonian equations (D27) and (D28) The probability ησ′σ that single magnon scatters an input spin-orbit-coupled-photon mode into another is described as ησ′σ = ζσ′σ 2π / Pσ ħomega0 −1 This dimensionless probability is determined by the product of the energy partitioning ratio and the BLS efficiency within the YIG sphere

How it works

The scattering efficiencies for all other cases can be calculated using the same procedure as those shown with gray arrows in Figs. 3(a)-3(d) Table III summarizes these calculated and experimental efficiencies for all scatterings observed in Figs. 3(a)-3(d) that are labeled with gray arrows The scattering efficiencies for all other cases can be calculated using the same procedure as those shown with gray arrows in Figs. 3(a)-3(d) Table III summarizes the calculated and experimental efficiencies for all scatterings observed in Figs.

1. Better modeling of nonreciprocal light transformation in optical systems using Equation (D4) and (D5). This improved model will allow AI systems to predict how an input Gaussian beam transforms into a specific optical vortex beam based on aperture angle, accounting for both spin-orbit coupling and the magneto-optic effect.

2. Quantitative prediction of scattering efficiencies based on the full theoretical framework described in Appendix D. The AI system will be able to calculate the overall scattering efficiency of the optical-vortex-Stokes scattering by combining the transition pathways as shown in Equation (D37).

3. Design of novel magnetic materials for topological photonics by optimizing parameters related to Faraday and Cotton-Mouton coefficients. The AI can use the derived relationships between these coefficients and experimental results to predict which material properties will yield specific scattering outcomes, enabling the design of materials that enable magneto-optical studies utilizing scattering rules for any magnetic materials.

4. Control of optical angular momentum in communications by predicting the required response speeds for magnon-based vortex generation. The AI can leverage the finding that Magnon-based optical vortex generation could be controlled with response speeds exceeding megahertz to design control schemes for high-speed OAM modulation.