SPICE Workshop on Spin textures: Magnetism meets Plasmonics, July 23rd - 25th 2024
Ady Arie
The dynamics of nonlinear sum frequency generation is analogous to spin current dynamics in magnetic fields [1]: the signal and idler complex amplitudes represent the two-dimensional spinor; the nonlinear coupling represents the strength and direction of the magnetization; and the transverse Laplacian of the beams represent the kinetic energy. Spin-up and spin-down is represented by signal-idler waves in-phase or out-of-phase. The control over the effective magnetization can be done by modulating the second-order nonlinear coefficient of ferroelectric crystals, either by electric field poling or by laser-induced writing [2].
This analogy can be useful for many different applications: Broadband frequency conversion; accumulation of geometric phase [3] and its application for non-reciprocal and asymmetric beam focusing [4]; spin-dependent deflection of signal-idler beams, representing the nonlinear-optics analogue of the Stern-Gerlach effect [5]; all-optical topological Hall effect in skyrmionics nonlinear photonics crystals [6]; and emulation of spin currents in disordered nonlinear crystals, representing the optical analogues of spin glass.
Moreover, we can realize new nonlinear optical devices that control the signal-idler pseudospin. These devices will act differently if the signal and idler waves are in-phase or put-of phase. Based on this concept we have recently studied all-optical spin valve [7], spin filters and spin waveguides. The spin valve is a device that can either transmit or reflect signal-idler beams that are in-phase, by turning on/off a control pump beam. Furthermore, the nonlinear structure can be configured to act as a spin filter that transmits in-phase signal-idler beams and reflects the out-of-phase signal-idler beams. A spin waveguide is a device that can guide signal-idler beams in a nonlinear photonic crystal, but only if they are in-phase. We have recently observed this effect experimentally in a KTP nonlinear photonic crystal.
The realization of optical analogies of the spintronic devices is not limited to the spatial domain, and can be also observed in the time domain [8], by relying on the well-known similarities between the diffraction of optical beams in space and the dispersion of optical pulses in time [9]. Specifically, we have observed the Stern-Gerlach effect for light pulses, using four-wave-mixing (with two pump pulses, a signal pulse and an idler pulse) in a 1 km long single-mode optical fiber. When these signal-idler pulses were in-phase (the 'spin-up' case), both of them were up-shifted in frequency, whereas when they were out-of-phase ('spin-down'), both of them were down-shifted in frequency.
[2] Y. Zhang, Y. Sheng, S. Zhu, et al., Optica 8, 372 (2021).
[3] A. Karnieli, Y. Li and A. Arie, Front. Phys. 17, 12301 (2022)
[4] A. Karnieli, S. Trajtenberg-Mills, G. Di Domenico and A. Arie, Optica 6, 1401 (2019)
[5] O. Yesharim et al, Nature Photonics 16, 582 (2022).
[6] A. Karnieli, S. Tsesses, G. Bartal and A. Arie, Nature Comm. 12, 1092 (2021)
[7] S. Izhak, A. Karnieli, O. Yesharim, S. Tsesses and A. Arie, Opt. Lett. 49, 1025 (2024)
[8] B. H. Kolner and M. Nazarathy, Opt. Lett. 14, 630 (1989).
[9] G. Bashan, A. Eyal, M. Tur and A. Arie, Optics Express, to be published (2024)