Polarization-Controlled Circular Second-Harmonic Generation from Metal Hole Arrays with Threefold Rotational Symmetry

Konishi, Kuniaki; Higuchi, Tohru; Li, Jia; Larsson, Jakob C.; Ishii, Shuntaro; Kuwata‐Gonokami, Makoto

doi:10.1103/physrevlett.112.135502

Cited by 122 publications

(107 citation statements)

References 34 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…For a circularly polarized FW propagating along the three-fold axis of a c-cut β-BBO crystal, we find that the SHG signal with the same polarization state as the FW (LCP-LCP and RCP-RCP) is much weaker than that with the polarization state opposite to the FW (LCP-RCP and RCP-LCP). This agrees well with the selection rules for harmonic generations of circularly polarized light demonstrated in previous works [29][30][31][32][33][34][35] . Theoretically, SHG of the same spin as the FW should be forbidden for a crystal with C3 rotational symmetry.…”

supporting

confidence: 79%

“…Although equation (4) shows that the Doppler shift is directly related to the harmonic generation order, the rotational symmetry of the nonlinear crystal also plays an important role. The reason is that crystals of certain rotational symmetry allow only nonlinear processes of certain orders according to the selection rule pertaining to harmonic generations with circularly polarized FWs 33,34 . Specifically, it has been shown that the allowed nonlinear generation orders are given by n = ml ± 1, where m is the rotational symmetry order, l is an arbitrary positive integer, and '+' and '−' signs correspond to the harmonic generation signal with the same and the opposite circular polarization as that of the fundamental beam, respectively 33 .…”

mentioning

confidence: 99%

“…For a circularly polarized FW that propagates along the rotation axis of a nonlinear optical crystal with three-fold rotational symmetry, only SHG with opposite circular polarization compared with the FW is allowed [29][30][31][32][33][34][35] . Hence, for a rotation frequency Ω of the nonlinear optical crystal along its rotation axis (Fig.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Rotational Doppler effect in nonlinear optics

2016

View full text Add to dashboard Cite

The translational Doppler e ect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies [1][2][3][4][5][6][7][8] , and for the Global Positioning System. The Doppler e ect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms 9 and has benefited cooling and trapping of atoms with laser light [10][11][12] . Despite numerous successful applications of the translational Doppler e ect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves 13-the so-called rotational Doppler e ect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.A beam of light with spin angular momentum (SAM) σ (σ = ±1), which corresponds to either left or right circular polarization (LCP and RCP) states respectively, flips its spin when it passes through a rotating half-wave plate (HWP). In this process, the circularly polarized light applies a torque on the HWP (refs 14,15) and in return experiences a frequency shift 16 . For circularly polarized light propagating along the normal axis of a rotating HPW at angular frequency Ω, it was predicted and experimentally confirmed that the transmitted circularly polarized light with the opposite sense has a frequency shift of ±2Ω (Fig. 1a), where the + and − signs correspond to the rotation direction of the HWP, being the opposite or same as that of the circularly polarized incident light [16][17][18][19] . In recent years, the rotational Doppler effect has been successfully used for probing and controlling the rotation of molecules 20 , and studying rotating quantum systems 21,22 . Recently, the observation of the rotational Doppler effect has been extended to light with orbital angular momentum [23][24][25][26][27][28] , which has shown the capability of remotely measuring the rotational frequency of a spinning object, such as air turbulence, rotating astronomical bodies and so on 27 . Compared with the rapid development and applications of the rotational Doppler effect in linear optics, it has received much less attention in the nonlinear optical regime since it was first predicted for second harmonic generation (SHG) processes more than four decades ago 29 . So far, t...

show abstract

supporting

confidence: 79%

mentioning

confidence: 99%

See 1 more Smart Citation

Rotational Doppler effect in nonlinear optics

2016

View full text Add to dashboard Cite

show abstract

“…Typical examples includes L-shaped gold nanoparticle [142,143], T-shaped nanoparticle [144], split-ring resonator (SPR) with electric or magnetic dipole resonance [145][146][147], and silver triangular nanoprisms and nanoholes [148,149]. A symmetry-breaking metasurface not only significantly enhances its nonlinear optical response but also shows strong spin-selectivity in the nonlinearly generated light [150]. Polarization-dependent selection rules for high harmonic generations on a metasurface have also been extensively studied [151].…”

Section: Symmetry-related Applications With Spin-orbit Interactionmentioning

confidence: 99%

Spin-dependent optics with metasurfaces

et al. 2016

View full text Add to dashboard Cite

Optical spin-Hall effect (OSHE) is a spindependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components.

show abstract

“…[24][25][26][27][28] It has already been demonstrated that for a circularly polarized fundamental wave (FW) propagating along the axis of molecules or artificial nanostructures with n-fold rotational symmetry, the allowed order (m) of harmonic generation can be determined from a selection rule m = nl ± 1, where l is an arbitrary integer, and the "+" and "-" signs represent that harmonic generation and FW possess the same and opposite circular polarization states, respectively. [29][30][31] In our case, the gammadion-shaped meta-atoms have four-fold rotational (C4) symmetry, and are arranged in a square lattice such that the symmetry of the structures and the lattice are consistent with each other [ Fig. 1(a)].…”

confidence: 99%

Controlling third harmonic generation with gammadion-shaped chiral metamaterials

Zhang

Yang

et al. 2016

AIP Advances

View full text Add to dashboard Cite

We theoretically investigated third harmonic generation (THG) from planar chiral metamaterials consisting of a square array of gammadion-shaped metal-insulator-metal multilayered nanostructures. We show that there exists strong circular dichroism (CD) for THG on the proposed chiral metamaterials. We also demonstrate that geometrically mirroring the gammadion -shaped meta-atoms can result in reversal of the THG-CD effect. Based on these CD effects in the optical nonlinear regime, we propose a design of a Fresnel zone plate (FZP) for intense focusing of the THG signals, in which adjacent zones of the FZP consist of gammadions with mirror symmetry and generate circularly polarized THG with opposite handedness. Furthermore, we demonstrate that the relative phase of the THG can be continuously changed by rotating the gammadion around its rotational axis, which could be used in the FZP to control the polarization of the output THG signals.

show abstract

Polarization-Controlled Circular Second-Harmonic Generation from Metal Hole Arrays with Threefold Rotational Symmetry

Cited by 122 publications

References 34 publications

Rotational Doppler effect in nonlinear optics

Rotational Doppler effect in nonlinear optics

Spin-dependent optics with metasurfaces

Controlling third harmonic generation with gammadion-shaped chiral metamaterials

Contact Info

Product

Resources

About