Fig. 1. Superchiral optical field generated by chiral nanostructures. (a), (b) Optical chirality enhancement by a planar Gammadion structure illuminated with left circularly polarized light and right circularly polarized light at a wavelength of 2.01µm^[37]; (c) top picture: dissymmetry between left and right circularly polarized light enhancement on two arrays of enantiomeric nanorod pairs. Middle picture: an achiral arrangement of equivalent nanorods. Bottom picture: finite element method (FEM) for standardized electromagnetic chirality is used to calculate chiral optical density of crystal cell center in plane 10 nm above nanorod pairs in nanostructures. Black line represents left hand and green line represents right hand^[38]

Fig. 2. Superchiral light field generated by non chiral nanostructures. (a) Chiral hotspots (orange blurry spots) appear in gaps between dimers under circularly polarized light irradiation; (b) volume average chirality spectrum of dimer gaps (black) under top irradiation of right circularly polarized light plane waves, as well as spectra of dimer scattering (red), absorption (blue), and extinction (green) cross-sections^[42]; (c) normalized E- and H-field intensity maps for dimers of nanodisks with separation of 20 nm at λ=579nm. White arrow represents vector field and direction of polarization of incident light is given by a double headed arrow (two pictures on the left). Simulated optical chirality enhancement for Si nanodisk dimers (D=100nm,h=20nm,g=579nm) at λ=140nm with an incident light angle of θ=π/4and3π/4 (two pictures on the right)^[44]; (d) scheme to generate superchiral field at vector EP using two beams of circularly polarized light exciting system from opposite directions; (e) average enhanced optical chirality in cylindrical pores with different thicknesses. Blue line corresponds to structure sustaining EP with h=154.2nm. Black, red, green, and pink lines correspond to cases deviating from vector EP; (f) near-field distribution of optical chirality near photonic crystal slab at vector EP under two beams of excitation from opposite directions^[46]; band structures of photonic crystal plates for (g) d=145.5nm and (h) d=145nm. Other parameters are a=270nm,np=2.02,ns=nb=1.47, and t=154nm. Illustration shows band structures of TEB and TMA expanding at point Γ; (i) chiral field enhancement of Si3N4 photonic crystal plates with parameters a=270nm,h=154nm,ns=nb=1.47,d=145nm,andk=0.0276rad/m^[48]

Fig. 3. Ultra sensitive detection of chiral molecules based on near field superchirality of hotspots. (a) Schematic diagram shows that a nanoparticle dimer generates a strong local electromagnetic hotspot in gap, where chiral molecules can undergo enhanced interactions with light^[22]; (b) extinction spectra (left) and CD spectra (right) of discrete gold nanospheres (blue solid line) and L-GNSs (black line) and D-GNSs (red line)^[23]; (c) schematic of system consisting of a Ag dimer and a chiral molecule. Radius of nanoparticles is set to Rs=15nm(left figure). CD (ED-EQ) and CD (ED-MD) of system as functions of wavelength (inset: CD (ED-MD) is from 360 to 400 nm) (right figure)^[24]; (d) coordinate and schematic diagram system of a complex composed of gold nanoparticles (left figure), gold dimers (right figure), and chiral molecules; (e) local OD signal as a function of wavelength for composite system of single chiral molecule and gold nanoparticles (two pictures on the left) and gold dimer (two pictures on the right) under OAM incident beams with l=±1 and l=±2, respectively. Insets represent calculated results for single chiral molecule without nanoparticles^[63]

Fig. 4. Ultra sensitive detection of chiral molecules based on near field superchirality of hotspots. (a) I¯(SE)ICP‑ROAαG, average α˜A˜(I¯(SE)ICP‑OAαA), mode average surface enhanced or unenhanced Raman scattering intensity (I¯(SE)RS), and corresponding surface enhanced mode averaged circular intensity differences Δ¯SE of SEROA spectra at d=8 nm, d=4 nm, and d=2 nm, respectively^[26]; (b) geometric shape and coordinate of a hybrid system composed of chiral molecules and nanospheres. Chiral molecules are placed at origin of coordinate. Nanosphere, with radius R, locates atRs. Enhanced CD spectra, chiral optical densities, and extinction spectra of Si (black line), Au (red line) single nanospheres (left), and dimers (right); (c) temperature increment of Si (black line), Au (red line) single nanospheres (left), and dimer (right) systems as a function of wavelength^[66]; (d) CD and extinction of chiral structure of gold spherical trimer induced by rotating nanoparticles with a gap of 1 nm are calculated as functions of wavelength. Parameters: a=17.5nm,b=17nm,αp=0.0025°. Solid line, dashed line, and dotted line represent total CD, structural chirality (CDNP-FF), and molecular induced plasma chirality (CDmol+CDNP-DD+CDNP-DF), respectively; red line represents extinction^[25]; (e) CD signal of dimer and molecular composite system of gold nanosphere, corresponding extinction spectra, and superchiral fields as functions of wavelength. A-E, B-E, and C-E represent electric field distribution at points A, B, and C on y-zplane under left circularly polarized light excitation. A-Ch, B-Ch,and C-Ch are corresponding optical chiralities^[43]

Fig. 5. Application of enhanced chiral optical force based on vector EPs to construct a superchiral field. (a) Contribution of each term of optical force on chiral particle. Bottom left illustration is schematic diagram of placement of chiral particle; (b) magnitude of electric field gradient force Fe, magnetic field gradient force Fh, and chiral gradient force Fk as a function of relative phase; (c) optical force component along x, y, and z directions on enantiomers (κ=+0.5 and κ=-0.5) changes with relative phase of incident light; (d-g) when relative phase is π/4, intensity distribution and direction of optical forces in three-dimensional space are indicated by arrows in case of κ=+0.5 and κ=-0.5. Optical force distribution under κ=+0.5 and κ=-0.5 conditions when relative phase is 5π/4^[31]; (h) spatially averaged enhancement of chiral field as a function of width w2 for different regions [arm1(C1/C10), slot between two arms (Cs/Cs0), and arm1 (C2/C20)]. Here, Ci0 represents spatial average of chiral field in different regions under left-right symmetry (w2=256nm); (i) spatially averaged enhancement of chiral gradient field in slot channel as a function of width w2; (j) electric field gradient force Fe, agnetic field gradient force Fh, and chiral gradient force Fk along x axis varying with width w2. Subscripts ± of force in figure represent chiral parameters κ=±0.5. Illustration is a schematic diagram of placement of chiral particles; (k) intensity distribution and direction of optical forces acting on a pair of enantiomers with κ=0.5 and κ=-0.5 in a gap channel. Illustration shows corresponding forces in two-dimensional x‑y plane^[32]

Fig. 6. Chiral embodiment of synthetic chiral light^[88]. (a) A locally chiral bichromatic electric field. Scheme illustrates how such fields are generated by two noncollinear beams of carrier frequencies ω and 2ω. Lissajou plot describes electric vector field's time-dependent polarization in a given point in space; (b) mirror twin diagram of chiral field in (a)

Fig. 7. Applications of synthetic chiral fields. (a) Experimental images of (L+R) image (PES) and (L-R) image (PXECD) at 200 fs pump-probe delay for (1S)-(+)-fenchone and (1R)-(+)-camphor. Characteristic forward-backward asymmetry of photoelectron is observed along light propagation direction z^[20]; (b) microscopic y-polarized HHG emission from model potential chiral ensemble, where y-polarized harmonics survive orientation averaging (left picture), and calculated harmonic ellipticities in x-y plane from (R) and (S) ensembles—helicity changes with medium's chirality (right picture)^[21]; (c) exactly 100%-efficiency inner-state enantioseparations. Probabilities occupying ground states of left-handed enantiomer P1Ltare denoted by blue line, and those of right-handed enantiomer P1R(t) are denoted by red line. Exactly 100%-efficiency inner-state enantioseparations [P1L(t)=1,P1R(t)=0] are achieved at t=2π4μs (black dashed line), when probabilities of two enantiomers experience integer (1) and half-integer (1/2) periods of their corresponding Rabi oscillations^[102]; (d) two-dimensional spectra of racemic mixtures with equal left-handed and right-handed chiral molecules. These spectra are obtained through two-dimensional fast Fourier transform and only absolute value of transformation result is taken.KL and KR correspond to ac Stark peaks of left- and right-handed molecules in mixed sample, respectively. By comparing intensity of peaks, ratios of left- and right-handed molecules in mixed sample can be obtained^[18]