Fig. 1. Twisted light cages. (a) Waveguides feature an axial twist with helical pitch distance P. Inset: CCD image of the core mode at λ=600nm. (b) SEM images of fabricated structures viewed from the top. (c) Photographic image of a twisted light cage sample integrated on a Si-chip via 3D nanoprinting. (d) Example of twist-induced resonances leading to CD in a twisted light cage. Simulated attenuation of the RCP and LCP fundamental mode at a wavelength of λ=770nm is shown.

Fig. 2. Definition of the two investigated twisted light cage variants. (a) Multimode strand light cages were experimentally implemented [lateral pitch distance Λmm=7μm, strand offset ρ=14μm, strand diameter 2rcmm=3.6μm (for ab initio simulations) and 3.8μm (implemented), number of strands 12]. (b) Single-mode strand light cages are used in simulations only and feature a smaller strand diameter of 2rcsm=0.4μm and a total of 108 strands. For clarity, the single-mode strand variant is represented by the simplified geometry shown at the bottom of panel (b) in subsequent figures. (c) Attenuation of the fundamental core mode in untwisted single-mode strand and multimode strand light cages. Corresponding modal dispersion is available in Fig. S2 in the Supplementary Material.

Fig. 3. Analysis of twist-induced resonances in single-mode strand light cages (2rc=0.4μm). (a) The real part of the effective index of the fundamental core modes (l=0) intersects with that of higher-order core modes (l≠0) at certain twist rates. (b) Attenuation of the involved modes. Left panels: first achiral resonance (Δs=0,Δl=6), right panels: first chiral LCP (Δs=+2,Δl=4) and RCP resonance (Δs=−2,Δl=8). The splitting between the modes is an inherent characteristic of the helicoidal coordinate frame [Eq. (1), gray dashed lines]. Curves for the higher-order modes on the right panels are only shown near the resonances to improve clarity. (c) Distributions of Poynting vector Sz, phase of Ex, and Stokes parameter S3 for four pairs of the fundamental mode and the relevant higher-order mode at twist rates indicated by the gray arrows. At the chiral resonances, the spin state of the oppositely polarized modes mixes to allow coupling (four panels in the bottom-right corner). The origin of the spiraling features in the phase patterns is explained in Sec. S5 in the Supplementary Material. The two remaining resonances between twist rates of 1 and 1.5 mm−1 are analyzed in Fig. S4 in the Supplementary Material. Wavelength: 770 nm, scale bar in (c): 10μm.

Fig. 4. Optical properties of twisted single-mode strand light cages (2rc=0.4μm) in the lab frame. (a) The real part of the effective index of the RCP and LCP fundamental mode transformed to the lab frame using Eq. (8). (b) Circular birefringence BC as a function of twist rate. The analytical prediction of four is shown as a light purple line. (c) Attenuation of the fundamental core modes. Vertical lines are predictions of the resonances according to Eq. (S9) in the Supplementary Material (blue: LCP, orange: RCP, gray: LCP and RCP). (d) Magnitude of the electric field of fundamental RCP modes at the indicated twist rates. Blue dots show the simplified geometry. (e) OAM and spin decomposition for the RCP fundamental modes of (d). The modes contain dominant RCP components (orange) as well as weak LCP components (blue). Twisting shifts the average of the OAM distribution toward negative values for a left-handed twist (gray-dashed lines are a guide to the eye).

Fig. 5. Experimental results for twisted multimode strand light cages with strand diameter 2rc=3.814μm. (a) CCD images of the LCP core mode along different axial (z) positions were recorded by moving the focal plane of the objective into (left) or out of (right) the waveguide. The intensity distribution follows the rotation of the right-handed twisted structure (blue lines). Full video sequence is available as a Supplementary Video (Video 1, MP4, 853 kB [URL: https://doi.org/10.1117/1.AP.7.4.046002.s1]). Aberrations arise due to the presence of the strands when imaging inside the waveguide (left image) or due to diffraction once the mode leaves the waveguide (right image). (b) SEM images of the four studied light cages with twist rates up to 11.4 mm−1. (c) Transmission spectra of RCP (orange) and LCP (blue) light through 5-mm long waveguide samples, normalized to the spectrum of the light source. Note that all four panels cover a range of 12 dB. (d) Simulated loss spectra of the same waveguides. Note that the used strand diameter is determined from the untwisted sample and might differ slightly in the twisted waveguides resulting in minor spectral shifts (gray-dotted lines). Arrows indicate the wavelength of the largest CD. Insets in panels (c) and (d) show the core mode at λ=770nm.

Fig. 6. Achieved twist rates for different twisted waveguide geometries (shown in Fig. S1 in the Supplementary Material). Solid-core waveguides are shown as filled triangles, hollow-core waveguides as rings, and theoretical investigations as stars. Blue denotes glass-based waveguides, whereas 3D-nanoprinted waveguides are shown in orange. Twisted light cages are shown in green. All works are listed in more detail in Table S1 in the Supplementary Material.

Fig. 7. Potential on-chip applications of twisted light cages. (a) Spectral distribution of the attenuation around a chiral resonance enabling strong CD in a centimeter-scale waveguide. (b) The real part of the effective index around an achiral resonance (calculated in the helicoidal frame). A waveguide with an adiabatically increasing twist rate could convert the fundamental core mode to a mode carrying OAM (here: l=−6). (c) Spectral distribution of the attenuation around an achiral resonance. Increasing the twist rate results in a shift of the resonance toward longer wavelengths (bottom panel). This effect can be applied for twist and tension sensing. The dashed gray line denotes the analytical model of Eqs. (2) and (S7) in the Supplementary Material. All subfigures show simulation results for the single-mode strand light cage.