Fig. 1. Origin of the CARR principle. (a) (I) F–P cavity and (II) relevant parameters; (III) the light source is set on the top of the F–P cavity for glancing incidence, and the antiresonant frequency components are guided out from the bottom of the cavity. (b) To accommodate the incident light beam from a point source on the tube axis, the parallel plates of the F–P cavity are bent into a fully enclosed cylindrical wall. (c) The main distinction between the proposed CARR theory and traditional antiresonance lies in the location of optical oscillations, occurring either (I) in the central core or (II) in the cladding. (d) Several representative ARROWs, including a cylindrical pipe^[5], a hexagonal cage^[6,7], a quadrilateral multilayer channel^{[810" target="_self" style="display: inline;">–10]}, and a ring-nested fiber^[1]. (e) Several representative tubular geometries wherein the proposed CARR effect is applicable rather than the traditional antiresonance, including a helix^[18,19], a multihole tube^{[2022" target="_self" style="display: inline;">–22]}, an ultrathin tube^[23,24], and a thick-wall hole^[25]. (d), (e) Adapted from Ref. [15] under the license CC BY 4.0.

Fig. 2. (a) Two examples to make cylindrical tubes by paper; (b) the CARR tube was tested in a typical THz-TDS setup. (c) The cage system for positioning the CARR cavity between the THz transmitter and receiver. (a), (b) Adapted from Ref. [15] under the license CC BY 4.0.

Fig. 3. Diversity of the CARR cladding materials. (a) Normalized transmission spectra (left) through tubes (right) made of different nonpolar materials with high transparency in the THz band; (b) similar spectra with (a) except for the cladding made by polar materials instead. Note that, the single-layer tinfoil tube on top is not a CARR cavity, and thus is without dips in its spectrum. (a), (b) Adapted from Ref. [15] under the license CC BY 4.0.

Fig. 4. (a) Parallel plates, (b) quadrilateral and (c) octagonal paper tubes, (d) hollow air hole with large wall thickness, (e) bent plastic tube, and (f) metallic spring with corresponding CARR spectra. (a)–(d) Adapted from Ref. [15] under the license CC BY 4.0.

Fig. 5. CARR-type applications on sensing the ambient stress by considering single or orthogonal polarization directions. (a) The CARR tubes used with different sensitivities S and pressure P ranges due to different structures (without/with folded-up ends) of the tube claddings; (b) correlations between resonant frequencies f_m and the applied P for the above tubes; (c), (d) folding process of an octagonal paper tube and its photos; (e), (f) THz spectra of orthogonally polarized components during the pressure-sensing process; (g) corresponding evolution of resonant frequencies (f_h and f_v) at m = 3; (h) distribution of Δf_{m = 3} with respect to the applied pressure P. (a), (b) Adapted from Ref. [15] under the license CC BY 4.0; (c)–(h) adapted with permission from Ref. [16], © The Optical Society.

Fig. 6. THz polarization modulations by the octagonal paper cavity. (a) Schematic of the external force applied on the rear of the cavity; (b), (c) time variation of the THz waveform peak retrieved from the orthogonal polarization components; (d) evolution of linear-elliptical-circular polarization states of the output cavity mode; (e) magnetism-driven scheme of THz polarization modulation by attaching a magnet at the tube port, which is then exposed to the external magnetic field; (f), (g) deformation of the tube’s cross section with orthogonal cavity lengths being varied. (a)–(d) Adapted with permission from Ref. [16], © The Optical Society.

Fig. 7. (a), (b) θ_m − f_m connection in the CARR principle; (c) THz transmission spectrum of the paper cavity with the THz source in Fig. 2; (d) corresponding resonant frequencies at different orders m retrieved from (c); (e) calculated θ − f distribution by data in (d) and Eq. (2); (f)–(h) an additional TPX lens was inserted into the THz beam to enhance the THz divergence angle, which was then detected by the CARR method; (i)–(k) THz radiation from a laser plasma filament was detected by the CARR method. (a)–(k) Adapted from Ref. [17] under the license CC BY 4.0.