Fig. 1. Polarization state of the double-mode vector beam.

Fig. 2. Schematic of the focusing system.

Fig. 3. Calculated intensity distributions of in the x-z plane with setting parameters β0 = 1.12, zd = 3λ, and t= 0.6. (a) Intensity of transverse component |Er|2+|Eφ|2, (b) intensity of longitudinal component |Ez|2, (c) total intensity distribution, (d) normalized intensity profile along the z and x axes [marked in (c) by the red and white dotted lines, respectively].

Fig. 4. Calculated intensity distributions with different parameters in the x-z plane. (a),(b) The same zd = 3λ and β0= 1.12, but different t = 0.3, and t = 0.8, respectively; (c),(d) The same zd = 3λ, and t= 0.6, but different β0 = 1.6, and β0 = 0.7, respectively; (e),(f) The same t = 0.55, and β0= 1.5, but different zd = λ, and zd = 5λ, respectively.

Fig. 5. Intensity distributions of multiple 3D optical cages generated in the focal volume. Left column: five cages in each of two transverse planes located, respectively, at z =+15λ and z =−15λ; (a) intensity distribution in the transverse plane at z =+15λ, (b) intensity distribution in the longitudinal plane at x =+15.6λ, (c) intensity distribution in the longitudinal plane at x =−15.6λ. Right column: 2 × 1 optical cages in each of four transverse planes at z = 45λ, 15λ, −15λ, and −45λ; (d) intensity distribution in the transverse plane at z = +15λ; (e) intensity distribution in the longitudinal plane at y = 0; (f) intensity distribution in the longitudinal plane at x =+13.8λ.