Polarization oscillating beams constructed by copropagating optical frozen waves

Polarization oscillating beams, namely, polarization standing waves, commonly formed by a pair of coherent counterpropagating light waves with orthogonal polarizations, oscillate their states of polarization periodically within a wavelength interval, offering conceptual and practical interests in light-matter interactions such as the nonreciprocal magnetoelectric effect, and impressive applications in optical imaging, sensing, and chirality detection. Here, we propose a new class of polarization oscillating beams that longitudinally vary states of polarization with spatial intervals within centimeters via the superposition of two copropagating optical frozen waves with preshaped longitudinal intensity profiles and transverse phase structures. The flexibility and manipulability are demonstrated by creating several polarization oscillating beams with different polarization structures. This work paves a new way to manipulate other waves and may be useful for applications of optical standing waves in optical manipulation, light guiding of atoms, polarization-sensitive sensing, etc.