Ultra-broadband, ultra-narrowband, and ultra-passband composite polarization half-wave plates, ultra-broadband composite polarization -rotators, and quantum-classical analogy.

Composite pulses, which produce ultra-broadband, ultra-narrowband and ultra-passband x-, y-rotations Rx(θ)=exp⁡{-iθσx/2}, Ry(θ)=exp⁡{-iθσy/2} by the rotational angle θ = π on the Bloch-Poincaré sphere, are presented. In polarization optics, the first class plays a role in the design of achromatic polarization retarders, while the second class corresponds to chromatic polarization filters. The third class is an assortment of the above two classes. Besides, composite pulses, which produce ultra-broadband z-rotations Rz(ζ)=exp⁡-iζσz/2 by the phasal angle ζ = π on the same sphere, are presented. These phasal pulses coincide with achromatic polarization π rotators. The evolution matrix and the Jones matrix have similar forms in quantum optics and polarization optics. In the context of quantum optics, quantum computing, and quantum information processing, following the quantum-classical analogy, we achieve ultra-robust, ultrasensitive, and ultrasquare quantum control of an X (NOT) gate, and ultra-robust control of a Z phase gate, with respect to pulse area error. Our proposed UBBN (BatN), UNBN (SnakeN), UPBN (OctopusN), and UBBPhN (BatPhN) sequences are novel due to the novel methods of derivation. They surpass and outperform the superior candidates of the similar subclass of altering variable rotations in literature - BB2, NB2, and PB2, in precision parameters such as broadness, narrowness, FWHM, or execution time. We suggest that, in general, the presented composite pulse sequences are interdisciplinary and can have other possible applications, such as nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and spectroscopy, quantum sensing, local addressing, optical switching, cold-atom interferometry, quantum communication, quantum cryptography, quantum image processing, and quantum steganography.