Electromagnetic spins, including longitudinal and transverse ones, have been playing important roles in light-matter interactions, leading to many intriguing phenomena and applications. Previously, the ordinary longitudinal and transverse spins of single polarized modes were distinguished by means of mean wavevector. However, our recent discovery argues that this method is incomplete for a generic electromagnetic field with hybrid polarization. Here, we demonstrate, both theoretically and experimentally, an extraordinary transverse spin oriented parallel to the mean wavevector and an extraordinary longitudinal spin perpendicular to the mean wavevector. Remarkably, the extraordinary transverse spin is locally helicity-dependent, resulting in a corresponding helicity-dependent spin-momentum locking, while the helical property of integral transverse spin is determined by the symmetry breaking of system. Furthermore, this extraordinary transverse spin determines the inverted helical component and thus is related to the geometric phase closely. The findings have deepened the understanding the underlying physics of spins and opened an avenue for chiral quantum optical applications.
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