An optical vortex (also known as an optical phase singularity, photonic quantum vortex, or screw dislocation) is a zero of an optical field; a point of zero intensity. The term is also used to describe a beam of light that has such a zero in it. The study of these phenomena is known as singular optics. The concept of "optical vortices" was first described by Coullet et al. in 1989, based on solutions of the Maxwell-Bloch equations. According to one review, studies in 1989-1999 mainly focused on fundamentals; studies in 1999-2009 developed many applications; and studies in 2009-2019 made a number of technological breakthroughs.
Explanation In an optical vortex, light is twisted like a corkscrew around its axis of travel. Because of the twisting, the light waves at the axis itself cancel each other out. When projected onto a flat surface, an optical vortex looks like a ring of light with a dark hole in the center. The vortex is given a number, called the topological charge, according to how many twists the light does in one wavelength. The number is always an integer, and can be positive or negative, depending on the direction of the twist. The higher the number of the twist, the faster the light is spinning around the axis. This spinning carries orbital angular momentum with the wave train, and will induce torque on an electric dipole. Orbital angular momentum is distinct from the more commonly encountered spin angular momentum, which produces circular polarization. Orbital angular momentum of light can be observed in the orbiting motion of trapped particles. Interfering an optical vortex with a plane wave of light reveals the spiral phase as concentric spirals. The number of arms in the spiral equals the topological charge. Optical vortices are studied by creating them in the lab in various ways. They can be generated directly in a laser, or a laser beam can be twisted into a vortex using any of several methods, such as computer-generated holograms, spiral-phase delay structures, or birefringent vortices in materials. Importantly, spin and orbital angular momentum are not properly defined for photons. In the context of vortex beams, these terms correspond to different quantities. By contrast, the total angular momentum projection and helicity are suitable quantities to characterize beams even outside the paraxial approximation.
Properties An optical singularity is a zero of an optical field. The phase in the field circulates around these points of zero intensity (giving rise to the name vortex). Vortices are points in 2D fields and lines in 3D fields (as they have codimension two). Integrating the phase of the field around a path enclosing a vortex yields an integer multiple of 2π. This integer is known as the topological charge, or strength, of the vortex. A hypergeometric-Gaussian mode (HyGG) has an optical vortex in its center. The beam, which has the form
ψ ∝ e i m ϕ e − r 2 , {\displaystyle \psi \propto e^{im\phi }e^{-r^{2}},\!}
is a solution to the paraxial wave equation (see paraxial approximation, and the Fourier optics article for the actual equation) consisting of the Bessel function. Photons in a hypergeometric-Gaussian beam have an orbital angular momentum of mħ. The integer m also gives the strength of the vortex at the beam's centre. Spin angular momentum of circularly polarized light can be converted into orbital angular momentum. Another important property of optical vortices is the transformation of their topological charge upon reflection, which depends on the type of reflecting surface.
Reflection of optical vortices The behavior of the topological charge upon reflection depends on the type of reflection. According to numerical simulations based on scalar diffraction theory, a conventional mirror reflection reverses the sign of the topological charge (e.g., a vortex with q = + 1 {\displaystyle q=+1} becomes q = − 1 {\displaystyle q=-1} ). This is because the mirror reverses the spatial structure of the wavefront relative to the propagation axis, changing the handedness of the vortex. In contrast, phase-conjugate reflection (e.g., from stimulated Brillouin scattering media) restores the original topological charge. In this case, the wavefront is inverted twice, which preserves the initial orbital angular momentum.
Creation Methods of creating optical vortices work by taking a plane wave or Gaussian beam and increasing the phase of the wave at each by point l ϕ {\displaystyle l\phi } , where l {\displaystyle l} is the orbital angular momentum of the beam and ϕ {\displaystyle \phi } is the angle along the plane transverse to the direction of light propagation. Generation methods include spiral phase plates, holograms, spiral fresnel lenses, cylindrical lenses, spatial light modulators, and q-plates, as well as others.
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