As we konw, an optical vortex beam is a structured beam with a spiral phase exp(−ilϕ) in the azimuthal direction ϕ perpendicular to the propagation direction. Such beams carried an orbital angular momentum (OAM) of lℏ per photon.
In many papers about optical vortex, the Laguerre Gauss (LG) mode is often metioned.
Such as, in the paper(Article Coherent optical vortices from relativistic electron beams
), it mentioned that the LG mode is the eigen mode of the free space by citing the paper (Article Orbital angular momentum of light and transformation of Lagu...
). However, in the latter one, it mentioned that the LG mode is the eigen mode of the angular momentum operator Lz instead of free space.So, why LG mode is important for the optical vortex?
Compared with the optical vortex which just have the spiral phase but the amplitude A(r) does not match LG modes (For example, a Gaussian mode with a spiral phase ), what benifit will it take when the pure LG beam is generated?
A Gaussian mode with a spiral phase does not satisfy the paraxial wave equation, and therefore, it will not preserve its shape under free-space propagation. This is actually what happens when you pass a Gaussian beam through a spiral phase plate (SPP). Immediately after the SPP, the Gaussian shape disappears and you have a donut-shaped intensity.
LG modes are the solution of paraxial wave equation in cylindrical coordinates. In the mathematical expression of its complex field, we can see the helical phase term, exp(−ilϕ) along with other terms. And this helical phase is the reason for phase singularity, which is referred as optical vortex. If a gaussian beam is modulated with helical phase, null intensity region will automatically appear as the beam propagates.
JOSA A 36(8):1447-1455,
DOI: 10.1364/JOSAA.36.001447
Hi,
As mentioned the gaussian modulated by SLM (+l OAM) has zero intensity in the center through propagation, so can we again produce gaussian by reverse phase plate (-l OAM)? or because of that singularity and zero intensity at center, we can not ?
Yes, we can produce Gaussian from OAM(+1) by using reverse phase plate.
This concept is often used for detection of OAM modes.
I see, but my question is how again we have intensity at center? because in papers mentioned because of singularity in phase, there is zero intensity there.
Here, intensity profile of beam is determined by its wavefront.
If wavefront is changed from helical to Gaussian, intensity profile of beam will change accordingly.
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