Estimation of dislocated phases in wavefronts through intensity measurements using a Gerchberg-Saxton type algorithm

Estimation of dislocated phases and tunable orbital angular momentum using two cylindrical lenses

A first-order optical system consisting of two cylindrical lenses separated by a distance is considered. It is found to be non-conserving of orbital angular momentum of the incoming paraxial light field. The first-order optical system is effectively demonstrated to estimate phases with dislocations using a Gerchberg-Saxton-type phase retrieval algorithm by making use of measured intensities. Tunable orbital angular momentum in the outgoing light field is experimentally demonstrated using the considered first-order optical system by varying the distance of separation between the two cylindrical lenses.

Realization of general first-order optical systems using thin lenses of arbitrary focal length and fixed free propagation distance

Any general first-order optical system can be represented using S∈Sp(4,R), where Sp(4,R) is the symplectic group with real entries in four dimensions. We prove that any S∈Sp(4,R) can be realized using not more than 18 thin lenses of arbitrary focal length and seven unit distance. New identities that realize S=S₁⊕S₂, where S₁,S₂∈Sp(2,R), are obtained. Also, it is proved any S of the form S₁⊕S₂ can be realized using a maximum of eight thin lenses of arbitrary focal length and three unit distance. Moreover, decompositions for examples such as differential magnifier, partial Fourier transform, and inverse partial Fourier transform are also provided. A "gadget" is proposed that can realize any S∈Sp(4,R) using thin lens transformations-which can be realized through the use of eight spatial light modulators (SLMs) and seven unit distance. Experimental limitation imposed by SLMs while realizing thin lens transformations is also outlined. The justification for the choice of unit distance according to the availability of thin lenses in a lab is given too.