Abstract: Polarization-independent focusing is advantageously achieved by a multifocal system having a polarization beam splitter (PBS) to split an unpolarized light beam into two orthogonally linearly-polarized (LP) light beams. The two LP light beams are reflected by mirrors to travel in opposite directions and enter into a variable-focusing module at two ends thereof, respectively. The module includes waveplates to convert the LP light beams into two circularly-polarized (CP) light beams at both ends of an optical assembly. The optical assembly is formed with a stack of birefringent optical elements including at least one geometric phase lens and one polarization selector that may be electrically modulated to select the optical power in focusing the two CP light beams. Followed by the waveplates converting two focused CP light beams to two focused LP light beams and upon mirror reflection, the beams are finally recombined by the PBS to form one focused light beam.

Abstract: Polarization-independent focusing is advantageously achieved by a multifocal system having a polarization beam splitter (PBS) to split an unpolarized light beam into two orthogonally linearly-polarized (LP) light beams. The two LP light beams are reflected by mirrors to travel in opposite directions and enter into a variable-focusing module at two ends thereof, respectively. The module includes waveplates to convert the LP light beams into two circularly-polarized (CP) light beams at both ends of an optical assembly. The optical assembly is formed with a stack of birefringent optical elements including at least one geometric phase lens and one polarization selector that may be electrically modulated to select the optical power in focusing the two CP light beams. Followed by the waveplates converting two focused CP light beams to two focused LP light beams and upon mirror reflection, the beams are finally recombined by the PBS to form one focused light beam.

Abstract: A rotational geometric phase hologram has geometric phase optical elements (GPOEs) serially cascaded along a common optical axis to form a GPOE cascade used for receiving a linearly-polarized light beam and generating output light beams at an exit surface of the last GPOE. Interference occurred in the output light beams creates a polarization interference pattern on the exit surface. A photoalignment substrate, when positioned in close proximity to the exit surface, records the pattern. Advantageously, each GPOE is rotatable about the common optical axis. Respective rotation angles of the GPOEs are determined according to a spatially-varying linear polarization orientation distribution selected to be generated for the polarization interference pattern.

Abstract: A rotational geometric phase hologram has geometric phase optical elements (GPOEs) serially cascaded along a common optical axis to form a GPOE cascade used for receiving a linearly-polarized light beam and generating output light beams at an exit surface of the last GPOE. Interference occurred in the output light beams creates a polarization interference pattern on the exit surface. A photoalignment substrate, when positioned in close proximity to the exit surface, records the pattern. Advantageously, each GPOE is rotatable about the common optical axis. Respective rotation angles of the GPOEs are determined according to a spatially-varying linear polarization orientation distribution selected to be generated for the polarization interference pattern.

Abstract: A device for controllably deflecting a first circularly-polarized (CP) light beam from an incident direction with fast response comprises a polarization selector (PS) to adjust the incident light beam's sense of rotation to a desired one to form a second CP light beam, and a polarization grating (PG) to deflect the second CP light beam according to the desired sense of rotation. The PS comprises an optical modulator sandwiched between two quarter-wave plates. The optical modulator has at least one ferroelectric liquid crystal (FLC) half-wave plate (HWP) being reconfigurable in fast axis orientation. The device has a fast response in beam steering due to a short time of reconfiguring the FLC HWP. Based on serially cascading multiple units each being this device, a beam-steering apparatus having fast response and enhanced steering resolution is obtained. The apparatus is usable for enhancing a field of view in projecting an image.