Generalized Matrix Transformation Formalism for Reflection and Transmission of Complex Optical Waves at a Plane Dielectric Interface

We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the incident constituent plane wave fields to obtain the reflected and transmitted constituent plane wave fields. We derive these matrices and describe the complete formalism by implementing these matrices. This formalism, though physically equivalent to Fresnel formalism, has greater mathematical elegance and computational efficiency as compared to the latter. We utilize exact 3D expressions of the constituent plane wavevectors and electric fields of the incident, reflected and transmitted waves, which enable us to seamlessly analyse plane waves, paraxial and non-paraxial beams, highly diverging and tightly focused beam-fields as well as waves of miscellaneous wavefront-shapes and properties using the single formalism. The exact electric field expressions automatically include the geometric phase information; while we retain the wavefront curvature information by using appropriate multiplicative factors. We demonstrate our formalism by obtaining the reflected and transmitted fields in a simulated Gaussian beam model. Finally, we briefly discuss how our generalized formalism is capable of analysing the reflection-transmission problem of a very large class of complex optical waves -- by referring to some novel works from the current literature as exemplary cases.Comment: 21 pages, 7 figure

Optical Singularity Dynamics and Spin-Orbit Interaction due to a Normal-Incident Optical Beam Reflected at a Plane Dielectric Interface

The degenerate case of normal incidence and reflection of an optical beam (both paraxial and non-paraxial) at a plane isotropic dielectric interface, which is azimuthally symmetric in terms of the momentum-spatial variation of Fresnel coefficients but not in terms of the fundamental polarization inhomogeneity of the incident field, requires in-depth analyses. In this paper, we use the reflection and transmission coefficient matrix formalism to derive an exact field expression of a normal-reflected diverging beam. The availability of the exact field information allows controlled variations of the system parameters, leading to significant dynamics of phase and polarization singularities hitherto unanticipated in the literature. We carry out a detailed exploration of these dynamics in our simulated system, and also verify them experimentally by using an appropriate setup. We then use Barnett's formalism to determine the associated orbital angular momentum (OAM) fluxes, leading to a subtle interpretation and mathematical characterization of spin-orbit interaction (SOI) in the system. Our work thus represents a non-trivial unification of the most fundamental electromagnetic reflection/transmission problem at a plane dielectric interface and the emerging areas of optical singularity dynamics with their understanding in terms of OAM flux and SOI. The normal-incidence--retro-reflection geometry being especially amenable to applications, these beam-field phenomena are anticipated to have applications in interface characterization, particle rotation/manipulation and other nano-optical processes.Comment: 16 pages, 13 figure

Rotational Doppler-effect due to selective excitation of vector-vortex field in optical fiber

Experimental demonstration of rotational Doppler-effect due to direct and simultaneous excitation of orthogonal elliptically-polarized fundamental and vortex modes in a two-mode optical fiber is presented here. The rotation frequency and the trajectory of the zero-intensity point in the two-mode fiber output beam measured as a function of analyzer rotation matches with the S-contour of polarization singularity in the beam, identified via Stokes parameter measurement. The characteristics of the S-contour around the C-point in the output beam is also measured as a function of rotating Dove prism and half-wave plate - Dove prism combination to highlight the role of polarization modifying components on the observed rotational Doppler-effect of vector-vortex beams.</p

Rotational frequency shift in cylindrical vector beam due to skew rays in few-mode optical fibers

We report here the demonstration of rotational Doppler Effect (RDE) and measurement of rotational frequency shifts (RFS) in single-charge helical-phased cylindrical vector beams directly generated using a two-mode optical fiber. The vector-vortex beam with a shifted vortex core, generated by propagating the Gaussian laser beam as an offset-skew ray selectively excites both the fundamental and first low-order waveguide modes simultaneously in the two-mode optical fiber. Rotation frequency of the output beam around a shifted axis of the beam is measured as a function the analyzer rotation for changing handedness of the input circular polarization to demonstrate RDE in the directly excited cylindrical vector-vortex beams. Even small variations in the input launch conditions were found to dramatically alter the stability of the vortex beams and hence the demonstration of RDE.</p

Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams