Novel approaches to amplify tiny spin optical effects

Pal, Mandira (2019) Novel approaches to amplify tiny spin optical effects. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Mandira Pal (12RS059)) 12RS059.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

The spin and the orbital angular momentum carried by a light beam can get coupled under certain circumstances leading to interesting consequences like the spin-orbit interaction of light (SOI). An interesting manifestation of SOI is the so-called spin Hall effect of light (SHEL) that leads to the spin (circular polarization) dependent splitting of a light beam and has been observed in various optical interactions. The simplest form of optical interactions where all the rich physics associated with SOI and SHEL can be observed are the refraction, partial reflection and total internal reflection (TIR) of light at dielectric interfaces. In this case, the SOI is manifested as a transverse (perpendicular to the plane of incidence) shift of the centre of gravity of a finite light beam depending upon the incident polarization state. The eigenpolarization states corresponding to this so-called Imbert- Federov (IF) shift are left (LCP)/right (RCP) circular polarizations and +45°/ - 45° linear polarizations. A variant of the IF shift is the spin Hall effect of light (SHEL), whose eigenpolarizations are LCP and RCP. In addition to the SHEL and the IF shifts, there is also a longitudinal (in the plane of incidence) shift of the beam, known as the Goos-Hänchen (GH) shift. The eigenpolarization modes of the GH shift are TM (traverse magnetic) or p and TE (transverse electric) or s linear polarizations. In general, these beam shifts may manifest as a spatial displacement (coordinate shift) or an angular deflection (momentum shift) of the beam depending upon the nature of the interaction. These beam shifts have evoked intensive investigations owing to fundamental interests and potential metrological applications. However, fundamental understanding of these effects and their ensuing applications are compromised due to: (a) these shifts are exceedingly small (typically in the sub-wavelength domain) and thus, accurate measurement of these shifts are extremely challenging, and (b) for any optical interaction, the spatial and the angular variants of the GH, IF, and the SHEL shifts contribute in a complex interrelated way making their unique interpretation extremely difficult. In this thesis, some of these outstanding issues pertaining to the optical beam shifts at planar dielectric interfaces have been addressed. We have employed optimized weak measurement schemes to selectively amplify the different variant of the beam shifts for faithful detection, quantification and their unambiguous physical interpretation. In the first phase of these studies, simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of fundamental Gaussian beam at planar dielectric interfaces are demonstrated using pre- and post-selection schemes with appropriate linear polarization basis states. In the next step, decoupling and selective weak value amplification of the two variants of the IF shifts and the angular GH shift are demonstrated using pre- and post- selections with both optimized elliptical and linear polarizations. This is achieved by selective conversion of the spatial to angular nature of the beam shifts and subsequent weak value amplification using optimized weak measurement schemes. The experimental results were analyzed via appropriate theoretical treatment of weak measurements. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via pre- and post-selected weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their optimized applications in sensing and precision metrology. Despite the success of the weak value amplification schemes in numerous experiments in the optical domain and beyond, it remains to be a rather enigmatic and hotly debated topic in physics. Moreover, there is an upper bound on the maximum achievable weak value amplification in the conventional linear response regime of weak measurements. For practical purposes, it is therefore important to explore ways to achieve weak value amplification that can exceed this conventional limit. On the conceptual ground, it is also equally important to understand the weak values through physically meaningful and experimentally accessible properties such as the system response function. In an attempt to address these issues, we have demonstrated a fundamental relationship between the weak value of an observable and complex zero of the response function of a system by employing weak measurement on SHEL of a Gaussian light beam. Using this relationship, it is shown that extremely large weak values far beyond its upper bound in the conventional linear response regime can be experimentally obtained from the position of the minima of the pointer intensity profile corresponding to the real part of the complex zero of the response function. The imaginary part of the complex zero, on the other hand, is related to the spatial gradient of the geometric phase of light, which evolves due to the weak interaction and the pre- and the post- selections of the polarization states. These relationships between the weak value and the complex zeros of the response function may provide new insights on weak measurements in a wide class of physical systems. Extraction of large weak values outside the usual domain of its validity and quantification of small interaction parameters using a physically meaningful and experimentally accessible system property such as the response function may open up a new paradigm of weak measurement enhancing its metrological applications. The SHEL effect is known to originate from the transverse spatial (or momentum) gradient of either the Pancharatnam- Berry (PB) geometric phase or the spin redirection Berry phase. SHEL produced via spin redirection Berry phase is generally weak and this rather weak SOI effect and the exceedingly small magnitude of SHEL is a major stumbling block towards their practical applications. Recent efforts towards enhancing the SOI and the SHEL effects, therefore, exploited the PB geometric phase in transversely inhomogeneous anisotropic medium, which can be considerably stronger. However, the realization of the tunable spin-dependent splitting of the light beam remains to be an outstanding challenge. We have observed a new variant of SHEL, namely, the spin specific beam shift and demonstrated its full tunability in an inhomogeneous anisotropic medium exhibiting user-controlled spatially varying birefringence level. The extraordinary spin specificity (shift occurs only for one circular polarization mode, keeping the other orthogonal mode unaffected) has been shown to arise due to the combined spatial gradients of the geometric and dynamical phases of light. In a simple yet elegant system of a twisted nematic liquid crystal based spatial light modulator, we have demonstrated that one can simultaneously generate desirable spatial gradients of both the geometric and the dynamical phases of light to produce spin specific beam shift in a regulated fashion. The effect is eventually manifested as a spin-dependent splitting of input linearly polarized beam, where the constituent two orthogonal circular polarization modes evolve in different trajectories leading to a large and tunable spin separation. The spin specificity of the beam shift and the demonstrated principle of simultaneously tailoring space-varying geometric and dynamical phase of light for achieving its tunability (of both magnitude and direction), may provide an attractive route towards the development of novel spin-optical devices.

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