A study of geometric phase topology using Fourier transform method

Transformation of a C-point singularity into its orthogonal state has been introduced recently. This non-trivial process of transformation naturally raises a question about its significance. In this paper we show that orthogonal C-point polarization singularities can be used to construct basis sets of polarization optics. The generic C-points namely lemons and stars are used to substantiate the idea. Here, we show homogeneous polarization distributions as superpositions of two orthogonal C-points. The Wronskian of the two orthogonal basis states is non-zero which indicates that the basis states are linearly independent. This novel idea where homogeneous polarization distributions are expressed as superpositions of singular polarization distributions may be useful in diverse fields beyond polarization optics. This exercise is shown to bring out hitherto unknown interesting structures like interconnections between polarization singularity, phase singularity and stereographic projection, in polarization optics.

mentioning

confidence: 65%

Basis construction using generic orthogonal C-points

Ruchi

Pal

Senthilkumaran

2019

“…The GP features of the weak value have been discussed in the context of both fundamental and applied physics [21][22][23][24][25][26][27][28]. The geometric topological aspects of the GP due to pure polarization projection were reported recently by our group, wherein it was shown that phase singularity is enclosed in orthogonal polarization state projection in two-dimensional parameter space of ellipticity η and ellipse orientation χ of a polarization ellipse [29,30]. The topological behaviour of GP from the projective transformation of a polarization state upon the weakly interacted state is shown here to give a unique insight into understanding the WM protocol.…”

Section: Introductionmentioning

confidence: 93%

Geometric phase topology in weak measurement

Samlan¹,

Viswanathan²

2017

Self Cite

The geometric phase visualization proposed by Bhandari (R Bhandari 1997 Phys. Rep. 281 1–64) in the ellipticity-ellipse orientation basis of the polarization ellipse of light is implemented to understand the geometric aspects of weak measurement. The weak interaction of a pre-selected state, acheived via spin-Hall effect of light (SHEL), results in a spread in the polarization ellipticity (η) or ellipse orientation (χ) depending on the resulting spatial or angular shift, respectively. The post-selection leads to the projection of the η spread in the complementary χ basis results in the appearance of a geometric phase with helical phase topology in the η − χ parameter space. By representing the weak measurement on the Poincaré sphere and using Jones calculus, the complex weak value and the geometric phase topology are obtained. This deeper understanding of the weak measurement process enabled us to explore the techniques’ capabilities maximally, as demonstrated via SHEL in two examples—external reflection at glass-air interface and transmission through a tilted half-wave plate.

“…and n 1.3999, cl = is shown in figures 3(a) and (b) respectively, where n co and n cl are the refractive indices of core and cladding of the step-index TMF. It is important to note here the nonlinear variation of the phase (figure 3(b)) in the beam cross-section as one radially approaches the fiber center, an indication of its topological character [16], which becomes an almost linear variation as one moves towards the fiber periphery.…”

Section: Bomentioning

confidence: 99%

Geometric phase due to orbit–orbit interaction: rotating LP₁₁modes in a two-mode fiber

Chakravarthy¹,

Naik²,

Viswanathan³

2017

Self Cite

Accumulation of geometric phase due to non-coplanar propagation of higher-order modes in an optical fiber is experimentally demonstrated. Vertically-polarized LP11 fiber mode, excited in a horizontally-held, torsion-free, step-index, two-mode optical fiber, rotates due to asymmetry in the propagating k-vectors, arising due to off-centered beam location at the fiber input. Perceiving the process as due to rotation of the fiber about the off-axis launch position, the orbital Berry phase accumulation upon scanning the launch position in a closed-loop around the fiber axis manifests as rotational Doppler effect, a consequence of orbit–orbit interaction. The anticipated phase accumulation as a function of the input launch position, observed through interferometry is connected to the mode rotation angle, quantified using the autocorrelation method.