Weak Measurements in Nano-optics

Abstract

Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to ‘weak value’ that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domain. The applications involves measuring an ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signal or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.

Interferometric weak value of polarization observable and differential Jones matrix algebra

“…Corresponding WVA approximation (∼ α cot a ) depicted as black dashed line shows a good agreement with the enhancement of U/I. Like other WVA protocols, here also the amplification of U/I breaks down beyond linear response regime [43,44,50], a → 0. The imaginary WVA of circular retardance effect is demonstrated as the variation of V /I with changing phase offset parameter p by the solid blue line in Fig 2 (b).…”

“…Although, like other WVA protocols, the enhancement of tiny polarization anisotropy effects comes at the cost of total intensity [52,53], but careful tuning of pre and post-selection enables to detect all possible polarization anisotropy effects, even if these appear simultaneously. Under linear approximation of WVA [27,44,54,50], all the present anisotropy effects leave their signature enhancements in the characteristic Stokes vector elements which can be quantified under clever choice of pre and post-selection. From the practical point of view, it is important to quantify simultaneously exhibiting multiple polarimetry effects as in most of the realistic scenarios, these effects appear jointly in space even for a single anisotropic unit.…”

“…Black dash-dotted line demonstrates the corresponding WVA approximation ∼ β cot p . Beyond the linear response regime [43,44,50], the WVA breaks down as depicted.…”

“…( 9). Corresponding linear response regime approximation of WVA [43,44,50] (∼ α cot p ) is given by black dash-dotted line. (b) Using Eq.…”

Interferometric weak value of polarization observable and differential Jones matrix algebra

“…Corresponding WVA approximation (∼α cot ϵ a ) depicted as black dashed line shows a good agreement with the enhancement of U/I. Like other WVA protocols, here also the amplification of U/I breaks down beyond linear response regime [43,44,50], ϵ a → 0. The imaginary WVA of circular retardance effect is demonstrated as the variation of V/I with changing phase offset parameter ϵ p by the solid blue line in figure 2(b).…”