Natural weak value amplification in Fano resonance and giant Faraday rotation in magneto-plasmonic crystal

Abstract

The extraordinary concept of weak value amplification can be formulated within the realm of wave interference as nearly destructive interference between the eigenstates of the measuring observable. Here we report on a phenomenon of interferometric weak value amplification of small polarization rotation in Fano resonance that evolves completely naturally due to near destructive spectral domain interference between a continuum and a narrow resonance mode having slightly different polarization response. In order to elucidate this, we first experimentally demonstrate an interferometric weak value amplification concept by generating nearly destructive interference of two paths of an interferometer having slightly rotated linear polarization states of light. The weak value amplification of polarization rotation effect is manifested as dramatic changes in the polarization state of light, which acts as the pointer. We go on to demonstrate that the manifestation of natural interferometric weak value amplification is an important contributing factor to the observed giant Faraday rotation and ellipticity in waveguided magneto-plasmonic crystals exhibiting prominent Fano resonance. The natural weak value interpretation of the enhanced Faraday rotation in hybrid magneto-plasmonic systems enriches the existing understanding on its origin. This opens up a new paradigm of natural weak measurement for gaining fundamental insights and ensuing practical applications on various weak interaction effects in rich variety of wave phenomena that originate from fine interference effects. The weak measurement concept, introduced by Aharonov, Albert, and Vaidman 1-5 involves three steps, quantum state preparation (pre-selection), a weak coupling between the pointer (device) and the measuring observable, and post-selection on a final state which is nearly orthogonal to the initial state 1-3. The outcome, the so-called weak value may lie far outside the eigenvalue spectrum of an observable and can also assume complex values. These strange characteristics have allowed a wide range of applicability of weak values in both classical and quantum contexts 6-15. The weak value amplification (WVA) has turned out to be a useful tool for addressing foundational questions in quantum mechanics 12,13 and for resolving quantum paradoxes 14,15. WVA is also finding widespread metrological applications 6-11 , to quantify small physical parameters, e.g., for precision measurements of angular rotation 6 , phase shift 8 , temporal shift 9 , frequency shift 10 , detection of ultra-sensitive beam deflections 11 , and so forth. Even though WVA is a quantum mechanical concept, it can be understood using the wave interference phenomena and can therefore be realized in classical optical setting also 2,3,6-11. In most of the optical weak measurements, Gaussian spatial modes of laser beams or Gaussian temporal pulse are employed as external pointer and associated polarization state of light is used as a pre-post selection mechanism, with tiny polarization dependent opti...

Interferometric weak value of polarization observable and differential Jones matrix algebra

“…As mentioned earlier, this protocol is realized in a standard Mach Zehnder interferometer [26,48]. Table 1 demonstrates the corresponding input electric fields and subsequent characteristic Stokes vector elements for extracting different polarization anisotropy effects [26].…”

“…1). The real WVA can be achieved by using a variable neutral density (ND) filter [26,48] which essentially varies the amplitude ratio a in path |1 and path |2 , thus varying the relative intensities. Variation in the relevant Stokes parameters(as in Table 1) as a function of amplitude offset parameter a provides the corresponding real WVA.…”

“…Variation in the relevant Stokes parameters(as in Table 1) as a function of amplitude offset parameter a provides the corresponding real WVA. Instead, the imaginary WVA can be probed by keeping the relative intensities in the paths same and recording the relevant Stokes parameters(as in Table 1) for different spatial positions slightly away from the point of minimum intensity of the interference fringes which provide the phase offset parameter p [26,48].…”

“…Up till now, it has been shown that simultaneously appearing multiple small polarization anisotropy effects can be modeled by a unitary evolution operator corresponding to the weak interaction Hamiltonian. Now, we complement the above weak measurement formalism dealing with simultaneous circular retardance α and circular diattenuation β effects with its corresponding classical field-based analog [26,48]. For describing such a sample with multiple anisotropy effects, it is required to define the differential Jones matrix N at every point, whereas the entire sample is represented by the exponential Jones matrix M [46,47].…”

“…Now, we consider near destructive interference of two paths of an interferometer having slightly different polarizations of light [26,48] with electric field vectors…”