Optical near fields as photon‐matter interacting systems

Abstract

A quantum theoretical formulation of an optical near-field system developed using the projection operator method is shown to be applicable to conventional problems in the optical near field in a unified way, and also addresses different quantum mechanical issues such as atom manipulation and nano-fabrication. To gain a clear insight, the effective mass of exciton-polaritons is introduced; this depends on the sizes of the probe tip and sample. We calculate the optical near-field intensity detected by (a) a probe sphere and (b) tapered probe modelled by two spheres. The results show that the size of the probe tip determines the spatial resolution, while the contribution of the tapered part causes degradation of the signal contrast. A size± resonance effect between the probe and sample is predicted. Furthermore, enhancement of the signal intensity is observed at the edges of a circular aperture perpendicular to incident polarization. These results are consistent with those obtained from different methods. The approach employed is shown to be a valuable tool in physical understanding and analysis of the near-field optical phenomena as well as experimental situations.

Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology

“…Since "Ricci tensor"R ν µ in this case is defined asR ν µ =R νσ σµ = −S σµ S νσ = S µσ S νσ and "scalar curvature"R becomesR ν ν = S στ S στ , we see that the first equation in ( 9) is rewritten asT ν µ =R ν µ −Rη ν µ /2 and is isomorphic to the second one. In addition, the divergence free condition ∂ νT ν µ = 0 which qualifiesT ν µ as the energy-momentum tensor of the Clebsch dual field corresponds to the second equation in (11). We conjecture that the above isomorphism ( 9) is a sort of "conjugated"manifestation of the isomorphism between the Coulomb force and the universal gravitation, since, as we already explained, the Clebsch dual field represents the longitudinal Coulomb modes of electromagnetic field.…”

“…Therefore, while S µν only contains the first derivatives of scalar fields φ and λ, the entire formulation of the Clebsch dual field covering, for instance, ∇ νT ν µ involves the first and second derivatives of them, for the latter of which the order of differentiation does not matter. We mentioned already that the simple bivector property of S µν is a crucial element for deriving the first equation in (11). In reference [5], we show that, not only for (11) but also for the other parts of the Clebsch dual formulation, the simple bivector property of S µν and the commutativity of the second derivatives of scalar fields λ and φ are essential elements.…”

“…The results showed that, in the initial stage of deposition, the deposition rate and the FWHM increased monotonically with time. When the FWHM reached the size of the fiber probe tip, the deposition rate was the maximum, which is the phenomenon known as size-dependent resonance between the fiber probe tip and the size of the NM [11]. Then, the deposition rate monotonically decreased and approached a constant value.…”

<p style="text-align: left;">History, current developments, and future directions of near-field optical science

“…By noting these two phenomena, spatial localization of the DP has been studied for a system composed of two NMs between which the DP energy is transferred 31,38 . This study assumed that a nanometer-sized subsystem (composed of two NMs and the DP) was buried in a macroscopic subsystem (composed of a macroscopic host material, incident light, and scattered light).…”

Excitation dynamics in a three‐quantum dot system driven by optical near‐field interaction: towards a nanometric photonic device

“…According to the theoretical framework developed in our previous studies (Kobayashi & Ohtsu, 1999; Kobayashi et al ., 2001; Sangu et al ., 2001; Ohtsu et al ., 2002), let us consider an interdot interaction due to the optical near‐field. The total Hamiltonian Ĥ for the system consists of Ĥ photon for incident photons, Ĥ matter for a surrounding macroscopic matter system, Ĥ QD for a nanometric QD system, and their interactions V̂ as given by the multipolar QED Hamiltonian (Cohen‐Tannoudji et al ., 1989; Craig & Thirunamachandran, 1998; Andrews & Demidov, 1999).…”