Notional Duette on Nanophotonics Fundamentals

A two-part Notional Synthesis on Nanophotonics Fundamentals is being carried out: On the one hand, a rather novel depiction of the Fermionic Quantum Causality is being attempted. On the other hand, a Nanophotonic Response Encoder is being devised: Illuminated Electrons are the original Protagonists.


Primo: On Fermionic Quantum Causality
With respect to the Causality of the Fermi-Dirac Distribution Function ( ) it can be easily observed that, since there holds that under the Initial Condition ( ) a Second-Order Constant-Coefficient Bernoulli Differential Equation (DE) emerg-Optics and Photonics Journal ing as embodying the (Quantum) Causality of f.Indeed, by defining ( ) ( ) ( ) e 1 leading to (1) through (6).
Easily verifiably, on the other hand, the Monoparametric Family of Con- ρ being an arbitrarily chosen Real Number different from both (−1) and 0, might be regarded as a Collective Generator of the Fermi -Dirac Distribution Function Causality (4) by virtue of the simple Transformation ( ) ( ) leading back to (4) for any such ρ.
with Probability f lying between 0 and 1 for any bound Real x) is overlappingly analogous both to the Occupancy Degree of Current Energy Level and (in parallel) to the Non-Occupancy Degree of Current Energy Level.
Such a (Simulative) Quantum Specific Equipotently Dual Proportionality of f' to f and (1 -f), the Non-Linearity of DE ( 4) not being overlooked and the brilliance of systematic Topical Research Studies (for example, Refs [1] [2] [3]) being enthusiastically acknowledged, could be ventured to be considered linked to the Pauli-Principle-respecting Singularity of the Fermionic Character.
As Dirac, Fermi, Einstein, Feynman, and their Peers, would comment upon, Nature favours (Inherent) Functional Symmetries, the echo of some of which may be appearing perceptible through (Phenomenological) Physical Relationships of Admirably Concise Purity.

Secondo: On a Nanophotonic Response Encoder
In previous studies of ours, there has been traced an approximate analogy between the Photonic Dose β Rate of Change (dη/dβ) of the Persistent Photocarrier Sheet Density η and the Average Conductivity Carrier Mobility μ [4], allowing for the expression of the Second Photonic Dose Derivative The physically meaningful Boundary Conditions reflect that the Photoinduced Electron Surface Concentration scans the scale from its naught Dark-Value to its Terminal Value η 0 compatible with the Capacity of the eventually (at Critical Total Photonic Dose β 0 ) saturated Fundamental Subband ( ) ( ) On the other hand, for the Complete Equation ( 16) holding under Conditions (17) there may be employed the respective Green's Function g(β, γ), which for a reference Cumulative Photonic Dose γ reads: being positive for any Real x, and only asymptotically tending to zero for x tending to plus infinity) there appears the Conjugate First-Order Constantby the sum of its (unconstrained) Partial Solution φ p = 1 and the Solution of its Respective Homogeneous DE (constrained through (8)) φ H = expx: already incorporates the experimentally monitored Limiting Linearity of η(β) for approaching the saturation of the Nanophotonic Device Fundamental Conduction Subband, signaled by the instantaneous vanishing of μ β .
13) Mathematically, the Solution of Equation (12) under the Inhomogeneous Boundary Conditions (13) is formulated as the Superposition of a function χ(β) ψ(β) verifying the Complete, Inhomogeneous 0 M 20) Β(β) being the Solution of the Homogeneous Equation 0 Γ being the Wronskian Determinant of functions Β and Γ evaluated at the reference Instantaneous Cumulative Photonic Dose γ.Thus, the Green's Function takes the form solution of Equation (16) consistent with Conditions (17) is derivable as the Convolution between the Green's Function g and the Stimulus Mμ β : of the fact that the Green's Function is Nanodevice-specific as parametrised by the characteristic Total Photonic Dose β 0 tantamount to the saturation of the Capacity of its Fundamental Conduction Subband, it appears meaningful to adopt g(β, γ) as a potentially Notionally Universal Nanophotonic Re-E. A. Anagnostakis DOI: 10.4236/opj.2018.811027