Circuit Elements at optical Frequencies: Nanoinductors,

Nanocapacitors and Nanoresistors

PRESENTED BY

MARYAM LIAQAT

Modular assembly of Optical Nanocircuits Matellic and dielectric nanoparticles ressembles as lumped elements

on the basis of permitivity of material and geometry, as

If permitivity is positive the dielectric behaved as nanocapacitor.

If permitivity is negative the dielectric behaved as nanoinductor

and nanoresistors are referred as ohmic losses.

Real part of permitivity calculate the polarization of material and

imaginary part calculate the ohmic losses/ploarization losses in

material

By applying simple circuit rules , nanoparticles

configured as nanocircuits on the bases of

spectral response or polarization of signals.

Scattering is effected by Size to wavelength

ratio

Kirchoff’s circuit laws are used to translate

electric circuit to optical frequencies.

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Electric current on Nanosphere

Electric Potenital and Impedance on the Sphere

ε>0

IimpIsph Ifring

G Cs Cfring

The Kirchhoff voltage law is also satisfied, since is locally near zero in this quasistatic approximation.

Therefore:

Inductance and Capacitace of Nanosphere

ε<0

Therefore:Iimp

Isph Ifring

G Le Cfringe

The rasonance condition for the LC

circcuit that is and

permitivity is

Coupled Nanocircuits for Multilayer Spheres Within the quasi-static Limits there are two case for coupled

nano-circuits. Depending on the external excitation and orientation of the nano-resonant. The possible arrangements are,

Case I : Parallel Resonant L-C Circuit Case II : Series Resonant L-C CircuitIn fused circuit Fringes always remain parallel to the

parallel/series lumped nano-circuit.

Conventional Circuit Theory

Lumped elements isolated from external world Interconnection( series/parallel) passes only

through their terminals depending on external applied field

Epsilon-near-zero (ENZ) nanocircuit elements are insulated from surrounding space as nano-insulator.

Epsilon-very-large (EVL) nanoconnector are terminals trough which the displacment current flows.

Closed-form Potential Distribution

Permittivity at interface is epsilon-I Potential determined by sum of two terms that

is Impressed Field is parallel or orthogonal to the interface

Background potential distribution fai-0 independent of epsilon-I and epsilon-1

epsilon-2= - epsilon-1 (for series ) Resonance frequency w=1 /(LC)^1/2 at which

outer circuit isnt distinguish b/w both elements

Series Resonant L-C Circuit When angle (b/w impinging electric

field and normal to the interface b/w 2 half-cylinders) is zero.

Electric field is perpendicular to sphere and therefore the lumped elements are in series

Same current flowing through the both/all components

Potential Difference at the surface is zero

Displacement current flows within the circuit

Equivalent local impedance of cylinder seems to be zero from outside

Potential distribution is epsilon-2= - epsilon-1= -2 epsilon-0

Effective impedance is infinity

Impressed current depend on epsilon-0

Displacement current depend on epsilon-2 inside the lower half cylinder

Energy is Stored inside the resonant pair

No current passes through the fringe capacitance

Parallel Resonant L-C Circuit Electric field is parallel to sphere

therefore the lumped elements are in parallel

A Potential Difference is Induced in the sphere

Total Electric Field is zero at the surface

At resonate point impedance is infinite

Net displacement current is zero As the case is considered lossless

then Imaginary part of permittivity is negligible

Voltage across the elements are same

Electric field lines are tangential to the surface of sphere

Impressed D. current flow through fringes which depends on specific value of permittivity (of outer material /background)

Thanks for

attention