1Lab

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PhC guided resonances discussion

Pierre Pottier

Laboratoire des Micro et Nano Systèmes 19/06/2008

2Lab

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Plan

Modelisation double layer slabGuided resonancesTuning & resonancesEnhancementQD localisationFluorescence enhancement ?

(summarise, analysis, article discussion)

3Lab

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Modelisation of PhC slabs

T double layer PhC

T single layer PhCT single layer slab

T double layer slab

Analytical formula (short)

Analytical formula (long)

Simulation (matrix transfer)

Model: T 1 slab + equiv. FP cavity

Analytical formula

Simulation (FDTD) + band structures

Model simplified: T 1 slab (background) + peaks position for r/a<<1 (from w.g. disp. curve)

backgroundcomparison

engineering of background Te.g.: AR coating

Analytical formula

Simulation (FDTD)

Model - near field regime ? - far field regime model equiv. FP cavity

OK

OK

OK

~

?

?

~

4Lab

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Double layer slab

t

d

t

n2

n2

slab transparent when t = kλ/2n2 kNslab reflective when t = (2k+1)λ/4n2

double slab:(weak) FP-like resonances when d ≈ λ/2n1

& around t = (2k+1)λ/4n2

n1

n1

n1

300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

wavelength (nm)

tran

smis

sio

n

thickness=0.4a

gap=0.5agap=0.6agap=0.7agap=0.8agap=0.9agap=1.0a

2n2t/2 2n2t/1

4n2t/3

5Lab

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Double layer slab

t

d

t

n2

n2

n1

n1

n1

deq.

ded. = f(λ)R = f(λ)

if d small (case of near field regime), no more FP modes

6Lab

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background fitted+peak shape analytical model (peak position & width simulation)

FDTD simulation

Article [1]

Single PhC slab: guided resonances

Analytical model of peak position and Q possible ?

7Lab

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Double PhC slab: resonances & tunabilityArticle [2]

Far field regime

1 PhC slab with high and wide Rr/a high

2 PhC slabs FP cavity

Near field regime

evanescent coupling between slabsh>0.5acoupling due to propagating waves

T independent of lateral displacement

PhC slab with high R big holeshigh distance between PhC slabsMEMS vertical actuation (only)

low Q guided resonances( more field between slabs) less enhancement (?)

short distance between PhC slabsMEMS vertical and/or horizontal actuation

8Lab

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Near field regime

Article [3]

Double PhC slab: resonances & tunability

9Lab

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Enhancement

Enhancement via Purcell factor only (?)

need high Q, small Vm

need QD coupled at max. of field

(http://qwiki.stanford.edu/wiki/Purcell_Factor)

10Lab

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QD localisation

SiNSiO2

Si

Si

SiNSiO2

11Lab

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Fluorescence enhancement ?

?

?

?