A One Dimensional Photonic Crystal - 台大電機系計算機中心

No band gaps ( no scattering in y)
No degeneracy (split: TMy & TEy )
Approximately linear at
long wavelengths
for all PhC
effectively homogeneous
lower modes concentrate
electrical energy in the
higher ε-region
ω TM < ω TE
Off-Axis Off Axis Propagation
NTU GIPO & EE 13 YPC Photonic Modeling and Design Lab.
Localized Modes at Defects
Defects + ω in band gap
may exist localized modes
0.2 a (ε=13) + 0.8a (ε=1)
Like two parallel perfect mirrors
discrete freq. (quantized)
thicker defect => more states
1.6a =
2*0.8a
E-field strength
Quantized like particle in a box (QM) or metallic cavity (μ-wave)
Defects by
Increase low/high-ε thickness
or lower/increase ε (same thick.)
or combined
Pull down/push up a sequence
of discrete modes from the
upper/lower bands
Max. exp. decay in mid-gap
Single peak associate with the defect
Used in dielectric Fabry-Perot filter
DOS
= # states / Δω
NTU GIPO & EE 15 YPC Photonic Modeling and Design Lab.
Short wavelength (high freq.)
Freq. difference
Below light line
* index guided
* decay exp.
* negligible overlap
* small coupling
Every mode become
a uncoupled
guided mode
Off-Axis Off Axis Propagation
Blue: (0, k y,0)
Green: (0, k y, π/a)
Red: light line
NTU GIPO & EE 14 YPC Photonic Modeling and Design Lab.
Localized Modes at Defects
Defects by
Increase low/high-ε thickness
or lower/increase ε (same thick.)
or combined
Pull down/push up a sequence
of discrete modes from the
upper/lower bands
Off-axis propagation
Still localized in z-direction
Can be guided in both
High and low ε regions (even air)
2D => photonic crystal fibers (PCF)
NTU GIPO & EE 16 YPC Photonic Modeling and Design Lab.