1. “Hybrid resonant photonic crystals:
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“Hybrid resonant photonic crystals:
a model of 1D mesochiral structure.”
Donatella Schiumarini, Norberto Tomassini and Andrea D’Andrea
ISTITUTO DEI SISTEMI COMPLESSI,CNR
Area della Ricerca di Roma 1 (Montelibretti)
“The hybrid (isotropic/anisotropic) periodic stacks with misaligned in plane optical C-axis and in resonance with Wannier exciton energy of 2D quantum wells, is able to combine the optical properties of the normal isotropic resonant Bragg reflectors (RBR), namely: giant dipole effect, spatial dispersion, strong radiation-matter interaction, super-radiance mode,… , with those observed in anisotropic multi-layers: high photon density of states, absolute photonic gap inside the Brillouin zone, negative refraction properties... .”
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2. isotropic/anisotropic layers, with misaligned in plane anisotropy and
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The manipulation of the optical properties in order to obtain coherent radiative coupling among a collection of emissive species was proposed by R.H. Dicke in 1954 (R. H. Dicke, Phys.Rev. 93, 99 ,1954 ).
If N-emitters are arranged periodically in an homogeneous dielectric background, with emission wavelength equal two times the spatial periodicity, a new collective coherent state (super-radiance mode) originates in the system (“resonant photonic Bragg reflector”-see ref.1).
Since the optical strength of N-oscillators concentrates into the super-radiant mode, increasing the number of emitters increases the radiation-matter interaction,and therefore polariton splitting energy can overcome the total broadening of the system giving the so called “strong coupling regime”.
The exciton-polariton propagation in resonant hybrid periodic stacks of
isotropic/anisotropic layers, with misaligned in plane anisotropy and
Bragg photon frequency in resonance with Wannier exciton of 2D quantum
wells, is computed by self-consistent theory and in the effective mass
approximation for symmetric and asymmetric elementary cells.
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3. Hybrid sample deposition:
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Hybrid sample deposition:
The improvements on plasma-assisted molecular-beam epitaxy allowed to deposit on a substrate of a buffer of one micron of GaN (1,-1,0,0), and 15 quantum wells of AlGaN/GaN with in-plane optical C-axis (P. Waltereit et al. J. of Crystal Growth 218, 143 , 2000).
It is well known that also isotropic Bragg structures become optically anisotropic when submitted to an intense mechanical constrain .
An hybrid material can also to be obtained by encapsulating liquid crystals in a solid isotropic periodic structure. X
N=1-elementary cell
l/4
-Anisotropic dielectric materials (blue)
-Isotropic dielectric materials (yellow) z
Fig.1
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4. A) Symmetric elementary cell:
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A) Symmetric elementary cell:
InGaAs/GaAs(001) high quality QWs
at low temperature
P polarization
at normal incidence:
transmittivity (blue) ,
reflectivity (red) ,
absorbance (green)
Fig.2
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5. At normal incidence, P polarized optical response, with
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At normal incidence, P polarized optical response, with
axis orientation
, shows the same spectra than that computed for S polarization
with
axis orientation
P polarization:
Fig.3
The orientation of in plane C-axis
of the uniaxial bilayer stack with
respect to the incident radiation
determines the reflection intensity
from 0% to 100% as shown by
the two limiting cases reported on
fig.3 and fig.2 respectively.
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6. SIF
In fact, the optical response, computed for C-axes misalignment a=p/4 , shows the reflection intensity as large as 50%, since the same contribution of ordinary and extraordinary waves, is expected. Moreover, the transmission peaks, close to the borders of the reflection stop band, maintain their high intensity value (giant transmission band edge-ref.2).
T : bleu
R : red
A : green
T+R+A=1
Fig.4
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7. S-polarization: Fig.5a P-polarization: Fig.5b Tss: green Tsp: red
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S-polarization: Fig.5a
Tss: green
Tsp: red
Rss: bleu
Rsp: grey
Tpp: red
Tps: green
Rpp: bleu
Rps: grey
P-polarization: Fig.5b
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8. (positive optical symmetry)
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B) Asymmetric elementary cell: in order to remove the symmetry due to the mirror plane parallel to z-direction (point group ) at least two in-plane uniaxial layers with misaligned optical axes must to be present in the elementary cell (ref.2). Moreover, we assume the two further conditions:
(positive optical symmetry)
Notice, that , at variance of the first condition, the second condition is
chosen in oder to make more simple the optical tailoring of the system
and, therefore the spectra interpretation. Moreover, we will point out that
some interesting optical properties (as: degenerate band edge, high
density of states,...) still remain also by removing the second condition,
since they are robust properties of the system.
Symmetry of the multilayer space group : i) mirror plane parallel to the (x,y) layers ( ) , ii) two-fold rotation about Z-axis ( ), and iii) time reversal ( ).
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9. SIF
B1) Symmetric case:
Fig.6a
Fig.6b
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10. reflectance/transmission spectra for S and P polarization are equal
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B2) Asymmetric case:
Fig.7a
Fig.7b
In a non-absorbing photonic crystal, for perpendicular optical axes, the
reflectance/transmission spectra for S and P polarization are equal
(degenerate case), since they feel the same sequence of dielectric
constants except for their order.
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11. The strong difference in the absorbance intensities for S and P
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B3) Degenerate case:
Fig.8b
Fig.8a
The strong difference in the absorbance intensities for S and P
polarization is due to the asymmetry of the elementary cell.
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12. a)-reciprocal symmetry:
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C) Dispersion curves:
(see ref.5, 6)
a)-reciprocal symmetry: ; ;
b) – non-reciprocal symmetry:
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13. a) reciprocal symmetry : The direct gaps drop inside the Brillouin
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a) reciprocal symmetry :
The direct gaps drop
inside the Brillouin
zone for in-plane
optical axes (see ref.3)
Fig.9
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14. normal incidence Fig.10a Fig.10b non-normal incidence
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normal incidence
Fig.10a
Fig.10b
non-normal incidence
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15. D) Intermediate dispersion curves: optical trapping (see ref.4 and 5)
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D) Intermediate dispersion curves: optical trapping (see ref.4 and 5)
Optical trapping on IDC
for misalignment a=p/2
and releasing for a=p/4
(see ref.3)
Maximum energy splitting
between the two IDCs.
Fig.11
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16. are performed and the misalignment of the optical axes provide the
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Conclusions:
i) The tailoring of the optical response for asymmetric elementary cell
are performed and the misalignment of the optical axes provide the
opportunity for a strong re-arrangement of the band structure.
ii) Investigating the exciton-polariton propagation and/or localization in
the asymmetric hybrid Bragg reflector, the dispersion curves evidence
two IDC in the lowest energy gap, very close to the exciton energy,
whose energy splitting is a strong function of the misalignment of the
two optical axes.
iii) For exciton energy in resonance with Bragg energy and optical
axes misalignment a=p/2 the absorbance is strongly dependent from
the light polarization.
iv) Non-reciprocal signature (ref.6) will be studied at the
interband energies of semiconductors in resonant hybrid Bragg reflectors .
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17. References: 1) L. Pilozzi, A. D'Andrea and K. Cho,
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References:
1) L. Pilozzi, A. D'Andrea and K. Cho,
“ Spatial dispersion effects on the optical properties of a resonant
Bragg reflector” Phys. Rev.B 69, (2004).
2) Alex Figotin and Ilya Vitebeskiy,
“Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers” Phys.Rev. E 72 , (2005).
3) Cédric Vandenbem, Jean-Pol Vigneron and Jea-Marie Vigoureux,
“Tunable band structures in uniaxial multilayer stacks”
J.Opt.Soc.Am B Vol.23, N.11 November 2006.
4) Z.S.Yang, N.H.Kwong, R. Binder and Arthur L. Smirl,
“Stopping, storing and releasing light in quantum well Bragg Structures” J.Opt.Soc.Am.B Vol.22, N.10 October 2005.
5) A.D’Andrea and N.Tomassini,
“Resonant Bragg quantum wells in hybrid photonic crystals”
arXiv: v1 26 Jan 2015
6) V.P.Kochereshko,V.N.Kats,A.V.Platonov,L.Besombes,D.Woverson,
H.Maritte, “Non reciprocal magneto-optical effects in quantum wells” Phys.Stat.Sol. (c) v.11,7-8, 1316 (2014)
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