Cristaux Photoniques, PO-014 Ecole doctorale photonique Romuald

Cristaux Photoniques, PO-014
Ecole doctorale photonique
Romuald Houdré
Semestre été 2007
IV Techniques de mesures
Plan
1 Introduction, survol du domaine.
•Introduction
•Histoire des cristaux photoniques
•Les principaux concepts
2 Théorie
•Cristal infini
-Equations de base
-Structure de bandes
-Ondes planes
•Cristal fini
-Matrice de transfert
-FDTD
3 Propriétés physiques
•Contrôle des ondes électromagnétiques
-Miroir
-Guide d’onde
-Résonateurs optiques
•Propriétés réfractives
•Diagramme de dispersion et nappes equi-fréquence
•Réfraction
•Analyse de Fourier des ondes de Bloch
•Superprisme, ultraréflectivité, réfraction négative
•Auto-collimation
4 Composants, fabrication et applications
•Techniques de fabrication
-écriture, gravure
-2D, III-V, Si, SOI
-3D, Opales
•Techniques de mesures
-Source interne
-Injection face clivée
•Guides d’onde à cristaux photoniques
•Composants
-Virages, diviseurs, coupleurs
-Filtres multiplexeurs / démultiplexeurs
-Spectromètres et interféromètres
-Coupleurs
-Polariseur et rotateur
-Lasers à cristaux photoniques
-Lasers 1D
-Amplificateurs
-Lasers cavités 0D
5 L'actualité
•Imagerie, Fourier, champ proche, résolu en temps
•Cavités à très grand facteur de qualité
•Modes lents
6 Sujets connexes
•Les matériaux 3D
•Les fibres à cristaux photoniques
•Les métamatériaux
Goal
Once our photonic crystal structure
has been (painfully) fabricated and
characterised (SEM etc...)
How can we measure its optical
properties, it was designed for ?
Which optical properties ?
Optical response
D()
• Transmission, T
• Reflection, R
I()
T()
• Diffraction, D
• Absorption, A
• Losses, L=1-T-R-D-A R()
I()
T()
R()
disp_tri_hole_TE.dat
0.8
0.35
0.7
0.3
0.6
even
odd
0.25
0.5
u=a /λ
Band structure
• Dispersion curve
• Group index
L()
0.4
0.2
0.15
even
0.3
0.1
0.2
0.05
0.1
M
0
-0.6
G
-0.4
-0.2
0
K
0.2
k
0.4
0.6
M
0.8
1
0
0
0.1
0.2
0.3
k
||
0.4
0.5
Which optical properties ?
Localised state
• Optical cavity
• Resonance frequencies
• Quality factor
Light propagation inside the
photonic crystal
QD in bulk
PL intensity ( a. u.)
Dynamic properties (time resolved)
Emission properties (spontaneous, amplified, laser)
Wavelength
• Visible / near infra-red
QD1
QD2
0
2
4
6
time (ns)
8
10
Which photonic crystal structure ?
3D photonic crystal
2D photonic crystal
Which photonic crystal structure ?
Material
• Dielectric / Semiconductor
•
Use
• Physics
• Device
B12
1st PhC
B23
2nd PhC
3rd PhC
Input
port
Through
port
1
2
3
4
L~18 μm
5
Techniques outline
Lithographic tuning
External light source
Reflectivity
End fire
Internal light source
Internal light source
Luminescence spectroscopy
Advanced techniques
Local probe, SNOM
Time resolved
Fourier imaging
Lithographic tuning
Scaling laws
r r'= r.s
(r) (r')
k k'= k /s
'= /s
H(r) H(r')
E(r) E(r')
Reduced units
Energy :
a a
u= =
2c
ka
˜
Wave vector : k =
2
a : lattice parameter
Lithographic tuning
Wavelength, energy scan
a a
Reduced energy : u = =
2c
either scan u in changing
the lattice constant. Often
more convenient.
either scan u in changing
the wavelength
a : lattice parameter
sample
External source
Reflectivity & transmission measurements
Simple R&T measurements to probe the photonic bandgap
I
T.I
R.I
Similar to the measurement of
a dielectric multi-layer sample
Planar GaAs/AlAs Fabry-Perot cavity
R.P. Stanley et al., Appl. Phys. Lett., 65, 1883, (1994)
External source
Reflectivity & transmission measurements
Spectral resolution
In a linear regime, light source can be a wavelength tuneable
source or a white light source and spectral resolution is
performed afterwards
I(
T( ).I( )
tuneable)
R( ).I( )
I(
T( ).I( )
white light)
R( ).I( )
External source
Reflectivity & transmission measurements
Quantitative measurements require a good measurement of
the reference (incoming intensity)
chopper f1
Reference
Incident
chopper f2
Many set-up designs, one example :
identical
optics
beam
splitter
Reflected
same
detector
Similar set-up in transmission with
a Mach-Zehnders like geometry
lock-in detection
at f1 and f2
R=S(f2)/S(f1)
External source
Reflectivity & transmission measurements
Quantitative measurement
Note: it is not easy to measure directly reflectivity
coefficients close to unity
This would imply being able to discriminate between e.g.
R=0.999 and R=0.997
Usually much more convenient to use the mirror to make a
high Q optical cavity and deduce R from Q
External source
Reflectivity & transmission measurements
Simple R&T measurements to probe the photonic bandgap
Note that:
• T=0 does not prove R=1
• No angular investigation
(full bandgap ?)
• Polarisation ?
First measurements performed on opals of
0.11μm polystyrene microspheres
I. Inanç Tarhan et al., Opt. Lett., 20, 1571, (1995)
External source
Reflectivity & transmission measurements
Simple R&T measurements to probe the photonic bandgap
inverted opal
Y.A.Vlasov et al., Nature, 414, 289, (2001)
External source
Angular reflectivity
Principle
Measurement :
• Intensity vs. angle(s) at constant wavelength
• Intensity vs. wavelength at constant angle(s)
Light is reflected according to the grating diffraction law
Conservation of the in-plane component of the wavevector
k//ref = k //inc + G = k//inc + miGi
i
G : vector of the reciprocal lattice
mi = 0 : specular reflection
mi 0 : diffraction
As such, it will provide information on the reciprocal
lattice but not the band structure (?)
• For some specific set of incident k and wavelength, light
can couple to a mode into the photonic crystal
• Giving rise to a dip in the reflected intensity spectrum
(Wood anomaly)
• Will provide information on the band structure k()
• Simple picture :
θ2
n2
n 1 > n2
k1
β1
θ1
k2
β2
sin θ1
n2
=
sin θ2
n1
in-plane k conservation
k0 n1 sin θ1 = k0 n2 sin θ2
β1 = β2
k//
medium 2
kx
k=
medium 1
n
c
medium 2
Total internal reflexion :
k<n2/c :
coupling 1 to 2 possible
k>n2/c :
coupling 1 to 2 impossible
medium 1
• In the case of a bi-dimensional medium 2, the equi-frequency
surface is reduced to a curve in the plane kx, ky, i.e. points in the
kx, kz plane
PhC EFS
air light cone
such an incidence wave can
only be reflected or diffracted
such a specific incident wave
can couple to a PhC mode
plane of incidence
ky
kx
k//
PhC
such resonant incidence wave
can couple to a PhC mode
such an incidence wave can
only be reflected or diffracted
air
k=
n
c
ky
kx
In real life experiment are not so straightforward to
interpret due to the complex shape of the reflectivity
spectrum
Macroporous silicon
TE, M orientation
M. Galli et al., Phys. Rev. B, 65, 113111, (2002)
Measurement limited
to the radiative cone
For 3D structures, the measurement probes mainly the
density of states and its associated singularities
Artificial opals
E. Pavarini. et al., Phys. Rev. B, 72, 045102, (2005)
Measurement above the light line limit
Extension to larger k-values
air light cone, n=1
ky
n
k=
c
nZnSe = 2.4
kx
dielectric light cone, n>1
M. Galli et al., Phys. Rev. B, 70, 081307, (2004), M. Galli et al., Phys. Rev. B, 72, 125322, (2005)
Measurement above the light line limit
Extension to larger k-values
nZnSe = 2.4
Si
SiO
2
air
Measurement above the light line limit
Extension to larger k-values
W1 waveguide
W1 waveguide
• Experiment is difficult
• Resolution is limited by the sphere astigmatism and field of view
• Analysis is delicate
• Experiment does not discriminate between true propagating slow modes
and localised defect modes