2328-13
Preparatory School to the Winter College on Optics and the Winter College on
Optics: Advances in Nano-Optics and Plasmonics
30 January - 17 February, 2012
BLOCH SURFACE WAVES ON PHOTONIC CRYSTALS
APPLICATIONS TO GAS SENSING AND BIOPHOTONICS
F. Michelotti
University Roma La Sapienza
Roma
Italy
BLOCH SURFACE WAVES ON PHOTONIC CRYSTALS
APPLICATIONS TO
GAS SENSING AND BIOPHOTONICS
SAPIENZA Università di Roma
Department of Basic and Applied Sciences for Engineering
Molecular Photonics Laboratory
Francesco Michelotti
International Centre for Theoretical Physics, Trieste, February 2010
Collaboration and Credits
SAPIENZA Università di Roma
'LSDUWLPHQWRGL6FLHQ]HGL%DVH$SSOLFDWHSHUO¶,QJHJQHULD
F.Michelotti, L. Dominici, A.Sinibaldi, G.Figliozzi
POLITECNICO di Torino
FLab and Dipartimento di Scienza dei Materiali ed Ingegneria Chimica
E. Descrovi, M. Ballarini, G. Digregorio, F. Frascella, P. Rivolo, B. Sciacca, F.
Geobaldo, F. Giorgis, M. Quaglio, M. Cocuzza and F. Pirri
IMT- Ecole Polytechnique Fédérale de Lausanne (EPFL) - Neuchatel
T. Sfez, L. Yu, and H.-P. Herzig
NAM- Ecole Polytechnique Fédérale de Lausanne (EPFL)
D. Brunazzo and O. J. F. Martin
IOF - Applied Optics and Fine Mechanics ± Jena
N.Danz
IWS - Materials and Beam Technology ± Dresden
F.Sonntag
Plasmonics
 DURING THESE TWO WEEKS MANY
PLASMONICS
EXPERIMENTS
AND
APPLICATIONS WERE OR WILL BE
DESCRIBED
 PLASMONICS RECENTLY BECAME A
VERY HOT RESEARCH FIELD. SO
POPULAR THAT «.
 APPLICATIONS BASED ON PLASMONS
SHOW SOME LIMITATIONS WHICH CAN
BE OVERCOME ADOPTING ALTERNATIVE APPROACHES
ONE OF THE POSSIBLE APPROACHES
ARE BLOCH SURFACE WAVES ON
PHOTONIC CRYSTALS
Examples ± SPR Biosensing
Z [ rad/s ]
2.5x10
16
Zspp
Zp
1 H2
TM
2.0x10
16
1.5x10
16
Zp
1.0x10
16
Zspp
0.5x10
16
0
T
Linea di luce
Z
c
Z2 Z 2
2Z Z
Dispersione del SPP
p
Dispersione della luce nel vuoto
2
Frequenza del plasmone2di superficie
Frequenza di plasma
p
q(Z )
0
0.5
1.0
7
ȁȁȁȁȁȁȁȁȁ
¸¸¸¸¸¸¸¸¸
R
1.5
-1
q [ 10 m ]
SPP dispersion at a
metal(ideal)/dielectric interface
T
Examples ± SPR Biosensing
2.0
Substrate
PAM, Otto
1.5
R [ arb.un. ]
Air
Metal Film
O = 1550 nm
1.0
0.5
Ti
TP
Substrate
Metal Film
PMA, Kretschmann
Au (40nm) + SiO2 (184nm)
Bare BK7 prism
0
-40
-30
-20
-10
0
Ti [ deg ]
10
20
30
Examples ± SPR Biosensing
Examples ± SPR Biosensing
 Absorption losses in metal layers give rise to broad resonances and limit the
sensitivity of SPR devices
 The limit of resolution is 'n=2#10-7 RIU (Biacore)
 The resolution does not permit to detect small molecules (<250 dalton)
 SPR devices never really accessed the Point-of-Care level
 The sensitivity can be improved by making use of long range surface
plasmon polaritons but problems due to the symmetry of dielectric layers
arise.
Examples ± Fluorescence Imaging
Bare Cover slip
Au coated Cover slip (45nm)
Surface Plasmon Coupled Emission
(SPCE)
and
Surface Plasmon Field-enhanced
Fluorescence (SPFS)
Examples ± SW-SPCF Fluorescence Imaging
Examples ± DLSPPW and LRSPP Waveguiding
Dielectric
thickness
500nm
Can we do similar things in a different way?
We can exploit the propagation of surface electromagnetic waves (SEW) at the
truncation interface of finite one dimensional photonic crystals (1DPC)
We shall refer to such waves with the name
Bloch Surface Waves (BSW)
To demonstrate such possibility in the following we will describe the:
Mon
10?? ± 1100
General properties of BSW on 1DPC (Theory)
Tue
1000 - 1100
Experimental techniques for the detection of SPP and
BSW (Experimental)
Tue
1130 ± 1230
Applications of BSW to gas sensing (Experimental)
Wed
1430 - 1530
Applications of BSW to biophotonics (Experimental)
Lecture 1
General properties of BSW on 1DPC
(Theory)
BSW at the truncation interface of 1DPC
Propagation of light in infinite 1DPC
cell n-‐1
cell n
n(x) = n2
n(x) = n1
with
for 0 < x < b
for
ďфǆфȿ
Ŷ;ǆнȿͿсŶ;ǆͿ
0
E x, z E x e iEz
In each layer the field can be expressed as the superposition of forward and backward propagating waves
( a n(D ) e ikDx ( xn/ ) bn(D ) e ikDx ( xn/ ) )e iEz
E ( x, z)
With
k Dx
^>Z / c n
D
@
2
E
`,
1
2 2
D=1,2
In a vectorial representation
§ a n(D ) ·
¨ (D ) ¸
¨b ¸
© n ¹
Propagation of light in infinite 1DPC
§ a n( 1 ) ·
¨
¸
¨ b( 1 ) ¸
© n ¹
For the sake of notation simplicity
§ a n 1 ·
¨¨
¸¸
© bn 1 ¹
§A
¨¨
©C
B ·§ a n ·
¸¸¨¨ ¸¸
D ¹© bn ¹
§A
¨¨
©C
B·
¸¸ T
D¹
§ an ·
¨¨ ¸¸
© bn ¹
§ a n( 2 ) ·
¨
¸
¨ b( 2 ) ¸
© n ¹
§ cn ·
¨¨ ¸¸
© dn ¹
The unit cell / translation operator is unimodular AD-‐CB=1
TE case
ª
º
k ·
1 §k
A e ik 1 x a «cos k 2 xb i ¨¨ 2 x 1x ¸¸ sin k 2 xb»
2 © k1 x k 2 x ¹
«¬
»¼
C
e
ik 1 x a ª 1
º
§ k 2 x k1 x ·
¨
¸
i
sin
k
b
« ¨
2x »
¸
2
k
k
«¬ © 1 x
»¼
2x ¹
B
D
ª 1 §k
º
k ·
e ik 1 x a « i ¨¨ 2 x 1x ¸¸ sin k 2 xb»
«¬ 2 © k1 x k 2 x ¹
»¼
e
ik 1 x a ª
º
1 § k 2 x k1 x ·
¸¸ sin k 2 xb»
«cos k 2 xb i ¨¨
2
k
k
«¬
»¼
2x ¹
© 1x
Propagation of light in infinite 1DPC
§ a n( 1 ) ·
¨
¸
¨ b( 1 ) ¸
© n ¹
For the sake of notation simplicity
§ a n 1 ·
¨¨
¸¸
© bn 1 ¹
§A
¨¨
©C
B ·§ a n ·
¸¸¨¨ ¸¸
D ¹© bn ¹
§A
¨¨
©C
B·
¸¸ T
D¹
C
e
ª 1 § n22 k1 x n12 k 2 x ·
º
¨
¸
i
sin
k
b
« ¨ 2
2x »
2
¸
2
n
k
n
k
«¬ © 1 2 x
»¼
2 1x ¹
§ a n( 2 ) ·
¨
¸
¨ b( 2 ) ¸
© n ¹
§ cn ·
¨¨ ¸¸
© dn ¹
The unit cell / translation operator is unimodular AD-‐CB=1
TM case
ª
º
1 §¨ n22 k1x n12 k 2 x ·¸
ik 1 x a
A e
2 ¸ sin k 2 xb» B e ik
«cos k 2 xb i ¨ 2
2 © n1 k 2 x n2 k1x ¹
¬«
¼»
ik 1 x a
§ an ·
¨¨ ¸¸
© bn ¹
D
e
1xa
ik 1 x a
ª 1 § n22 k1 x n12 k 2 x ·
º
¨
¸
i
sin
k
b
«
2x »
2
¨ n2 k
¸
2
n
k
«¬
»¼
2 1x ¹
© 1 2x
ª
º
1 §¨ n22 k1x n12 k 2 x ·¸
2 ¸ sin k 2 xb»
«cos k 2 xb i ¨ 2
2
© n1 k 2 x n2 k1 x ¹
¬«
¼»
Propagation of light in infinite 1DPC
Only one vector is independent
§ an ·
¨¨ ¸¸
© bn ¹
§c ·
Note that: ¨¨ n ¸¸
© dn ¹
§ A'
¨¨
© C'
B' ·
¸
D' ¸¹
n
§ c0 ·
¨¨ ¸¸
© c0 ¹
§A
¨¨
©C
and that:
B·
¸¸
D¹
§ A'
¨¨
© C'
n
§ a0 ·
¨¨ ¸¸
© b0 ¹
§ D
¨¨
© C
B' · § A
¸¸ z ¨¨
D' ¹ © C
B·
¸¸
A ¹
B·
¸¸
D¹
The unit cell translation operator is such that:
Tx
x l/
T  E ( x)
E (T 1 x)
E ( x l/).
Floquet theorem for a wave propagating in a periodic medium:
 E K ( x , z ) E K ( x )e iKx e iEz
®
¯E K ( x / ) E K ( x )
K := Bloch wavenumber
n
§ a0 ·
¨¨ ¸¸
© b0 ¹
Propagation of light in infinite 1DPC
Periodicity
§ an ·
¨¨ ¸¸
© bn ¹
e
iK /
§ a n 1 ·
¨¨
¸¸
© bn 1 ¹
Eigenvalues
§A
¨¨
©C
B ·§ a n ·
¸¸¨¨ ¸¸
D ¹© bn ¹
Eigenvectors

½
1
°ª 1
º
iK /
A D r ®« A D » 1°¾
e
2
°̄¬ 2
°
¼
¿
Unimodularity of T implies that:
2
1
§ a0 ·
¨¨ ¸¸
© b0 ¹
2
1
ª1
º
cos 1 « A D »
/
¬2
¼
K (E , Z )
B
§
·
¨¨ iK/
¸¸
A¹
©e
Dispersion relation
The field in the n1 layer of the n-‐th cell is:
E K ( x)e iKx
>a e
0
ik1 x ( x n/ )
@
b0 e ik1x ( xn/ ) e iK ( xn/ ) e iKx
e
iK /
§ an ·
¨¨ ¸¸
© bn ¹
Propagation of light in infinite 1DPC
TE Case
1
A D 1  K  R
2
TE
Propagating waves (permitted)
1
A D ! 1  K
2
mS
iK i  C
/
Evanescent waves (forbidden in 1DPC)
1
A D 1
2
Band edges
TM
BSW at the truncation interface of 1DPC
z
na n2 n1
x
y
If the 1DPC is finite the evanescent solutions are
permitted at the interface and decay in the 1DPC
with an envelope (Bloch Surface Wave -‐ BSW):
e Ki x
The BSW field has the transverse structure:
 E ( x ) De qa x
xd0
with q a
®
iKx
xt0
¯ E ( x ) E K ( x )e
K C Continuity of
E and 0E/ 0x ^E
2
>Z / c na @
Æ
BSW live in the forbidden bands
Æ
BSW dispersion relation qa
qe iK/ A B / e iK/ A B 2
`
1
2
EXAMPLE: a-Si1-xNx :H 1DPC
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
10 periods
Glass
Band Diagram
Finite and non periodic 1DPC
z
na n1 n2 ... n N
In the case the 1DPC is finite and/or non periodic
the analytical approach from Yariv cannot be
applied. The solution must be seeked numerically.
x
y
We can applied the Transfer Matrix Method (TMM)
to calculate the reflectance of an arbitrary
structure.
Ti
Suppose we wish to calculate the reflectance of a
finite 1DPC in the Kretschmann prism coupling
configuration.
T
Substrate
1DPC
PMA, Kretschmann
Finite and non periodic 1DPC
Step 1 ±
The single layer transfer matrix is:
Interface matrix
Propagation matrix
TE case
Finite and non periodic 1DPC
Step 2 ±
The multilayer transfer matrix is:
Finite and non periodic 1DPC
Step 3 ±
The reflectance and transmittance are calculated imposing
that bN+1=0:
R
T
r
2
t
2
Finite and non periodic 1DPC
Step 4 ±
The field distribution at any position inside the structure is
calculated imposing that a0=1 and b0=r:
EXAMPLE: a-Si1-xNx :H 1DPC
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
1
0.9
10 periods
0.8
0.7
R
0.6
0.5
0.4
Glass
0.3
0.2
0.1
30
35
40
45
50
55
Angle ( deg )
60
65
70
EXAMPLE: a-Si1-xNx :H 1DPC
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
10 periods
Glass
EXAMPLE: a-Si1-xNx :H 1DPC
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
10 periods
Glass
Transfer Matrix Method on MATLAB
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
10 periods
Glass
«a small preview of Lecture 2
L
t=294nm n=1.75 @ O=1530nm
H
t=240nm n=2.23 @ O=1530nm
10 periods
Glass
Band Diagram
Hydrogenated amorphous silicon nitride ( Si1-xNx :H) by PECVD
F.Giorgis, E.Descrovi
Politecnico di Torino
NH 3 +SiH 4
x=N/(Si+N)
0.6
50 nm
T=200 C
NH 3 +SiH 4 +H 2 T=200 C
0.4
0.2
0.0
0
20
40
60
80
100
a-Si1-xNx:H alloy
13.56 MHz PECVD
(SiH4+NH3)
material with tunable optical gap
and refractive index varying the N
content
growth of a-Si1-xNx:H thin films
and multilayers with an excellent
control of the thickness and
composition
refractive index at 1500 nm
Ammonia fraction in the reactor (NH 3 %)
3.5
3.0
2.5
2.0
1.5
0.0
0.1
0.2
0.3
0.4
x=N/(Si+N)
0.5
0.6
a-Si1-xNx :H based 1D Photonic Crystal
Linewidths are smaller than
observed for SPPs
O=1530nm
TE 
T
BSW
Kretschmann
a-Si1-xNx :H based 1D Photonic Crystal
a-Si1-xNx :H ± Kretschman reflectance
633 nm
SE W
G uided Modes
830 nm
a-Si1-xNx :H ± Kretschman reflectance
1300 nm
1550 nm
Kretschman Reflectance Map
2.0
TE 
T
R [ arb.un. ]
R [ arb.un. ]
1.5
2.0
1.0
1.5
0.5
1.0
0
30
SEW
40
0.5
SEW
Kretschmann
50
O=1550nm
60
70
T [ deg ]
SPP on Au @ O=1550 nm
Bare BK7 prism
0
30
40
50
T [ deg ]
60
70