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OPTO-ELECTRONICS REVIEW 14(3), 243–251
DOI: 10.2478/s11772-006-0032-y
Energy transport in plasmon waveguides on chains of metal nanoplates
W.M. SAJ*, T.J. ANTOSIEWICZ, J. PNIEWSKI, and T. SZOPLIK
Faculty of Physics, Warsaw University, 7 Pasteura Str., 02-093 Warsaw, Poland
An interest in energy transport in 3D chains of metal nanoparticles is oriented towards future applications in nanoscale optical devices. We consider plasmonic waveguides composed of silver nanoplates arranged in several geometries to find the
one with the lowest attenuation. We investigate light propagation of 500-nm wavelength along different chains of silver
nanoplates of subwavelength length and width and wavelength-size height. Energy transmission of the waveguides is analysed in the range of 400–2000 nm. We find that chain of short parallel nanoplates guides energy better than two electromagnetically coupled continuous stripes and all other considered nonparallel structures. In a wavelength range of 500–600 nm,
this 2-µm long 3D waveguide transmits 39% of incident energy in a channel of l ´ l/2 cross section area.
Keywords: surface plasmons-polaritons, waveguides, nano-optical devices, plasmon resonance, evanescent waves.
1. Introduction
Surface plasmon waves are collective oscillations of electrons
excited within a thin metal layer of metal-dielectric interface.
Plasmons are coupled with polaritons that are electromagnetic
waves with high field amplitude propagating in the direction
tangential to metal-dielectric interface. In the direction normal
to the surface, plasmon-polaritons are evanescent [1–4]. Propagation of long range surface plasmon waves on thin and infinite metal films have been studied since more than two decades [5–7]. It was motivated by a search for methods of signal distribution in very low size channels. Dielectric waveguides with non-plasmonic propagation of optical signals
have size limited to half a wavelength due to diffraction phenomenon. Resolution beyond the optical diffraction limit is
possible when plasmons are distributed along metal circuits
fabricated with e-beam patterning technique. Interest in plasmonic energy transport in channels of limited volume resulted
in theoretical description and experiments on 3D chains of
metal nanoparticles and 3D metal nanostrips [8–31]. In such
structures, it is expected that signals can propagate in transmission lines with a diameter one order of magnitude smaller
than a wavelength.
In this paper, we analyse several geometries of plasmon
waveguides composed of flat silver nanoplates. They are illuminated with the light of 500-nm wavelength polarized
perpendicularly to plate walls. A chain of short parallel
nanoplates has the lowest attenuation. Then, we investigate
propagation and attenuation of light of 400–2000-nm wavelengths in two electromagnetically coupled long stripes and a
chain of short parallel nanoplates. A 3D chain of nanoplates
guides optical frequencies in a channel of width below the
diffraction limit. We investigate influence of scaling down the
optimum structure on efficiency of energy transport.
*e-mail:
2. Geometries of plasmon waveguides on silver
nanoplates
The first geometry considered is a chain of 2D nanorods of
100-nm diameter arranged in the hexagonal lattice, Fig.
1(a) [27]. The chain of nanorods of 3.5-µm length transmits
more than 50% of energy of optical wavelengths in the
range of 500–600 nm [27], thus it has lower attenuation
than that available in chains of nanoparticles [e.g., 8.23].
However, the hexagonal chain of nanorods bends at p/3
and the bends introduce considerable losses. Therefore we
consider several geometries of plasmon waveguides in the
form of chains of nanoplates that allow non-discrete bending. Two types of chains with funnel-like nonparallel nanoplates are shown in Fig. 1(b) and 1(c). Nanoplate length
and width are 380 and 60 nm, respectively. Chain links are
separated by 40 nm. An angle between waveguide axis and
each nanoplate is 10°. Then, a chain of parallel short
nanoplates of similar size, shown in Fig. 1(d), is compared
with two continuous nanoplates of 60-nm width of Fig. 1(e).
Nanoplate parameters are chosen to meet the possibilities
of technological processes that might be involved in a fabrication process. With resolution of standard e-beam lithography, nanoplate thickness of 60 nm is achievable. With
nowadays etching and deposition techniques, fabrication of
500-nm, 750-nm, and 1-µm high metal plates is possible.
3. FDTD simulations
We use the finite difference time domain (FDTD) method
[32] to investigate properties of waveguides illuminated
with the light, polarized perpendicularly to plate walls. The
permittivity of silver is described using the single pole
Drude model
e (w) = e ¥ - w 2p [w(w + iG )] -1 ,
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(1)
Energy transport in plasmon waveguides on chains of metal nanoplates
Fig. 1. Isometric views and cross sections of waveguides: (a) nanorods of 100-nm diameter in hexagonal lattice, (b) nanoplates in
herring-bone pattern, (c) nanoplates in foot-step pattern, (d) parallel pairs of nanoplates, and (e) continuous parallel stripes.
with the parameters e¥ = 3.70, wp = 13673 THz, and G = 27.35
THz calculated from the work of Johnson and Christy [33].
In each case, the simulation volume is 780´1400´2225 nm
discretized with Dr = 5 nm step surrounded by 10 layers of
UPML absorbing conditions at all boundaries. Simulation
time step is Dt = Dr/2c = 8.34´10–18 s. The source has a
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Gaussian field distribution with a half width of 372 nm. It
is placed in the z = 0 nm plane with small misalignment
Dr/2 = 2.5 nm along the x axis. The source is introduced
with total/scattered field split of a simulation volume. Energy guidance of the considered waveguides is calculated
for a wavelength of 500 nm. Field intensities in the wave-
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guides are calculated as the values of z-axis components of
Poynting vector averaged over three periods of the source.
Light transmissions of 2-µm long waveguides are calculated using a broadband source. Energy transmission coefficients are calculated as a ratio (E x2 + E y2 ) out /
(E x2 + E y2 ) in of intensities integrated at the output (z =
2225 nm) and the input (z = 0 nm) planes, where Ex and Ey
are the time Fourier transforms of field components.
4. Analysis of energy guidance
On a plane metal-dielectric interface, small frequency plasmons-polaritons propagate with group velocities close to the
speed of light in the dielectric. When frequency reaches the
resonance plasmon frequency, the energy of electromagnetic
plasmon-polariton undergoes transition to energy of electrons.
Then, plasmon wave vector tends to infinity and the group
and phase velocities of the plasmons tend to zero.
Whichever mechanism decides upon transmission of
light in a fibre, either total internal reflection or photonic
band gap guidance, a beam diameter is diffraction limited.
Plasmon waveguides may transport light below the diffraction limit in a surrounding dielectric with energy densities a
few orders of magnitude higher than those available in optical fibres. High energy concentration results from long
wave vectors of plasmons. In Fig. 2, we show the simulation volume containing several nanoplates and vertical (z =
1500 nm) and horizontal (y = 700 nm) cross section planes
of energy flow in the z direction.
Figure 3 presents distribution of energy in the vertical
cross section plane at z = 1500 nm (left column) and flow
of energy along a few links of waveguides (right column)
shown in the horizontal cross section at y = 700 nm. For
geometries with oblique position of nanoplates, losses connected with radiating into the far field are obviously higher
than for parallel plates. Surprisingly, a chain of short parallel nanoplates concentrates energy inside the waveguide
[Fig. 3(c) left] better than continuous metal stripes [Fig.
3(d) left]. Right column of Fig. 3 visualizes attenuation of
energy in the analysed structures. Radiation losses into the
far field are the smallest in a chain of short parallel
nanoplates. Ohmic losses are supposedly similar in all
structures because plate dimensions are the same. We note
that subimages within each column of Fig. 3 are normalized independently.
Transmission characteristics of the waveguide with
plates arranged in herring-bone pattern are calculated for
the plates rotated by 10°, with respect to the waveguide
axis. Figure 3(a) (left) shows the dominance of edge guiding, similarly as in case of continuous plates of Fig. 3(d)
(left). Figure 3(a) (right) shows that the output beam has
central minimum with side maxima. We observe strong
coupling between tops and bottoms of both plates of a single link. It is stronger than coupling between top and bottom edges of the same plate. Intensity distribution on the
outer walls of plates is higher than on inner walls and results in high radiation losses into the far field.
Opto-Electron. Rev., 14, no. 3, 2006
Fig. 2. Scheme of two cross sections through a simulation volume,
where Poynting vectors averaged over a wave period are
calculated.
Figure 3(b) shows the dominance of edge guiding in the
waveguide arranged in foot-step pattern. Spatial shift of
subsequent nanoplates results in serpent-like flow of energy. Similarly as in the previous geometry, intensity distribution on the outer walls of plates is higher than on inner
walls what results in high radiation losses. Output beam is
asymmetric and has central minimum with the side maxima.
The waveguiding chain of short parallel nanoplates
[Fig. 3(c)] attenuates less than all the other analysed nanoplate structures. Moreover, energy guiding on outside walls
is lower than in the case of continuous plates. This can be
interpreted as counterintuitive energy flow from the waveguide outside to its centre through openings between plates.
The output beam has a distinct central maximum with
small side lobs in the x-axis direction.
In the waveguide of two parallel continuous plates [Fig.
3(d)], coupling between tops and bottoms of both plates is
stronger than that between top and bottom edges of the
same plate. Bound modes in continuous plates have energy
concentrated between edges of both plates and on the outer
walls of plates.
In all cases, the Gaussian source is not located exactly
on the system axis. The mismatch of the Gaussian source
and bound modes results in energy leaks from the centre of
the waveguides and in field asymmetry.
5. Influence of scaling the structures on energy
guiding
It was shown in the previous section that a chain of parallel
nanoplates has better guiding properties than all the other
structures. For a chain of parallel nanoplates and two paral-
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Energy transport in plasmon waveguides on chains of metal nanoplates
Fig. 3. Z-axis components of Poynting vector averaged over a wave period and calculated at two planes shown in Fig. 2, in waveguides (a)
in herring-bone pattern, (b) in foot-step pattern, (c) parallel pairs of nanoplates, and (d) continuous parallel stripes. All plates are separated
by 260 nm, embedded in a medium with the refractive index n = 1 and illuminated with Gaussian beam of 500-nm wavelength.
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Fig. 4. Z-axis components of Poynting vector averaged over a wave period and calculated at the horizontal y = 700 nm cross section plane in
the chain of parallel pairs of nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of
500-nm wavelength. In rows, the distance between plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of
nanoplates decreases from 1000 nm to 500 nm for every 250 nm.
lel unbroken stripes we continue search for optimum relation between guided wavelength and the separation a and
the height h of plates for both structures. We scan three
separation values 160, 210, and 260 nm and three heights
1000, 750, and 500 nm. Thus, the area ah of transversal
channel cross section changes from l ´ l/3 to 2l ´ l/2.
Figure 4 shows isolines of guided energy calculated at
the horizontal cross section plane at y = 700 nm of the
chain of parallel pairs of nanoplates. The narrowest channel
is not efficient in energy guiding independently of the plate
heights. The best results are observed for l high plates separated by l/2. Distribution of energy at the vertical cross
section of this chain of plates shown in Fig. 5 confirms the
observation. For 260-nm separation of plates we observe
that with decrease in the plate heights, energy concentrates
on the waveguide axis. For l/2 high plates guided modes
differ distinctly. With increase in plate separation, weak
coupling of edge plasmons on outer sides of plates changes
to strong plasmon coupling between top and bottom parts
of plates. This results in energy concentration within the
waveguide.
Similar calculations of z-axis components of Poynting
vector averaged over a wave period and calculated at the
horizontal and vertical cross section of a waveguide on two
continuous stripes are shown in Figs. 6 and 7, respectively.
Opto-Electron. Rev., 14, no. 3, 2006
It is clear that none of combinations of the separation a and
the height h is helpful to decrease attenuation. Figure 6
shows a horizontal cross section on half-height of the
waveguide, thus, poor guidance is observed because continuous plates transport energy with edge plasmons mostly.
When height of plates decreases, the energy transport
moves from inner to outer space. Figure 7 shows that with
decrease in height of plates, plasmon coupling between
neighbouring plates decreases. For 2l high plates, there is
a coupling between top and bottom edges of plates. The
plates of l height do not guide plasmons on their inner
walls. There is an outer coupling between top and bottom
edges of the same plate.
6. Light transmission in plasmon waveguides
Figure 8 shows spectral transmission plots calculated using
FDTD for all the geometries of waveguides presented in
Fig. 1. For the hexagonal chain of nanorods, the transmission is calculated for optical wavelengths of 380–750 nm
and for nanoplate structures for the range from 400 nm to 2
µm. Chain of nanorods has the best efficiency and bandwidth of transported wavelengths, however, it has no bending abilities. Therefore calculations made in 2D are not recalculated for 3D case. The nanoplate structures are calcu-
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Energy transport in plasmon waveguides on chains of metal nanoplates
Fig. 5. Z-axis components of Poynting vector averaged over a wave period and calculated at the vertical cross z = 1500 nm section plane in
the chain of parallel pairs of nanoplates embedded in a medium with refractive index n = 1 and illuminated with Gaussian beam of 500-nm
wavelength. In rows, the distance between plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of nanoplates
decreases from 1000 nm to 500 nm for every 250 nm.
Fig. 6. Z-axis components of Poynting vector averaged over a wave period and calculated at the horizontal cross section plane in parallel
continuous nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of 500-nm
wavelength. In rows, the distance between plates increases from 160 to 260 nm for every 50 nm. In columns, the height of nanoplates
decreases from 1000 nm to 500 nm for every 250 nm.
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Fig. 7. Z-axis components of Poynting vector averaged over a wave period and calculated at the vertical cross section plane in parallel
continuous nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of 500-nm
wavelength. In rows, a distance between the plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of nanoplates
decreases from 1000 to 500 nm for every 250 nm.
Fig. 8. Transmission of broadband Gaussian beam through 2-µm long waveguides of (a) nanorods in hexagonal lattice, (b) nanoplates in
herring-bone pattern, (c) in foot-step pattern, (d) parallel pairs of nanoplates, and (e) continuous parallel stripes, all embedded in vacuum.
Opto-Electron. Rev., 14, no. 3, 2006
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Energy transport in plasmon waveguides on chains of metal nanoplates
Acknowledgements
This research was sponsored by Polish grant 3 T08A 081 27.
We also acknowledge the support from the 6FP Network of
Excellence Metamorphose, EC Contract #500 252.
References
Fig. 9. Propagation in a bent herring-bone pattern waveguide with
angle of rotation of subsequent segments equal six degrees. An
angle between waveguide axis and each nanoplate is 5°.
lated in 3D. Funnel-like waveguides analysed because of
bending possibilities are very lossy in comparison to parallel plate geometries.
Transmission plot of a waveguide made of short parallel plates has a few maxima [Fig. 8(d)]. After 2-µm propagation distance, the highest transmission values close to
39% are observed in the wavelength range of 500–600 nm.
Single infinite length plate is considered, e.g., in Refs. 15
and 18. Here, we analyse the propagation properties of two
parallel continuous plates. We observe that transmission
along the plates of finite length not only increases with decreasing wavelength but also exhibits Fabry-Perot resonances [Fig. 8(e)].
Figure 9 illustrates confined propagation of light along
bent plasmon waveguide composed of nanoplates in a herring-bone pattern with subsequent segments rotated by six
degrees. In the wavelength range of 600–780 nm, attenuation in the bent waveguide is close to 2 dB/µm.
7. Conclusions
Photonic crystal waveguides, operating on photonic bandgap mechanism, require at least three layers of cladding
to achieve attenuation at the level of 0.1 dB/mm. For a
lattice constant equal to light wavelength, the waveguide
is 7l wide [34]. Plasmon waveguides on silver nanoparticles demand less space, however, they have higher
attenuation of energy. In this paper, we analyse a few geometries of plasmon waveguides made of nanoplates embedded in the vacuum. A chain of parallel short nanoplates is promising for applications in nanophotonic devices. Future research should lead to minimization of energy losses when nanoplates are embedded in a dielectric
and investigation of properties of bent, y-junction and
coupler structures.
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1. H. Raether, Surface Plasmons, Springer, Berlin, 1988.
2. C. Sönnichsen, “Plasmons in metal nanostructures”, PhD
Thesis, Ludwig-Maximilians-Universtät München,
München, 2001.
3. A.V. Zayats and I.I. Smolyaninov, “Near-field photonics:
surface plasmon polaritons and localized surface plasmons”, J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
4. W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface
plasmon subwavelength optics”, Nature 424, 824–830
(2003).
5. D. Sarid, “Long-range surface-plasma waves on very thin
metal films”, Phys. Rev. Lett. 47, 1927–1930 (1981).
6. J.J. Burke, G.I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films”, Phys.
Rev. B33, 5286–5301 (1986).
7. W.L. Barnes, S.C. Kitson, T.W. Preist, and J.R. Sambles,
“Photonic surfaces for surface-plasmon polaritons”, J. Opt.
Soc. Am. A14, 1654–1661 (1997).
8. M. Quinten, A. Leitner, J.R. Krenn, and F.R. Aussenegg,
“Electromagnetic energy transport via linear chains of silver
nanoparticles”, Opt. Lett. 23, 1331–1333 (1998).
9. J.R. Krenn, A. Dereux, J.C. Weeber, E. Bourillot, Y. Lacroute, J.P. Goudonnet, G. Schider, W. Gotschy, A. Leitner,
F.R. Aussenegg, and C. Girard, “Squeezing the optical
near-field zone by plasmon coupling of metallic nanoparticles”, Phys. Rev Lett. 82, 2590–2593 (1999).
10. J.C. Weeber, A. Dereux, C. Girard, J.R. Krenn, and J.P.
Goudonnet, “Plasmon polaritons of metallic nanowires for
controlling submicron propagation of light”, Phys. Rev.
B60, 9061–9068 (1999).
11. B. Lamprecht, J.R. Krenn, G. Schider, H. Ditlbacher, M.
Salerno, N. Felidj, A. Leitner, F.R. Aussenegg, and J.C.
Weeber, “Surface plasmon propagation in microscale metal
stripes”, Appl. Phys. Lett. 79, 51–53 (2001).
12. J.C. Weeber, J.R. Krenn, A. Dereux, B. Lamprecht, Y.
Lacroute, and J.P. Goudonnet, “Near-field observation of
surface plasmon polariton propagation on thin metal
stripes”, Phys. Rev. B, 64045411 (2001).
13. J.C. Weeber, M.U. González, A.L. Baudrion, and A.
Dereux, “Surface plasmon routing along right angle bent
metal strips”, Appl. Phys. Lett. 87, 221101 (2005).
14. T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide
for optical far/near-field conversion”, Appl. Phys. Lett. 79,
4583–4585 (2001).
15. P. Berini, “Plasmon-polariton waves guided by thin lossy
metal films of finite width: bound modes of symmetric
structures”, Phys. Rev. B61, 10484–10503 (2000).
16. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Skrzek, “Experimental observation of plasmon-polariton
waves supported by a thin metal film of finite width”, Opt.
Lett. 52, 844–846 (2000).
Opto-Electron. Rev., 14, no. 3, 2006
© 2006 COSiW SEP, Warsaw
Unauthenticated
Download Date | 6/17/17 8:14 AM
17. P. Berini, “Plasmon-polariton waves guided by thin lossy
metal films of finite width: bound modes of asymmetric
structures”, Phys. Rev. B63, 125417 (2001).
18. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini,
“Demonstration of integrated optics elements based on
long-ranging surface plasmon polaritons”, Opt. Express 13,
977–984 (2005). http://www.opticsinfobase.
org/abstract.cfm?URI=oe-13-3-977.
19. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi,
“Characterization of long-range surface-plasmon polariton
waveguides”, J. Appl. Phys. 98, 043109 (2005).
20. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M.S.
Larsen, and S.I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons”, J.
Lightwave Technol. 23, 413–422 (2005).
21. K. Leosson, T. Nikolajsen, A. Boltasseva, and S.I.
Bozhevolnyi, “Long-range surface plasmon polariton
nanowire waveguides for device applications”, Opt. Express
14, 314–319 (2006). http://www.opticsinfobase.
org/abstract.cfm?URI=oe-14-1-314.
22. M.L. Brongersma, J.W. Hartman, and H.A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle
chain arrays below the diffraction limit”, Phys. Rev. B62,
R16356–R16359 (2000).
23. S.A. Maier, “Guiding of electromagnetic energy in
subwavelength periodic metal structures”, PhD Thesis, California Institute of Technology, Pasadena, 2003.
24. S.A. Maier, P.G. Kik, and H.A. Atwater, “Optical pulse
propagation in metal nanoparticle chain waveguides”, Phys.
Rev. B67, 205402 (2003).
25. S.A. Maier, M.D. Friedman, P.E. Barclay, and O. Painter,
“Experimental demonstration of fiber-accessible metal
Opto-Electron. Rev., 14, no. 3, 2006
26.
27.
28.
29.
30.
31.
32.
33.
34.
nanoparticle plasmon waveguides for planar energy guiding
and sensing”, Appl. Phys. Lett. 86, 071103 (2005).
A. Degiron and D.R. Smith, “Numerical simulations of
long-range plasmons”, Opt. Express 14, 1611–1625 (2006).
http://www.opticsinfobase.org/abstract.
cfm?URI=oe-14-4-1611.
W. Saj, “FDTD simulations of 2D plasmon waveguide on
silver nanorods in hexagonal lattice”, Opt. Express 13,
4818–4827 (2005). http://www.opticsinfobase.
org/abstract.cfm?URI=oe-13-13-4818.
W.M. Saj, T.J. Antosiewicz, J. Pniewski, and T. Szoplik,
“Plasmon waveguides on silver nanoelements”, Proc. SPIE
6195, 227–237 (2006).
L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration”, Opt. Express 13, 6645–6650
(2005). http://www.opticsinfobase.org/abstract.scfm?URI=oe-13-17-6645.
R. Zia, M.D. Selker, P.B. Catrysse, and M.L. Brongersma,
“Geometries and materials for subwavelength surface
plasmon modes”, J. Opt. Soc. Amer. A21, 2442–2446 (2004).
J.A. Dionne, L.A. Sweatlock, H.A. Atwater, and A. Polman,
“Plasmon slot waveguides: Towards chip-scale propagation
with subwavelength-scale localization”, Phys. Rev. B73,
035407 (2006).
A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method,
Artech House, Norwood, 2000.
P. Johnson and R. Christy, “Optical constants of the noble
metals”, Phys. Rev. B6, 4370–4379 (1972).
D. Gerace and L. Andreani, “Low-loss guided modes in
photonic crystal waveguides”, Opt. Express 13, 4939–4951
(2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4939.
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W.M. Saj
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