Transmission of surface plasmon polaritons through a nanowire array: - - PowerPoint PPT Presentation
Transmission of surface plasmon polaritons through a nanowire array: mechano- optical modulation and motion sensing D Yu Fedyanin and A V Arsenin Laboratory of Nanooptics and Femtosecond Electronics, Department of General Physics, MIPT e-mail:
e-mail: feddu du@mail.r .ru
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anti-symmetric mode symmetric mode
For IMI waveguide structures with ε2=ε3, dispersion relation can be easily simplified and rearranged as two branches: 7
Long Range SPPs
Bulk and surface sensitivities of surface plasmon waveguides, New Journal of Physics 10 (2008) 105010 (37pp)
8 Kyungsuk Yum, et.al. J. Appl. Phys. 96, 3933
Nanobelts,” in Dekker Encyclopedia of Nanoscience and Nanotechnology, (Taylor&Francis, 2004).
harmonic resonance (n1 = 1.21 MHz), and (c) the second harmonic resonance (n2 = 5.06 MHz). (d) The traces of a uniform one-end fixed elastic beam at the first two resonance modes, as predicted by the continuous elasticity theory.
Typical dimensions of nanowires are 5-100 nm in diameter (width) and 1-50 μm in length. Such a small size, combined with unique electrical, mechanical and
scientific community for their potential in different applications from microelectronic to nanooptics. We focus here on the mechanical properties of nanowires. There are two main reasons for this. Firstly, the resonance frequency of mechanical oscillations is usually in the kilohertz or megahertz range and the amplitude of oscillations may exceed ten micrometers. Secondly, nanowire cantilevers are very sensitive and can be used even for single-atom mass sensing and tiny force measurements.
9 Kyungsuk Yum, et.al. J. Appl. Phys. 96, 3933 (2004) Z. L. Wang, “Mechanic Properties of Nanowires and Nanobelts,” in Dekker Encyclopedia of Nanoscience and Nanotechnology, (Taylor&Francis, 2004).
harmonic resonance (n1 = 1.21 MHz), and (c) the second harmonic resonance (n2 = 5.06 MHz). (d) The traces of a uniform one-end fixed elastic beam at the first two resonance modes, as predicted by the continuous elasticity theory.
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Dekker Encyclopedia of Nanoscience and Nanotechnology, (Taylor&Francis, 2004).
vx1 = 622 kHz, and (d) the first harmonic resonance in the y direction, vy1 = 691 kHz. (e) An enlarged image of the nanobelt and its electron diffraction pattern (inset). The projected shape of the nanobelt is
11 Schematic operation of the mechano-optic modulator, β is the SPP wavevector, h1>h2. (a). If the distance h between the nanowire array and the metal film is very large, there is no interaction between the SPP and the nanowires and we do not have any effect. (b). When the distance decreases, the effect
waveguide and the coupling between guided and radiation modes occurs. Changing the distance h, one can control the intensity of the transmitted SPP. A number of methods to do this have been proposed, including all-optical
incident optical radiation, etc. change optical properties, e.g. the refractive index or polarization tensor, of the materials used. We propose a different technique.
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York, 1974).
York, 1982).
13 AS guided mode S guided mode AS radiation mode S radiation mode
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Since the radiation losses interest us, the amplitude coefficients should be related to the power carried by the mode. For each pair ν and µ of guided modes, we require and for for each pair of radiation modes
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Assuming β to be positive, introduce now amplitude coefficients A (for the forward- running mode (β>0)) and B (for the backward-running mode (β<0)), so that In general case, the system of coupled mode equations is written as
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We have an infinite number of differential equations, since we have an infinite number of radiation modes. To solve the problem, we have to simplify the above
AS of the transmitted SPP to be
much less than unity, i.e. assume a weak coupling regime (|Ag
AS|
A ≫
ν,Bν), and only
Integration of Eq. (13) gives the exact expressions for the amplitude coefficients A and B:
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We have an exponentially decaying term exp(−κ2
gASh), consequently, the radiation
loss power decreases as h increases. However, there are oscillating terms in braces and therefore oscillations in Kz
η(h,β) as a function of h are expected. The form of the
dependence can be approximately expressed as
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Dependence of the normalized total radiation loss power on the gap between the nanobelt array and the metal film for different values of the nanobelt transverse size, l = 500 nm, N = 10, 2πc/ω = 800 nm.
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Dependence of the normalized total radiation loss power on the gap between the nanobelt array and the metal film for different values of the nanobelt transverse size, l = 500 nm, N = 10, 2πc/ω = 800 nm. Results of direct calculations show that it is possible to achieve a modulation depth
high sensitivity of the system can be used for the detection of the mechanical motion
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Dependence of the normalized total radiation loss power on the number of nanobelts, h=500 nm, l=500 nm, N=10, 2πc/ω=800 nm. (b). Dependence of the normalized total radiation loss power on the permittivity of the nanobelts, h=500 nm, l=500 nm, N=5, 2πc/ω=800 nm.
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