In this report, we summarize recent findings regarding the use spherical microcavities in the amplification of light that is inelastically scattered by either fluorescent or Raman-active molecules. This discussion will focus on Raman scattering, with the understanding that analogous processes apply to fluorescence. Raman spectra can be generated through the use of a very strong light source that stimulates inelastic light scattering by molecules, with the scattering occurring at wavelengths shifted from that of the source and being most prominent at shifts associated with the molecules natural vibrational frequencies. The Raman signal can be greatly enhanced by exposing a molecule to the intense electric fields that arise near surfaces (typically of gold or silver) exhibiting nanoscale roughness. This is known as surface-enhanced Raman scattering (SERS). SERS typically produces gain factors of 103 - 106, but under special conditions, factors of 1010 - 1014 have been achieved

Fuller, Kirk A.

NASA Technical Reports Server

 
 
 
 
 
2004 
 
NASA FACULTY FELLOWSHIP PROGRAM 
 
 
 
 
MARSHALL SPACE FLIGHT CENTER 
 
THE UNIVERSITY OF ALABAMA  
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE 
ALABAMA A&M UNIVERSITY 
 
 
 
 
 
  LOCAL INTENSITY ENHANCEMENTS IN SPHERICAL
MICROCAVITIES: IMPLICATIONS FOR PHOTONIC
            CHEMICAL AND BIOLOGICAL SENSORS
 
 
 
 
 
 
 
 
 
         
 
 
XVI-1 
https://ntrs.nasa.gov/search.jsp?R=20050215321 2019-08-29T19:47:13+00:00Z
Introduction
In this report, we summarize recent findings regarding the use spherical microcavities in the am-
plification of light that is inelastically scattered by either fluorescent or Raman-active molecules.
This discussion will focus on Raman scattering, with the understanding that analogous processes
apply to fluorescence.
Raman spectra can be generated through the use of a very strong light source that stimulates
inelastic light scattering by molecules, with the scattering occurring at wavelengths shifted from
that of the source and being most prominent at shifts associated with the molecules’ natural
vibrational frequencies. The Raman signal can be greatly enhanced by exposing a molecule to
the intense electric fields that arise near surfaces (typically of gold or silver) exhibiting nanoscale
roughness. This is known as surface-enhanced Raman scattering (SERS). SERS typically pro-
duces gain factors of 103 − 106, but under special conditions, factors of 1010 − 1014 have been
achieved (Felidj, 2003).
An intriguing mechanism for near-field enhancement arises from microcavity whispering gallery
modes (WGMs). Also known as morphology-dependent resonances (MDRs), these modes appear
at sharply defined spectral positions for any sufficiently large and lossless spherical particle.
(MDRs also appear in cylindrical and spheroidal microstructures.) A key feature of a resonator
is its quality factor Q, which is the ratio of stored energy to the energy lost per cycle through
the cavity. Microspheres can sustain Qs approaching 1010 (cf. Vernooy et al., 1998). The
dramatic increases in photon densities within these microcavities have been shown to produce
low-threshold nonlinear optical effects such as stimulated Raman scattering, lasing, spectral
hole burning, and cavity quantum electrodynamic effects. In addition to very high photon
densities in the mode volumes of microcavities, very strong evanescent fields reside on and
near their outer surfaces. Vigorous research has begun into ways to use these strong surface
fields to detect and analyze minute amounts of molecular species adsorbed onto the resonator.
Optical shifts in MDRs have been used to detect adsorption of proteins onto glass spheroids and
resonant enhanced evanescent wave fluorescence has been proposed for photonic biosensing, as
have integrated optical microcavities.
Calculations presented below indicate that the absorption cross sections of metal nanoparticles
immobilized onto dielectric microspheres can be greatly enhanced by cavity resonances in the mi-
crospheres. Molecules attached to the immobilized nanoparticles would thus experience cascaded
surface-photoenhancements (CSPs), leading to increased gains in Raman scattering of several
orders of magnitude over conventional SERS effects. Gain factors of 103 − 104 are predicted
for realistic, though challenging, experimental conditions using homogenous microspheres. Our
calculations further indicate that carefully structured cladded microspheres, acting as coupled
microcavities, could produce a further gain of 3 or 4 orders of magnitude. Cascaded surface
photoenhancement thus has the potential of pushing sensitivities of chemical and biological
detectors to dramatically lower thresholds.
XVI-2
Enhanced absorption by nanoparticles on a microcavity
The electric field at any point may be expanded in vector spherical harmonics Nnp. The vector
spherical harmonics may be written as Nnp = RgNnp + i IgNnp, where Rg and Ig stand for
‘regular’ (finite at the origin) and irregular. The expansion for the incident field (here, an infinite
plane wave) is
Einc =
∑
np
qnpRgNnp, (1)
and for the external and internal fields of a homogeneous sphere, respectively,
Esca =
∑
np
qnp anpNnp, (2)
Ecor =
∑
np
qnp cnpRgNnp (3)
where the expansion coefficients anp and anp are functions of the sphere’s refractive index m,
radius a, and the wavelength λ. These coefficients and the qnp are well-known (cf. Fuller
and Mackowski, 2000), and are also used in calculating the cross sections for scattering and
absorption, Csca and Cabs, respectively.
Figure 1: Absorption efficiency spectrum of a 10 nm Au sphere on a 5 µm latex microbead.
The position of the nanoparticle (not drawn to scale) relative to the incident beam is shown in
the inset in the lower left corner of the graph. The absorption efficiency of the nanoparticle in
the absence of the sphere is given by the black curve. The calculations are based on an exact
formulation for compounded sphere systems (Fuller and Mackowski, 2000).
Figure 1 shows how the absorption efficiency Qabs (= Cabs divided by, in this case, the micro-
sphere’s geometric cross section) of a Au nanoparticle may be enhanced near the surface of a
microcavity as the wavelength of the incident beam is tuned through a series of microsphere
WGMs. There is no absorption in the microsphere itself, and so this graph shows that the Au
nanoparticle is being exposed to greatly enhanced local intensities.
XVI-3
For illustrative purposes, latex beads were chosen as the microcavities for this calculation. In
practice, one must choose microcavities that are made from materials, such as silica, that will
not themselves produce a strong Raman background signal. The Qabs spectra and local energy
densities will be similar for equivalent modes, regardless of the dielectric chosen.
The electromagnetic ‘terrain’ responsible for this resonance-enhanced absorption is shown in
Fig. 2, which is a plot of the ratio of the energy density near or in the microcavity to that of
the incident field. This calculation was made with an existing version of the author’s computer
program for scattering and absorption by a sphere. That this is a 3rd-order resonance may be
inferred from the presence of three concentric rings in the mode volume of the cavity.
Figure 2: Electromagnetic energy density in the equatorial plain of a microsphere tuned to a
3rd-order TE69 resonance. The incident field propagates parallel to the z-axis. In order to better
illustrate the structure of the mode volume of the resonance, only enhancements of greater than
103 are shown.
Internal and near fields of homogeneous and core-shell microspheres on resonance
The geometry of the problem is illustrated in Figure 3 for the case of a sphere with a concentric
spherical inclusion. The field associated with a particular n may be written as a sum of partial
waves multiply reflected between the surface of the core and the outer (concave) surface of the
shell. Defining
fnp =
cnp
1− 2anp aˇnp (4)
we have shown (Fuller and Smith, 2003) that the fields in the core and shell may be written,
respectively, as
Eshl =
∑
np
qnp fnp
(
RgNnp +
2anpNnp
)
and Ecor =
∑
np
qnp fnp
2cnpRgNnp. (5)
XVI-4
Figure 3: Geometry of the core-shell problem along with two illustrations of mode splitting
by coupled concentric microcavities that have been tuned to co-resonance. The equation for
the absorption cross section at a particular distance from the center of the microcavity is also
provided, and was developed by Fuller and Smith (2003). Evaluation of the equation at the
outer surface of the shell and at the surface of the core then gives the total absorption cross
section of the layered sphere and of the core, respectively. The difference of these two cross
sections then gives the absorption cross section of the shell.
Also shown in Fig. 3 is the spectrum of slightly absorbing microcavities. The mode splitting
displayed Fig. 3 is potentially of great consequence to the future development of Raman-based
detection and analysis: The enhancement of the intensity of Raman scattering by metal nanopar-
ticles is expressed in terms of incident and scattered local electric field amplitudes Eloc as
ISERS ∝ GSERS ∝ |Eloc(ωexc)|
2
|E0(ωexc)|2
|Eloc(ωRS)|2
|E0(ωRS)|2, (6)
where ωexc and ωRS are the circular frequencies of the incident (excitation) and Raman scattered
light, respectively. Excitation of the nanoparticle-microsphere systems discussed above results
in a gain of
|Eloc(ωexc)|2/|E0(ωexc)|2 ≈ 102 − 104. (7)
If, however, one were able to tune coupled cavity resonators to co-resonance, such that the
excitation frequency coincided with the left peak in Fig. 3 and the right peak were centered on
a Raman-active band, then that spectral feature would be amplified by a factor of 104 − 108
beyond the gain already realized from SERS alone.
Fig. 4 provides a view of the local intensity enhancement for both homogeneous and co-resonant
concentric microcavities. For this part of the work, the author’s computer program for calcu-
lating scattering and absorption by a homogeneous sphere was modified to allow calculation of
the internal and near fields of core-shell systems. The modifications were made in a way that
should allow for easy extension of the program to the case of multilayered structures.
XVI-5
Figs. 3 and 4 as well as Figs. 1 and 2 indicate that an order-of-magnitude jump in absorption
efficiency relates roughly to an order-of-magnitude increase in |E|2 near the surface of the cavity
and so the absorption spectrum of a nanoparticle on the surface of the microsphere may be used
to predict SERS gain factors. Calculations also indicated that coupling between the nanoparticle
and the resonator will spoil the cavity Q if the diameter of the Au particle exceeds ≈ 150 nm.
Also from Figs. 2 and 4 it should be noted that considerably larger (by yet another order of
magnitude) gain factors are present near the poles of the microcavities.
Figure 4: Enhancement factors in resonant homogeneous sphere and in co-resonant core-shell
microcavity
Acknowledgments
The author wishes to express his great appreciation for the many valuable discussions with Dr.
David D. Smith, and for the productive environment provided by MSFC for the performance of
this research.
References
Fe´lidj, N., J. Aubard, G. Le´vi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R.
Aussenegg, Optimized surface-enhanced Raman on gold nanoparticle arrays, Appl. Phys. Lett.
82 3095–3097(2003).
Fuller, K. A. and D. W. Mackowski, “Electromagnetic Scattering by Compounded Spherical
Particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and
L. D. Travis, Eds., Academic Press, NY 2000.
Fuller, K. A. and D. D. Smith, ‘Partial wave analysis of coupled photonic structures,’ in The
2002 NASA Faculty Fellowship Program Reasearch Reports, J. Bland Ed., Marshall Space Flight
Center, 2003.
Smith, D. D. and K. A. Fuller, Photonic bandgaps in Mie scattering by concentrically stratified
spheres, accepted for publication, J. Opt. Soc. Am. B, 19 No. 10. (2002).
Vernooy, D. W., V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, High-Q measure-
ments of fused-silica microspheres in the infrared, Opt. Lett. 23, 247–249( 1998)
XVI-6


Local Intensity Enhancements in Spherical Microcavities: Implications for Photonic Chemical and Biological Sensors

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