A nonlinear theory for the optical properties of gold nanorods at various aspect ratios is used to calculate the refractive index sensitivity of surface plasmon resonance (M) which is found to be 100 to 1000 nm/RIU and proportional to the aspect ratio (R). Based on Gans theory, the calculated figure of merit, defined by the ratio of M and the resonance spectral width, has a range of 1.0 to 10 and has a maximum value at the optimum aspect ratio of 3.5 to 4.5. Numerical results are fit for analytic equations for the peak wavelength and sensitivity showing their nonlinear dependence on the surrounding medium refractive index (n) and R. The calculated optimal condition for the figure of merit provides useful guideline for the design of biosensors.
Analysis and applications of vision correction via accommodating intraocular lens (AIOL) are presented. By Gaussian optics, analytic formulas for the accommodation rate function (M) for two-optics and three-optics systems are derived and compared with the exact numerical results. In a single-optics AIOL, typical value of M is (0.5-1.5) D/mm, for an IOL power of (10-20) diopter. For a given IOL power, higher M is achieved in positive-IOL than negative-IOL. In the dual-optics AIOL, maximum accommodation is predicted when the front positive-optics moves toward the corneal plan and the back negative-optics moves backward. Our analytic formulas predict that greater accommodative rate may be achieved by using a positive-powered front optics, a general feature when either front or back optics is mobile. The M function is used to find the piggy-back IOL power for customized design based on the individual ocular parameters. Many of the new features demonstrated in this study can be easily realized by our analytic formulas, but not by raytracing method.
Analytic formulas for spherical nanoshell (Au/silica) resonance wavelength and refractive index sensitivity were derived and compared with a numerical nonlinear theory. A universal scaling law was deduced in terms of a normalized thickness defined by the ratio of the shell thickness and its core diameter. The calculated figure of merit shows a maximum at an optimal value of the resonance wavelength and normalized thickness. The nonlinear theory of nanoshells improves the accuracy of the linear theory in the short wavelength regime (500 to 650 nm).
This study evaluated the effectiveness of near-infrared laser-excited gold nanorods as the active target to selectively kill
the cancer cells. The key parameters of laser and sample to be measured include the absorption coefficient, the laser
fluence and irradiation time, and the temperature profiles. The optimal laser operation for the surface and volume heating
was achieved by a novel pulsed-train technique using an auto-controlled laser on-off time to meet the desired
temperatures. The measured temperature is an increasing function of laser fluence and irradiation time. For a fixed laser
influence, GNRs solution with smaller extinction coefficients (A) provides higher volume temperature, but slower
surface raising speed. This novel measured features are predicted by our theory based on a heat diffusion equation, which
was solved numerically, for volume heating.
A nonlinear theory for the optical properties of gold nanorods is presented. The refractive index sensitivity of the
associated surface plasmon resonance is calculated to be 100-1000 nm/RIU for the aspect ratio range of 1-10. According
to Gan's theory, the figure of merit, defined by the refractive index sensitivity divided by the FWHM value of the
extinction coefficient, is calculated to be 1.0-12.0, which has a maximum value at the optimum aspect ratio of 3.5-4.5
depending on refractive index the surrounding medium.
Using raytracing method (ZEMAX program), the reduction of SA of the whole human eye may be reduced via the
combined effects of asphericity (Q) and the ratio of the front and back surface of an IOL. The overall SA for best image
quality may be defined by Q* when the image position off axis is reduced to that of the paraxial. Our calculations show
the following general features: (1) For a give Q value, the influence on the SA is proportional to the surface power; (2) for minimal whole eye SA, negative Q is needed in IOL; (3) for a given IOL power, the Q* is smaller when the front surface has a smaller power. All above features derived from numerical raytracing method are consistent with analytic formulas.