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CST – Computer Simulation Technology

Electromagnetic Field Simulation of Nanometric Optical Tweezers

This article shows how the frequency domain solver of CST MICROWAVE STUDIO® (CST MWS) can be used to calculate the near field distribution of metallic and dielectric objects at optical frequencies. This article is based on the work presented in [1].

The test structure is a laser-illuminated metal tip. The vacuum wavelength of the illuminating light is 810 nm (Ti:sapphire laser). At this frequency, the dielectric constant of the gold tip is -24.9 + 1.57i. The structure is calculated in a water environment with a dielectric constant of 1.77. The problem setup takes a just a few minutes in the modeller. In CST MWS the material properties of metals at optical frequencies can be defined using Drude dispersive materials. The Drude material parameters can be calculated from the dielectric constants eps1 and eps2, or the reflective index n and absorption coefficient k by using a macro. Figure 1 shows the interface of this Macro. At 810 nm the resonance and collision frequencies are calculated as 1.19E16 rad/s and 1.41e14 Hz respectively....



Figure 1: Macro for calculating Drude material parameters

Figure 3 shows the absolute component of the E-field in the near field of the tip when illuminated by a plane wave with a field strength of 1 V/m. As shown in the paper, the E-field will be enhanced if the incident E-field is polarized along the axes of the tip (Figure 3). CST MWS calculates a maximum field enhancement of around 75. For an E-field polarization perpendicular to the tip axes, the field is not enhanced. 19E16 rad/s and 1.41e14 Hz respectively.



Figure 2: Polarization of the incident E-field perpendicular to the tip axes


Figure 3: E-field in the near field of the tip when illuminated by plane wave with a field strength of 1 V/m, polarised along the axes of the tip

The localised field enhancement might be used for trapping a particle underneath the tip. Figures 4 and 5 show the amplitude of the electric field if a dielectric or a metallic particle is moved underneath the tip. To take into account the strongly varying field, the mesh is refined around the apex of the tip. The total model is resolved by more then 250 000 tetrahedrons. Calculation time for each sphere position is about 20 minutes.



Figure 4: Amplitude of the electric field for a dielectric sphere underneath the tip


Figure 5: Amplitude of the electric field for a metallic sphere underneath the tip

This article has shown that the CST MWS frequency domain solver is well suited for calculating nano-optical problems. The combination of time and frequency domain solvers gives the user greater flexibility when performing optical simulations. It also demonstrates the powerful post-processing possibilities available in CST MWS. All animations can be generated directly within the program by using macros and template based post-processing steps.

References

[1] L. Novotny, R. X. Bian, X. Sunney Xie, “Theory of Nanometric Optical Tweezers,” Physical Review Letters, Vol. 79, No. 4, 28 July 1997.

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