本篇論文的研究目的是使用掃描式近場光學顯微鏡觀察經過電子束微影製成的結構在1064奈米的恩斯-高斯雷射照射下其激發的表面電漿的特性。本論文嘗試了六種不同週期的狹縫結構，研究發現在第五組結構傳播現象特別明顯，得到要在1064奈米雷射下要激發出表面電漿所設計的金屬光柵結構其週期要滿足a(週期)=n微米，n為整數。接著針對第五種設計出新的結構，再以IGe0,0、IGe1,1、IGe2,2打在結構上激發出表面電漿，發現可以利用結構控制其傳播方向。並在實作上找出了製作微奈米結構的流程及製成參數，可供未來欲從事相似微奈米結構之研究者參考。

This article aims to use the scanning near-field optical microscope to observe properties of surface plasmon on the microstructure made by E-beam lithography, induced by Ince Gaussian laser-excited surface plasmon with periodic Ag structure surface

Author: Yi-Hua Chen
Advisor: Shu-Chun Chu, Ph.D
National Cheng Kung University, Department of Physics

Summary
This article aims to use the scanning near-field optical microscope to observe properties of surface plasmon on the microstructure made by E-beam lithography, induced by a beam of 1064 nm Ince-Gaussian laser. In this research, thin-slit microstructures of 6 different periods were taken into experiment, the fifth is shown to have the most significant results. In order to induce surface plasmon with a 1064 nm laser, the periodic structure must obey a(period)=n micrometers, where n is an integer. Next, light of modes IGe0,0、IGe1,1、IGe2,2 are aimed onto the structures to induce surface plasmon, and the direction of propagation isfound to be controllable via the structure.

Key word: Ince-Gaussian Modes,SNOM, surface plasmon

INTRODUCTION
Hermite-Gaussian Modes (HGMs) and Laguerre-Gaussian Modes (LGMs) are solutions to Paraxial Wave Equations (PWEs) in Cartesian coordinates and Cylindrical coordinates, respectively. Ince Gaussian Modes (IGMs), which we manipulate in this article, are solutions of PWEs that are expanded in elliptic cylindrical coordinates.
Consider a sample of two layers formed by metal and dielectric material, respectively. When an electromagnetic wave from the outside interacts with the layers, the diodes near the border between layers will exhibit group oscillation. This phenomenon is known as surface plasmon oscillation. The phenomenon exists owing to the high density of free electrons in the metal layer, which become instantly induced diodes under the effect of the electromagnetic wave.
A periodic structure must fulfill the following equation in order to induce surface plasmon oscillation: ω/c √(ε_1 ) sin⁡θ+n 2π/a=ω/c √((ε_1 ε_2)/(ε_1+ε_2 ))=k_sp, where ω is the angular frequency of incident light, c is the speed of light in vacuum, ε_1 is the electric permittivity in the dielectric, ε_2 is the electric permittivity in the metal, n is a integer variable, and a stands for the period of the structure. Under a 1064 nm laser, the structure must fulfill a=n (micrometers) for induction.

MATERIAL AND METHODS
The manufacturing process of the sample is divided into two parts. First, we make a double cross pattern on the sample as shown in the picture below(Fig.1):

Fig.1 double cross pattern
This pattern will be easy to locate when performing the experiment. This process is carried out by masked photolithography. The second part of the process creates the periodic microstructure. We implement the E-beam lithography system to write the pattern on the PMMA photoresist. Then, the photoresist is dipped into the developer. Afterwards, a 60 nm thick layer of silver is plated on top. The dimensions of the pattern is 50(um)*50(um). The picture below(Fig.2) shows the pattern after lithography seen under an SEM.

Fig.2 microstructure
The experimental structure is shown in the picture below. First, we use He-Ne laser as reference and two apertures to collimate the 1064 nm laser. Next, two lenses are implemented to reduce the size of the light source. A 20x objective lens is used to focus the laser beam onto the sample surface, inducing the surface plasmon field.

Fig.3 Experimental setup
The experiment consists of two parts. The first part is to verify that the microstructure satisfies a=n(um) so that surface plasmon can be induced. The second part is to find the best period of the structure in order to design a new structure, in order to control the propagation direction of the surface plasmon.

RESULTS AND DISCUSSION
For the first part of the experiment, structures of six different periods were tested, the periods are a =1, 2, 2.5, 3, 4, 5 (um), respectively. From the picture below, it can be seen that when n=2.5(um), surface plasmon propagation will not be induced. Thus we know that a=n(um) is correct. When n=2.0(um), propagation is most apparent.

Fig.4 Graph of intensity to position for different periods
For the second part, we design the pattern based on a=2.0(um). The pattern consists of two periodic structures placed side to side within a varying distance. The distance variable, s, have values of 14, 10, and 6(um), respectively. In the pictures below, we make the right half of the light source hit the upper half of the structure, while the left half of the source does not hit the structure. First, we use IGe0,0 as the source:

Fig.6 Graph of intensity to position for distance variable
Next, we use IGe1,1 as the source:

Fig.7 Graph of intensity to position for distance variable
And finally, IGe2,2 as the source

Fig.8 Graph of intensity to position for distance variable
Within different s values and different sources, it can be seen that light that does not hit the structure helps the induced light propagate to its direction.

CONCLUSION
In this article, the manufacturing process makes amends for the lack of manufacturing experience in our laboratory, which makes a standard procedure for micro-sized manufacture, allowing newcomers to spend less time exploring.
The results from this research verifies that in order to induce surface plasmon on a surface of silver, the period of the structure pattern, a, must be equal to n micrometers, where n is an integer. When a=2(um), better propagation results are obtained. The larger the period, the weaker the propagation.
From the second part of the experiment, a phenomenon has been observed: light that does not hit the microstructure makes the induced light propagate to its direction, providing us with an effective method to control the surface plasmon propagation.

[1] X.-Y. Wu, L. Sun, Q.-F. Tan, and J. Wang, "A novel phase-sensitive scanning near-field optical microscope",Chin. Phys. B 24(5), pp. 6128-6133 (2015).
[2] P. Dvořák, "Control and near-field detection of surface plasmon interference patterns", Nano Lett. 13(6), 2558 (2013).
[3] R. W. Wood, "On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum ", Philos. Mag. 4, 396 (1902).
[4] M. A. Bandres, and J. C. Gutiérrez-Vega, "Ince–Gaussian modes of the paraxial wave equation and stable resonators," JOSA A 21, 873 (2004).
[5] S.-C. Chu, and K. Otsuka, "Numerical study for selective excitation of Ince-Gaussian modes in end-pumped solid-state lasers," Optics express 15, 16506 (2007).
[6] E. H. Synge, "A suggested method for extending the microscopic resolution into the ultramicroscopic region," Phil. Mag. 6, 356 (1928).
[7] J. A. O'Keefe, "Letters to the Editor,". J. Opt. Soc. Am. 46, 359 (1956).
[8] D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: Image recording with resolution λ/20," Appl. Phys. Lett. 44, 651 (1984).
[9] 蔡定平，科儀新知，"掃描式近場光學顯微儀"，第二十一卷第五期(17-23) (2000).
[10] U. Fano, "The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces," J. Opt. Soc. Am. 31, 213 (1941).
[11] A. Hessel and A. A. Oliner, "A New Theory of Wood’s Anomalies on Optical Gratings," Appl. Opt. 4, 1275 (1965).
[12] R. H. Ritchie, "Plasma Losses by Fast Electrons in Thin Films," Phys. Rev. 106, 874 (1957).
[13] H. A. Atwater, "The Promise of Plasmonics", Scientific American 296, 56 ( 2007).
[14] W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[15] 邱國斌，蔡定平，物理雙月刊，"金屬表面電漿簡介"，二十八卷二期，472(2006).