1. 3D Micromanufacturing Laboratory School of Mechatronics Gwangju Institute of Science and Technology (GIST), KOREA 이 용 구이 용 구 Calculation of optical trapping forces summary Yong-Gu Lee

2. 3D Micromanufacturing Lab. Rayleigh, Mie, and Ray-optics regimes With Rayleigh scattering, the electric field is assumed to be invariant in the vicinity of the particle Taken from the course notes of Radar Metrology by Prof. Bob Rauber (UIUC) http://www.atmos.uiuc.edu/courses/atmos410-fa04/presentations.html

3. 3D Micromanufacturing Lab. Electromagnetic forces + Electric forceMagnetic force

4. 3D Micromanufacturing Lab. Electromagnetic forces

5. 3D Micromanufacturing Lab. Dielectric material ( 유전체 )  Dielectric material: poor conductor of electricity but an efficient supporter of electrostatic fields  Examples are: porcelain (ceramic), mica, glass, plastics, and the oxides of various metals. Dry air is an excellent dielectric. Distilled water is a fair dielectric. A vacuum is an exceptionally efficient dielectric.  Metals can be thought as dielectric at their outermost shells

6. 3D Micromanufacturing Lab. Induced electric field in a dielectric object E1E1 Incident plane wave Dielectric Sphere + - - +

7. 3D Micromanufacturing Lab. Potential due to dipole Dielectric Sphere - charge + charge

8. 3D Micromanufacturing Lab. Electric field inside dielectrics 1 2 Image from: Julius Adams Stratton, Electromagnetic theory, McGraw-Hill Book Company Inc. 1941

9. 3D Micromanufacturing Lab. Gradient force (Rayleigh regime)

10. 3D Micromanufacturing Lab. Scattering force (Rayleigh regime) Incident plane wave Dielectric Sphere Scattered spherical wave

11. 3D Micromanufacturing Lab. Calculating C pr

12. 3D Micromanufacturing Lab. This slide is taken from the lecture notes of Optical Tweezers in Biology by Prof. Dmitri Petrov https://www.icfo.es/courses/biophotonics2006/html/

13. 3D Micromanufacturing Lab. Mie (scattering) theory Spherical harmonics: Waves in spherical structures

14. 3D Micromanufacturing Lab. Ray optics regime Medium index of refraction n 1 Sphere index of refraction n 2

15. 3D Micromanufacturing Lab. Scattering of a single incident ray  Why is this θ?  Scattered rays make angles relative to the incident forward ray direction of Π+2 θ, α, α+ β, …, α+n β, …  The powers of the scattered rays are PR, PT 2, PT 2 R,…,PT 2 R n,… Medium index of refraction n 1 Sphere index of refraction n 2

16. 3D Micromanufacturing Lab. Total scattering force  Force due to a single ray of power P hitting a dielectric sphere at an angle of θ incidence with incident momentum per second of n 1 p/c

17. 3D Micromanufacturing Lab. Total scattering force

18. 3D Micromanufacturing Lab. Total scattering force Gradient force Scattering force

19. 3D Micromanufacturing Lab. Force is towards the focal point

20. 3D Micromanufacturing Lab. Integrate along the beam diameter

21. 3D Micromanufacturing Lab. Metal trapping An electronic field attenuates e-times in the skin layer This slide is adapted from the lecture notes of Optical Tweezers in Biology by Prof. Dmitri Petrov https://www.icfo.es/courses/biophotonics2006/html/

22. 3D Micromanufacturing Lab. Numerical solutions  We can obtain the complete electromagnetic solution in time and space using FEM and FDTD methods.  By integrating the Maxwell stress tensor at the surface (S) of the scattering object the optical force as well as momentum can be computed. Fig. 1. Solid and medium under an incident field. Ref. Seung-Yong Sung and Yong-Gu Lee, "FDTD 방법을 이용한 광집게의 포획 힘 계산," Hankook Kwanghak Hoeji, Vol. 19, No. 1, pp 80-83, 2008 Feb (Written in Korean) Seung-Yong Sung and Yong-Gu Lee, “Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method,” Optics Express, Vol. 16, No. 5, pp 3463-3473, 2008 Seung-Yong Sung “Calculations of the trapping force using the FDTD method and its applications,” 2008.02 Master’s thesis, GIST

23. 3D Micromanufacturing Lab.