Surface-waves generated by nanoslits

1. Surface-waves generated by nanoslits Philippe Lalanne Jean Paul Hugonin Jean Claude Rodier INSTITUT d'OPTIQUE, Palaiseau - France Acknowledgements : Lionel Aigouy , 40 100 Béziers

2. Basic diffraction problem

3. Basic diffraction problem

4. Motivation : providing a microscopic description of the interaction between nanoslits

5. Motivation : ET =l/3 L = 750 nm 320-nm-thick Ag film Ebbesen et al., Nature 391, 667 (1998)

6. 20 µm Motivation : beaming effect calculation Garcia-Vidal et al., APL 83, 4500 (2003) measurements H. Lezec et al., Science 297, 820 (2002) Gay et al., Appl. Phys. B 81, 871-874 (2005)

7. Outline Try to answer basic questions Nature of the surface waves SPP?

8. Outline Try to answer basic questions Nature of the surface waves SPP? – other waves?

9. Outline Try to answer basic questions Nature of the surface waves SPP? – other waves? Influence of the geometrical parameter w slit width

10. Outline Try to answer basic questions Nature of the surface waves SPP? – other waves? Influence of the geometrical parameter Influence of the metal dielectric property silver or gold visible or IR illumination

11. d d Outline Try to answer basic questions Nature of the surface waves SPP? – other waves? Influence of the geometrical parameter Influence of the metal dielectric property Experimental validation Young’s experiment slit groove experiment

12. SPP generation n1 n2

13. SPP generation n1 r0 a-(x) a+(x) n2

14. SPP generation n1 t0 b -(x) b+(x) n2

15. Easy generalization S S S = b+ [t0a exp(2ik0neffh)]/ [1-r0exp(2ik0neffh)]

16. General theoretical formalism (a) (b) • 1) Calculate the transverse (Ez,Hy) near-field • 2) make use of the completeness theorem for the normal modes of waveguides • Hy=  • Ez=  • 3) Use orthogonality of normal modes P. Lalanne, J.P. Hugonin and J.C. Rodier, PRL 95, 263902 (2005)

18. n1 a-(x) a+(x) n2 Analytical model 1) assumption : the near-field distribution in the immediate vicinity of the slit is weakly dependent on the dielectric properties 2) Calculate this field for the PC case 3) Use orthogonality of normal modes describe material properties -The SP excitation probability |a+|2scales as |e(l)|-1/2 -Immersing the sample in a dielectric enhances the SP excitation (n2/n1) P. Lalanne, J.P. Hugonin and J.C. Rodier, JOSAA23, 1608 (2006)

19. n1 a-(x) a+(x) n2 Analytical model 1) assumption : the near-field distribution in the immediate vicinity of the slit is weakly dependent on the dielectric properties 2) Calculate this field for the PC case 3) Use orthogonality of normal modes describe material properties describe geometrical properties -A universal dependence of the SPP excitation that peaks at a value w=0.23l. -For w=0.23l and for visible frequency, |a+|2 can reach 0.5, which means that of the power coupled out of the slit half goes into heat

20. Results obtained for gold Total SP excitation efficiency model : solid curves vectorial theory : marks total SP excitation probability

21. SPP? - other waves?

22. H = HSP + Hc HSP = Hc= Integral over a single real variable Green function (1D) z H(x,x’,z=0) x x’=0

23. HSP Hc (x/l)-1/2 100 10-1 |H| (a.u.) |H| (a.u.) 10-2 l=1 µm l=0.633 µm 10-3 x/l x/l 100 10-1 |H| (a.u.) |H| (a.u.) 10-2 l=3 µm l=9 µm 10-3 100 101 102 100 101 102 x/l x/l (result for silver) Green function (1D) z P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

24. plane wave illumination (l) 1 w=100 nm 0 l -1 0.5 0 -0.5 l=0.852 µm x/l w=352 nm l l=3 µm x/l P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

25. (d/l) -1/2 PC l=9 mm l=3 mm |S/S0|2 l=1.5 mm l=1 mm l=0.852 mm d/l ….. SPP only computational results l = 852 nm l = 852 nm d S0 S P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

26. d d Outline Try to answer basic questions Nature of the surface waves SPP? – other waves? Influence of the geometrical parameter Influence of the metal dielectric property Experimental validation Young’s experiment slit groove experiment

27. d=4.9 µm d d=9.9 µm gold glass d=14.8 µm TM incident light d=19.8 µm Validation : Young’s slit experiment H.F. Schouten et al., PRL. 94, 053901 (2005).

28. b+ a - gold S d=4.9µm d S ***semi-analytical model o o oSchouten’s experiment numerical results d=9.9µm S Validation : Young’s slit experiment S = |t0 + a- b+ exp[ikSPd)]|2 P. Lalanne, J.P. Hugonin and J.C. Rodier, PRL 95, 263902 (2005)

29. d |S/S0|2 d(µm) Slit-Groove experiment Fall off for d < 5l silver l=852 nm d frequency = 1.05 k0 kSP=k0 [1-1/(2eAg)] 1.01k0 |S|2 |S0|2 G. Gay et al. Nature Phys. 2, 262 (2006) promote an other model than SPP

30. l = 852 nm l = 852 nm d S0 S computational results o o oexperiment ….. SPP theory |S/S0|2 d (µm) SPP theory and computational results are in perfect agreement P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

31. 2 µm Gwénaelle Julié, Véronique Mathet Institut d’Electronique Fondamentale, Orsay, France 2 µm TM incident light Near field validation Lionel Aigouy, Laboratoire ‘Spectroscopie en Lumière Polarisée’ ESPCI, Paris gold slit slit

32. ----- extracted from fit computational results Real part Imaginary part total field Real part Imaginary part creeping wave ONLY distance distance Field at a single aperture

33. Conclusion • The surface wave is a combination of SPP [exp(ikSPx)] and a creeping wave with a free space character [exp(ik0x)]/x1/2 • SPP is predominant at optical frequency for noble metal • The creeping wave is dominant for l>1.5 µm and for noble metals • The SPP generation probability can be surprisingly high for subwavelength slits (50%) at optical wavelengths • The probability scales as |e(l)|-1/2 • The probability is enhanced when immersing the sample • Experimental validation is difficult but on a good track