Shiwei Tang1, David J. Cho2, Hao Xu1, Wei Wu3, Y. Ron Shen2, and Lei Zhou1*

1Physics Department, Fudan University, Shanghai 200433, China 2Department of Physics, University of California, Berkeley, California 94720, USA 3Quantum Science Research, Hewlett-Packard Laboratories, Palo Alto, California 94304, USA

(2) (2) 2( , 2 ) : :[ ( , )]S locp L r E r dr

(2) (2)(2 ) : ( ) ( )p E E

2(2) (2)( , 2 ) : : ( , )SL r L r dr

Mirror planes at x = 0 and y = 0, nonvanishing elements:

None contributes to PS and SS SHG.

(2)

zzzX (2)

zyyX

(2) (2)

xzz xxzX X

(2)

zxxX(2) (2)

yzy yyzX X

Break mirror planes at x=0

(2) (2)2x xxz x zp E E (2)

x xzz z zp E E (2)

x xxx x xp E E (2)

z zzz z zp E E (2)

z zxx x xp E E (2) 2z zzx z xp E E

Calculated (lines) and measured (symbols) SHG spectra for different polarization combinations.

( )( , ) ( )

r

B rL r A r

i

4

1 2

( ) [ ]PP C DS B

i i

References: S. W. Tang, D. J. Cho, H. Xu, W. Wu, Y. R. Shen, and L. Zhou, submitted to Plasmonics

L R

x xE EL R

z zE E

with inclined plane without inclined plane