Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Formation principles of two-dimensional compound photonic lattices by one-step holographic lithography

W. D. Mao, J. W. Dong, Y. C. Zhong, G. Q. Liang, and H. Z. Wang

Open Access Open Access

Abstract

From the view of crystallography, a systematic theoretical study on one-step formation of two-dimensional compound photonic lattices by four noncoplanar elliptical waves is presented. A general formula for the interference intensity of N elliptically polarized waves, and relevant phase shifts that compensate for the initial phases and control the relative position and size of the motifs, have been deduced. Using appropriate polarization configurations, four kinds of beam geometries can be used to form various compound lattices. This provides an ideal new experimental platform for fabricating large-area compound photonic lattices.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Crystallography of two-dimensional photonic lattices formed by holography of three noncoplanar beams

Weidong Mao, Yongchun Zhong, Jianwen Dong, and Hezhou Wang
J. Opt. Soc. Am. B 22(5) 1085-1091 (2005)

Formation of all fourteen Bravais lattices of three-dimensional photonic crystal structures by a dual beam multiple-exposure holographic technique

Ashish Dwivedi, Jolly Xavier, Joby Joseph, and Kehar Singh
Appl. Opt. 47(12) 1973-1980 (2008)

Fabrication of photonic crystals with functional defects by one-step holographic lithography

Juntao Li, Yikun Liu, Xiangsheng Xie, Peiqing Zhang, Bing Liang, Li Yan, Jianying Zhou, Gershon Kurizki, Daniel Jacobs, Kam Sing Wong, and Yongchun Zhong
Opt. Express 16(17) 12899-12904 (2008)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)
Fig. 1.
Fig. 1. (a) Beam geometry for 2D compound lattices. Four laser beams are placed around Z axis and make the same angle with OZ. (b) Primitive rectangular compound lattice. (c) 3D structure of the square compound lattice. (d) Change of the relative size (left) and position (right) of the motifs in two unit cells due to the phase shifts.

Download Full Size | PDF

Fig. 2.
Fig. 2. (a) Hexagonal compound lattice. (b) Schematic illustration of the choices of the G ij vectors for the hexagonal compound lattice. Inset, the change of the relative size and shape of the motifs in a unit cell. (c) Compound rectangular p-lattice. (d) G ij vector choices for the lattice in (c).

Download Full Size | PDF

Fig. 3.
Fig. 3. (a) New hexagonal compound lattice. (b) Schematic illustration of the G ij vector choice for the hexagonal compound lattice. Inset is the superposition of two different simple lattices corresponding to the top left corner of (a). (c) Compound rectangular c-lattice. (d) G ij vector choices for the lattice in (c).

Download Full Size | PDF

Fig. 4.
Fig. 4. (a) Square compound lattice that contains four simple lattices. (b) G ij vector choices and the determination of corresponding k j vectors projected onto the xy-plane. Inset, the change of relative size of the motifs in a unit cell.

Download Full Size | PDF

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I ( r ) = ∣ ∑ j E aj exp [ i ( k j · r + δ j ) ] e aj + ∑ j E bj exp [ i ( k j · r + δ j − π ⁄ 2 ) ] e bj ∣ 2
= ∑ j E aj 2 + ∑ j E bj 2 + ∑ i < j 2 E ij 2 cos [ ( k j − k i ) · r + δ j − δ i − t shift _ ij ]
i , j = 1 , 2 , 3 , ⋯ , N ,
E ij 2 = ( E ai E aj cos θ aiaj + E bi E bj cos θ bibj ) 2 + ( E ai E bj cos θ aibj − E bi E aj cos θ biaj ) 2 ,
cos t shift _ ij = E ai E aj cos θ aiaj + E bi E bj cos θ bibj E ij 2 ,
cos [ ( δ 2 − δ 1 + δ 4 − δ 3 ) ⁄ 2 ] · cos [ ( k 2 − k 1 ) · r + ( δ 2 − δ 1 + δ 3 − δ 4 ) ⁄ 2 ]
cos [ ( δ 3 − δ 2 + δ 1 − δ 4 ) ⁄ 2 ] · cos [ ( k 3 − k 2 ) · r + ( δ 3 − δ 2 + δ 4 − δ 1 ) ⁄ 2 ]
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use