TAILIEUCHUNG - composite 2012 Part 4

Tham khảo tài liệu 'composite 2012 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Manipulating Nematic Liquid Crystals-based Magnetophotonic Crystals 53 For a monochrome light propagating along the z - axis with a given frequency O based on Maxwell s equations we have 71 dtylz iu . 2 az c where F z is the field vector provided as J . ii . i . and A z is the Berrmeman matrix which is the function of the permittivity permeability of the material and the incident wave vector. The subscript t denotes the transpose operator. The components of the Berreman matrix are provided with 71 til uxS5 33 t12 - - u22 - t 1Z 33 33 Í13 -Vx x ÍU 21 11 - 22 - x 23 e12- 24 0 . . 3 31 0 32 -M12 Í33 x 777 ứơ X 33 34 MU- 41 621 - 42 -v v x 33 x 33 43 622 - - 44 -v Eq. 2 has a solution of the form - . 211 4 Within the frame of transfer matrix method the field vector can be expressed as 5 where T z z0 is the transfer matrix provided with the Cauchy and Hamilton theorem 71 ill 4 4ị4Ạ 6 54 New Developments in Liquid Crystals These coefficients Pi are - E A E AjAfc AjA AfcAf . ỂJtAi fa - E Aj Afc A a. a. fa Ayi Au- where Ajj At Aj 8 i j k l 1 2 3 4. Xi are the eigenvalues of the Berreman matrix. In contrast with the isotropic materials it is more complicate due to the existence of the non-diagonal elements in the dielectric permittivity or magnetic permeability tensors. Even the incident plane wave is a linear polarization it will form the non-linear polarized waves. Therefore it typically yields the four solutions for the anisotropic materials two of which represent left- and right- handed polarized forward propagating waves and another two are the corresponding backward propagating waves. If the individual layer occupies the spatial region of Zo z zo d the field vectors k zt d and k zo can be connected with TiCfi where Ti is the single-layer transfer matrix and d is the thickness of this layer. For the finite photonic crystals the total transfer matrix Ttotai of the system can be achieved by multiplying the individual transfer matrix together. The NLC is of .

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