1. Total Internal Reflections in Liquid Crystals Optics and Photonics Presented in Partial Fulfillment of the Second Midterm Clinton Braganza Liquid Crystal Institute, K.S.U. 4/4/2004

2. Reflection Coefficients ii rr tt SIGMA Polarization ErEr HrHr E H 1 2

3. Reflection Coefficients Pi Polarization ii rr tt 1 2 HiHi EiEi HrHr ErEr HtHt EtEt

4. Total Internal Reflection SIGMA polarization Writing  t explicitly using Snell’s law If n 1 > n 2, all the incident power is reflected if the incident angle is greater than arcsin (n 2 / n 1 ).

5. TIR in Liquid Crystals: Glass to LC. Note that liquid crystals are birefringent, therefore reflections will depend of the orientation of the liquid crystal with respect to the direction of light propagation. Let us consider this liquid crystal: n e = 1.7 n o = 1.5 n glass = 1.7 

6. TIR in LC’s: Orientation We will consider the following configurations: A homeotropic cell With sigma and pi polarized light incident on the cell surface A planar cell –With director parallel to y-axis and sigma and pi polarized light incident on the cell surface –With director parralel to x-axis And sigma and pi polarized light incident on the cell surface. y z y z

7. TIR in LC’s Homeotropic Cells This encounters n o, therefore when the incident angle is greater than arcsin (n o /n g ) = 61.9º, all the light is reflected. E i, S - polarization E

8. TIR in LC’s Homeotropic Cells This encounters This increase from n o to n e, which is the same as glass, therefore TIR does not take place. E i, P - polarization  n k

9. TIR in LC’s Planar Cell : director parallel to y-axis Here the electric field always encounters n o, therefore if the incident angle is greater than the critical angle we have 100% reflectance. E i, S - polarization y z

10. TIR in LC’s Planar Cell : director parallel to y-axis As the incidence angle is increase, the refractive index decreases from n e to n o as the electric field becomes parallel to the director, therefore TIR happens here. E i, Pi - polarization

11. TIR in LC’s Planar Cell : Director parallel to x-axis Here the electric field is always parallel to n e, therefore we do not have TIR E i, S - polarization y z

12. TIR in LC’s Planar Cell : Director parallel to x-axis Here the electric field always encounters n o, therefore TIR occurs at incident angles greater than the critical angle. E i, Pi - polarization

13. TIR in LC’s: LC to Glass Let us consider a different liquid crystal n o =1.5 n e =1.8 Therefore the critical angle is arcsin(n glass /n e ) = 70.81º

14. TIR in LC’s : LC to Glass Homeotropic cell In the liquid crystal the light encounters n o, which is less than n glass, therefore no TIR occurs here. E i, S - polarization E

15. TIR in LC’s : LC to Glass Homeotropic cell In the liquid crystal the light encounters n eff, which increases from n o to n e. Therefore TIR occurs. E i, p - polarization

16. TIR in LC’s: LC to Glass Planar Cell: director parallel to y-axis In the liquid crystal the light encounters n o, therefore no TIR occurs E i, S - polarization y z

17. TIR in LC’s: LC to Glass Planar Cell: director parallel to y-axis In the liquid crystal the light encounters n eff, which decreases to n o as the incident angle increase, therefore no TIR occurs E i, p - polarization y z

18. TIR in LC’s: LC to Glass Planar Cell: director parallel to x-axis In the liquid crystal the light encounters n e, therefore TIR occurs In the liquid crystal the light encounters n o, therefore no TIR occurs E i, S - polarization E i, p - polarization y z

19. TIR in ChLC’s: Glass to LC  Knowing the orientation of the liquid crystal at the boundary we treat the planar texture as the previous nematic cases.  Focal Conic Texture I expect a periodic behavior here, for example, for s- polarization:  If director is parallel to cell normal we have TIR  if director is parallel to polarization of light we will have no TIR. Planar Texture Focal Conic Texture

20. Some applications Switchable fiber optic cables –too expensive A more economical use would be for optical switches. –Shown below is a telecom optical switch designed by Baker, that can switch light to two different positions without changing the polarization. ITO

21. Conclusions Total internal reflection was solved by carefully analyzing the orientation of the liquid crystal director with respect to light propagation. It would be nice to get a general solution for TIR in LC’s, without first knowing the director orientation. For the case of cholesterics this problem would involve studying the effect of the evanescent wave from one chiral layer to another.

22. References Yang, D-K, J. Opt. A: Pure and Appl. Opt, 5(2003) 402-408 Baker, A. P., 1998 Liquid Crystal Optical Switch Having Reduced Crosstalk, USA Patent # 4,720,171 Xianyu, H., et al, Optics Letters, 28 10 (2003) Boiko, Y., et al, Optics Letters, 27 19 (2002)