Where L Is the Crystal Length Along the Y-Axis

ELEC425/6261

Assignment 6

1. Wave plates: Calculate and compare the thickness of quarter -wave plates made from calcite, quartz and LiNbO3 crystals all operating at a wavelength of   590 nm. What is your conclusion?

2. Transverse Pockels cell with LiNbO3 Suppose that instead of the configuration in Figure 7.20, the field is applied along the z-axis of the crystal, the light propagates along the y-axis. The z-axis is the polarization of the extraordinary wave and x-axis that of the ordinary wave. Light propagates through as o- and e-waves. Given that Ea = V/d, where d the crystal length along z, the indices are  1 3  1 3 no  no  2 nor13Ea and ne  ne  2 ne r33Ea Show that the phase difference between the o- and e-waves emerging from the crystal is, 2L 2L 1 V      n  n  n3r  n3r  e o  e o  2 e 33 o 13 d where L is the crystal length along the y-axis. Explain the first and second terms. How would you use two such Pockels cells to cancel the first terms in the total phase shift for the two cells. If the light beam entering the crystal is linearly polarized in the z-direction, show that

2n L 2L (n3r ) V   e  e 33   2 d Consider a nearly monochromatic light beam of the free-space wavelength = 500 nm and polarization along z-axis. Calculate the voltage V needed to change the output phase  by given a LiNbO3 crystal with d/L = 0.01 (see table 7.2).

z x L L d Ea z Light Ea Light d  y y x T w o t r a n v e r s e P o c k e l s c e l l p h a s e m o d u l a t o r s t o g e t h e r c a n c e l t h e n a t u r a l b i r e f r i n g e n c e i n e a c h c r y s t a l . Figure Q2

1 ELEC425/6261

3 Longitudinal Pockels cell a Sketch schematically the structure of a longitudinal Pockels cell in which the applied field is along the direction of light propagation, both parallel to z-axis (optic axis). Suggest schemes that would allow light to enter the crystal along the applied field direction. b Suppose that a LiNbO3 crystal is used. LiNbO3 is uniaxial and n1 = n2 = no (polarizations parallel to x and y)and n3 = ne (polarization parallel to z) Neglecting the rotation of the axes (same principal axes in the presence of an applied field), the new ordinary refractive index is  1 3 no  no  2 nor13Ea Calculate the half-wave voltage required to induce a retardation of  between the emerging and incident waves if the free space wavelength is 1 m. What are their polarizations? -12 [ Note: For LiNbO3 at 633 nm, no  2.28, r13  910 m/V. c Suppose that a KDP crystal is used. KDP is uniaxial and n1 = n2 = no (polarizations parallel to x and y)and n3 = ne (polarization parallel to z). The principal axes x and y are rotated by 45 to become x and y as in Figure 7Q16-1 and  1 3  1 3 n1  no  2 nor63Ea n2  no  2 nor63Ea and n3 = n3 = ne Calculate the half-wave voltage required to induce a retardation of  between the emerging components of the electric field, for free space wavelength of 633 nm if for KDP at -12 633 nm, no  1.51, r63  10.510 m/V.

y E a y  x  y n = n n 2 2 o n 2 n 1 4 5 

x z x x z n = n z 1 o E a n 1

K D P , L i N b O 3 K D P L i N b O 3

(a) (b) (c)

( a ) C r o s s s e c t i o n o f t h e o p t i c a l i n d i c a t r i x w i t h n o a p p l i e d f i e l d , n 1 = n 2 = n o ( b ) T h e a p p l i e d e x t e r n a l f i e l d m o d i f i e s t h e o p t i c a l i n d i c a t r i x . I n a K D P c r y s t a l , i t r o t a t e s t h e

p r i n c i p a l a x e s b y 4 5  t o x  a n d y  a n d n 1 a n d n 2 c h a n g e t o n 1 a n d n 2 . ( c ) A p p l i e d f i e l d a l o n g y i n L i N b O 2 m o d i f i e s t h e i n d i c a t r i x a n d c h a n g e s n 1 a n d n 2 c h a n g e t o n 1 a n d n 2 . Figure Q3