lecture31

# lecture31 - 3 1 M o r e I n t e r f e r e n c e M i c h e l...

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Unformatted text preview: 3 1 . M o r e I n t e r f e r e n c e M i c h e l s o n I n t e r f e r o m e t e r r e v i s i t e d T h e f i e l d a u t o c o r r e l a t i o n S e n s i t i v e m e a s u r e m e n t s o f p h a s e d i s t o r t i o n s T h e w o r l d ’ s l a r g e s t i n t e r f e r o m e t e r : L I G O O t h e r i n t e r f e r o m e t e r s M a c h- Z e h n d e r S a g n a c Y o u n g ’ s d o u b l e s l i t e x p e r i m e n t I r r a d i a n c e o f a s u m o f t w o w a v e s { } 2 * 2 1 1 R e c E E I I I ε = + + ⋅ D i f f e r e n t w a v e l e n g t h s D i f f e r e n t p o l a r i z a t i o n s S a m e w a v e l e n g t h S a m e p o l a r i z a t i o n s 1 2 I I I = + 1 2 I I I = + 1 2 I I I = + I n t e r f e r e n c e o n l y o c c u r s w h e n t h e w a v e s h a v e t h e s a m e w a v e l e n g t h a n d t h e s a m e p o l a r i z a t i o n . T h e M i c h e l s o n I n t e r f e r o m e t e r ( M i s a l i g n e d ) S u p p o s e w e m i s a l i g n t h e m i r r o r s , s o t h e b e a m s c r o s s a t a n a n g l e w h e n t h e y r e c o m b i n e a t t h e b e a m s p l i t t e r . A n d w e w o n ' t s c a n t h e d e l a y , s o t h e l e n g t h s a r e e q u a l . B e a m- s p l i t t e r I n p u t b e a m M i r r o r M i r r o r θ z x F r i n g e s ( i n p o s i t i o n ) x I o u t ( x ) ( ) ( ) * R e e x p c o s s i n e x p c o s s i n − − − − + E j t k z k x E j t k z k x ω θ θ ω θ θ I f t h e i n p u t b e a m i s a p l a n e w a v e , t h e c r o s s t e r m b e c o m e s : ] R e e x p 2 s i n c o s ( 2 s i n ) ∝ − ∝ j k x k x θ θ C r o s s i n g b e a m s m a p s d e l a y o n t o p o s i t i o n I f t h e p a t h l e n g t h d i f f e r e n c e c h a n g e s , t h e f r i n g e s s h i f t . T h e " U n b a l a n c e d " M i c h e l s o n i n t e r f e r o m e t e r M i s a l i g n m i r r o r s , s o b e a m s c r o s s a t a n a n g l e . z x B e a m- s p l i t t e r I n p u t b e a m M i r r o r M i r r o r θ P l a c e a n o b j e c t i n t h i s p a t h e x p [ j φ ( x , y ) ] D i s t o r t e d f r i n g e s ( i n p o s i t i o n ) I o u t ( x ) x S u p p o s e a n o b j e c t i s p l a c e d i n o n e a r m o f a n i n t e r f e r o m e t e r ....
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## This note was uploaded on 11/23/2009 for the course ELEC 262 taught by Professor Mittleman during the Spring '09 term at Rice.

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lecture31 - 3 1 M o r e I n t e r f e r e n c e M i c h e l...

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