Investigation of spatial coherence and phase change in the modes of a HeNe laser

Volume 20, n u m b e r 6

PHYSICS

INVESTIGATION

LETTERS

1April 1966

OF SPATIAL COHERENCE IN THE MODES OF A He-Ne ,

•

AND PHASE LASER

CHANGE

p

L. C S I L L A G , M . J A N O S S Y a n d K . K A N T O R Central Research Institute of Physics, Budapest Received 22 F e b r u a r y 1966

M e a s u r e m e n t s of spatial coherence in the modes TEM and TEM i0 showed this to be very nearlv ideal. 00 A phase difference of y was o b s e r v e d between the two p a r t s of the mode pattern TEM10.

In a n e a r l i e r e x p e r i m e n t w e h a v e m e a s u r e d t h e s p a t i a l c o h e r e n c e of a H e - N e l a s e r o p e r a t i n g a t ~ = 1.15 # i n t h r e e l o w - o r d e r t r a n s v e r s e m o d e s [1]. T h e d e g r e e of c o h e r e n c e o b t a i n e d t h e n d e v i a t e d i n g e n e r a l b y 5 - 6% f r o m i d e a l c o h e r e n c e . We therefore repeated our measurements on a H e - N e l a s e r o p e r a t i n g n o w a t ~ = 0 . 6 3 2 8 ~t a n d s l i g h t l y m o d i f i e d t h e a p p a r a t u s d e s c r i b e d i n [1] i n o r d e r to o b t a i n h i g h e r a c c u r a c y . W i t h t h e h e l p of a l e n s of f = 30 c m f o c a l d i s t a n c e t h e l a s e r b e a m leaving the Mach-Zehnder interferometer was e n l a r g e d i n s u c h a w a y t h a t t h e d i a m e t e r (0.4 m m ) of t h e a p e r t u r e of t h e d e t e c t i n g p h o t o m u l t i p l i e r ( E M I 6 2 5 6 B ) w a s e q u a l to a b o u t 1 / 4 0 t h of t h e d i a m e t e r of t h e l a s e r b e a m . Fig. 1 shows the measuring results. The degree of c o h e r e n c e ~12t o b t a i n e d i n t h e m o d e T E M o o w a s p r a c t i c a l l y 1, w h i l e i t w a s 0.98 i n t h e m o d e

3

I

1,0) J~.~\ A

"LO0

itl

d

I

Ir~l I t.~?~ TEMoo

0.96-

0

f

~

2

,

,

,

id

#ram

Fig. 1. The degree of coherence ~121 obtained at v a r ious distances d between two points on the c r o s s s e c tion of the l a s e r b e a m {right) and the intensity d i s t r i bution I of the modes (left). 636

I

8

A

Fig. 2. Location of mode p a t t e r n s TEM10 with r e s p e c t to each other shaded part showing where i n t e r f e r e n c e was investigated (inset). The c o r r e s p o n d i n g intensity distributions; dotted line and thin full line mode patterns, thick full i n t e r f e r e n c e pattern (lower figure).

~m

"I

-!

tn~

T E M 1 0 . T h e d e v i a t i o n of 2% f r o m i d e a l c o h e r e n c e i n t h e l a t t e r m o d e m a y b e a t t r i b u t e d to t h e e f f e c t of s o m e o t h e r w e a k l y e x c i t e d t r a n s v e r s e m o d e s and the same effect may have been responsible also for the deviation observed in our previous m e a s u r e m e n t [1]. Fig. 2 describes the interesting case observed i n t h e m o d e T E M 10 w h e n t h e l a s e r b e a m i s s p l i t b y t h e i n t e r f e r o m e t e r a n d o n e p a r t of t h e m o d e p a t t e r n of o n e of t h e b e a m s p r o d u c e s a n i n t e r f e r e n c e p a t t e r n w i t h b o t h p a r t s of t h e m o d e p a t t e r n of t h e o t h e r b e a m . It m a y b e s e e n t h a t t h e i n t e n s i t y d i s t r i b u t i o n of t h e i n t e r f e r e n c e p a t t e r n

Volume 20, number 6

PHYSICS LETTERS

has a m a x i m u m , for i n s t a n c e , at A and a m i n i m u m at B although the path difference between the i n t e r f e r i n g b e a m s is the s a m e in these p o i n t s , i n d i c a t i n g that there is a phase difference between the two p a r t s of the mode p a t t e r n TEM10. The q u a n t i t a t i v e e v a l u a t i o n of the i n t e r f e r e n c e p a t t e r n gives a p p r o x i m a t e l y the value of z for this phase

RESONANCES

IN T H E

1 April 1966

d i f f e r e n c e , in a g r e e m e n t with the theory of optical r e s o n a t o r s [2]. 1. M. Jtinossy, L. Csillag, K.K~intor, Physics Letters 18 (1965) 124. 2. G.D. Boyd, Proc. Third Int. Congr. on Quantum electronics, Paris, Vol. II (Dunod-Columbia Press, 1964) p. 1179.

INELASTIC

e-He

SCATTERING

G. DRUKAREV, T. ~.IKARJEVA

Physical Institute, Leningrad State University Received 22 February 1966

The three-channel system is considered as consisting of 11S-23S-33S or 11S-21S-33S states of He, the incident electron being in flae p-state. Resonances in the 23S or 21S-excitation cross sections are found near the 33S threshold.

The r e s o n a n c e s in the i n e l a s t i c e - H e s c a t t e r i n g w e r e o b s e r v e d r e c e n t l y by Schulz and P h i l b r i c k [1] and C h a m b e r l a i n [2] n e a r 22eV. These r e s o n a n c e s as well, as the r e s o n a n c e s in e l a s t i c s c a t t e r i n g [3] in the s a m e r e g i o n , a r e due to the v i r t u a l f o r m a tion of the q u a s i - s t a t i o n a r y negative h e l i u m ion He-. The s i m p l e s t model to d e m o n s t r a t e the o c c u r r e n c e of the r e s o n a n c e s in the e l a s t i c and i n e l a s t i c s c a t t e r i n g is a t h r e e - c h a n n e l s y s t e m with coupling b e t w e e n all c h a n n e l s . In this p a p e r we c o n s i d e r as an e x a m p l e of such a t h r e e - c h a n n e l s y s t e m the 11S-23S-33S and 11S-21S-33S s t a t e s of He atom, the incident e l e c t r o n being in the p - s t a t e . The p a r t i a l c r o s s s e c t i o n for the i - j t r a n s i t i o n is given by

aiJ _ 4 ~ 2 l i + 1 ) ]Tij]2 , ki2

(1)

where Tij is the m a t r i x e l e m e n t of the f a m i l i a r T-matrix. It is convenient to e x p r e s s the T - m a t r i x in t e r m s of the m a t r i x , introduced by Ross and Shaw

[4]

r-- kl+ ( -ik 2l+l)'lkl+ ,

(2)

1 1 2 is the e n e r g y of the incident e l e c t r o n ; ~k

k22 = k l 2 - 2 ( E 2 - E 1 ) ;

k32 = k l 2 - 2 ( E 3 - E 1 ) ,

E l , E2, E 3 a r e the e n e r g i e s of n o r m a l , f i r s t excited and second excited s t a t e s r e s p e c t i v e l y .

33.¢

(3)

I '

~205

~2~

z h: a.u.

Fig. 1. 23S excitation. 637