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Nonlinear scattering of electrons by laser beam
Volume24A, number 2
PHYSICS LETTERS
[14] r e l a t i n g the f i e l d on one m i r r o r to that one on the other m i r r o r . The gain of the m e d i u m was i n t r o d u c e d by s t a r t i n g f r o m r a t e equations, thus excluding r e s o n a t o r e f f e c t s . T h e i r a n a l y s i s i n v o l v e s a lengthy a l g e b r a . It can be shown, h o w e v e r , that fo r al l p r a c t i c a l c a s e s the effect of M 3 can be d e r i v e d d i r e c t l y f r o m t h e i r i n t e n sity d e t e r m i n i n g equation if (R2)½ is r e p l a c e d by the a m p l i t u d e r e f l e c t i v i t y r of the e x t e r n a l i n t e r f e r o m e t e r , s i m i l a r l y as was done in our s i m p l e a n a l y s i s *. Th e g e n e r a l shape of the modulation s i g n a l s t u r n e d out to be s i m i l a r in t h e i r and our c a l c u l a t i o n s , s i n c e it is c l o s e l y r e l a t e d to the t i m e - v a r y i n g r e f l e c t i v i t y of the e x t e r n a l i n t e r ferometer. It m i g h t be of i n t e r e s t to c o n s i d e r e x t e r n a l m o v i n g m i r r o r modulation in t e r m s of e x t e r n a l signal i n j e c t i o n [15],
We a r e greatly indebted to N. V. P h i l i p s ' Gloeilampenfabrieken for t h e i r courtesy in supplying the 1.15 ~ l a s e r .
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
1
* The quantityA in ref. 13 is equal to (R2)~/r , where r is assumed to be real at the laser oscillation f r e quency. This was not noticed by Hooper and Bekefi. The minus sign in the denominator of their eq. (18) has to be replaced by a plus sign (E.B.Hooper. private communication).
16 January 1967
12. 13. 14.
15.
P.T.Bolwijn, Phys. Letters 19 (1965) 384. P.T. Bolwijn, IEEE J. Quant. Elec. QE 2 (1966). P.T. Bolwijn, J. Appl. Phys. 37 (1966} 4487. P.G.R.King and G.J.Steward, New Scientist 17 (1963) 180, M.Born and E.Wolf, Principles of optics (Pergamon Press Ltd., London, 1959)pp. 322-326. D.M.Clunie and N.H.Rock, J. Sci. lnstrum. 41 (1964) 489. G.Bouwhuis, Philips Res. Repts. 19 (1964) 422. W.E,Lamb Jr., Phys. Rev. 134 (1964) A1429. H.G.Van Bueren, J,Haisma and H.De Lang, Phys. Letters 2 (1962) 340, P.T. Bolwijn, Th. H. Peek and C. Th. J. Alkemade, Phys. Letters 23 (1966) 88. Th. H. Peek, P.T. Bolwijn and C. Th. J. Alkemade, to be published. J.B.Gerardo and J.T.Verdeyen, Proc. IEEE 52 (1964) 690. E.B.Hooper and G.Befeki, J. Appl. Phys. 37 (1966) 4083. A.G.FoxandT.Li, Bell System Tech. J. 40 (1961) 453. T,Uehida, IEEE J. Quant. E1ec,, to be published.
* * * * *
NONLINEAR
SCATTERING
OF
ELECTRONS
BY L A S E R
BEAM
P. T. CHANG
Systems Development Division, International Business Machines Corporation, Poughkeepsie, New York Received 15 December 1966
D i r e c t observation of nonlinear s c a t t e r i n g of e l e c t r o n s by a l a s e r b e a m has been r e p o r t e d [1], but the p r o b a b i l i t y of r e f l e c t i o n a p p e a r e d m u c h h i g h e r than what was p r e d i c t e d by the K a p i tz a and D i r a c f o r m u l a [2]. S i n c e it is well known that the i n t e n s i t y of a l a s e r b e a m has a G a u s s i a n d i s t r i b u t i o n [3], it can be shown that e n e r g y c o n s e r vation is p r e s e r v e d if this d i s t r i b u t i o n taken e x p l i c i t l y into acco u n t in the c a l c u l a t i o n . * * * * *
130
References 1. H. Schwarz,H. A. Tourtelotte, W. W. Gaertner, Physics Letters 19 (1965) 202. 2. P.L.Kapitza and P.A.M. Dirac. Proc. Cambridge Phil, Soc. 29 (1933) 297. 3. Spectra-Physics, Inc., Laser Technical Bulletin No. 2.
PHYSICS LETTERS
[14] r e l a t i n g the f i e l d on one m i r r o r to that one on the other m i r r o r . The gain of the m e d i u m was i n t r o d u c e d by s t a r t i n g f r o m r a t e equations, thus excluding r e s o n a t o r e f f e c t s . T h e i r a n a l y s i s i n v o l v e s a lengthy a l g e b r a . It can be shown, h o w e v e r , that fo r al l p r a c t i c a l c a s e s the effect of M 3 can be d e r i v e d d i r e c t l y f r o m t h e i r i n t e n sity d e t e r m i n i n g equation if (R2)½ is r e p l a c e d by the a m p l i t u d e r e f l e c t i v i t y r of the e x t e r n a l i n t e r f e r o m e t e r , s i m i l a r l y as was done in our s i m p l e a n a l y s i s *. Th e g e n e r a l shape of the modulation s i g n a l s t u r n e d out to be s i m i l a r in t h e i r and our c a l c u l a t i o n s , s i n c e it is c l o s e l y r e l a t e d to the t i m e - v a r y i n g r e f l e c t i v i t y of the e x t e r n a l i n t e r ferometer. It m i g h t be of i n t e r e s t to c o n s i d e r e x t e r n a l m o v i n g m i r r o r modulation in t e r m s of e x t e r n a l signal i n j e c t i o n [15],
We a r e greatly indebted to N. V. P h i l i p s ' Gloeilampenfabrieken for t h e i r courtesy in supplying the 1.15 ~ l a s e r .
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
1
* The quantityA in ref. 13 is equal to (R2)~/r , where r is assumed to be real at the laser oscillation f r e quency. This was not noticed by Hooper and Bekefi. The minus sign in the denominator of their eq. (18) has to be replaced by a plus sign (E.B.Hooper. private communication).
16 January 1967
12. 13. 14.
15.
P.T.Bolwijn, Phys. Letters 19 (1965) 384. P.T. Bolwijn, IEEE J. Quant. Elec. QE 2 (1966). P.T. Bolwijn, J. Appl. Phys. 37 (1966} 4487. P.G.R.King and G.J.Steward, New Scientist 17 (1963) 180, M.Born and E.Wolf, Principles of optics (Pergamon Press Ltd., London, 1959)pp. 322-326. D.M.Clunie and N.H.Rock, J. Sci. lnstrum. 41 (1964) 489. G.Bouwhuis, Philips Res. Repts. 19 (1964) 422. W.E,Lamb Jr., Phys. Rev. 134 (1964) A1429. H.G.Van Bueren, J,Haisma and H.De Lang, Phys. Letters 2 (1962) 340, P.T. Bolwijn, Th. H. Peek and C. Th. J. Alkemade, Phys. Letters 23 (1966) 88. Th. H. Peek, P.T. Bolwijn and C. Th. J. Alkemade, to be published. J.B.Gerardo and J.T.Verdeyen, Proc. IEEE 52 (1964) 690. E.B.Hooper and G.Befeki, J. Appl. Phys. 37 (1966) 4083. A.G.FoxandT.Li, Bell System Tech. J. 40 (1961) 453. T,Uehida, IEEE J. Quant. E1ec,, to be published.
* * * * *
NONLINEAR
SCATTERING
OF
ELECTRONS
BY L A S E R
BEAM
P. T. CHANG
Systems Development Division, International Business Machines Corporation, Poughkeepsie, New York Received 15 December 1966
D i r e c t observation of nonlinear s c a t t e r i n g of e l e c t r o n s by a l a s e r b e a m has been r e p o r t e d [1], but the p r o b a b i l i t y of r e f l e c t i o n a p p e a r e d m u c h h i g h e r than what was p r e d i c t e d by the K a p i tz a and D i r a c f o r m u l a [2]. S i n c e it is well known that the i n t e n s i t y of a l a s e r b e a m has a G a u s s i a n d i s t r i b u t i o n [3], it can be shown that e n e r g y c o n s e r vation is p r e s e r v e d if this d i s t r i b u t i o n taken e x p l i c i t l y into acco u n t in the c a l c u l a t i o n . * * * * *
130
References 1. H. Schwarz,H. A. Tourtelotte, W. W. Gaertner, Physics Letters 19 (1965) 202. 2. P.L.Kapitza and P.A.M. Dirac. Proc. Cambridge Phil, Soc. 29 (1933) 297. 3. Spectra-Physics, Inc., Laser Technical Bulletin No. 2.