Selection rules in a Cherenkov laser

Volume 140, number 5

PHYSICS LETFERS A

25 September 1989

SELECTION RULES IN A CHERENKOV LASER S.G. OGANESYAN and N.H. SARGSYAN NPO “Lasernaya Tekhnika’~Yerevan State University, Shopron str. 21, 375090 Yerevan, USSR Received 2 June 1989; accepted for publication 27 July 1989 Communicated by D. Bloch

It is shown that the photon absorption process in a Cherenkov laser is suppressed when a polarized electron beam and circularly polarized amplifying light are propagated in the same direction.

The investigation carried out in refs. [1,2] shows that in a Cherenkov laser two amplification mech-

spins, respectively. If an electron is polarized along the z axis (S1~=~h) and a photon is left-hand cir-

anisms are realized. If the light beam characterizing spreads are much less than those of an electron beam the first can be described as a plane wave. In this case amplification is possible because the energies of the particles (and their numbersrespectively) taking part in the processes of photon emission and absorption are different [1]. In the reverse case we can assume that the particle beam is monoenergetic and does not have an angular spread and the light beam is a sum of plane waves. Here amplification is possible because the same electron emits and absorbs photons with different wave vectors (their numbers are different, too) [2]. It is obvious that in both cases the efficiency of a free-electron laser (FEL) depends on the possibility of separating the photon emission and absorption. The gain of a FEL will increase sharply if a way of full suppression of photon absorption is found. In this paper we show that such an effect is possible in the case when a polarized electron beam amplifies a circularly light beam. isNevertheless, the value ofthepolarized gain in such a device not large because it is based on the Cherenkov radiation of an electron magnetic moment. We consider first the possibility ofthis effect from the law ofconservation ofparticle angular momenta. If both particles (photon and electron) move along

cularly polarized (4= 1~)then the emission process is allowed only with electron spin flipping. The same discussion for different polarizations of electrons and photons leads to the selection rules shown in table 1. As an example we shall obtain the gain in the first case, when the electromagnetic wave A =A0 x exp ( icot— ikz) + c.c. is left-hand circularly polarized and moves in a dielectric medium with a refractive index n. We assume that the electron beam has a Gaussian energy spread,

the z axis, the z-projection sum of their angular momenta is conserved: S1~ ±4 = S2~.Here S2 ±3M and 4= ± h are z-projections of the electron and photon

1/2

g(~)=(

~_!~—~) It

-~-

exp(_~in 2

A

A

(1) and moves along the z axis. The small signal gain is calculated from the self-consistent system of Dirac and Maxwell equations [31.The current of the electron beam is ~

f eA1~( (1 —nfl) (1 — 2/fl~)2 ep0c .1 2~\. 1 nfl+ (~ko/2~‘) (mc — (1 —nfl) (1 + ~) 1 —.nfl— (haI/2~)(mc2/fl~)2 xg( ~) exp (kot ikz) d~+c.c. (2)

=

0~

—

—

,

where J 0 and Po are the initial electron beam current and density, respectively, /1= v/c, V is the particle yelocity, c is the velocity of light in vacuum, C~is the z-projection of the electron polarization vector ~ [3]. 249

Volume 140, number 5

PHYSICS LETTERS A

first of the mechanisms mentioned in the introduction and / mc2 ~ hw 1=6.6

Table 1 Emission S (h) 1r(h)

Absorption

‘

I

I

I

12

—i2

—i2

12

25 September 1989

PoroAcTj~t,~-~-—) ~

(4)

The comparison of eqs. (3) and (4) shows that the The second term in eq. (2) describes photon absorption and the third one emission. It appears that if all electrons are polarized along the z axis the second term equals zero and the gain is maximum, ~

~o (mc2)2

absorption process suppression allows the gain to increase by A/hw times. The authors wish to thank Professor V.M. Arutunyan for helpful discussions.

(3)

A ~ References

Here r 2/mc2 is the classical electron radius and 0= e = h/mc is the Compton wavelength ofan electron. Notice that this expression is applicable only if the angular spread ô of the electron beam ~<< (~~-,/ I /2• If the z-projection of the polarization vector = 0 then the amplification process is based on the

250

[1] V.M. Arutunyan and S.G. Oganesyan, Pis’ma Zh. Eksp. Teor. Fiz. 7 (1981) 539. L2] J.E. Walsh and J.B. Murphy, IEEE J. Quantum Electron. QE18 (1982)1259. [3] Al. Akhiezer and V.B. Berestetskii, Kvantovaya elecktrodinamika (Nauka, Moscow, 1969) p. 623.