GB2225440A

GB2225440A - High frequency coherent light source

Info

Publication number: GB2225440A
Application number: GB8925699A
Authority: GB
Inventors: Shui-Yin Lo
Original assignee: Apricot SA
Current assignee: Apricot SA
Priority date: 1988-11-14
Filing date: 1989-11-14
Publication date: 1990-05-30
Also published as: GB8925699D0

Abstract

A method of generating a high frequency beam of coherent light 30, comprises directing first and second coherent light beams 16, 18 one into the other whereby said high frequency beam of coherent light is generated by scattering among the photons forming the first and second beams and is of higher frequency than the light of at least one of said first and second beams. Each beam 16, 18 may be generated by a respective laser 1, 2 the beams being brought together by mirrors 20, 22 or be generated by a single laser combined with a beam splitter. <IMAGE>

Description

HIGH FREQUENCY COHERENT LIGHT SOURCE BACKGROUND OF THE INVENTION (i) Field of the invention This invention relates to a high frequency coherent light source.

(ii) Prior Art The specification of International application PCT/AU86/00212 describes scattering among coherent bosons. The mechanism of the present invention is in some ways analogous but this invention is, rather, concerned with scattering among coherent light.

BRIEF SUMMARY OF THE INVENTION The present invention provides a method of generating a high frequency beam of coherent light, comprising directing first and second coherent light beams one into the other whereby said high frequency beam of coherent light is generated by scattering among the photons forming the first and second beams and is of higher frequency than the light of at least one of said first and second beams.

The invention also provides said means for generating first and second coherent light beams comprises first and second lasers.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS The invention is further described by way of example only with reference to the accompanying drawings in which: Figure 1 is a Feynman diagram for photon-photon.

scattering; Figure 2 is a Feynman diagram for multiphoton scattering; Figure 3 is a diagram of an apparatus constructed in accordance with the invention, for generation of high frequency coherent light from scattering of two laser beams; and Figure 4 is a diagram of an alternative apparatus for generation of high frequency coherent light from scattering of two laser beams.

DETAILED DESCRIPTION Two beams of coherent light can be focused into a very small area where they interact and scatter off one another.

nlY (k) + n2Y (p) nlY(k') + n2Y (p') (Equation 1) where k,p,k',p', are the momenta of initial and final photons, and nl, n2 are the number of photons in the two photon beams.

The Feynman diagram for single photon scattering off another single photon is shown in Figure 1. Its cross section is given to be:

(Equation 2) where a = 1/137 re = classical electron radius = 2.8 x 10~13cm X = Angular frequency of light m = mass electron If we take # = 1 eV, the cross section o is 7.0 x 10-66 cm2. The normal cross section of a nucleus is 10-26 cm2, so C is 10-4 times smaller than a nuclear cross section, a very small number indeed.

From work by Schwinger, on Gauge Invariance and Vacuum Polarization, Phys. Rev. 82, 664(1951), for a general discussion see: C. Itzykson and J.B. Zube, Quantum Field Theory, it is possible to deduce an effective Lagrangian, W. Heisenberg and H. Euler, Z.

Plysik 98, 714(1936) for photon-photon scattering to all orders. In the nth order in the fine structure coupling, the effective Lagrangian density is given by:

(Equation 3) where m is the mass of the electron, α=1/137, ( are Riemann function, and a, b are functions of electric field and magnetic field a1-b1 s ab (Equation 4) For an estimate of order of magnitude, it is convenient to treat a scalar theory of photons where E=B=|E| so that a=b, a-b=0. ab=|E|. Then the Lagrangian density becomes:

(Equation 5) (Equation 6) =0 for n-odd ~0(1) for n=even.

And the term a2n is evaluated by substituting the values of electric fields of the two scattering photons:

i 1,2 (Equation 7) where n1 and n2 are the numbers of coherent photons in laser pulses. Z 2 are their energies and Vi the normalization volume.

(Equation 8) Two cases n1=n2=n/2, and nl # n2, are now examined (a) nl=n2=n/2 case.

The effective Lagrangian is

(Equation 9) (Equation 10) In quantum electrodynamics, higher order (large n) generally imply a smaller effect and can be neglected.

This is due to the smallness of the fine structure coupling X1/137. The 2nth order of an electromagnetic process means that its amplitude is 10-2n smaller.

Coupling is incorporated in 2, and 2 is less than 1.

However, for two intense photon beams interacting through a vacuum, polarization fluctuations as given by Equation 3, there is a difference. The number of diagrams increases drastically as the number of photons is increased. For the lowest order n=2 diagram (Figure 1), we have 3! because the permutation of external photon lines. If there are 2n photons connected to the electron loop, then there are (2n-1)! different diagram. This is thought to be the origin of the (2n-3)! factor in Equation 3. There are far more diagrams for the nth order process as shown in Figure 2.More particularly, in Figure 2, Feynman diagrams are shown for photon-photon scattering through an electron loop, for the following cases: (a) 4th order process (b) 6th order process (c) 8th order process (d) 2nth order process By the use of Stirling formulae, this reflects in Equation 10, where Z is proportional to n2. The larger n is, the larger Z becomes. For a coherent beam, the electric field contains a factor Pn in Equation 6, therefore there is an additional factor n multiplying in the factor Z. Given the expression Z n3, then it is possible that, for a sufficiently intense laser pulse, a critical condition is reached where Z > 1 or

(Equation 11) the nth process dominates.

For #=lev, V=100 cm x l m x lWm the critical number is n#10" (Equation 12) For a 1 Joule laser pulse with #=leV, n-i019, so this number of photons is not hard to achieve. For the case Z > 1, the Lagrangian density L(2n) is proportional to zn, and therefore becomes extremely large. In the Dirac-Feynman path integral formulation of quantum mechanics, this implies the quantum mechanical scattering of photon-photon becomes classical in nature.

The trajectories of photons will follow a classical path where the Lagrangian attains its extreme value. The two laser pulses will bounce off each other like two balls bounce off each other.

We may also note that in classical electromagnetic theory, electromagnetic waves of frequency X will bounce off a plasma with plasma frequency cop if the critical condition

(Equation 13) where

(Equation 14) and ne/V is the density of electron in the plasma. Our critical condition Z 2 1 can be regarded as similar and equation (11) can be derived alternatively from the following argument to equation (13). We have intense electric field from the laser pulse, which will cause the vacuum to fluctuate and create electron-positron pain.

The probability amplitude for vacuum fluctuation is

(Equation 15a) where E-E is the energy density of the electric field, and its chance to create e±e pair then is divided by the electron mass ln. Because of energy-momentum there cannot be real e + -e - pair even though there is enough energy. The uncertainty principle tells us, however that this result is possible in a fraction of the time ss T in the period of the light T.

AT m ~ 1 (Equation 15b)

(Equation 15c) So the plasma density ne in equation (14) become

(Equation 15d) If we substitute (15d) into (14) and (13), we will get the critical condition equation (11) up to some numerical constant.

For the case of photon-photon scattering with unequal intensity, the critical condition for two photon beams with photons number nl and n2 at frequencies and and 2 is modified to become:

(Equation 16) for n > > n2 The kinematic for scattering of two photon beams: n1 photons with momentum p1 and n2 photons with momentum K n1 (p)+n2 (k)#n1 (p')+n2(k') (Equation 17) into n1 photons with momentum p' and n2 with momentum k' can be evaluated by the conservation of energy and momentum: at the laboratory frame n1p@+n2k@ = n1p'@+n2k'@ (Equation 18) n1p@-2k@ = -n1p'@+n2k'@ (Equation 19) where po, ko, p'o, k'o are energies of n1, n2 photons before and after scattering respectively. The result is that the energy of backscattered photons are

(Equation 20) So if nl n2, the backscattered n2 photon beam will increase its energy by nl/n2 times.

Numerically, if n2=1015, n1=1018, n1/n2=103, ko=po=leV, one has k'o=103 eV, p'o=10-3 eV.

This means that, starting with two laser pulses, each with photons of leV in energy, after scattering, the backscattered beam with smaller number of photons will become an X-ray laser with energy in kev, and the backscattered beam with larger number of photons essentially loses most of its energy.

In Figure 3, two lasers 12, 14 emit respective beams 16, 18 of coherent light.

It is possible to use either a mirror or a prism to bend the light beam from the second laser 14 so that it collides at 180e with the coherent light beam from first laser 12. In this case, two mirrors 20, 22, are shown.

Lenses 24, 26, are positioned in the paths of the light beams 16, 18, to focus the respective light beams to a small area at the location 28 shown. The backscattered light from this interaction of light beams 14, 16, at location 28, passes in the direction of beam 16 back through mirror 22 to emerge as a beam 30. This backscattered light has a much higher frequency than the two incident light beams. Because of this high frequency it has greater penetrating power and can pass through the mirror 22 as the useful beam 30.

It is also possible to use a single laser to produce high frequency coherent light. Thus, in figure 4 a single laser 40 is shown generating a single beam 42, which is split by a beam splitter 44 to form two, unequal, beams 46, 48. The beams 46, 48 are-directed by mirrors 50, 52 to meet in a line after focusing by lenses 54, 56.

The scattering resulting from this interaction causes a back-scattered beam to be formed. That is to say, higher frequency (w-n2/n1 0) coherent light will emerge from the backscattering and penetrate through the mirror 52 to become a useful beam 58.

Generally, when practising the method of the invention by use of two beams of light (whether generated separately or by splitting a single beam), it is preferred that the beams be unequal in the sense that one has more photons that the other or is more powerful than the other. This is not essential however, as equal. beams may be employed. Generally the light in each beam may be of the same frequency or of different frequencies.

Claims

1 CLAIM:

1. A method of generating a high frequency beam of coherent light, comprising directing first and second coherent light beams one into the other whereby said high frequency beam of coherent light is generated by scattering among the photons forming the first and second beams and is of higher frequency than the light of at least one of said first and second beams.

2. A method of generating a high frequency beam of coherent light as claimed in claim 1 wherein said first and second beams are generated by separate lasers and means is provided deflecting the beams, as emerging from the lasers, to direct them one into the other.

3. A method of generating a high frequency beam of coherent light as claimed in claim 1 or claim 2 wherein said beams are focussed before incidence one upon the other.

4. A method of generating a high frequency beam of coherent light as claimed in any one of claims 1 to 3 wherein said directing of beams is effected by the use of mirrors through one of which mirrors said high frequency beam of coherent light is caused to emerge.

5. Apparatus for generating a high frequency beam of coherent light comprising means for generating first and second coherent light beams and means for directing the beams as so generated one into the other whereby said high frequency beam of coherent light is generated by scattering among the photons forming the first and second beams and is of higher frequency than the light of at least one of said first and second beams.

6. Apparatus as claimed in claim 5 wherein said means for generating first and second coherent light beams comprises first and second lasers.

7. Apparatus as claimed in claim 6 wherein said means for generating coherent light beams comprises a laser generating a beam of coherent light, together with a beam splitter arranged for production from that beam of said first and second beams of coherent light.

8. Apparatus as claimed in any one of claims 5, 6 and 7 wherein means is provided for diverting at least one of said first and second beams from relative orientations which are not 1800 displaced one relative to the other to an effective displacement of 180e.

9. Apparatus as claimed in any one of claims 5, 6 and 7 wherein focussing means is provided for focussing said first and second beams prior to incidence thereof one upon the other.

10. Apparatus as claimed in claim 8 wherein focussing means is provided for focussing said first and second beams prior to incidence thereof one upon the other.