paul l. csonka- suggestion for x-ray laser holography

8/3/2019 Paul L. Csonka- Suggestion for X-ray laser holography

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Particle Accelerators1978, Vol. 8, pp. 161-165

Gordon and Breach, Science Publishers Ltd.Printed in the United Kingdom

SUGGESTION FOR X-RAY LASER HOLOGRAPHYPAUL L. CSONKA

Stanford Linear Accelerator Center,Stanford Synchrotron Radiation Project,Stanford, California 94305andInstitute of The.?retical Science,University ofOregon,Eugene, Oregon 97403(Received April 5, 1977; infinalform July 19,1977)

It seems that synchrotron radiation from electron s torage rings will soon be used to pump soft X-ray lasers. Thesecould serve in holographic studies ofmicrostructures, e.g., biological samples. Storage rings best adapted for such experiments would also be suitable for free electron laser experiments. The two types of experiments might profitably sharethe same ring. Radiation for X-ray laser pumping should originate in a low-beta section.

t The critical length of the laser is that length which a signalof coherent photons, initiated by a single photon, has to travelin the laser before the signal is amplified so much that thereafter it de-excites (by stimulated emission of coherent photons)essentially all optically inverted atoms.

ifdz is chosen (as in Ref. 1) to satisfy dz ;c 21c ' wherelc is the critical length of the lasertDenote by Eyx , Eyy respectively the horizontal andvertical emittance of the synchrotron radiationwhich pumps the laser. It turns out,! and it isintuitively clear, that the pumping of the laser isefficient, if

where (J "IX is the (rms) horizontal radius of thephoton beam at the center of the laser, (J;,x is the(rms) spread of the horizontal half angle there, andthe quantities with subscript yare defined analogously. Equation (1 b) is simply a statement of thefact that both the x and y phase-space ellipse of thepumping X-ray radiation is "upright ", i.e., the xaxis is a symmetry axis of the first of these ellipses,and so is the y axis for the second. Equation (1 c)

(lc)i = x, y),. (i = x, y) (1b)

1 d,


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162 P. L. CSONKAsays that the height and width of the pumpingphoton beam matches the laser volume at itscenter and that the angular divergence is smallenough so that most of the pumping photonstraverse the whole length of the laser.

From Eqs. (1)(2)

t We will find that for our purposes the best place to takesynchrotron radiation from the ring is at the center of a low-betasection. Equation (4) is usually satisfied there.

Consider synchrotron radiation with wavelengthnear Ao, emitted by circulating electrons of energyE(,. The characteristic angle of emission is ec ' Then

a ~ = [(a?')2 + e;]1/2. (3b)Assume that at the point where the synchrotronradiation is emitted, t

The above quantities are related to the param-eters characterizing the electron beam at the pointwhere the synchrotron radiation is emitted. Letthe horizontal (rms) electron beam radius be ax,and the corresponding (rms) spread in the halfanglea ~ . , etc. Denote by a superscript 0 quantit ies referr ing to the region where the synchrotron radiationis emitted, e.g., a means the electron beam radiuswhere synchrotron radiation originates. Clearly,

(6a)i = x, y)hP>-,...."" A 'tla;or scattering angles

Pi AocP;


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X-RAY LASER HOLOGRAPHY 163II Semi- transparent"

Xl mirrol U ~ ~ ~ ~ i ~ ~ : dObject

-Laser ".:.. .___ _ . : . _ . : . . . - - : . : . ~ . . . . . . > ._ __ -""'-4>...... ~ - - -, r RecordingMirror s u r f a c e s - - - -

FIGURE 2 X-rays produced by the laser travel parallel to thez axis. Some of them reach the object of diameter h directly(these we call "undeviated photons") and are scattered by it.The scattering angle is (dash-dot line). The other photonsare diverted by a "semitransparent" mirror (actually, it may bea simple mirror intercepting only part of the photons emittedby the laser) and reach the object traveling at an angle +(XII - (Xs. We call these the "unscattered photons" (dashed line).The recording surface records the interference pattern betweenthe scattered and unscattered photons reaching it at a grazingangle (Xs and (XII respectively.

measured from the surface parallel to the (x, z)plane will generate an electromagnetic field whichis periodic along the surface, with a periodicityAs = Ao/cos as. Similarly, photons arriving at thesurface with a grazing angle au produce a fieldperiodic along the surface with Au = Ao/cos au.The interference pattern of these two fields willtherefore be periodic along the surface with a"beat" periodA = IAs - Au I = IcO;oIXu _ cO;oIXs 1- 1

2Ao1X,; - I X I' (8)The la st p iece of this equation is valid as as,all O. When as, au 1, then A Ao, and theinterference pattern can be recorded provided thatA 2 ~ l even if Ao ~ 1 . 5 Rotating the mirrors willdirect the unscattered photons successively to theseveral recording plates, and so record the patternproduced by photons scattered at various anglescjJ. Holographic reconstruction of the image ispossible using the several recording plates: illuminate each with coherent radiation ofwavelength Ao,reaching the surface at a grazing angle au. Moreimportantly, enlarged reconstruction is also possible: En la rge the interference pattern on eachsurface by a factor p, e.g., by geometrical magnification produced by (not necessarily coherent)radiation of wavelength A Ao. Arrange the en-

larged surface patterns so that they form a p-timesenlarged version of the original recording pla tea rrangement . Il lumina te each surface with coherent radiation whose wavelength is pAo. Then ap-times enlarged image of the original object willresult. If PAo is in the optical range, then this imagecan be viewed with optical instruments, includingth e human eye. The image can also be recorded ona s ingle plate (us ing a coherent reference beam ofwavelength pAo). Thereaf te r the image can berecreated with a single coherent beam of wavelength PAo and viewed as a conventional hologram(i.e., one which is produced as shown in Figure 1).In this manner, one can visualize details of dimension Ao, in spite of the fact th at the recordingmedium may have resolution ~ Ao.This method could be called "three-wavelengthmicroscopy", because radiation of three differentwavelengths is used: radiation with wavelength Aoproduces the original recorded interference pattern,radiation with wavelength A Ao is used to enlargethis pattern by a factor p', and the enlarged patternis viewed in a radiation with wavelength pAo. It is ageneralizationof the "two-wavelengthmicroscopy"in which radiation of two different wavelengths isemployed,4,6 one with wavelength Ao to producethe original recorded interference pattern, the otherwith wavelength A to view this pattern. In threewavelength microscopy p' :f. p is possible. However, when the original pattern is recorded onseveral plates (as in Figure 2), reconstruction iseasier when p' = p. This is why p' = p was assumedin the previous paragraph.

The interference pat te rn a t the holograph willbewashed out, unless the photon beamproduced bythe X-ray laser is sufficiently monochromatic: 4

()A < Ao (9)Ao 2 LH(ris - riu) .At a distance L from the center of the laser as

measured along z, the radius of the laser beam willbe (10)Substitute for in Eq. (lc). Then with Eqs.(lb), (lc), and (10) we have

a;(L) tdi(l + ~ ) (11)Let L s be the distance of the object from the centerof the laser, and LH the distance of the object fromthe holographic surface. At the holographic surface L = L s + LH The laser beam will cover a


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164 P. L. CSONKAholographic surface whose projection on a surfaceperpendicular to the propagation direction of thephotons has a radius R, provided that

.1d.(l + L s + LH ) > R (12)2 l d 1'-1'zThose photons which do not reach the holographicsurface are wasted. Therefore choose the sign inEq. (12).Let Ao be the undeviated photon amplitude atthe object. Then the undeviated photon intensitythere is 1' -1 lAo 12 The amplitude of the unscatteredphotons at the object is Au, their intensity I'-IIAuI2.The object scatters a fraction f of all photonsreaching it, so that the scattered photon amplitudeat the object will bef1 /2(Ao + Au)' Assume ~ h a t theamplitudes Ao(H) and Au(H) of undeviated andunscattered photons at the holographic surface willbe approximately Ao and Au respectively (as when.Ls ri)' Denote the corresponding intensities byIo(H) .and Iu(H). Assume (see Fig. 2) also hi ri'and hx/rx = h,/r" == hire The absolute value of theamplitude of scattered photons at the holographicsurface will be of the order of I(h/r)fI /2(A o + Au)l.If, furthermore, IAu(H)I/IAo(H)1 == g1 /2 1, thisexpression can be simplified to (h/r)f 1/2 IA o l. Thephoton intensity variation, I int(H), a t tha t surfacedue to interference between unscattered and scattered photons will be proportional to A;(H)As(H),and

IintCH) 1' -1 h f1/2 1/2 (13)Io(R) 1' -1 -; g.One needs n)' photons/cm 2 impinging on therecording surface to imprint a meaningful record.

The term "meaningful record" here means arecord from which a recognizable image can bereconstructed holographically. The value of n ydepends on the recording medium.Suppose that ~ Ao. Then, by Eq. (8), we needexu' exs 1. Assuming exu exs ' we require

e::Y!2 ;


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X-RAY LASER HOLOGRAPHY 165Then the needed number of photons would bedelivered by the laser approximately within 2.5 sec.We conclude that holographic study of microstructures appears feasible.For purposes of such studies the electron ringdoes not need high circulating electron energy, Ee .It suffices to have Ee such that the critical energy ofsynchrotron radiation be ;(: 100 eV.The photon emittance should be as small aspossible, because the number of pumping photonsneeded is roughly proportional1 to (8)IX8yy)1/2 forfixed A. The photon beam emittance being relatedto the electron.beam emittance and the latter beinggenerally smaller at lower Ee , this argues in favorof a ring which emits synchrotron radiation with alow critical energy.To achieve low (8,'x8yy)1/2, the photons shouldbe taken out from a low-beta section of the ring[Eq. (5)]. This is contrary to common practicetoday.Pumping the X-ray laser uses only a relatively

narrow energy band of the emitted synchrotronradiation.t Therefore, for purposes of X-ray laserholography, it is desirable to enhance synchrotronradiation in that narrow band. This can be donewith wiggler magnets, provided that the momentumspread of the circulating electron beam is smallenough, another argument in .favor of a smallemittance ring.Thus, for purposes of holography, one would

t Nevertheless, the pumping bandwidth is several orders ofmagnitude broader than the bandwidth of the emitted coherentX-ray photons.

like to have a ring with relatively low energy, lowemittance, and high instantaneous current. Thesecharacteristics would also make the ring well suitedfor free electron laser experiments (producing intense coherent radiation mostly in the infrared, andup to the ultraviolet).It seems reasonable to suggest that if an electronring were to be built for free electron laser experiments, at least a section of it should be designedfor pumping X-ray lasers which could then be usedfor holographic studies of microstructures, as wellas for other purposes.

ACKNOWLEDGEMENTSI wish to thank B. W. Matthews, V. Rehn, H. Wiedemann, andH. Winick for discussions concerning this subject.

REFERENCES1. Paul L. Csonka, Phys. Rev. 13A, 405 (1976), and Opportunities to Produce Coherent Soft X-Rays at Stanford, SSRP

Report No. 77/03 (1977).2. Paul L. Csonka, University of Oregon, I.T.S. Preprint N.T.065/75 (1975).3. Paul L. Csonka, University of Oregon, I.T.S. Preprint N.T.059/75 (1975).4. D. Gabor, Proc. Roy. Soc. London, A197, 454 (1949).5. A. V. Baez and H. M. A. EI-Sum, in X-Ray Microscopy andMicro Radiography by V. Cosslett et al.. [Academic Press,

N.Y., 1957], p. 347.6. M. J. Buerger, J. Appl. Phys., 21, 909 (1950).

paul l. csonka- suggestion for x-ray laser holography

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