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Practical design of optical diagnostics for chirped-pulse free-electron lasers
NUCLEAR INSTRUMENTS &METHODS I PHYSICS RESEARCH
Nuclear Instruments and Methods in Physics Research A319 (1992) 914-920 North-11olland
Se ction A
ractical design o free-electron lasers
tical diagnostics for chirped-pulse
Erie B. Szarmes and John M .J. Madey
Duke Uniueositr Free Electron Laser Lccborawn., Durham. ,N'('27706. USA
In recent years there have been several proposals to operate rf-linac-driven FELs with chirped electron and optical micropulses for use in fast time-resolved experiments . We have been actively pursuing this application on the Mark-III infrared FEL at Duke Universitv, and have designed and procured an apparatus to achieve broad-band compression of chirped optical pulses between roughh, 2.5 p.m and 4.1 tLm . with subsequent measurement of pulse widths as short as 2011 fs . The principles of design for this experiment will be reviewed, and extensions of the design to other wavelengths will be considered .
1.Int
uctiion
In recent years there have been several proposals to operate rflinac-driven free:-electron lasers (FEW with chirped-energy electron micropulses for applications in fast time-resolved spectroscopy, in which the output optical pulses possess appreciable frequency chirps and are susceptible to pulse compression in an external dispersive delay line [1-3] . The physical principles governing these e=xperiments are generally not specific to a particular wavelength. because substantial energy chirps can be achieved at a given energy simply by dephasing the electron bunches relative to the accelerating field in the accelerator . Consequently, the most practical realizations of these experiments should employ broad-band optics in both the optical-transport and diagnostic apparatus in order to fully exploit the inherent tunability of the FEL. In this paper we describe the implementation of this experiment on the Mark-III FEL for wavelengths between 2.5 and 4.1 Wm, using a broad-band sapphire prism pulse compressor which has been designed and procured for applications in a user-oriented program at Duke University. The diagnostic apparatus consists primarily of an autocorrelator to measure the compressed pulse widths. We review the physical principles Building the design of these experiments, and suggest some possible extensions to other wavelength regimes in the near and far infrared . 2. Pulse parameters A chirped optical pulse is most conveniently characterized by a chirp parameter `h' and a pulse width
parameter 'a' [4J defined by to(t) =w,+(22h)t
(2 .1)
and a = (2 log, 2)/-,,,
(2 .2)
where w(t) is the time-dependent optical frequency and se, is the FWHM pulse width . The spectrum of an optical pulse, %` .(t)=E(t) exp[i(w t+W)l,
(2 .3)
can then be written in the general form
r' (w) = E(w)
h 4[ f(a,
h) +h - l
- i0(w-w
(2.4)
where f(a, h) is a form factor that depends on the pulse shape. for example, f(a, h) = a' for Gaussian pulses. The first-order term in the exponent can be omitted because it affects only the centroid of the pulse, and if the fre=quency chirp is large and purely linear, then the higher-order terms are usually negligible. Second-order- phase compensation means the elimiw(,), nation of the term - i[ . . . ](w in the spectral phase factor, and is the usual manner of compressing the pulse . This is accomplished by sending the pulse through a dispersive delay line, which has the effect of multiplying the spectrum by a phase factor of the form 1 d-'0 _ cxp -, i 2 dw(ar - wo) - 'O(w
0168-9()1)2/92/$()5 .1)11 ~0 1992 - Elsevier Science Publishers B .V . All rights reserved
;
(2 .5)
E.B. S.-armes, J.MJ. Mudcy / Oplicul dicrgtwslic:s for chirped-puise FEL .D
0 U _cß
30
and fig . 2 displays the corresponding pulse compression ratios ; in all cases, optimum compression was defined as yielding the maximum compressed peak power, not the minimum FWHM pulse duration. The curve fits appearing in those figures arc given below for I alb j < 1, and may be useful in the design and adjustment of phase compensators for chirped-pulse experiments in which the shape and duration of the optical pulses can be inferred from optical autocorrelation measurements .
o Tophat Parabolic * Gaussian o s Sech 2
20
c 10 0 c a E
0 U
iic"llStilllll :
Fig. I . Optimum quadratic phase compensation factors Ma . h) from eq . (2.6) for various ideal pulse shapes. defined as yielding the maximum compressed peak powers. The data and curve fits were obtained numerically.
K(a, b) = 4 T
The spectral width (as determined from I f (to) 1 2 ) is unaltered by this propagation, but the compensated optical pulse has essentially no frequency chirp, since h = 0 in the absence of the second-order term in eq. (2.4). As a result, the original spectral content of the pulse is effectively transferred from the optical phase to the optical envelope, and the pulse is compressed. The coefficient of the quadratic frequency term in eq. (2.5) which compensates the corresponding term in eq. (2.4) can be written phcnolnellologically as 1 ( d-(hi d w`
1
1
rum
where Ma, b) is a factor that depends on the pulse shape and on the ratio of alb, and has a limiting value of K -> 4 as alb - 0. Figure 1 displays the numerically derived values of Ma, b) for several ideal pulse shapes,
(2.7a)
t~
h )2
-
+1
Scch-' : K(a . b) = 4 0.76 ,- min Tp
lcl
''- .Iql
0.784
'n
h a
+ I]
11 .~11
(2.7b)
ti, .
)2 + 0.31111/2
Parabolic :
a
(2 .6)
bK(a
cl ' + [(b
min
P Tt,
u
2
915
t .t+ .t
10 .50
~b1
T
(2.7c)
P
Top hat : a ,.min '"
P
T
1
10
100
b/a Fig. 2. Optimum pulse compression ratios corresponding to the phase compensation factors in fig. I.
11 .6(1
.611
2.12 b ) 4/3 + 11 .7 _ cl _
3/4
(2.7d)
The equations for the Gaussian case are exact analytical results [4] . The only conditions assumed in the form of the remaining equations are that they depend only on the ratio of alb, and that they approach the limits .p,'"/Tp a ( alb I as alb - 0; these Ma. h ) - 4 and 7 conditions are heuristic and agree with the Gaussian case. 3é 1. FEL OPTIC S
E.B. Szartnes, J.M.J. Madey / Optical diagnostics for chirped-pulse FEL
916
3. Mark-III design parameters Simulations of the optical-pulse generation using chirped-energy electron pulses on the Mark-III FEL have been described previously [3]. Those simulations were based on the practical operating configurations of the Mark-III linac, in which the electron pulses are compatible with the dispersion in the downstream transport line and yield chirped optical pulses with large spectral widths at saturation . For experiments near A - 3.35 j,Lm, the electron pulses in the wiggler have a duration of 4 ps and a linear-energy chirp of 8y/y = + 2% with higher energies towards the trailing edge. e simulations assumed top-hat electron pulses, since optical autocorrelation measurements on the Mark-III FEL have indicated that the optical pulses at saturation are essentially top hat in shape [5] . The dura : .,- of the optical pulses (-,p - 3.4 ps) is slightly shorter mean 4 ps due to lethargy, but the magnitude of that positive frequency chirp (Jw/w " +4.7% over 4 ps) is slightly larger than would be predicted by assuming that the resonance condition determines the lasing wavelength during the pulse-, this frequency chirp is determined numerically from the simulations by fitting a least-squares parabola to the optical phase over the FWHM duration of the optical pulse. The corresponding chirped-pulse parameters from the simulations at A = 3.35 jam are 1 .2 x 10 =' s --'. h= +33 1024 s-2, K(a . b) =4 .3. = +7.0 x 10 - -' s-',
30 v
and the compressed optical pulses have a duration of about 230 fs. The simulated profiles of the chirped output pulses, and the results of pulse compression, are illustrated in fig . 3. For designing experiments over a range of wavelengths, it is in fact useful to assume that the resonance condition determines the lasing wavelength during the pulse; this will actually be a fairly good approximation if the slippage parameter is sufficiently small . The wavelength dependence of the chirp parameter h then becomes explicit : h(A) _
2,rrc 1 dy A
y dt
,
(3 .2)
where ymc- is the electron energy, and if one also assumes that the duration of the optical pulses at saturation is equal to the duration of the electron pulses (appropriate for long electron pulses), then the compensation factor in eq. (2.6) can be readily evaluated using eqs. (3.2) and (2.7) .
4. Pulse compressor design The two general designs for pulse compressors employ either grating pairs or Brewster angle prism pairs [6]. The latter choice is preferred in the present application because of the possibility of achieving substantial compression ratios over a wide range of wavelengths . In contrast, the diffractive geometry of a given grating system is very sensitive to wavelength, and the corresponding dispersions can be too large to yield practical compressor designs in chirped-pulse FEL experiments . For example, a double-pass Littrow grating system at 3.35 Wm, designed to compensate the pulse parameters in eq. (3.1), would have a slant spacing of only a few millimeters . The design of prism pulse compressors has been treated extensively in the literature [6-9] . A typical minimum deviation, single pass, Brewster angle prism
L-
-6
-4
-2
0 Time (ps)
2
4
6
Fig. 3. Simulations of FEL pulse compression experiments on the Mark-III FEL at 3.35 p.m, including shot noise in the electron beam. The experiment is described in the text. The uncompressed pulses have a duration of 3.4 ps and an average power of 2.5 MW. The compressed pulses havi~ a duration of 230 fs and a peak power of 28 MW, and result from propagation through the same dispersive delay line.
devielion, Br,wr'f- angle ps'a pa; r
Fig . 4. Typical prism configuration for a single-pass dispersive delay line. The prisms are in the minimum deviation geometry to avoid astigmatism in the transmitted beam.
E.B. Szarmes, J.M.J. Madey / Optical diagnostics for chirped-pulse FEL
917
Brewster angle, minimum deviation sapphire prism
rernovab4e mirror
to experiment
Fig. 5. Double-pass. sapphire prism. dispersive delay line for the Mark-III experiments between 2.5 and 4 .1 Rm . The set-up includes removable mirror assemblies to interchange the compressed and uncompressed pulses between the autocorrelator and the experimental sample .
system is shown in fig . 4 . The second-order dispersion for a corresponding doublepass system is given by 1 d -'46 2 do) ' _
d`n 1 )(dn 11P , 2 , + 2rt - )'` sin /3 dA` n3 dA 2rrc ` A3
dr:` .1) -4 (4 Ip cos (3 , (
n
where A is the vacuum wavelength, n(A) is the refractive index, and lp and 6 are shown in fig . 4. For a given set of system parameters, the LHS of eq. (4.1) should equal the required compensating factor from eq. (2.6). The contribute .^,ns to the dispersion arise from material dispersion and angular dispersion, the latter leading to wavelength-dependent geometrical paths through the system . In particular. material dispersion in the crystals yields the d`rz/dA` term in eq. (4.1), angular dispersion in the crystals yields the (1/n ; Xdn/dA) 2 term, and angular dispersion in air,
comprising the dominant contribution in most systems, yields the two remaining terms. The angle /3 is usually determined by the clear aperture of the beam through the system, for example, by setting 1p sin ß _ 4wheam, where w bean, is the mode radius . If 1p is much larger than o beam, one may then set cos ß - 1 . The pulse compressor for the Mark-III experiments consists of four minimun !-deviation sapphire prisms arranged as shown in fig. 5. The prisms are cut at the Brewster angle for 3.35 Wm, which yields no more than 0.03% total reflection losses for the double-pass system between 2.5 and 4.1 Wm. The optic axis of the crystal is perpendicular to the triangular faces to within 30 minutes, so that the horizontally polarized ray is ordinary. A double-pass system is required in order to eliminate the presence of lateral spectral walk-off in the output beam ; this walk-off can significantly increase the duration of the compressed optical pulses [161 according to Tcom p r Tmin
1 +
Ti rait ( Tmin
where 7,,, .,,p and
Train
(4.2) are the durations of the comX1 . FEL OPTICS
918
E. B. Szarntes. J.MJ. Afadey / Optical diagnostics for chirped-pulse FEL
3.0 3.5 Wavelength (ttm)
4.0
4.5
Fig. 6. Estimated apex-to-apex prism separations for Mark-111 experiments between ? .5 and -t .1 p.m .
the
pressed pulses in the presence and absence, respectively, of spectral walk-off, Tini, is: the duration of the input pulse, and z,i is the Rayleigh range . For example, a single-pass system designed to compensate the pulse parameters in eq. (3.1) would compress the optical pulses to no less than 1 .5 times the minimL:m duration that could be achieved in the absence of spectral walk-off. The mounting of the prisms on translation stages allows the experimenter to vary the dispersion of the system by changing the path length through all four prisms without changing the position or direction of the output beam. The size of the prisms was chosen so that roughly 70% of the required dispersion at 3.35 p.m could be provided by moving the prisms in this fashion . The removable mirror assembly at the input to the system allows the quick interchange of compressed or
AgGaSe 2 crystal; 0.45 mm thick; 90 ° phase match
motor driven translation stage
from pulse compressor
sI s. mirror
Fig. 7. Layout of the autocorrelator for measuring pulse durations as short as 200 fs.
thickness sin Optical experimental ameasuring factor all 7,apredicted are the path also (33by 200 by wavelengths, is ain this isfrequencies 3high angle to estimated need have crystals, between -focussing limited background-free 90° shown altering equating the fringes, shown equating used silver remain 5cr),, at required the and fs p,m diagnostics included of (W,) internal length angle to of degree The optical 3numerical phase-matched the not designed By A, is 1Rayleigh pulses 3prism or from to pulse gallium in waves, respectively in important by = p,m and sample in so doubling moving the constant, prism Rayleigh the calculate greater of the be geometry and 450 the within fig angle fig the pof to that dispersion the pulse, eq to so spacing path durations into prism adjusted fundamental collimation prism account [Lm, 7constants a67and selenide isminimum range spacing The optical (2 it clear the can autocorrelation crossed-beam appropriate The the The crystal than which length the should because and range h(A) this dispersion (19 isabasic through lower be dispersion LiNb0 increases FWHM ischosen where spacing aperture crossed-beam autocorrclator is for with from the as 3is as changed (AgGaSe,) pulse much yields and appearing isthe deviation be the increases external) For component with atranslation short the prism athe (o),) function mm wavelength p,m, possible eq for 90° coherence eq the internal Ma, bandwidth to with wavelengths crystals larger widths for adeviation afor beam from autocorrelator of as from accept (3 trace digitized-data type-1 phase-matchspacings beam system and one (3 The 3in the h) geometry) decreasing at wafer ingeometry the 200 of than eq to radius 3eq or arrange3and arc (adjustcrossedwith stage can dispersecondinverse or pwavecorrewhose phasethe fs length mainprism using onto (4 from (4 Here This with For the are eq asbeless Ag[Lm use no 1isin is
Experiments short FEL crystal focus the 7marginally dispersions radius experimental -the should their iscan ,'puke duration (note previously in [11]) the near are optical are at pulse pulse isitfront exactly in has ranges beam of group Note any down +designed fundamental shown from principle provide that and critical durations compression aduration wide at of pulses, wavelength Idn/dA Percent that negligible far direcily the velocity to (assuming outer design the noted, of inathe beams, infrared waists importance transparency, the fig be to crossover radius because wavelengths will Ifor performed greatest deliver FWHM 8of described group overestimates of from chirped-pulse effect of experiments the cross be Gaussian At several the of [12-15] ,the grossly the fundamental 190 point) if present, velocity wavelengths for overestimate wavelength pulse on beam focussed the on which pulse above, pthe the infrared As temporal rbeams overestimated This durations, measurement at of angles dispersion FEL fundamental Fig several suggested compressor FEL were the beams prism the focussing pulses flexibility materials through9are can OPTICS crystal experiof shows calcupulse comsuch and are too sys3be in by
919
E.B. S .-armes, J.MJ Made" / Optical diagnostics for chirpeclpulse FEL
uncompressed the The length found with lp Cam sponding 2 m total other sumed found sion (2.7) ments were Brewster's Although wavelengths, proportion tain radius consideration usually height .
0
. .
70
. "
.35
W neam =
. .
1 .5
.1),
.m
.
.1)
70 cm
.
.
.6),
.2)
. .
.
.
c
20 10 0 0 .0
0 .2
.
. .5°
.7° . .35 .
.5° (9 .2° .35 3 .5
0 .6
0.8
1 .0
1 .2
Fig . K . Calculated errors in the measured pulse widths for beams with a spot size of 1911 p.m at the crystal. The calcula tions assume a Gaussian temporal profile for the compressed pulses .
.m . .
loge 2 a " heam ,~ , "group
where "group the . the . pulse pressed-pulse and .5°
0.5
0 .4
Fundamental pulse width (ps)
mm and surface located geometry of wide For calculated profiles
Ak = 2k 1(W ,) cos(a/2) - k,((o,) is the phase mis
.1
30 ~
'meat
for
match harmonic beam fig . external) without than .1 BTYPel < GaSe ., The
w
.1)
c
[(Ak)l,/ 2 ]
50 40
U
.
60
â
n
.35 .m. . .
sin '`[(Ak )l,/2]
72 U
5. We for tween .1 ment yields intensity acquisition . matched a for ing
80
(5 .2)
.5
. .
6. As ments systems systems out the tems in the over
.f.-linac-driven
. .
.
X1.
.
E. B. Szannes, LAI.J. Madey / Optical diagnostics for chirped-pulse FEL
920
lengths can most likely be designed within convenient dimensions on a laboratory bench. Acknowledgment The authors wish to gratefully acknowledge the support of this research by the Army Research Office under Contract No DAAL03-88-K-0109.
r
References 1
10
Wavelength (microns)
100
Fig. 9. Dispersion of several low- or non-hygroscopic infrared materials over their range of transparency, all of these materials also transmit at 633 nm, and may be suitable as prism delay lines for chirped-pulse FEL experiments in the near and far infrared .
lated from the published Sellmeier equations [161. These materials also transmit at 632 nm, so that alignment is possible using a I-le-Ne laser. For a given material, the most useful wavelength range is the one in which the dispersion increases with wavelength . owever, materials that transmit at longer wavelengths generally have lower dispersions. This is not a serious problem in the design of long-wavelength pulse compressors, because the dominant contribution to the prism dispersion comes from the last term in (4.1), i.e. 1 d=rb
A'
d'a
'
2 dca2-c- dA Therefore. the reduction in dispersion due to decreased (dn/dA)2 is compensated by the presence of the factor A;. Even for electron pulse lengths or energy chirps that do not change greatly with wavelength, the required dispersion from eq. (2.6) and eq. (3.2) is proportional only to A, so that the prism spacing 1p is roughly proportional to I /A:!. Therefore, broad-band pulse compressors for experiments at other wave-
[11 G.T. Moore. Nucl . Instr. an d Meth. A272 (1988) 302. [21 G.T. Moore, Phys. Rev . Lett ., 60 (1988) 1825 . [31 E.B. Szarmes, S .V . Benson, and J .M.J . Madey, Nucl. Instr. and Meth. A296 (1990) 755. [41 A.E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986) ch . 9. [51 B.A. Richman, J.M .J . Madey and E. Szarmes, Phys . Rev. Lett . 63 (1989) 1682 . [61 R.L. Fork . C.H. Brit o Cruz, P.C. Becker and C.V . Shank, Opt. Lett. 12 (1987) 483. [71 O.E. Martinez, J.P . Gordon and R.L. Fork, J. Opt. Soc. Am . A 1 (1984) 1003 . [81 R.L . Fork, O.E . Martinez and J.P. Gordon, Opt. Lett . 9 (1984) 150. [91 J.D. Kafka and T. Baer, Opt. Lett. 12 (1987) 401 . [101 O.E . Martinez, J . Opt . Soc. Am. B 3 (1986) 929. [111 J. Janszky, G. Corradi and R.N . Gyuzalian, Opt. Commun. 23 (1977) 293. [121 C. Brau, these Proceedings (13th Int. Free Electron Laser Conf., Santa Fe, USA, 1991) Nucl . Instr. and Meth . A318 (1992) 38 . [131 A.F.G . van der Meer et al., The FELIX Project-Status Report October 1990, FOM-Instituut Voor Plasmafysica Rijnhuizen Report 90-199, 1990 ; P.W . van Amersfoort et al ., Nucl. Instr. and Meth . A304 (1991) 163. [141 M. Castellano et al ., Nucl . Instr. and Meth . A304 (1991) 204. [151 A.H . Lumpkin et al ., Nucl . Instr. and Meth . A296 (1990) 181. [16] W.G . Driscoll (ed.) Handbook of Optics (McGraw-Hill, New York, 1978).
Nuclear Instruments and Methods in Physics Research A319 (1992) 914-920 North-11olland
Se ction A
ractical design o free-electron lasers
tical diagnostics for chirped-pulse
Erie B. Szarmes and John M .J. Madey
Duke Uniueositr Free Electron Laser Lccborawn., Durham. ,N'('27706. USA
In recent years there have been several proposals to operate rf-linac-driven FELs with chirped electron and optical micropulses for use in fast time-resolved experiments . We have been actively pursuing this application on the Mark-III infrared FEL at Duke Universitv, and have designed and procured an apparatus to achieve broad-band compression of chirped optical pulses between roughh, 2.5 p.m and 4.1 tLm . with subsequent measurement of pulse widths as short as 2011 fs . The principles of design for this experiment will be reviewed, and extensions of the design to other wavelengths will be considered .
1.Int
uctiion
In recent years there have been several proposals to operate rflinac-driven free:-electron lasers (FEW with chirped-energy electron micropulses for applications in fast time-resolved spectroscopy, in which the output optical pulses possess appreciable frequency chirps and are susceptible to pulse compression in an external dispersive delay line [1-3] . The physical principles governing these e=xperiments are generally not specific to a particular wavelength. because substantial energy chirps can be achieved at a given energy simply by dephasing the electron bunches relative to the accelerating field in the accelerator . Consequently, the most practical realizations of these experiments should employ broad-band optics in both the optical-transport and diagnostic apparatus in order to fully exploit the inherent tunability of the FEL. In this paper we describe the implementation of this experiment on the Mark-III FEL for wavelengths between 2.5 and 4.1 Wm, using a broad-band sapphire prism pulse compressor which has been designed and procured for applications in a user-oriented program at Duke University. The diagnostic apparatus consists primarily of an autocorrelator to measure the compressed pulse widths. We review the physical principles Building the design of these experiments, and suggest some possible extensions to other wavelength regimes in the near and far infrared . 2. Pulse parameters A chirped optical pulse is most conveniently characterized by a chirp parameter `h' and a pulse width
parameter 'a' [4J defined by to(t) =w,+(22h)t
(2 .1)
and a = (2 log, 2)/-,,,
(2 .2)
where w(t) is the time-dependent optical frequency and se, is the FWHM pulse width . The spectrum of an optical pulse, %` .(t)=E(t) exp[i(w t+W)l,
(2 .3)
can then be written in the general form
r' (w) = E(w)
h 4[ f(a,
h) +h - l
- i0(w-w
(2.4)
where f(a, h) is a form factor that depends on the pulse shape. for example, f(a, h) = a' for Gaussian pulses. The first-order term in the exponent can be omitted because it affects only the centroid of the pulse, and if the fre=quency chirp is large and purely linear, then the higher-order terms are usually negligible. Second-order- phase compensation means the elimiw(,), nation of the term - i[ . . . ](w in the spectral phase factor, and is the usual manner of compressing the pulse . This is accomplished by sending the pulse through a dispersive delay line, which has the effect of multiplying the spectrum by a phase factor of the form 1 d-'0 _ cxp -, i 2 dw(ar - wo) - 'O(w
0168-9()1)2/92/$()5 .1)11 ~0 1992 - Elsevier Science Publishers B .V . All rights reserved
;
(2 .5)
E.B. S.-armes, J.MJ. Mudcy / Oplicul dicrgtwslic:s for chirped-puise FEL .D
0 U _cß
30
and fig . 2 displays the corresponding pulse compression ratios ; in all cases, optimum compression was defined as yielding the maximum compressed peak power, not the minimum FWHM pulse duration. The curve fits appearing in those figures arc given below for I alb j < 1, and may be useful in the design and adjustment of phase compensators for chirped-pulse experiments in which the shape and duration of the optical pulses can be inferred from optical autocorrelation measurements .
o Tophat Parabolic * Gaussian o s Sech 2
20
c 10 0 c a E
0 U
iic"llStilllll :
Fig. I . Optimum quadratic phase compensation factors Ma . h) from eq . (2.6) for various ideal pulse shapes. defined as yielding the maximum compressed peak powers. The data and curve fits were obtained numerically.
K(a, b) = 4 T
The spectral width (as determined from I f (to) 1 2 ) is unaltered by this propagation, but the compensated optical pulse has essentially no frequency chirp, since h = 0 in the absence of the second-order term in eq. (2.4). As a result, the original spectral content of the pulse is effectively transferred from the optical phase to the optical envelope, and the pulse is compressed. The coefficient of the quadratic frequency term in eq. (2.5) which compensates the corresponding term in eq. (2.4) can be written phcnolnellologically as 1 ( d-(hi d w`
1
1
rum
where Ma, b) is a factor that depends on the pulse shape and on the ratio of alb, and has a limiting value of K -> 4 as alb - 0. Figure 1 displays the numerically derived values of Ma, b) for several ideal pulse shapes,
(2.7a)
t~
h )2
-
+1
Scch-' : K(a . b) = 4 0.76 ,- min Tp
lcl
''- .Iql
0.784
'n
h a
+ I]
11 .~11
(2.7b)
ti, .
)2 + 0.31111/2
Parabolic :
a
(2 .6)
bK(a
cl ' + [(b
min
P Tt,
u
2
915
t .t+ .t
10 .50
~b1
T
(2.7c)
P
Top hat : a ,.min '"
P
T
1
10
100
b/a Fig. 2. Optimum pulse compression ratios corresponding to the phase compensation factors in fig. I.
11 .6(1
.611
2.12 b ) 4/3 + 11 .7 _ cl _
3/4
(2.7d)
The equations for the Gaussian case are exact analytical results [4] . The only conditions assumed in the form of the remaining equations are that they depend only on the ratio of alb, and that they approach the limits .p,'"/Tp a ( alb I as alb - 0; these Ma. h ) - 4 and 7 conditions are heuristic and agree with the Gaussian case. 3é 1. FEL OPTIC S
E.B. Szartnes, J.M.J. Madey / Optical diagnostics for chirped-pulse FEL
916
3. Mark-III design parameters Simulations of the optical-pulse generation using chirped-energy electron pulses on the Mark-III FEL have been described previously [3]. Those simulations were based on the practical operating configurations of the Mark-III linac, in which the electron pulses are compatible with the dispersion in the downstream transport line and yield chirped optical pulses with large spectral widths at saturation . For experiments near A - 3.35 j,Lm, the electron pulses in the wiggler have a duration of 4 ps and a linear-energy chirp of 8y/y = + 2% with higher energies towards the trailing edge. e simulations assumed top-hat electron pulses, since optical autocorrelation measurements on the Mark-III FEL have indicated that the optical pulses at saturation are essentially top hat in shape [5] . The dura : .,- of the optical pulses (-,p - 3.4 ps) is slightly shorter mean 4 ps due to lethargy, but the magnitude of that positive frequency chirp (Jw/w " +4.7% over 4 ps) is slightly larger than would be predicted by assuming that the resonance condition determines the lasing wavelength during the pulse-, this frequency chirp is determined numerically from the simulations by fitting a least-squares parabola to the optical phase over the FWHM duration of the optical pulse. The corresponding chirped-pulse parameters from the simulations at A = 3.35 jam are 1 .2 x 10 =' s --'. h= +33 1024 s-2, K(a . b) =4 .3. = +7.0 x 10 - -' s-',
30 v
and the compressed optical pulses have a duration of about 230 fs. The simulated profiles of the chirped output pulses, and the results of pulse compression, are illustrated in fig . 3. For designing experiments over a range of wavelengths, it is in fact useful to assume that the resonance condition determines the lasing wavelength during the pulse; this will actually be a fairly good approximation if the slippage parameter is sufficiently small . The wavelength dependence of the chirp parameter h then becomes explicit : h(A) _
2,rrc 1 dy A
y dt
,
(3 .2)
where ymc- is the electron energy, and if one also assumes that the duration of the optical pulses at saturation is equal to the duration of the electron pulses (appropriate for long electron pulses), then the compensation factor in eq. (2.6) can be readily evaluated using eqs. (3.2) and (2.7) .
4. Pulse compressor design The two general designs for pulse compressors employ either grating pairs or Brewster angle prism pairs [6]. The latter choice is preferred in the present application because of the possibility of achieving substantial compression ratios over a wide range of wavelengths . In contrast, the diffractive geometry of a given grating system is very sensitive to wavelength, and the corresponding dispersions can be too large to yield practical compressor designs in chirped-pulse FEL experiments . For example, a double-pass Littrow grating system at 3.35 Wm, designed to compensate the pulse parameters in eq. (3.1), would have a slant spacing of only a few millimeters . The design of prism pulse compressors has been treated extensively in the literature [6-9] . A typical minimum deviation, single pass, Brewster angle prism
L-
-6
-4
-2
0 Time (ps)
2
4
6
Fig. 3. Simulations of FEL pulse compression experiments on the Mark-III FEL at 3.35 p.m, including shot noise in the electron beam. The experiment is described in the text. The uncompressed pulses have a duration of 3.4 ps and an average power of 2.5 MW. The compressed pulses havi~ a duration of 230 fs and a peak power of 28 MW, and result from propagation through the same dispersive delay line.
devielion, Br,wr'f- angle ps'a pa; r
Fig . 4. Typical prism configuration for a single-pass dispersive delay line. The prisms are in the minimum deviation geometry to avoid astigmatism in the transmitted beam.
E.B. Szarmes, J.M.J. Madey / Optical diagnostics for chirped-pulse FEL
917
Brewster angle, minimum deviation sapphire prism
rernovab4e mirror
to experiment
Fig. 5. Double-pass. sapphire prism. dispersive delay line for the Mark-III experiments between 2.5 and 4 .1 Rm . The set-up includes removable mirror assemblies to interchange the compressed and uncompressed pulses between the autocorrelator and the experimental sample .
system is shown in fig . 4 . The second-order dispersion for a corresponding doublepass system is given by 1 d -'46 2 do) ' _
d`n 1 )(dn 11P , 2 , + 2rt - )'` sin /3 dA` n3 dA 2rrc ` A3
dr:` .1) -4 (4 Ip cos (3 , (
n
where A is the vacuum wavelength, n(A) is the refractive index, and lp and 6 are shown in fig . 4. For a given set of system parameters, the LHS of eq. (4.1) should equal the required compensating factor from eq. (2.6). The contribute .^,ns to the dispersion arise from material dispersion and angular dispersion, the latter leading to wavelength-dependent geometrical paths through the system . In particular. material dispersion in the crystals yields the d`rz/dA` term in eq. (4.1), angular dispersion in the crystals yields the (1/n ; Xdn/dA) 2 term, and angular dispersion in air,
comprising the dominant contribution in most systems, yields the two remaining terms. The angle /3 is usually determined by the clear aperture of the beam through the system, for example, by setting 1p sin ß _ 4wheam, where w bean, is the mode radius . If 1p is much larger than o beam, one may then set cos ß - 1 . The pulse compressor for the Mark-III experiments consists of four minimun !-deviation sapphire prisms arranged as shown in fig. 5. The prisms are cut at the Brewster angle for 3.35 Wm, which yields no more than 0.03% total reflection losses for the double-pass system between 2.5 and 4.1 Wm. The optic axis of the crystal is perpendicular to the triangular faces to within 30 minutes, so that the horizontally polarized ray is ordinary. A double-pass system is required in order to eliminate the presence of lateral spectral walk-off in the output beam ; this walk-off can significantly increase the duration of the compressed optical pulses [161 according to Tcom p r Tmin
1 +
Ti rait ( Tmin
where 7,,, .,,p and
Train
(4.2) are the durations of the comX1 . FEL OPTICS
918
E. B. Szarntes. J.MJ. Afadey / Optical diagnostics for chirped-pulse FEL
3.0 3.5 Wavelength (ttm)
4.0
4.5
Fig. 6. Estimated apex-to-apex prism separations for Mark-111 experiments between ? .5 and -t .1 p.m .
the
pressed pulses in the presence and absence, respectively, of spectral walk-off, Tini, is: the duration of the input pulse, and z,i is the Rayleigh range . For example, a single-pass system designed to compensate the pulse parameters in eq. (3.1) would compress the optical pulses to no less than 1 .5 times the minimL:m duration that could be achieved in the absence of spectral walk-off. The mounting of the prisms on translation stages allows the experimenter to vary the dispersion of the system by changing the path length through all four prisms without changing the position or direction of the output beam. The size of the prisms was chosen so that roughly 70% of the required dispersion at 3.35 p.m could be provided by moving the prisms in this fashion . The removable mirror assembly at the input to the system allows the quick interchange of compressed or
AgGaSe 2 crystal; 0.45 mm thick; 90 ° phase match
motor driven translation stage
from pulse compressor
sI s. mirror
Fig. 7. Layout of the autocorrelator for measuring pulse durations as short as 200 fs.
thickness sin Optical experimental ameasuring factor all 7,apredicted are the path also (33by 200 by wavelengths, is ain this isfrequencies 3high angle to estimated need have crystals, between -focussing limited background-free 90° shown altering equating the fringes, shown equating used silver remain 5cr),, at required the and fs p,m diagnostics included of (W,) internal length angle to of degree The optical 3numerical phase-matched the not designed By A, is 1Rayleigh pulses 3prism or from to pulse gallium in waves, respectively in important by = p,m and sample in so doubling moving the constant, prism Rayleigh the calculate greater of the be geometry and 450 the within fig angle fig the pof to that dispersion the pulse, eq to so spacing path durations into prism adjusted fundamental collimation prism account [Lm, 7constants a67and selenide isminimum range spacing The optical (2 it clear the can autocorrelation crossed-beam appropriate The the The crystal than which length the should because and range h(A) this dispersion (19 isabasic through lower be dispersion LiNb0 increases FWHM ischosen where spacing aperture crossed-beam autocorrclator is for with from the as 3is as changed (AgGaSe,) pulse much yields and appearing isthe deviation be the increases external) For component with atranslation short the prism athe (o),) function mm wavelength p,m, possible eq for 90° coherence eq the internal Ma, bandwidth to with wavelengths crystals larger widths for adeviation afor beam from autocorrelator of as from accept (3 trace digitized-data type-1 phase-matchspacings beam system and one (3 The 3in the h) geometry) decreasing at wafer ingeometry the 200 of than eq to radius 3eq or arrange3and arc (adjustcrossedwith stage can dispersecondinverse or pwavecorrewhose phasethe fs length mainprism using onto (4 from (4 Here This with For the are eq asbeless Ag[Lm use no 1isin is
Experiments short FEL crystal focus the 7marginally dispersions radius experimental -the should their iscan ,'puke duration (note previously in [11]) the near are optical are at pulse pulse isitfront exactly in has ranges beam of group Note any down +designed fundamental shown from principle provide that and critical durations compression aduration wide at of pulses, wavelength Idn/dA Percent that negligible far direcily the velocity to (assuming outer design the noted, of inathe beams, infrared waists importance transparency, the fig be to crossover radius because wavelengths will Ifor performed greatest deliver FWHM 8of described group overestimates of from chirped-pulse effect of experiments the cross be Gaussian At several the of [12-15] ,the grossly the fundamental 190 point) if present, velocity wavelengths for overestimate wavelength pulse on beam focussed the on which pulse above, pthe the infrared As temporal rbeams overestimated This durations, measurement at of angles dispersion FEL fundamental Fig several suggested compressor FEL were the beams prism the focussing pulses flexibility materials through9are can OPTICS crystal experiof shows calcupulse comsuch and are too sys3be in by
919
E.B. S .-armes, J.MJ Made" / Optical diagnostics for chirpeclpulse FEL
uncompressed the The length found with lp Cam sponding 2 m total other sumed found sion (2.7) ments were Brewster's Although wavelengths, proportion tain radius consideration usually height .
0
. .
70
. "
.35
W neam =
. .
1 .5
.1),
.m
.
.1)
70 cm
.
.
.6),
.2)
. .
.
.
c
20 10 0 0 .0
0 .2
.
. .5°
.7° . .35 .
.5° (9 .2° .35 3 .5
0 .6
0.8
1 .0
1 .2
Fig . K . Calculated errors in the measured pulse widths for beams with a spot size of 1911 p.m at the crystal. The calcula tions assume a Gaussian temporal profile for the compressed pulses .
.m . .
loge 2 a " heam ,~ , "group
where "group the . the . pulse pressed-pulse and .5°
0.5
0 .4
Fundamental pulse width (ps)
mm and surface located geometry of wide For calculated profiles
Ak = 2k 1(W ,) cos(a/2) - k,((o,) is the phase mis
.1
30 ~
'meat
for
match harmonic beam fig . external) without than .1 BTYPel < GaSe ., The
w
.1)
c
[(Ak)l,/ 2 ]
50 40
U
.
60
â
n
.35 .m. . .
sin '`[(Ak )l,/2]
72 U
5. We for tween .1 ment yields intensity acquisition . matched a for ing
80
(5 .2)
.5
. .
6. As ments systems systems out the tems in the over
.f.-linac-driven
. .
.
X1.
.
E. B. Szannes, LAI.J. Madey / Optical diagnostics for chirped-pulse FEL
920
lengths can most likely be designed within convenient dimensions on a laboratory bench. Acknowledgment The authors wish to gratefully acknowledge the support of this research by the Army Research Office under Contract No DAAL03-88-K-0109.
r
References 1
10
Wavelength (microns)
100
Fig. 9. Dispersion of several low- or non-hygroscopic infrared materials over their range of transparency, all of these materials also transmit at 633 nm, and may be suitable as prism delay lines for chirped-pulse FEL experiments in the near and far infrared .
lated from the published Sellmeier equations [161. These materials also transmit at 632 nm, so that alignment is possible using a I-le-Ne laser. For a given material, the most useful wavelength range is the one in which the dispersion increases with wavelength . owever, materials that transmit at longer wavelengths generally have lower dispersions. This is not a serious problem in the design of long-wavelength pulse compressors, because the dominant contribution to the prism dispersion comes from the last term in (4.1), i.e. 1 d=rb
A'
d'a
'
2 dca2-c- dA Therefore. the reduction in dispersion due to decreased (dn/dA)2 is compensated by the presence of the factor A;. Even for electron pulse lengths or energy chirps that do not change greatly with wavelength, the required dispersion from eq. (2.6) and eq. (3.2) is proportional only to A, so that the prism spacing 1p is roughly proportional to I /A:!. Therefore, broad-band pulse compressors for experiments at other wave-
[11 G.T. Moore. Nucl . Instr. an d Meth. A272 (1988) 302. [21 G.T. Moore, Phys. Rev . Lett ., 60 (1988) 1825 . [31 E.B. Szarmes, S .V . Benson, and J .M.J . Madey, Nucl. Instr. and Meth. A296 (1990) 755. [41 A.E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986) ch . 9. [51 B.A. Richman, J.M .J . Madey and E. Szarmes, Phys . Rev. Lett . 63 (1989) 1682 . [61 R.L. Fork . C.H. Brit o Cruz, P.C. Becker and C.V . Shank, Opt. Lett. 12 (1987) 483. [71 O.E. Martinez, J.P . Gordon and R.L. Fork, J. Opt. Soc. Am . A 1 (1984) 1003 . [81 R.L . Fork, O.E . Martinez and J.P. Gordon, Opt. Lett . 9 (1984) 150. [91 J.D. Kafka and T. Baer, Opt. Lett. 12 (1987) 401 . [101 O.E . Martinez, J . Opt . Soc. Am. B 3 (1986) 929. [111 J. Janszky, G. Corradi and R.N . Gyuzalian, Opt. Commun. 23 (1977) 293. [121 C. Brau, these Proceedings (13th Int. Free Electron Laser Conf., Santa Fe, USA, 1991) Nucl . Instr. and Meth . A318 (1992) 38 . [131 A.F.G . van der Meer et al., The FELIX Project-Status Report October 1990, FOM-Instituut Voor Plasmafysica Rijnhuizen Report 90-199, 1990 ; P.W . van Amersfoort et al ., Nucl. Instr. and Meth . A304 (1991) 163. [141 M. Castellano et al ., Nucl . Instr. and Meth . A304 (1991) 204. [151 A.H . Lumpkin et al ., Nucl . Instr. and Meth . A296 (1990) 181. [16] W.G . Driscoll (ed.) Handbook of Optics (McGraw-Hill, New York, 1978).