- Email: [email protected]
VUV optical ring resonator for the Duke storage ring free electron laser
Nuclear Instruments
and Methods
in Physics
Research
A 375 (1996) 487-491
NUCLEAR INSTRUMENTS 8 METHOOS IN PHYSICS
VUV optical ring resonator for the Duke storage ring free electron laser* S.H. Park”‘* ,V.N. Litvinenko”,
J.M.J. Madey”, B.E. Newnamb
“FEL Laboratory, Box 90319, Duke University, Durham, NC 27708-0319, hL.os Alumos National Laboratory, Los alamos. NM 87545, USA
USA
Abstract The
conceptual
expected
of a multifaceted-mirror ring resonator for the Duke storage ring VUV FEL is presented. of the OK-4 FEL with the ring resonator is described.
design
performance
1. Introduction The Duke FEL Storage Ring is designed to drive UV and VUV FEL devices. Successful operation of UV and VUV FELs requires a high quality electron beam, a high precision undulator, and high reflectivity, low damage cavity mirrors in the VUV spectral range. We have successfully stored an electron beam current up to 115 mA in the energy range 250 MeV with low emittante and energy spread. We will use the optical klystron (OK-4) as a high gain medium. The OK-4 was developed at Novosibirsk, Russia, and is presently being installed on the Duke storage ring. The design of the optical ring resonator using multifaceted mirrors, as proposed by Newman [l], is being developed at the Duke FEL laboratory. As compared to the visible-wavelength FEL ring resonator designed and operated by Boeing [3], a multifaceted resonator offers the possibility of substantially reduced losses, particularly at short wavelength. In this paper we discuss the conceptual design of the optical ring cavity.
The
exception of the first downstream mirror which is exposed to the spontaneous synchrotron radiation. A flat mirror, which is easy to design as well as to align, is used as the first reflector rather than a hyperboloidal mirror. Ellipsoidal mirrors are used for focusing. The multifacet-mirror in our design includes ten flat mirrors and a focusing mirror. The instabilities of the optical cavities when the first flat mirror is misaligned are analyzed below. As shown in Fig. 1, a type 1 resonator uses two focusing mirrors and type 2 uses three. In type 2, the cavity design depends on the Rayleigh length, /3,. between the two different focusing mirrors and the beam waist, w,, at the second focusing mirror. The Rayleigh length is determined by the value of wr, which satisfies the geometrical condition of the Duke storage ring. We choose I, = l2 = 26.865 m and w, = w, where w, and w, are the beam size at the first ellipsoidal mirror and the second, respectively. As shown Fig. 2 and Table 1, there are two values of p, in the type 2 resonator: type 2(a) has a small spot size at the
2. Geometry of the optical cavity Fig. 1 illustrates the geometry of the resonator we have examined. The average power of the VUV storage ring FEL is small due to the growth of the energy spread of the electron beam [2] and the optical intensity on a mirror with an incident angle 0, is decreased by a factor cos 0,. Therefore, we can assume that the thermal effect on the mirrors in Fig. I is small for 80” 5 19,<90”, with the
” This work is supported by Office of Naval Research Contract #NOOl4-94-1-0818. * Corresponding author. Tel + 1 9 I9 660 2667, fax + 1 9 19 660 267 1, e-mail [email protected]. 016%9002/96/$15.00 Copyright SSDl 0168-9002(95)01348-2
Fig. 1. Layout of optical ring resonator
(E%J:ellipsoidal
mirror).
0 1996 Elsevier Science B.V. All rights reserved VII. FEL TECHNOLOGY
488
S.H. Park et al. I Nucl. Instr. und Meth. in Phy.
Res. A 375 (1996) 487-491
(b)
v
A8
NEW CLOSED ORBIT
Fig. 3. New closed orbit of optical cavity tilted by AH.
16
Fig. 2. Beam propagation
(p,, = 4 m, on a single round trip).
point and type 2(b) has a large one. The basic idea for calculating the exact ray-tracing had been presented by Gabardi and Shealy [4]. We calculated the exact ray tracing using Mathematics [S].
from Cz where C, (i = 1,2) is the center of curvature of mirror M,. As a result, the focal point of the Gaussian beam is shifted to I&, as shown in Fig. 3b. For a symmetrical cavity of length L and mirror radius of curvature RC (R, = R, = R2), with one spherical mirror tilted by A@ the new closed orbit of the optical cavity is
focal
2.1. New closed orbit The lowest order optical mode in a cavity traces out a trajectory through the cavity in each round trip as shown in Fig. 3a. By analogy with particle trajectories in circular particle accelerators, we call this trajectory the closed orbit of the optical beam. However, their trajectories will move around inside the cavity if one of two spherical mirrors, MI, is tilted by A& In this case, we can easily calculate the new closed orbit, which is the new optical axis connected between C, and Ci shifted by A0
sint)_
=(h)
sinA0.
where 8,,,, is the angle of the new closed orbit assuming 0,,, = 0. Hence, we can find the new position of the focal point of the cavity by calculating x and x’. Similarly, for the optical ring cavity with a first downstream flat mirror located at z = z, and misaligned by A@
closed
(;)=M.(;)+R,,, R,,
=M(;
-;r)(,“,,)
The matrix M is a ray-transfer
(2) (3) matrix of the ring resonator
[6,71:
Table 1 Parameters of the optical cavity and new closed orbit of the optical cavity tilted by A0. q,: beam waist at the center of OK-4. w,,~: beam waist between two focusing mirrors, p,,: Rayleigh length of FEL, p,: Rayleigh length between the two different focusing mirrors, f,: focal length of the first mirror, f?: focal length of the second mirror, fl: phase advance of the transverse oscillations Parameters P,, [ml W, [cm1
TYPO 1 4 0.03 192
P, [ml q0 [cm1 h [ml fi [ml sin(p/2)
A0 (mrad)
x [mm1
13.7303 0.29133 0.06279
Type 2(a)
Type 2(b)
4 0.03192 0.98356 0.01583 9.05263 6.75226 0.95710 0.13452
4 0.03 I92 183.448 0.21614 21.1644 1259.40 0.99999 0.12850
0.00472
-0.00495
= 0.005 n’ (mrad)
-0.11046
S.H. Park et al.
M=
I Nucl. Instr.
and Meth.
L I ;
;
M,,M,,MtMmM,,~
=
for type 1, (4)
fortype2.
M,,M,,M,,M,,M,,M,,M,,.
where M,, is the ray matrix for a focusing mirror of radius of curvature R,, and M,, is the ray matrix for a drift space of length 1, (i = I, 2). The new closed orbit can be calculated from Eqs. (2) and (3). 2.2. Stabilitv
ofthe resonator
The stability condition
for the resonator
(
l -i(a+d)
>
,
cosp=+(a+d),
x
(6)
In the short wavelength range we can get the high reflectance of the mirror by using the total external reflection method. The reflectance of aluminum film on a silicon substrate was measured by Scott et al. [S] using A = 58.4 nm light. We must reduce the thermal effects that limit the lifetime of the mirror and distort the optical wave-front. Aluminum is a good choice for a multifacetmirror cavity because the imaginary part, k, of the index of refraction which causes the thermal distortion of the mirror surface is small in the VUV spectral range. As a substrate. silicon is good because the k value of Si is greater than Al. We also use the total external reflection method to increase the reflectance of mirror and to reduce the intensity on the mirror, as we mentioned in previous section. The optical ring resonator in the Duke storage ring FEL is designed normal to the plane of the electron orbit because the S-wave gives higher reflectance than P-wave. We calculated [9] the reflectance vs. the incident angle of evaporated Al film on the Si substrate at 80 nm and 200 nm using optical data [ IO,1 I] and shown in Fig. 5 and Table 2. We choose the film thickness 70 nm, because the reflectance at fII2 80” is almost constant for the film thickness greater than 30nm at 80 and 200nm. The
(7)
(8)
4 sin’(p/2)
The amplitude of x,,, is inversely proportional to sin’(jJ 2) and the optical cavity becomes unstable for p = 2mrr (m: integer), while the system is the most stable for /* = 2(m + 1 )rr. 2.3. Results We calculate the new closed orbit and the stability for two types of optical cavities. With a Rayleigh length & = 4 m, the new orbit for the 0.005 mrad misaligned to x = 0.06279 mm and x’ = cavity is shifted 0.11046 mrad in the type 1 resonator, x = 0.13459 mm and x’ = 0.004724 mrad in type 2(a), and x = 0.12850 mm and
2
x’ = -0.004948 mrad in type 2(b). Because x’ in Type I is 20 times greater than in type 2(a) and 2(b), we can prove that the type 2 resonators are more stable than type I. Comparing the amplitude of x,,, between type I and type 2(a) and 2(b), the stability of the optical cavity is improved by a factor of IO by inserting the second focusing mirror. We also examine x’ vs. & in Fig. 4 which has opposite dependence on /3,,: the type 1 resonator and the type 2(b) tend to become more stable as p,, is increased, while type 2(a) tends toward instability. However. we can see the overall stability is better in type 2(a) and 2(b) than in type I.
3. Cavity mirrors
Al9
=
X'
489
(5)
where p is the phase advance per round trip. Using Eqs. (2), (3) and (7), we can calculate x and x’:
0
487-491
is
O
in Phvs. Res. A .Z75 (1996)
~...Ib.A.Q.Adr..,.,4.4.A.~.A.+,,,
0
2
3
4
5
6
Rayleigh length (m) Fig. 4. Plot of x’ w.r.t. /3,,
7
8
9
Fig. 5. Plots of calculated reflectance, transmittance, and absorption w.r.t. incident angle of evaporated Al film on the Si substrate at A = 80 nm (film thickness: 70 nm).
VII. FEL TECHNOLOGY
S.H. Park et al. I Nucl. Instr. and Meth. in Phys. Res. A 375 (1996) 487-491 Table 2 (a) The calculated mirrors)
values of the optical properties
Angle [deg]
n
Reflectance
80 85 87.5
16 2 4
98.4575 99.2322 99.6162
After a round trip
22
75.6147
(b) The calculated
values of optical properties
Angle [deg]
n
Reflectance
80 85 87.5
16 2 2
98.7806 99.3872 99.6930
After a round trip
22
80.1800
(c) Optical constants
of aluminum
Wavelength
[nm]
of Al film on Si substrate
[%]
Transmission
80
1.94692 0.87277 0.42500
[%]
Transmission
[lo- ‘%I
[%]
I.2 18960 0.612588 0.306919
Si
n
k
n
k
0.25750 0.12115
0.07798 2.30146
0.32292 0.97571
0.45022 2.92122
light
Al film substra* 2D Amy
Absorption
and silicon [12]
Front
s
[%]
1.54053 0.76689 0.38340
4.54394 2.24701 1.12122
of the mirrors in the optical cavity is designed to keep the incident angle of the optical field greater than 80” to provide better reflectance. The calculated reflectance is over 98% at an incident angle greater than 80” in S-wave. In the type 1 resonator, the principle optical beam is incident on 16 flat mirrors at 80”. 4 flat mirrors at 87.5”. and 2 focusing mirrors at 85”. Total reflectance in type I, therefore, is greater than 75.6% at 80 nm. In practice, this value will decrease due to the effects of astigmatism, thermal distortion and mirror degradation. Thermal absorption is inversely dependent on the incident angle of the optical field. As shown in Table 2a. the absorption on the first flat mirror at 6: = 87.5” and A =
0
Absorption
70 nm (n: number of
of Al film on Si substrate at A = 200 nm with Al film thickness 70 nm (n: number of mirrors)
alignment
-
[ lo-‘%I
Al
200
Incident
at A = 80 nm with Al film thickness
heater
Fig. 6. Layout of the multichannel
heater array.
ofMinor
80 nm is 0.3834% which is four times less than at 0, = 80”. In addition to keeping the incident angle 0, 2 80”, we will use a 2-dimensional array heater to stabilize the dimensions of the front surface. As illustrated in Fig. 6, each element of the array will be computer-controlled to introduce a temperature profile in the substrate which compensates for the distortion due to the incident optical and X-ray power.
4. Conclusion We present here the stability for two types of the optical ring resonators and the new closed orbit only in the case that the first flat mirror at z = Z, is misaligned. From the result, we can prove that the optical cavity is more stable when we put a second focusing mirror between two symmetric ellipsoidal mirrors. In type 2(a), we can see the misalignment of the first mirror must be less than kO.005 mrad in order not to have critical effect on the optical resonator. As a second choice, we can easily correct the problem by finding the new closed orbit of the optical beam, but the astigmatic effect due to the focusing mirror and thermal effects must be analyzed. We choose the type 2(a) resonator in which the radius of curvature of focusing mirror is small enough to fabricate.
S.H. Park et al. / Nucl. Instr. and Meth. in Phys. Res. A 31.5 (19%) 487-491
References [II BE. Newman, in: Laser Induced Damage in Optical Materials: 1985, eds. H.E. Bennett, A.H. Guenther, D. Millam and B.E. Newnam, NBS Spec. Publ. 746 (1988) p. 261. VI V.N. Litvinenko, Nucl. Instr. and Meth. A 304 (1991) 40. I31 D.H. Dowel1 et al., Nucl. Instr and Meth. A 304 (1991) 1: J. Quantum Electron. 27( 12) (1991) 2613. [41 D.R. Gabardi and D.L. Shealy. Proc. SPIE 1160 (1989) 337. [51 S. Wolfram, Mathematics: A System for Doing Mathematics by Computer (Addison-Wesley, 1991). Lasers (Academic Press, Boston, [61 C.A. Brau, Free-Electron 1990) Chap. 7.
491
[71 A. Siegman, Lasers (Univ. Sci., Mill Valley, CA, 1986). PI M.L. Scott. P.N. Arendt. B.J. Cameron, J.M. Saber and B.E. Newnam, Appl. Opt. 27 (1988) 1503. [91 M. Born and E. Wolf, Principles of Optics (Pergamon, 1980). [lOI D.Y. Smith, E. Shiles and M. Inokuti, in: Handbook of Optical Constants of Solids, ed. E.D. Palik (Academic Press, 1985) p. 369. [Ill D.F. Edwards, in: Handbook of Optical Constants of Solids, ed. E.D. Palik (Academic Press, 1985) p. 547. [I21 E.D. Palik (ed.), Handbook (Academic Press, 1985).
of Optical
Constants
of Solids
VII. FEL TECHNOLOGY
and Methods
in Physics
Research
A 375 (1996) 487-491
NUCLEAR INSTRUMENTS 8 METHOOS IN PHYSICS
VUV optical ring resonator for the Duke storage ring free electron laser* S.H. Park”‘* ,V.N. Litvinenko”,
J.M.J. Madey”, B.E. Newnamb
“FEL Laboratory, Box 90319, Duke University, Durham, NC 27708-0319, hL.os Alumos National Laboratory, Los alamos. NM 87545, USA
USA
Abstract The
conceptual
expected
of a multifaceted-mirror ring resonator for the Duke storage ring VUV FEL is presented. of the OK-4 FEL with the ring resonator is described.
design
performance
1. Introduction The Duke FEL Storage Ring is designed to drive UV and VUV FEL devices. Successful operation of UV and VUV FELs requires a high quality electron beam, a high precision undulator, and high reflectivity, low damage cavity mirrors in the VUV spectral range. We have successfully stored an electron beam current up to 115 mA in the energy range 250 MeV with low emittante and energy spread. We will use the optical klystron (OK-4) as a high gain medium. The OK-4 was developed at Novosibirsk, Russia, and is presently being installed on the Duke storage ring. The design of the optical ring resonator using multifaceted mirrors, as proposed by Newman [l], is being developed at the Duke FEL laboratory. As compared to the visible-wavelength FEL ring resonator designed and operated by Boeing [3], a multifaceted resonator offers the possibility of substantially reduced losses, particularly at short wavelength. In this paper we discuss the conceptual design of the optical ring cavity.
The
exception of the first downstream mirror which is exposed to the spontaneous synchrotron radiation. A flat mirror, which is easy to design as well as to align, is used as the first reflector rather than a hyperboloidal mirror. Ellipsoidal mirrors are used for focusing. The multifacet-mirror in our design includes ten flat mirrors and a focusing mirror. The instabilities of the optical cavities when the first flat mirror is misaligned are analyzed below. As shown in Fig. 1, a type 1 resonator uses two focusing mirrors and type 2 uses three. In type 2, the cavity design depends on the Rayleigh length, /3,. between the two different focusing mirrors and the beam waist, w,, at the second focusing mirror. The Rayleigh length is determined by the value of wr, which satisfies the geometrical condition of the Duke storage ring. We choose I, = l2 = 26.865 m and w, = w, where w, and w, are the beam size at the first ellipsoidal mirror and the second, respectively. As shown Fig. 2 and Table 1, there are two values of p, in the type 2 resonator: type 2(a) has a small spot size at the
2. Geometry of the optical cavity Fig. 1 illustrates the geometry of the resonator we have examined. The average power of the VUV storage ring FEL is small due to the growth of the energy spread of the electron beam [2] and the optical intensity on a mirror with an incident angle 0, is decreased by a factor cos 0,. Therefore, we can assume that the thermal effect on the mirrors in Fig. I is small for 80” 5 19,<90”, with the
” This work is supported by Office of Naval Research Contract #NOOl4-94-1-0818. * Corresponding author. Tel + 1 9 I9 660 2667, fax + 1 9 19 660 267 1, e-mail [email protected]. 016%9002/96/$15.00 Copyright SSDl 0168-9002(95)01348-2
Fig. 1. Layout of optical ring resonator
(E%J:ellipsoidal
mirror).
0 1996 Elsevier Science B.V. All rights reserved VII. FEL TECHNOLOGY
488
S.H. Park et al. I Nucl. Instr. und Meth. in Phy.
Res. A 375 (1996) 487-491
(b)
v
A8
NEW CLOSED ORBIT
Fig. 3. New closed orbit of optical cavity tilted by AH.
16
Fig. 2. Beam propagation
(p,, = 4 m, on a single round trip).
point and type 2(b) has a large one. The basic idea for calculating the exact ray-tracing had been presented by Gabardi and Shealy [4]. We calculated the exact ray tracing using Mathematics [S].
from Cz where C, (i = 1,2) is the center of curvature of mirror M,. As a result, the focal point of the Gaussian beam is shifted to I&, as shown in Fig. 3b. For a symmetrical cavity of length L and mirror radius of curvature RC (R, = R, = R2), with one spherical mirror tilted by A@ the new closed orbit of the optical cavity is
focal
2.1. New closed orbit The lowest order optical mode in a cavity traces out a trajectory through the cavity in each round trip as shown in Fig. 3a. By analogy with particle trajectories in circular particle accelerators, we call this trajectory the closed orbit of the optical beam. However, their trajectories will move around inside the cavity if one of two spherical mirrors, MI, is tilted by A& In this case, we can easily calculate the new closed orbit, which is the new optical axis connected between C, and Ci shifted by A0
sint)_
=(h)
sinA0.
where 8,,,, is the angle of the new closed orbit assuming 0,,, = 0. Hence, we can find the new position of the focal point of the cavity by calculating x and x’. Similarly, for the optical ring cavity with a first downstream flat mirror located at z = z, and misaligned by A@
closed
(;)=M.(;)+R,,, R,,
=M(;
-;r)(,“,,)
The matrix M is a ray-transfer
(2) (3) matrix of the ring resonator
[6,71:
Table 1 Parameters of the optical cavity and new closed orbit of the optical cavity tilted by A0. q,: beam waist at the center of OK-4. w,,~: beam waist between two focusing mirrors, p,,: Rayleigh length of FEL, p,: Rayleigh length between the two different focusing mirrors, f,: focal length of the first mirror, f?: focal length of the second mirror, fl: phase advance of the transverse oscillations Parameters P,, [ml W, [cm1
TYPO 1 4 0.03 192
P, [ml q0 [cm1 h [ml fi [ml sin(p/2)
A0 (mrad)
x [mm1
13.7303 0.29133 0.06279
Type 2(a)
Type 2(b)
4 0.03192 0.98356 0.01583 9.05263 6.75226 0.95710 0.13452
4 0.03 I92 183.448 0.21614 21.1644 1259.40 0.99999 0.12850
0.00472
-0.00495
= 0.005 n’ (mrad)
-0.11046
S.H. Park et al.
M=
I Nucl. Instr.
and Meth.
L I ;
;
M,,M,,MtMmM,,~
=
for type 1, (4)
fortype2.
M,,M,,M,,M,,M,,M,,M,,.
where M,, is the ray matrix for a focusing mirror of radius of curvature R,, and M,, is the ray matrix for a drift space of length 1, (i = I, 2). The new closed orbit can be calculated from Eqs. (2) and (3). 2.2. Stabilitv
ofthe resonator
The stability condition
for the resonator
(
l -i(a+d)
>
,
cosp=+(a+d),
x
(6)
In the short wavelength range we can get the high reflectance of the mirror by using the total external reflection method. The reflectance of aluminum film on a silicon substrate was measured by Scott et al. [S] using A = 58.4 nm light. We must reduce the thermal effects that limit the lifetime of the mirror and distort the optical wave-front. Aluminum is a good choice for a multifacetmirror cavity because the imaginary part, k, of the index of refraction which causes the thermal distortion of the mirror surface is small in the VUV spectral range. As a substrate. silicon is good because the k value of Si is greater than Al. We also use the total external reflection method to increase the reflectance of mirror and to reduce the intensity on the mirror, as we mentioned in previous section. The optical ring resonator in the Duke storage ring FEL is designed normal to the plane of the electron orbit because the S-wave gives higher reflectance than P-wave. We calculated [9] the reflectance vs. the incident angle of evaporated Al film on the Si substrate at 80 nm and 200 nm using optical data [ IO,1 I] and shown in Fig. 5 and Table 2. We choose the film thickness 70 nm, because the reflectance at fII2 80” is almost constant for the film thickness greater than 30nm at 80 and 200nm. The
(7)
(8)
4 sin’(p/2)
The amplitude of x,,, is inversely proportional to sin’(jJ 2) and the optical cavity becomes unstable for p = 2mrr (m: integer), while the system is the most stable for /* = 2(m + 1 )rr. 2.3. Results We calculate the new closed orbit and the stability for two types of optical cavities. With a Rayleigh length & = 4 m, the new orbit for the 0.005 mrad misaligned to x = 0.06279 mm and x’ = cavity is shifted 0.11046 mrad in the type 1 resonator, x = 0.13459 mm and x’ = 0.004724 mrad in type 2(a), and x = 0.12850 mm and
2
x’ = -0.004948 mrad in type 2(b). Because x’ in Type I is 20 times greater than in type 2(a) and 2(b), we can prove that the type 2 resonators are more stable than type I. Comparing the amplitude of x,,, between type I and type 2(a) and 2(b), the stability of the optical cavity is improved by a factor of IO by inserting the second focusing mirror. We also examine x’ vs. & in Fig. 4 which has opposite dependence on /3,,: the type 1 resonator and the type 2(b) tend to become more stable as p,, is increased, while type 2(a) tends toward instability. However. we can see the overall stability is better in type 2(a) and 2(b) than in type I.
3. Cavity mirrors
Al9
=
X'
489
(5)
where p is the phase advance per round trip. Using Eqs. (2), (3) and (7), we can calculate x and x’:
0
487-491
is
O
in Phvs. Res. A .Z75 (1996)
~...Ib.A.Q.Adr..,.,4.4.A.~.A.+,,,
0
2
3
4
5
6
Rayleigh length (m) Fig. 4. Plot of x’ w.r.t. /3,,
7
8
9
Fig. 5. Plots of calculated reflectance, transmittance, and absorption w.r.t. incident angle of evaporated Al film on the Si substrate at A = 80 nm (film thickness: 70 nm).
VII. FEL TECHNOLOGY
S.H. Park et al. I Nucl. Instr. and Meth. in Phys. Res. A 375 (1996) 487-491 Table 2 (a) The calculated mirrors)
values of the optical properties
Angle [deg]
n
Reflectance
80 85 87.5
16 2 4
98.4575 99.2322 99.6162
After a round trip
22
75.6147
(b) The calculated
values of optical properties
Angle [deg]
n
Reflectance
80 85 87.5
16 2 2
98.7806 99.3872 99.6930
After a round trip
22
80.1800
(c) Optical constants
of aluminum
Wavelength
[nm]
of Al film on Si substrate
[%]
Transmission
80
1.94692 0.87277 0.42500
[%]
Transmission
[lo- ‘%I
[%]
I.2 18960 0.612588 0.306919
Si
n
k
n
k
0.25750 0.12115
0.07798 2.30146
0.32292 0.97571
0.45022 2.92122
light
Al film substra* 2D Amy
Absorption
and silicon [12]
Front
s
[%]
1.54053 0.76689 0.38340
4.54394 2.24701 1.12122
of the mirrors in the optical cavity is designed to keep the incident angle of the optical field greater than 80” to provide better reflectance. The calculated reflectance is over 98% at an incident angle greater than 80” in S-wave. In the type 1 resonator, the principle optical beam is incident on 16 flat mirrors at 80”. 4 flat mirrors at 87.5”. and 2 focusing mirrors at 85”. Total reflectance in type I, therefore, is greater than 75.6% at 80 nm. In practice, this value will decrease due to the effects of astigmatism, thermal distortion and mirror degradation. Thermal absorption is inversely dependent on the incident angle of the optical field. As shown in Table 2a. the absorption on the first flat mirror at 6: = 87.5” and A =
0
Absorption
70 nm (n: number of
of Al film on Si substrate at A = 200 nm with Al film thickness 70 nm (n: number of mirrors)
alignment
-
[ lo-‘%I
Al
200
Incident
at A = 80 nm with Al film thickness
heater
Fig. 6. Layout of the multichannel
heater array.
ofMinor
80 nm is 0.3834% which is four times less than at 0, = 80”. In addition to keeping the incident angle 0, 2 80”, we will use a 2-dimensional array heater to stabilize the dimensions of the front surface. As illustrated in Fig. 6, each element of the array will be computer-controlled to introduce a temperature profile in the substrate which compensates for the distortion due to the incident optical and X-ray power.
4. Conclusion We present here the stability for two types of the optical ring resonators and the new closed orbit only in the case that the first flat mirror at z = Z, is misaligned. From the result, we can prove that the optical cavity is more stable when we put a second focusing mirror between two symmetric ellipsoidal mirrors. In type 2(a), we can see the misalignment of the first mirror must be less than kO.005 mrad in order not to have critical effect on the optical resonator. As a second choice, we can easily correct the problem by finding the new closed orbit of the optical beam, but the astigmatic effect due to the focusing mirror and thermal effects must be analyzed. We choose the type 2(a) resonator in which the radius of curvature of focusing mirror is small enough to fabricate.
S.H. Park et al. / Nucl. Instr. and Meth. in Phys. Res. A 31.5 (19%) 487-491
References [II BE. Newman, in: Laser Induced Damage in Optical Materials: 1985, eds. H.E. Bennett, A.H. Guenther, D. Millam and B.E. Newnam, NBS Spec. Publ. 746 (1988) p. 261. VI V.N. Litvinenko, Nucl. Instr. and Meth. A 304 (1991) 40. I31 D.H. Dowel1 et al., Nucl. Instr and Meth. A 304 (1991) 1: J. Quantum Electron. 27( 12) (1991) 2613. [41 D.R. Gabardi and D.L. Shealy. Proc. SPIE 1160 (1989) 337. [51 S. Wolfram, Mathematics: A System for Doing Mathematics by Computer (Addison-Wesley, 1991). Lasers (Academic Press, Boston, [61 C.A. Brau, Free-Electron 1990) Chap. 7.
491
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of Optical
Constants
of Solids
VII. FEL TECHNOLOGY