With the prospect of high-intensity isolated attosecond pulses XUV pump-XUV probe spectroscopy as well as novel methods for controlling atomic-scale currents seem feasible paving the way for new physical, chemical, biological, and medical applications such as attosecond X-ray diffraction, non-invasive imaging and cancer therapy.
To reach these ambitious goals, optical parametric chirped pulse amplifcation (OPCPA) in combination with high harmonic generation (HHG) seems like a promising route. But this approach puts stringent demands on the pump laser driving it. To overcome these challenges Yb:YAG as active laser medium in a thin-disk geometry is often used offering a lot of favourable properties for high power applications with excellent beam quality.
Yb:Yag can be pumped at either 940 nm or, more recently, since the advent of Volume-Bragg-Grating stabilized diodes, at its Zero-Phonon-Line with a wavelength of 969 nm. These two wavelengths excite different transitions in the 5 F 1/2 electronic shell each exhibiting its own assets and drawbacks. This thesis will focus on a comparison between them.
A theoretical model of the conditions in the pumped thin-disk is created. Absorption of the pump light is calculated numerically. Amplified spontaneous emission and thermal effects are considered, too. The structure of the 5 F 1/2 energy manifold is accounted for thus allowing predictions for two different pumping wavelengths at 940 nm and 969 nm. To gauge the accuracy of the model the numerical calculations are compared with measurements conducted at LMU’s newly-built Laboratory for Extreme Photonics. A regenerative amplifer is set up to quantify the roundtrip gain at different pumping powers and wavelengths. The temperature of the pumped disk and its deformations as well as the single pass gain are measured, too. All measurements are in reasonable agreement with theory.
After the motivation for this work some basic properties of lasers are introduced. In chapter 3 the basics of thermodynamics and its application to laser gain media, especially Yb:YAG, will be covered. The previous considerations will be numerically applied to the case of a thin-disk regenerative amplifer in the 4. chapter. Additional aspects, like its cavity and nonlinear effects, will be considered, too. Chap. 5 will give a description of the experimental methods and setups used to check the numerical predictions while the raw measured data and its interpratation are stated chap. 6 and 7
P t
ss t
t rP
sr Prt tt Prt t t qr
ts r t r
str
t t
srstät ü
t Pss
stt
rt rr
tts
tt
t Prt ss s
s qts
tr rs
str
tt
s
sss
P tst ss
r ts
rr rts
r rr rts
tr
sr r
t ttsts
st ts
t qts
s r st
ts ss
t
trtr
3+
r s
s tr
rt r
t qts t t trs
t rt
ts ss
t t
tr
rt
rt r t
ts
t P t
srt
t tr
Pss
rt sr srt
r
rt sts
rtr
Prr
Pss
t tr
rts t s
trrtt
P t str
Prr
srt
Pss
t tr
rtr
r ts
r s
rts
r t
t t tr
ttrs
sr tr
s rts
st rs
st s
r
tt
t s ts t rt s t t ts strtr
tt r sr strtrs rs s r srtr rs
t ss r r r ss t trs srt t
st t t s ts t rs s s st
tr r st rt tt s r rstrt r rss
sttr tr s
t r t t r t rt
t r ts
rs ts rt s t ttr rst s
t s s t s srtr ss 10
-18
s r
rs 10
14
sr s rt t r rt srtt tst ss s ts r
t tt tr rss r rt tsts
rtsss rst rt t t
s s r
t s r s rts t rr rss r
r t st r tr rt r t s t t s t
t t st
t s s
r t t rtr rt t ss t s
s trt r t srs tr r t s s
t
rrs t st s t t Ps rs
rr t t t r Ps t P
t tts rrr s r rt s trst
sr ss tt s trts s r rt
rrt s st tts s =
-18
s ss t tr tr
t r rt t trt str r t st sst
strts r r ttr r t
r t s s srt t
ss tr s sr tr q t
rs sts ss
s s s ttr
s ts
ss r rt rt t ss
rtr rs s t t s t t r r
r t rr
-7
t
-5
t tr ts r t srs
r rtst trs rt trts sr ss tt s
trts
ts r s t t rst tst s
t tts ss r strs s s ts
r tr ts rrts s s
t r s
ts s s tts r rt
s r tr
tt
rs rt trs rt tst ss s
r rtst s t rtr r s t PP
ts r t r s ss r strt t
tst ss rst tr srr r rss
rss rt rs t trtt r
ts rss s t t srt r s t r t s t
st st t srts r str t t rr
s t ts
ts srt rst s t s tt strt s t
sr r t tst ss t rs t st t t r
srt s rts s r rtr rqrt s r st
r s t PP s tst
s s s rrs t
ts sst rts
r t tst sss
ts sr t r ts t qt
s r
r ts ts s t ssts t s 0.1
t t s rst st s t
tr rrts s
tt s stt sr st
s r s rt sr ts tr ts t s ts
t srt st s ss t t r tt
r t r ts t r s rr trs
t t rtss stt
s s s t
rtt rts
6
s s ss t r rrts r r ts
s t s r ts t tr tt
strss rsst r str t t r s
r ts srs t t tr r r rt
s t t rrt st s t ts rP
t t
s t ts t rt trsts
t
5
F
1/2
tr s t ts ssts rs s tss
s rs t t
r tt trt t ts t ts s
rt srt t t s t r st
s ss tr ts r sr t strtr t
5
F
1/2
tt
r s t r ts rts r t rt
ts t t r t t r
ts r r t srts t t s t
rtr r tr Pts rrt r s st t qt t
rtr t rt rs ts trtr t
s ts rts s s t s ss r sr t
srts r rs rt t tr
s tss ssts t rts
t t tt r srt sr t rrts t
ss s tr tt s s t
sr rt r s s s s t r tr tr
t ss trs ts t t sr s
r rs srts r
t t s ts rrt r t rt tr t
sts ts t r ts sr t tr
srt t rt ts sts s t t r
rts t r sr t s stt tr ts trrtt
t s r tr srt s tr
tt ts t
t Prt ss s
s trt t s trt rs t t s
sr ss trs ts s sst
tr t s rs tr r t t
t ss s t ss tr t ts t srt
rstrs s t ts r t t t t tr
rrts stt r str t srts t tr
s qts
tr st r t s r s qts
rtt s
· (
0
E) = -P + ,
× E = -µ
0
H
t
- µ
0
M
t
,
· (µ
0
H) = -(µ
0
M ),
× H =
0
E
t
+
P
t
+ j,
t t tr rttt
0
t r st t tr rrt
st j t tr E t sst r rss t r
t P =
0
XE t tr sstt X t r t
tr st
D =
0
E + P =
0
(1 + X)E =
0
r
E.
sr t t B rss tr t t
H
t tt M s
B = µ
0
(H + M ),
r µ
0
sts r t t rttt s t tt
r rrt ( = 0, j = 0) ss rt t st r
t rqs s tt qs rtt
s
× E = -µ
0
H
t
× H =
D
t
.
t Prt ss s
s qts
t
0
µ
0
= 1/c
2
× ( × A) = (A) -
2
A
t qt
r
c
2
2
E(x, t)
t
2
-
2
E(x, t) = 0
r rss t tr s
E(x, t) = A(x)n exp(-i(kz - t)),
r n ts t tr t t rt rt A(x) s
t q rtt s
-
2
r
c
2
A(x) -
2
A(x)
z
2
+ 2ik
A(x)
z
+ k
2
A(x) -
2
y
2
A(x) -
2
x
2
A(x) = 0.
ss k = 2/ = n/c =
r
/c
t t rrt n t trrs
s r t A(x) t rt rt z r
st t rr t t
ts
2
A(x)
z
2
k
A(x)
z
,
q s rs t t r qt
-
2
T
A(x) + 2ik
A(x)
z
= 0.
ts st rtt st s t sr t
ss tst strt
s t r rt x
2
+ y
2
z
2
t t trsrs rts st
|x| = x
2
+ y
2
+ z
2
= z
1 +
r
2
z
2
z +
r
2
2z
.
tr t rtr q = z +iz
0
t st q rtt
s
A(x) =
A
0
q
exp(
-ikr
2
2q
).
t Prt ss s
s qts
1
q
=
1
z + iz
0
=:
1
R
- i
k(z)
2
R(z) = z 1 +
z
0
z
2
,
2
(z) =
2
0
1 +
z
z
0
2
,
2
0
=
2z
0
k
=
z
0
,
and (z) = arctan(
z
z
0
)
q s
A(x) = A
0
0
(z)
exp(-
r
2
2
(z)
) exp(-ik
r
2
2R(z)
) exp(i(z)).
strt
2z
0
R(z)
0
2
(z)
r stts tr ss t z
0
= 50
= 30
ss t t tr q s q t rt stt
t (z) ts t rrt st s t rt z z
0
=
2
0
/
t
r R(z) t s rts rs rtr = /
0
t r
r |z| 0 s ss st s t s r t srt sr
s
t Prt ss s
s qts
strt
tst
r stts t tr trsrs tst
t
01
ss
strt
tst
r stts t tr trsrs tst
t
21
ss
r r r t s r sr
t trsrs t tt ts s t
t ss st t r rt s
H
0
(u) = 1
H
1
(u) = 2u
H
2
(u) = 4u
2
- 2
H
l+1
(u) = 2uH
l
(u) - 2lH
l-1
(u)
t trsrs ss s s t t rtr t
ss s st t t r qt tt t
t Prt ss s
s qts
ts rtt s
A(x) = A
0
H
m
(
2x
(z)
)H
n
(
2y
(z)
) exp (iZ(z))
·
0
(z)
exp(-
r
2
2
(z)
) exp(-ik
r
2
2R(z)
) exp(i(z))
t Z(z) = (m+n)(z) rst rt trsrs s r
mn
t m, n t rr t rt t x, yrt r r
r t r s s r strt s s
ts s r rr s
rstr tr r t sr trsrs s rst t t s t
t trr t tr rs rt st rt
sr ts r st t st t
00
s rrr s t rs t
st r st t t sst r s t rt
t st s t srs t r rr s r st
t t s s s
t Prt ss s
tr rs
tr rs
t s r ts rrts ss tr t t
rs s t sr tt s tr t rr tr
ts t r t ss s
optical axis
z
1
(z)
r
1
(z)
2
(z)
r
2
(z)
A
B
C
D
r rts s t tr rs
t t ts ss r rrrs rs s t r
trsrs st ts s tr ts rtr
t r rt st s trs r s sr
tr t rst rt rrsts t st t t t s r
i
(z)
t
sst t s t
i
(z)
t rst t t s ts r sss
tr t t ts st r t
A B
C D
·
r
1
(z)
1
(z)
=
r
2
(z)
2
(z)
,
r r
2
(z)
2
(z)
r t st t r tr t t t
ts t t t r rss s tr tt
t st rtt trsrts r st t
t sr t ts sr t s r t
rst trs r t t rrt rr t t tr t
r rt t tr t t ss rst t t r rt strt
r rt t t
s s tr r tr t ss s t t s r t t
sr ts s t rtr q tr q
ss t rtr q
1
s tr tt t
t sr tr t ts A
1
, B
1
, C
1
, D
1
t t rtr
q
2
=
A
1
q
1
+ B
1
C
1
q
1
+ D
1
t Prt ss s
str
t t
tr
Prt st d
tr t stt
rrt
0
1
t r r rrr
t rs R
-2/R
1
t r t rrr
0
1
s t t f
-1/f
1
rt t r tr
t rs R rrt
s n
1
, n
2
t rrs
(n
1
- n
2
)/Rn
2
n
1
/n
2
trs t ts
s t t ts rtr t
tr tts r rt s q s r s s s
t t t s t t st r ts tss s t
str
t rstr ssts t st t rrrs rt t ts s
t t sr rs rstr s t r st
t rqs t t t s tr t
s t s rt sr ts r t rrrs tr r st
s t rt rs rqs s st ttrs r s
sr r t s
tt
rstr ssts s t ts s t tr r
s s r ts rtrt t r t t
rs st s tr M
total
t ts A
total
B
total
C
total
D
total
sr t t t t r ts trs r
s rrst st ttrs tt r rt tss
t Prt ss s
str
tr rtr rtrst qrtr s ss
q
2
= q
1
=: q
ts rtt s
q =
qA
total
+ B
total
qC
total
+ D
total
.
s s t t qrt qt
q
2
C
total
- q(A
total
- D
total
) - B
total
= 0
tt s s
q
1,2
=
A
total
- D
total
± (A
total
- D
total
)
2
+ 4B
total
C
total
2C
total
!
= z + iz
0
,
r t st st s st t t q z
0
t s r ss
s t tr r t sqr rt s t t
(A
total
- D
total
)
2
+ 4B
total
C
total
< 0.
s rt rrt ts trs det (M
total
) = A
total
D
total
-
B
total
C
total
= 1
rs t
(A
total
+ D
total
)
2
- 4 < 0,
s t t r stt rtr
-2 < A
total
+ D
total
< 2.
s r t s rstr sst t r
rrrs t rs R
1
R
2
r srt st d tr
sr rtr strt t R
2
s
M
total
=
A
total
B
total
C
total
D
total
=
1 d
0 1
1
0
2
R
1
1
1 d
0 1
1
0
2
R
2
1
=
(1 + 2d/R
1
)(1 + 2d/R
2
)
d(2 + 2d/R
1
)
2(1 + 2d/R
2
)/R
1
+ 2/R
2
2d/R
1
+ 1
.
t Prt ss s
str
s ts q s r g
1
= 1 + d/R
1
g
2
= 1 + d/R
2
0 < g
1
g
2
< 1.
r rrstt s r s r rs r
rs t st rstr rts r t rs rtr
t rrrs r ss st rstrs r s r
sr strs t t t t t
g
1
g
2
concentric
planar
confocal
area of stability
r tt sr rstr g
1
g
2
s
s s st rstr rtr r t
ts sts t rt rt rts r sts
trsrs s s r t tr s r r
trsrs s r ss ts sstt srs
r rqr rt t t
00
t trsrs
s r rr tr t rs rr st
rstrt t r r t sr st r ts r
s rtr tr t t rstr t t s t
t s rtrs rs sss st ts r
t st rs t r s t srss r rr s
st r t sr t t s t
rs tt tt r t t t s t t r rtss s
t
00
rs t st r st t t sst r
t Prt ss s
str
t s t t rt t rt s t
rt ts tr rtr s s tt ts
t tt t t t t t t rrrs st
i
n
i
d
i
= p
2
r s s t rr n
i
s t rrt rst
t t d
i
rq s t t t t
s s t
=
c
2
i
n
i
d
i
t rs r rr trsrs s q s
=
c
2
i
n
i
d
i
p +
1
(m + n) arccos 1 -
i
n
i
d
i
R
t m, n t t trsrs s q R st
t rs rtr t rrrs s s st s
t t s s r rr r t t
st t r r t st sts
t rs t str
00
01
10
11
20
02
TEM
mnp
00
01
10
11
20
02
TEM
mn(p+1)
00
01
10
11
20
02
TEM
mn(p+2)
=
c
2
i
n
i
d
i
r t rrstt t rs str rstr
trsrs m, n t p s
sss
r tr rtr t s ts sss t ts
t s ts t rt t s s tr r
rtrs t t sss r tr t t r
t t t ts t trsss ts r s srt
r t r st ts ts ts tt rtr
t Prt ss s
str
t t rs st tst r rtr rr t s
r t rt ts sss t s s ss
rtr
rtr s rstr s trs sss t st t rrt
r t r ts tss s s t ts rtrs r rst
st t t ts r t st s s rt st t t
t t t ts s rt
r t t Ps s t s trt rsts
r ss r r t tr ts s t s ss t
r rtr ts sss t t s s s ss
rtr t ttr s sr rtr t ss trsrs
tst r t ss sr
I(x) = I
0
exp(-x
2
)
x
I
0.135I
0
I
0
2
-
2
d
Beam
n
2
-n
2
d
Aperture
r Pt ss tst strt ts ts
tr
t rtr ts t s ss s rs
d
Beam
s t s t st t tr s ts p
beam
1,2
t
t Prt ss s
str
t tst s r t
2
t tst r t
rts t xs s
p
beam
1,2
= ± 2/.
rtr t s t tr s ss t ts ts tr
p
Aperture
1,2
= n · p
beam
1,2
s t tst tt s t ss tr t
t trsrs s rtt s
I(±n 2/) = I
0
p
Aperture
-p
Aperture
exp(-x
2
) dx,
s exp(-x
2
)
s str t s q t
I(n
2/) = 2I
0
n
2/
0
exp(-x
2
) dx.
= x r s d = dx q s
I(n2) = I
0
2
n2
0
exp(-
2
) d,
s t ss rrr t s s t r t s trsrs
rt y s t trt s t sqr t rrr ts s
r s t
d
Aperture
/d
Beam
r(2d
Aperture
/d
Beam
)
r
2
(2d
Aperture
/d
Beam
)
s t ss rrr t ts sqr
tr s rrss t 2
t rtr trs rt sss
t r t ts
tr s s t s t rr trt sss t
t s s s ss r rt t r rtr t t
s rt sss st t
t st
tt r r stts t t rs rs r tr
t rtr
t Prt ss s
P tst ss
P tst ss
ts s sr s r t ss t tt tst
r st trt t rts t t
tst tt ss trsrs tst r s r s
tr s t tr
ss trsrs tst r s ss rss sr t
t rs st s
I
G
= I
Gauss
· exp(-r
2
).
r rts r s s tt r t tt tst tt
ts rr t t rt rt s trt
r ts
P
total
=
0
2
0
I
G
rdr d =
I
Gauss
.
tr s t t tr s ts t
I(r
0
) = I
Gauss
/e
2
t r
0
=
2/
r t tt r t t s
rs
I
f.t.
= I
f lat-top
· (r) - (r - 2/) ,
t (r) t t s t s r t tt r
P
total
=
2/
0
2
0
I
f.t.
rdr d = 2
I
f lat-top
.
P
total
s t q t ss t s rt r t tst
t ss r
I
Gauss
= 2I
f lat-top
.
s s st t s r t trrtt t
srt rsts
t Prt ss s
r ts
x
y
Intensity
I
Gauss
/e
2
I
flat-top
I
Gauss
r ss tt tst strt r t t s
r
r ts
sr ss r r tsts t rr 10
20
2
t
r rss trrs r rr r rsss
r strt t s ts t sr tsts 10
8
2
t
t t r t r t rss tr t
t t s t r r t r
srst s t r rt rrsts t sr
tr t t rtt r r
P =
0
XE s s t s rss r srs st
P =
0
X
1
E + X
2
E
2
+ X
3
E
3
+ . . .
=: P
1
+ P
2
+ P
3
+ ··· =: P
1
+ P
N L
.
r sstt s rr X
2
s tr s
X
2
E
2
:=
jk (nm)
X
2
ijk
(
n
+
m
,
n
,
m
)E
j
(
n
)E
k
(
m
),
r t r rrs s
r rtr ts t tsr tr
X t t ts r trs t qt s
2
E -
r
c
2
2
E
t
2
=
1
0
c
2
2
P
N L
t
2
,
t t r rt t s sr tr t rt s
ts qt s rs t rt r t ts
t Prt ss s
r ts
t t strr r rts r t rrs
t r sr r
rr rts
rr rts r ss rsts s rs s
tr
st rtt r
r rt t rq t s s
t trrss rst rq srs t r t
t s s r sr r ts r t
rs
t Prtr t P r t rst rts
t t rs s rq t t s rq ts
t rt r st t s rt s t
rst ts tq s s t rt trts sr ss
rq rt t srq t t s
s rt t s r strs
Ps t t srs t t rrt t
tr t rst t tr
n = -
1
2
· n
3
0
· r
eff
· E,
t t trs rrt n
0
t t tr tsr
r
eff
t tr strt E st t t tr s rst
t t t s tt trs s
t tr s ts rst s rr tt tr
tr t s rt
ts Ps s r
sts
t t tr s t rt t
rr t tr strt s t t rtr
t trsrt trs r rqr
trsrs t tr ts rr t t
r ts r rqr t rr rtrs r
t t t rss rrs ts t s t s s st
trt st s r s s ts tss t srt
t ss t rrt r rtr tr
t rst stts t rt tr
s ts t tr t rr s t t t
rtss t st ss
r
t Prt ss s
r ts
r t r trsrs Ps t rt
r r s rst
t t ts trs rts s rrt
r rr rts
ts r tr rr rt st t rsts t tt
rs str s s
r r rt t tr r t
s rt t s t rt t s r
t rs
tstt rt t rrt tt s r
trt ts tstt trt
n = n
0
+ n
2
I.
s s t rs ts str r ss n
2
> 0
tst s s str t ts
Ps t P t r rrt n
2
s t
tr s st t sr s s t s r str
r tst sr s s s r t
r r t s t rt rssr r t
st r str tr rss t srtr s
tr
tr s t tt s r s st t s r
t s s
B =
2
n
2
I(z) dz
t Prt ss s
r ts
t t r rrt n
2
tst I(z) t s t s s
ss r r ts r t t str qt
s t r sr r r srs s t tr t
r r t
stt t tr t rrt
r st ts tss s s
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- Quote paper
- Martin Schmidberger (Author), 2013, Pumping Yb:YAG thin-disks at 940 nm and the Zero-Phonon-Line, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/288672
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