Leseprobe
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
Ende der Leseprobe aus 123 Seiten
- Arbeit zitieren
- Martin Schmidberger (Autor:in), 2013, Pumping Yb:YAG thin-disks at 940 nm and the Zero-Phonon-Line, München, GRIN Verlag, https://www.grin.com/document/288672
Ähnliche Arbeiten
Kostenlos Autor werden
✕
Leseprobe aus
123
Seiten
Kommentare