changes with concentration from about 3.9 ns at low concentration (10~5 mol/dm3 ) to about 1 ... between 1 and 10 ns. ..... (reduction of input light to 1/e value).
Appl. Phys. B 40,85-93 (1986)
*
n r J a H
/\PPII6Q
physics
Physics B S Ä © Springer-Verlag 1986
Saturable Absorbers with Concentration-Dependent Absorption Recovery Time A . Penzkofer Naturwissenschaftliche F a k u l t ä t II - Physik, Universität Regensburg, D-8400 Regensburg, Fed. Rep. Germany Received 28 October 1985/Accepted 22 February 1986
Abstract. The ground-state bleaching of highly concentrated rhodamine 6 G solutions i n methanol is studied with intense picosecond light pulses. The ground-state recovery time changes with concentration from about 3.9 ns at low concentration (10~ mol/dm ) to about 1 ps at high concentration (0.6 mol/dm ). The shortening of the absorption recovery time is determined by the concentration dependent quenching of the S -state population due to unbound dimers and by the intensity dependent longitudinal and transverse amplified spontaneous emission. 5
3
3
1
PACS: 42.65, 42.70, 42.20
The bleaching of absorbing media by intense light pulses is a general phenomenon. The only requirement for reduction of absorption with increasing light signal is that the ground-state absorption cross-section is larger than the excited-state absorption cross-section [1-5]. F o r laser pulse durations At short compared to the absorption recovery time z the bleaching behavior is determined by the input pulse energy density e [6]. A t a pulse energy density s = hv /o
1
NT
1(T
CONCENTRATION
1(T C
10"
t mol/dm ] 3
Fig. 5. Concentration dependence of cross-sections. o from [24], 2n). With increasing dye concentration the sample length reduces. As soon as the beam diameter d becomes larger than the longitudinal interaction length, the amplified spontaneous emission dominates i n a rotational symmetric section transverse to the pump pulse propagation direction. One speaks of transverse amplified spontaneous emission. The solid angle AQ of the transverse amplified spontaneous emission is determined approximately by a cylinder surface of length lj and radius l , that is
NT
10"
5
Ilo
0
10"
A
pl0
CONCENTRATION
NT
3
10"
2
1
C [mol/dm ] 3
0
x
pM
ll
0
L
l 0
Itr
A Q ^ l n l ^ J ^ l n l j J l ^ .
(2)
Fig. 8a-c. Longitudinal amplified spontaneous emission. Curves belong to T =0.01 and r = 0 . 5 e x p ( - < 7 i V / ) . (a) Longitudinal interaction length l . It is identical to sample length /. (b) Solid angle AQ^ for beam diameters. d = 1 mm (solid curve), 0.1 mm (dashed curve), and 0.25 urn (dash-dotted curve), (c) Shortening of Si-state lifetime T ^/T due to longitudinal amplified spontaneous emission. Dye parameters as in Figs. 2 and 5. Refractive indices n from [24]. Solid curve, d = l m m , dashed curve, d = 0.1 mm, dash-dotted curve, d = 25 urn o
ex>F
0
Ittr
0
F
3 >
0
0
0
Si-state lifetime T (equal to T ) to a value shorter than the propagation time t = nd /c across the beam diameter then the transverse interaction length is limited to l = l ^T c /n. A t very high concentration 0.1 m o l / d m the longitudinal interaction length h,io becomes comparable and shorter than the pump laser wavelength (Fig. 8a, / = 0.49 |im for C = 0.6 mol/dm ). Under these conditions the transverse interaction length reduces to the diffraction length l = l /sm9 ~lj n/X . The relevant transverse interaction length is lj = mm(d J ,l ). A n illustration of the longitudinal and transverse solid angles of amplified spontaneous emission is given i n Fig. 7. The longitudinal and transverse interaction lengths, l and l , together with the sample length / and beam diameter d are indicated. A theoretical analysis of the longitudinal forward amplified spontaneous emission is given i n [27]. A
3
ptr
htr
p
3
0
0
0
3
3
D
Ilo
D
ao
L
t r
Itl0
The maximum transverse interaction length l is approximately given by the beam diameter d . If the process of amplified spontaneous emission reduces the
3
IJo
Itr
0
0
p
D
Extension of the theory of pump pulse propagation under conditions of longitudinal and transverse amplified spontaneous emission leads to a very time consuming computer program. Here were restrict to estimate the absorption recovery time under conditions of longitudinal and transverse amplified spontaneous emission (shortening of S -state lifetime) from a crude analytical analysis [27, 28]. The depopulation of the S state (level 3 of Fig. 4) after passage of the pump pulse is considered (time region t>t ~At /2). The population density N [cm ] decays due to radiative and radiationless relaxation [time constant T , first term of (3)] and amplified x
1
- 3
0
L
with t Sili,io fulfilled at lower concentration). In an intermediate concentration region (d >l ) the shortening is so large that the transverse propagation distance within T becomes shorter than d and 0
Itr
0
p
D
Iftr
0
p
Ijtr
D
±
L
Iftr
I 0
>
±
I tr
±
Iftr
3 > ±
D
F
3 > 1
f
0
t
htr
0
3
T
CONCENTRATION
C
ljo
1
0
1 1—I 1 I I I
I
1
1 1—I I I I I
I
I 10
I
I
I mol/dm ] 3
Fig. 9a-c. Transverse amplified spontaneous emission. Curves belong to T = 0.01 and T=0.5 exp(-(7 AT /). (a) Transverse interaction length l . (b) Solid angle AQ for three different beam diameters. d = 1 mm (solid curve), 0.1 mm (dashed curve), and 25 jam (dash-dotted curve), (c) Shortening of S -state lifetime 3 , I / F due to transverse amplified spontaneous emission. Dye parameters as in Fig. 8. Beam diameters as in (b) o
ex>F
Itr
3
L
0
1
t
T
[25]. The fluorescence lifetime r is included in Fig. 6 (Trad- 4.3 ns). Figure 8 illustrates the longitudinal amplified spontaneous emission. The bleached transmission is set to F
T=0.5exp[-(j
eXfF
iV3(to,/j/2)q.
In F i g . 8a the longitudinal interaction length Z = min(/, Z ) is shown. It is equal to /. The solid angle AQp (1), is depicted i n Fig. 8b for three different beam diameters d = l mm, 0.1 mm, and 25 Jim. The shortening of the S^state lifetime T | / T is given by the curves in Fig. 8c. A t low concentration (small AQ^) the S state lifetime shortening is small. I n an intermediate concentration range (AQ^ large, x large) the lifetime shortening is maximal. A t very high concentrations z becomes short and the lifetime shortening by amplified spontaneous emission reduces. The situation of transverse amplified spontaneous emission is displayed i n Fig. 9 for 7 l o
eff
0
3
(
f
x
F
eXsF
Ar3(t ,/ /2)/]. 0
/
I
BLEACHING
I I III
RATIO
I
I I I I il
100
Texp ( o
N l)/T
e xF
3
0
Fig. 10. Intensity dependence of Si-state lifetime. The lifetime shortenings T | | / T , T 3 >
F
3 J 1
/ T , and T / T = ( T / T „ H - T ^ A S , ! f
A
F
F
3 j
- 1
)
- 1
are plotted versus the bleaching ratio TQxp(a N l)/T . T = 0.01. d = \ mm. The parameters for C = 0.04 mol/dm are used exF
3
3
o
r=0.5exp[-(7
I
L 1
F
0
0
limits the shortening. A t high concentrations the transverse interaction length is limited by diffraction and Tp decreases. The lifetime shortening by amplified spontaneous emission reduces. In the described model of F i g . 4 the S -state lifetime T is equal to the absorption recovery time x
3
needed value by use of a thin cell of variable thickness. The dye rhodamine 6 G i n methanol with variable absorption recovery time may be applied as saturable absorber i n mode-locked dye lasers or for pulse shortening of second harmonic light pulses of modelocked Nd-glass and N d - Y a g lasers. The concentration quenching of the S -state lifetime is a general phenomenon [11, 12] and it should be possible for many dyes to tailor the absorption recovery time to the experimental needs. The use of highly concentrated dyes i n thin cells of variable thickness as saturable absorbers may be very interesting i n situations where saturable absorbers with fast monomeric absorption recovery time are not available. In recently reported experiments the occurance of strong transverse amplified spontaneous emission was applied to picosecond-pulse generation [30-33]. x
In F i g . 6 a calculated T curve is included for a laser beam diameter of d = 1 m m and T=0.5exp[-(7 N3(to///2)/]. The curve aggrees reasonably with the x points. The correct description of the low absorption recovery times at 10" m o l / d m and 4 x 10" m o l / d m and the equality of absorption recovery time and fluorescence lifetime at high concentrations should be noticed. The strong dependence of x on the beam diameter (Fig. 9) gives a possibility to change the absorption recovery time by changing the beam diameter (focusing). The intensity dependence of the absorption recovery time is illustrated i n Fig. 10. The S -state lifetime shortenings T | | A F > T ,±AF> and T / T versus normalized transmission T x exp(cr , N l)/T is plotted for a concentration of C = 4 x 10" m o l / d m and a beam diameter of d = 1 mm. A t low intensities (T->T = 0.01) no amplified spontaneous emission occurs. A t high intensities (larger T/T values) the longitudinal and the transverse amplification of spontaneous emission shorten the S -state lifetime. The longitudinal shortening levels off when the penetration length Z becomes equal to /. The transverse shortening is finally limited by the transverse light propagation time. The transverse amplified spontaneous emission was studied experimentally for the 0.04 molar rhodamine 6 G solution. The dye was contained in a glass cell and the sideward fluorescence was imaged to a photodetector. Strong emission occured transverse to the direction of pump pulse propagation within an opening angle of about 3 degree. The total light emission within this angle summed up over the circumfirence of emission was estimated to be about 50% of the input pump light. A
0
eXiF
A
2
3
2
3
A
t
3>
A
3
ex F
3
F
0
2
3
Acknowledgements. The author is grateful to Prof. W . Kaiser for helpful discussions. He thanks the "Deutsche Forschungsgemeinschaft" for financial support and the "Rechenzentrum" of the University for disposal of computer time.
0
0
0
t
eff
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
4. Conclusions
14.
The absorption recovery time of rhodamine 6 G i n methanol may be varied between about 3.9 ns at low concentration to about 1 ps at high concentration. The change of absorption recovery time along concentration is due to intensity independent S -state lifetime quenching by dimer formation and due to intensity dependent S -state lifetime shortening by longitudinal and transverse amplified spontaneous emission. The small signal transmission may be adjusted to any
15. 16.
t
17. 18. 19.
x
20.
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21. 22. 23. 24. 25.
B. Kopainsky, W . Kaiser: Chem. Phys. Lett. 88, 357 (1982) A . Penzkofer, Y . L u : Chem. Phys. (1986) (to be published) A Penzkofer, W . Falkenstein: Opt. Commun. 16,247 (1976) Y . L u , A . Penzkofer: Chem. Phys. (to be published) J. Wiedmann, A . Penzkofer: Nuovo Cimento 63B, 459 (1981) 26. M . E . Mack: Appl. Phys. Lett. 15, 166 (1969) 27. A Penzkofer, W . Falkenstein: Opt. Quant. Electron. 10,399 (1978) 28. A . Penzkofer, W . Blau: Opt. Quant. Electron. 15,325 (1983)
29. W . Falkenstein, A . Penzkofer, W . Kaiser: Opt. Commun. 27, 151 (1978) 30. H J . Polland, T . Elsaesser, A . Seilmeier, W . Kaiser: Appl. Phys. B32, 53 (1983) 31. Zs. Bor, S. Szatmari, A Müller: Appl. Phys. B32,101 (1983) 32. T. Elsaesser, H J . Polland, A Seilmeier, W . Kaiser: I E E E J. QE-20, 191 (1984) 33. S. Szatmari, F . P . Schäfer: Opt. Commun. 49, 281 (1984) 34. H . E . Lessing, A . von Jena: In: Laser Handbook, Vol. 3, ed. by M . E . Stitch (North-Holland, Amsterdam 1979) p. 821
