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Estimating the Peak Intesity and Energy Content of Short Duration Pulses Using Saturable Absorbers
Volume 5, number
3
OPTICS CON hIUNICATIONS
June 1972
ESTIMATING THE PEAK INTENSITY AND ENERGY CONTENT OF SHORT DURATION PULSES USING SATURABLE ABSORBERS* R.J.HARRACH, T.D.hlacVICAR, G.I.KACHEN and L.L.STEINh!ETZ Lauvrence Livennore Laboratory, Uf~iversity o f California, Livernlore, California 94550, USA Received 11 April 1972
\Ye describe a simple scheme to estimate the mode-locked pulse peak intensity, beam noise level, and ratio of pulsoto-noise energy from a measurement of the transmission of laser beam energy through various thicknesses of saturable absorber. The filtering process increases this ratio in the transmitted beam, and the necessary trade-off between beam energy attenuation versus pulse-to-noise enhancement is considered.
In a-recent article [l],.Penzkofer et al., have shown that the peak intensity IOof energetic, shortduration laser pulses can be determined from measurements of energy transmitted through a saturable absorber. The cases they consider involve "clean" isolated pulses. Interesting additional results arise when the mode-locked pulse is accompanied by a sub\stantial noise level. By measuring the laser beam ener\gy t~ansmittedthrough various thicknesses of saturable absorber, it is possible to estimate the pulse peak intensity (IO)p, the effective or average intensity (IO), of the noise, and the fraction EO of the total beam energy that is carried by the pulse [2]. The technique consists of splitting the beam from a mode-locked oscillator into a "reference" beam and a "signal" beam, the latter being filtered through different thicknesses of saturable absorber on successive laser shots. Both beams are directed into energy calorimeters, resulting in data on energy transmission T as a function of absorber path length 1 traversed by the signal beam. An adequate theoretical model [2,3] for our purpose is to treat the saturable absorber as a resonant. two-energy-level system of N molecules per cm3, characterized by a saturation intensity, IQt= (2ar)-l (photons/cm2 sec), and a saturation energy density
* Work performed under the auspices of the U.S. Energy Commission.
Atomic
EQt= hvoa01/2a, where a is the absorption cross section per absorber molecule, T is the time required for the absorber to return to equilibrium after excitation, and a. = N o is the small signal absorption coefficient. The laser beam is assumed to have its energy divided between a relatively intense mode-locked pulse and a quasi-continuous low intensity noise component. Further, the laser pulse duration At is assumed to be greater than the absorber recovery time T. Under these conditions, the intensity transmission function T(z) = I(z)/Io describing an optically thick absorber, for which the laser beam intensity I is a function of the penetration distance z into the absorbing medium, satisfies the transcendental equation [29 31 In [TdT(z)l + (Id/,t)[I
- nz)1
=0
.
(1)
Here lois the incident beam intensity in the boundary plane z = 0 of the absorbing medium, and To = exp [- q,z] is the transmission function for low level (IOImt. Solutions for T(z) as a function of absorber length z are shown in fig. 1 for a variety of values of IdIQf' 175
Volume 5, number 3
OPTICS COkihlUNICATIONS
Pig. 1. Transmitted intensity T =1(1)/10as a function of absorber thickness I, for particular values of the normalized incident intensity, I&,~.(aO= N D is the small signal absorption coefficient.) When the input beam intensity has distinct pulse @) and noise (n) components, describable by (IO)p and (Io),, then the resulting T(z) will be a linear superposition of curves of the type in fig. 1, weighted according to the fractional beam energy in each component. If e0 is the fraction of total beam energy that is carried by the pulse, then the observed transmission should be given by
(The intensity'transmission function is the same as the energy transmission function, since the change in pulse width on traversing the absorber is negligible for our stated conditions.) 176
.
June 1972
Our experiments measured the transmission of Ndglass laser radiation through various thicknesses of undiluted Kodak 9740 saturable dye*. For this dye, u x 2 X 10-l6 cm2/molecule and 7 = 8 X 10-l2 sec, so the saturation intensity at the Nd-glass laser wavelength of ho = 1.06 pm = c/vd is I,thvo = 4.5 X lo7 W/cm2, and the saturation energy density is EQt= (0.47)a01 ( m ~ / c r n ~The ) . laser oscillator, described in ref. [4], was Q-switched and mode-locked by a 2 mm cell of this same dye in a 1:10 solution of chlorobenzene, and was frequency selected using intracavity etalons. The laser output beam from this oscillator consists of an intense 70 psec pulse (determined by two-photon fluorescence) per 10 nsec period of the output beam (200 nsec total duration), in a 4 mm diameter beam. The transmitted energy was measured with an ITT F-4000 photodiode with an integrating circuit. Transmission data for dye thicknesses as large as 3 cm were recorded, as shown in fig. 2, using the full 200 nsec pulse train without amplification. Satisfactory agreement with the data is obtained = 5 IUt, (IO), = (0.05) IUt, and by by taking (Io)p taking the fractional energy in the pulse to be eo= 0.1 5 to 0.20. While the fit to the data is neither highly precise nor unique, reasonably good values are obtained because the different parameters (IO)P,(Io)n, and eo have a sensitive effect on different portions of the curve. For aO1> 1 the slope of the In T(z) versus 1 curve is primarily determined by the choice of (IO)p, while the actual range of values of In T(z) in this region is sensitive to the choice of eo. Similarly, for aO1< 1, the most relevant parameters are (IO),an'd (1 - e0). For our saturable dye, % was measured t o be about 3 cm-l, so the q,l values ranged from near zero to 9. The conclusions we draw from the data fit are therefore that the peak intensity of the modelocked pulse (averaged over the full pulse train) is 2.25 X lo8 w/cm2, the noise intensity is at least 100 times smaller, and the fraction of beam energy carried by the pulse is only 15 to 20%. These values are consistent with the required saturation energy density to penetrate 3 cm of dye, and with the total energy output and beam diameter of this laser. Filtering the beam through the saturable dye increases the fraction of beam energy carried by the
* Eastman Kodak data release. The undiluted solution consists of a proprietary dye of molecular weight 762 dissolved in chlorobenzene.
June 1972
OPTICS COhIhIUNICATIONS
Volume 5, number 3
-(
this becomes
-
- eO)laoT
~~OI
x exp {-lo[ 1 - T~(OI/I.~,)
-1
-
(4)
In our case these inequalities are not well satisfied, so we solve for E(C) in eq. (3) numerically. This result, along with the result for total beam energy attenuation is shown in fig. 3. For example, after filtering the beam through 10 mm of Kodak 9740 dye, the beam energy is attenuated to about 14%of its initial value, and about 68% of the remaining energy resides in the pulse.
--
-
--
1+
=i I-
0.01
0.001
-
0
I 2
4I
I 8
I
6
10
Fig. 2. Fit t o the data for transmitted energy as a function o f = absorber thickness 1 (cm), using ( 1 0 ) ~= 5 Isat, (0.05)lsat, and € 0 as indicated. The measured value of or0 is 3 cm-1. Data points have been corrected for a residual transmission of 0.3% that is present even for very large a01 values.
pulse, since the noise is more severely attenuated. Af) ter filtering through a thickness I , the fraction ~ ( lof ' transmitted beam energy in the pulse is given by
40 = €0 Tp(l)/[€oTp(O
+ (1
-ao) Tn(OI
.
(3)
In the special case that (Io)p3 IUtwhile (IO),
Fig. 3. Calculated fraction € ( I ) of energy in the pulse, and total energy attenuation, as a function of absorber tllickness, for the case ( 1 0 ) ~= 5 Isat, ( I o ) ~= (O.OS)lsat, and € 0 as indicated.
In conclusion, it has been shown that filtering the beam from a mode-locked laser through a fastrelaxing saturable dye provides estimates of the peak pulse intensity, average noise level, and fraction of beam energy carried by the pulse. hlore sophisticated and accurate methods of determining the fraction of
.-
Volume 5, number 3
OPTICS COhIhlUNICATIONS
energy carried by the pulse have been described in the literature [ S ] . The method given here is recommended by its straight-forward simplicity, and by the fact that while obtaining the diagnostic information, the pulse-to-noise ratio is simultaneously improved.
References [ l ] A.Penzkofer, D.von der Linde and A.hubereau, Opt. Commun. 4 (1972) 377. [2] R.J.lIarrach, T.D.hIacVicar, G.I.Kachen and L.L.Steinmetz, Univ. of California Rad. Lab., Rept. 5 1008 (1971)., [3] R.W.Keyes, IBhl J. Res. Develop. 7 (1963) 334;
June 1972
E.U.Condon, Proc. Natl. Acad. Sci. 5 2 (1964) 635; hl.Iiercher, .4ppl. Opt. 6 (1967) 947; A.C.Selden, Brit. J. Appl. Phys. 18 (1967) 743; J.D.hIacomber, J. Appl. Phys. 38 (1967) 3525. [4] G.I.Kachen and J.O.Kysilka, lEEE I. Quantum Electron. QE-6 (1970) 84. [5] D.II.Auston, Appl. Phys. Letters 18 (1971) 249; R.C.Eckardt and C.II.Lee, Appl. Phys. Letters 15 (1969) 425; P.hl.Rentzepis, C.J.hIitschele and A.C.Saxman, Appl. Phys. Letters 17 (1970) 122; G.Dubc', Appl. Phys. Letters 18 (1971) 69; D.von der Linde, IEEE J. Quantum Electron. QE-8 (1972) 328; hl.A.Duguay, J.W.IIansen and S.L.Shapiro, IEEE J. Quantum Electron. QE-6 (1970) 725.
3
OPTICS CON hIUNICATIONS
June 1972
ESTIMATING THE PEAK INTENSITY AND ENERGY CONTENT OF SHORT DURATION PULSES USING SATURABLE ABSORBERS* R.J.HARRACH, T.D.hlacVICAR, G.I.KACHEN and L.L.STEINh!ETZ Lauvrence Livennore Laboratory, Uf~iversity o f California, Livernlore, California 94550, USA Received 11 April 1972
\Ye describe a simple scheme to estimate the mode-locked pulse peak intensity, beam noise level, and ratio of pulsoto-noise energy from a measurement of the transmission of laser beam energy through various thicknesses of saturable absorber. The filtering process increases this ratio in the transmitted beam, and the necessary trade-off between beam energy attenuation versus pulse-to-noise enhancement is considered.
In a-recent article [l],.Penzkofer et al., have shown that the peak intensity IOof energetic, shortduration laser pulses can be determined from measurements of energy transmitted through a saturable absorber. The cases they consider involve "clean" isolated pulses. Interesting additional results arise when the mode-locked pulse is accompanied by a sub\stantial noise level. By measuring the laser beam ener\gy t~ansmittedthrough various thicknesses of saturable absorber, it is possible to estimate the pulse peak intensity (IO)p, the effective or average intensity (IO), of the noise, and the fraction EO of the total beam energy that is carried by the pulse [2]. The technique consists of splitting the beam from a mode-locked oscillator into a "reference" beam and a "signal" beam, the latter being filtered through different thicknesses of saturable absorber on successive laser shots. Both beams are directed into energy calorimeters, resulting in data on energy transmission T as a function of absorber path length 1 traversed by the signal beam. An adequate theoretical model [2,3] for our purpose is to treat the saturable absorber as a resonant. two-energy-level system of N molecules per cm3, characterized by a saturation intensity, IQt= (2ar)-l (photons/cm2 sec), and a saturation energy density
* Work performed under the auspices of the U.S. Energy Commission.
Atomic
EQt= hvoa01/2a, where a is the absorption cross section per absorber molecule, T is the time required for the absorber to return to equilibrium after excitation, and a. = N o is the small signal absorption coefficient. The laser beam is assumed to have its energy divided between a relatively intense mode-locked pulse and a quasi-continuous low intensity noise component. Further, the laser pulse duration At is assumed to be greater than the absorber recovery time T. Under these conditions, the intensity transmission function T(z) = I(z)/Io describing an optically thick absorber, for which the laser beam intensity I is a function of the penetration distance z into the absorbing medium, satisfies the transcendental equation [29 31 In [TdT(z)l + (Id/,t)[I
- nz)1
=0
.
(1)
Here lois the incident beam intensity in the boundary plane z = 0 of the absorbing medium, and To = exp [- q,z] is the transmission function for low level (IO
Volume 5, number 3
OPTICS COkihlUNICATIONS
Pig. 1. Transmitted intensity T =1(1)/10as a function of absorber thickness I, for particular values of the normalized incident intensity, I&,~.(aO= N D is the small signal absorption coefficient.) When the input beam intensity has distinct pulse @) and noise (n) components, describable by (IO)p and (Io),, then the resulting T(z) will be a linear superposition of curves of the type in fig. 1, weighted according to the fractional beam energy in each component. If e0 is the fraction of total beam energy that is carried by the pulse, then the observed transmission should be given by
(The intensity'transmission function is the same as the energy transmission function, since the change in pulse width on traversing the absorber is negligible for our stated conditions.) 176
.
June 1972
Our experiments measured the transmission of Ndglass laser radiation through various thicknesses of undiluted Kodak 9740 saturable dye*. For this dye, u x 2 X 10-l6 cm2/molecule and 7 = 8 X 10-l2 sec, so the saturation intensity at the Nd-glass laser wavelength of ho = 1.06 pm = c/vd is I,thvo = 4.5 X lo7 W/cm2, and the saturation energy density is EQt= (0.47)a01 ( m ~ / c r n ~The ) . laser oscillator, described in ref. [4], was Q-switched and mode-locked by a 2 mm cell of this same dye in a 1:10 solution of chlorobenzene, and was frequency selected using intracavity etalons. The laser output beam from this oscillator consists of an intense 70 psec pulse (determined by two-photon fluorescence) per 10 nsec period of the output beam (200 nsec total duration), in a 4 mm diameter beam. The transmitted energy was measured with an ITT F-4000 photodiode with an integrating circuit. Transmission data for dye thicknesses as large as 3 cm were recorded, as shown in fig. 2, using the full 200 nsec pulse train without amplification. Satisfactory agreement with the data is obtained = 5 IUt, (IO), = (0.05) IUt, and by by taking (Io)p taking the fractional energy in the pulse to be eo= 0.1 5 to 0.20. While the fit to the data is neither highly precise nor unique, reasonably good values are obtained because the different parameters (IO)P,(Io)n, and eo have a sensitive effect on different portions of the curve. For aO1> 1 the slope of the In T(z) versus 1 curve is primarily determined by the choice of (IO)p, while the actual range of values of In T(z) in this region is sensitive to the choice of eo. Similarly, for aO1< 1, the most relevant parameters are (IO),an'd (1 - e0). For our saturable dye, % was measured t o be about 3 cm-l, so the q,l values ranged from near zero to 9. The conclusions we draw from the data fit are therefore that the peak intensity of the modelocked pulse (averaged over the full pulse train) is 2.25 X lo8 w/cm2, the noise intensity is at least 100 times smaller, and the fraction of beam energy carried by the pulse is only 15 to 20%. These values are consistent with the required saturation energy density to penetrate 3 cm of dye, and with the total energy output and beam diameter of this laser. Filtering the beam through the saturable dye increases the fraction of beam energy carried by the
* Eastman Kodak data release. The undiluted solution consists of a proprietary dye of molecular weight 762 dissolved in chlorobenzene.
June 1972
OPTICS COhIhIUNICATIONS
Volume 5, number 3
-(
this becomes
-
- eO)laoT
~~OI
x exp {-lo[ 1 - T~(OI/I.~,)
-1
-
(4)
In our case these inequalities are not well satisfied, so we solve for E(C) in eq. (3) numerically. This result, along with the result for total beam energy attenuation is shown in fig. 3. For example, after filtering the beam through 10 mm of Kodak 9740 dye, the beam energy is attenuated to about 14%of its initial value, and about 68% of the remaining energy resides in the pulse.
--
-
--
1+
=i I-
0.01
0.001
-
0
I 2
4I
I 8
I
6
10
Fig. 2. Fit t o the data for transmitted energy as a function o f = absorber thickness 1 (cm), using ( 1 0 ) ~= 5 Isat, (0.05)lsat, and € 0 as indicated. The measured value of or0 is 3 cm-1. Data points have been corrected for a residual transmission of 0.3% that is present even for very large a01 values.
pulse, since the noise is more severely attenuated. Af) ter filtering through a thickness I , the fraction ~ ( lof ' transmitted beam energy in the pulse is given by
40 = €0 Tp(l)/[€oTp(O
+ (1
-ao) Tn(OI
.
(3)
In the special case that (Io)p3 IUtwhile (IO),
Fig. 3. Calculated fraction € ( I ) of energy in the pulse, and total energy attenuation, as a function of absorber tllickness, for the case ( 1 0 ) ~= 5 Isat, ( I o ) ~= (O.OS)lsat, and € 0 as indicated.
In conclusion, it has been shown that filtering the beam from a mode-locked laser through a fastrelaxing saturable dye provides estimates of the peak pulse intensity, average noise level, and fraction of beam energy carried by the pulse. hlore sophisticated and accurate methods of determining the fraction of
.-
Volume 5, number 3
OPTICS COhIhlUNICATIONS
energy carried by the pulse have been described in the literature [ S ] . The method given here is recommended by its straight-forward simplicity, and by the fact that while obtaining the diagnostic information, the pulse-to-noise ratio is simultaneously improved.
References [ l ] A.Penzkofer, D.von der Linde and A.hubereau, Opt. Commun. 4 (1972) 377. [2] R.J.lIarrach, T.D.hIacVicar, G.I.Kachen and L.L.Steinmetz, Univ. of California Rad. Lab., Rept. 5 1008 (1971)., [3] R.W.Keyes, IBhl J. Res. Develop. 7 (1963) 334;
June 1972
E.U.Condon, Proc. Natl. Acad. Sci. 5 2 (1964) 635; hl.Iiercher, .4ppl. Opt. 6 (1967) 947; A.C.Selden, Brit. J. Appl. Phys. 18 (1967) 743; J.D.hIacomber, J. Appl. Phys. 38 (1967) 3525. [4] G.I.Kachen and J.O.Kysilka, lEEE I. Quantum Electron. QE-6 (1970) 84. [5] D.II.Auston, Appl. Phys. Letters 18 (1971) 249; R.C.Eckardt and C.II.Lee, Appl. Phys. Letters 15 (1969) 425; P.hl.Rentzepis, C.J.hIitschele and A.C.Saxman, Appl. Phys. Letters 17 (1970) 122; G.Dubc', Appl. Phys. Letters 18 (1971) 69; D.von der Linde, IEEE J. Quantum Electron. QE-8 (1972) 328; hl.A.Duguay, J.W.IIansen and S.L.Shapiro, IEEE J. Quantum Electron. QE-6 (1970) 725.