Ultrafast Laser Energy Density and Retinal Absorption Cross-Section Determination by Saturable Absorption Measurements

Laser pulse nonlinear transmission measurements through saturable absorbers of known absorption parameters allow the measurement of their energy density. On the other hand, nonlinear transmission measurements of laser pulses of known energy density through absorbing media allow their absorption parameter determination. The peak energy density w0P of second harmonic pulses of a mode-locked titanium sapphire laser at wavelength λP = 400 nm is determined by nonlinear energy transmission measurement TE through the dye ADS084BE (1,4-bis(9-ethyl-3-carbazovinylene)-2-methoxy-5-(2’-ethyl-hexyloxy)-benzene) in tetrahydrofuran. TE(w0P) calibration curves are calculated for laser pulse peak energy density reading w0P from measured pulse energy transmissions TE. The ground-state absorption cross-section σP and the excited-state absorption cross-section σex at λP, and the number density N0 of the retinal Schiff base isoform RetA in pH 7.4 buffer of the blue-light adapted recombinant rhodopsin fragment of the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii were determined by picosecond titanium sapphire second harmonic laser pulse energy transmission measurement TE through RetA as a function of laser input peak energy density w0P. The complete absorption cross-section spectrum σλ of RetA was obtained by absorption coefficient spectrum measurement αλ and normalization to the determined absorption cross-section σP at λP [σ(λ) = α(λ)σP/αP].


Introduction
Saturable absorption measurements may be used to determine the peak intensity or peak energy density of laser pulses [1].For peak intensity detection saturable absorbers with ground-state absorption recovery time τ A short compared to the laser pulse duration Δt P are appropriate.For peak energy density detection saturable absorbers (dyes) with fluorescence lifetime τ F long compared to the laser pulse duration are suited.The fast saturable absorber technique was applied to determine the peak intensity of picosecond Nd:glass lasers at 1054 nm [2] (saturable absorber: mode-locking dye A9860 in 1,2-dichloroethane) and ruby lasers [3] (saturable absorber DDI in methanol).The slow saturable absorber technique was applied to measure the peak pulse energy density of Nd:glass lasers (fundamental: BDN I in 1,2-dichloroethane, second harmonic: rhodamine 6G in ethanol, third harmonic: dimethyl POPOP in cyclohexane, fourth harmonic: 9,10-dimethylanthracene in cyclohexane) and ruby lasers (fundamental: DDI in glycerol, second harmonic: dimethyl POPOP in cyclohexane) [4].
Here the peak energy density w 0P of picosecond second harmonic pulses of a mode-locked Ti:sapphire laser (wavelength λ P = 400 nm, pulse duration Δt P ≈ 5 ps) was measured using the dicarbazavinylene-MEH-benzene dye ADS084BE (from American Dye Source Inc., Quebec, Canada) in tetrahydrofuran (THF).The structural formula of ADS084BE is shown in Figure 1.Its absorption cross-section spectrum is shown in Figure 2 (from [5]).Further relevant parameters of ADS084BE required for the calculation of the energy transmission T E versus input pump pulse peak energy density w 0P are collected in Table 1 (from [5]).Two curves of T E (w 0P ) were determined for two different small-signal transmissions T 0 of ADS084BE in THF.
The structural formula of RetA is displayed in Figure 1.Relevant parameters of RetA cofactor in HKR1 rhodopsin for the absorption cross-section determination are collected in Table 1 (from [6] [7]).Detailed information on the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii and its retinal Schiff base cofactor isoforms is found in [6] [7] and is not repeated here.

Experimental
The nonlinear energy transmission measurements were carried out with a mode-locked titanium sapphire laser oscillator-regenerative amplifier system (Hurricane from Spectra Physics).The experimental arrangement is sketched in Figure 3.The laser was operated at wavelength of 800 nm and pulse duration of ≈ 5 ps.The laser pulses were frequency doubled in a BBO crystal (phase-matched β-BaB 2 O 4 crystal, from Eksma, crystal length: 3 mm).The fundamental laser light was blocked off (filter BF) and the second harmonic light passed to the sample S. The second harmonic laser pulse intensity at the sample position S was varied by working with and without lens L1 and with and without neutral density filters NF.The second harmonic laser pulse input pulse signal height S P,in was measured with the silicon photodiode PD1, and the transmitted pulse signal height S P,out was measured with the silicon photodiode PD2.The energy transmission T E through the sample was obtained by the ratio T E = S P,out /S P,in .The fused silica sample cell S of 2 mm path length was either filled with the dye ADS084BE in THF or the HKR1 rhodopsin in pH 7.4 HEPES/DDM buffer.The laser was operated in singleshot mode.It was fired every 10 seconds.Each energy transmission data point shown in Figures 5 and 6 was obtained as an average over about 30 laser shots.The retinal cofactor in HKR1 rhodopsin was brought and kept in the RetA isoform by continuous sample irradiation at 470 nm with an intensity of I exc = 1.5 mW cm −2 using a light emitting diode LED (from Thorlabs).
The absorption dynamics was simulated by using the absorber energy level scheme of Figure 4. Level 1 describes the S 0 ground-state.Its population number density is N 1 .Level 2' is the excited Franck-Condon state in the S 1 band (population number density N 2' ).Level 2 is the thermally relaxed state in the S 1 band (population number density N 2 ).Level 3 is a higher excited state in the singlet band S n (population number density N 3 ).σ P indicates the ground state absorption cross-section at the pump laser at wavelength λ P (frequency = where c 0 is the vacuum light velocity).σ ex denotes the excited absorption cross-section for S 1 -S n transition of the pump laser at the wavelength λ P .τ FC is the Franck-Condon relaxation time within the S 1 band.τ F is the ground-state absorption recovery time constant (fluorescence lifetime).The picosecond pump pulse temporal and spatial intensity distribution is assumed to be Gaussian shaped ( ( ) ( ) ( )    where ℓ is the sample length.The equation system for the level populations and the nonlinear pump pulse transmission through the sample is given in [8] and is not repeated here.It was solved numerically.The applied parameters in the calculations are collected in Table 1.

Calibration Curves for Pump Pulse Peak Energy Density Determination
In Figure 5 two calculated energy transmission curves belonging to the dye ADS084BE in THF are shown for two different small-signal transmissions T 0 (ground-state absorption cross-section σ P = 2.236 × 10 −16 cm 2 , sample length ℓ = 0.2 cm).The dye parameters used in the calculations are listed in Table 1.The excited state absorption cross-section σ ex of ADS084BE in THF was fitted to the experimental energy transmission results.For this purpose the T E energy transmission data points were determined with the two photodiodes, PD1 and PD2, as a function of the photodiode signal height S P,in of PD1.T E (S P,in ) was scaled to the input peak energy density abscissa w 0P .In the calculations σ ex was varied until the best agreement between the shapes of experimental T E (S P,in ) data and calculated T E (w 0P ) curves was obtained.The best fit was found for σ ex = 4.35 × 10 −17 cm 2 .After having the calculated calibration curves, the procedure of input pump pulse energy density determination is now the following: A sample of ADS094BE in THF is prepared with small-signal transmission of T 0 ( P ) = 0.115 or 0.409, then the energy transmission T E is measured and w 0P is read from the relevant curve (w 0P abscissa to T E ordinate).

Absorption Cross-Section and Number Density Determination of RetA
The energy transmission measurement results on a HKR1 rhodopsin sample with the retinal Schiff base cofactor in the RetA isoform (blue-light adapted) are displayed in Figure 6.The input peak energy densities for the data points were obtained by subsequent energy transmission measurements under the same experimental conditions on the dye ADS084BE.The solid curves in Figure 6 are calculated energy transmission curves with the fixed parameters of Table 1 for RetA and the varied parameters listed in the caption.Thereby the small signal transmission was set to the experimental value of T 0 = 0.695 and the limiting high pump pulse energy transmission of T e = 0.79.A comparison of the calculated energy transmission curves with the experimental data gives σ P = (2.0 ± 0.3) × 10 −16 cm 2 and σ ex = (1.29 ± 0.2) × 10 −16 cm 2 .The molar absorption coefficients [9]

Conclusions
The presented laser pulse peak energy density calibration curves for ADS084BE at λ P = 400 nm were calculated for a pulse duration of Δt P = 5 ps.But the energy transmission is nearly independent of the pulse duration as long as the laser pulse duration Δt P is short compared to the absorption recovery time τ F and the molecular reorientation time τ or , and longer than the higher excited-state relaxation time τ ex .Therefore they may be used with reasonable accuracy in the laser pulse duration range of 100 fs < Δt P < 50 ps (see ADS084BE parameters of Table 1).
The described method of ground-state absorption cross-section σ P , excited-state absorption cross-section σ ex , and absorbing entity number density N 0 determination by T E (w 0P ) measurement and numerical T E (w 0P ) simulation of the excitation an relaxation dynamics for the level-system of Figure 4 with known ground-state absorption recovery time τ F, , approximate molecular reorientation time τ or and approximate higher excited-state recovery time τ ex is generally applicable.It works for samples with σ P > σ ex (saturable absorption [10]) and for samples with σ P < σ ex (reverse saturable absorption [11]).It only fails for samples with σ P ≈ σ ex since in this case, the energy transmission is approximately independent of the pump pulse energy density (T E (w 0P ) ≈ T 0 ).

Figure
Figure 4. Energy level scheme.σ P : ground-state absorption cross-section.σ ex : excited-state absorption cross-section.τ F : ground-state absorption recovery time.τ FC : Franck-Condon relaxation time in first excited state.τ ex : higher excited-state relaxation time.ν P : pump laser frequency. are

Figure 7 .
Figure 7. Absorption cross-section spectrum of RetA cofactor of HKR1 rhodopsin in pH 7.4 HEPES/DDM buffer.Experimental data points of σ P (circle) and σ ex (triangle) at λ P = 400 nm are included.