¹Faculty of Physics, University of Regensburg, Regensburg, Germany

²Institute of Biology/Experimental Biophysics, Humboldt University to Berlin, Berlin, Germany

³Department of Exact Sciences/Biophysics, Vrije Universiteit, Amsterdam, The Netherlands

Email: ^*alfons.penzkofer@physik.uni-regensburg.de

Copyright © 2014 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received 7 January 2014; revised 7 February 2014; accepted 15 February 2014

Abstract

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 w_0P of second harmonic pulses of a mode-locked titanium sapphire laser at wavelength λ_P = 400 nm is determined by nonlinear energy transmission measurement T_E through the dye ADS084BE (1,4-bis(9-ethyl-3-carbazovinylene)-2-methoxy-5-(2’-ethyl-hexyloxy)-benzene) in tetrahydrofuran. T_E(w_0P) calibration curves are calculated for laser pulse peak energy density reading w_0P from measured pulse energy transmissions T_E. The ground-state absorption cross-section σ_P and the excited-state absorption cross-section σ_ex at λ_P, 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 T_E through RetA as a function of laser input peak energy density w_0P. 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 σ_P at λ_P [σ(λ) = α(λ)σ_P/α_P].

Keywords:Laser Pulse Peak Energy Density Determination; Ground-State Absorption Cross-Section Determination; Excited-State Absorption Cross-Section Determination; Saturable Absorption; ADS084BE Dye; Histidine Kinase Rhodopsin HKR1; Retinal Schiff Base RetA Cofactor; Number Density Determination

1. 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 T₀ of ADS084BE in THF.

The energy transmission, T_E(w_0P), of picosecond titanium sapphire second harmonic laser pulses (λ_P = 400 nm, Δt_P ≈ 5 ps) through retinal Schiff base RetA in pH 7.4 HEPES/DDM buffer (20 mM 2-[4-(2-hydroxyethyl)- 1-pipererazin-1-yl]ethansulfonic acid, 100 mM NaCl, 10 vol-% glycerol containing 0.03 m/v-% DDM (n-dodecyl-ß-D-maltoside)) of the blue-light adapted rhodopsin fragment of the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii [6] was measured to determine its ground-state absorption cross-section σ_P, excited state absorption cross-section σ_ex, and number density N₀ (concentration C₀ = N₀/N_A where N_A is the Avogadro constant). Knowing the absolute absorption cross-section of RetA at the fixed wavelength λ_P, its whole absorption cross-section spectrum is obtained by measuring the absorption coefficient spectrum α(λ) with a conventional spectrophotometer and calculation of the absorption cross-section spectrum by the relation since the number density of RetA is given by. The absorp

a: of HKR1 rhodosin. b: mean excited-state lifetime [7] . Abbreviations: M_m: molar mass. η: viscosity. ρ: mass density. V_m: molecule volume. J: temperature. k_B: Boltzmann constant. λ_P: pump laser wavelength. Δt_p: pump laser pulse duration (FWHM). σ_p: ground-state absorption cross-section at pump laser wavelength. σ_ex: excited-state absorption cross-section at pump laser wavelength. τ_F: fluorescence lifetime. τ_FC: Franck-Condon relaxation time. τ_ex: higher excited-state lifetime. τ_or: molecular reorientation time.

tion cross-section spectrum of RetA was needed in the analysis of the photo-dynamics of HKR1 rhodopsin [7] . 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.

2. 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-BaB₂O₄ 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 S₀ ground-state. Its population number density is N₁. Level 2’ is the excited Franck-Condon state in the S₁ band (population number density N_2’). Level 2 is the thermally relaxed state in the S₁ band (population number density N₂). Level 3 is a higher excited state in the singlet band S_n (population number density N₃). σ_P indicates the ground state absorption cross-section at the pump laser at wavelength λ_P (frequency where c₀ is the vacuum light velocity). σ_ex denotes the excited absorption cross-section for S₁-S_n transition of the pump laser at the wavelength λ_P. τ_FC is the Franck-Condon relaxation time within the S₁ 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 (,. The pump pulse energy transition through the sample is defined as

, (1)

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 Table1

3. Results and Discussion

3.1. 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 T₀ (ground-state absorption cross-section σ_P = 2.236 × 10⁻¹⁶ cm², sample length ℓ = 0.2 cm). The dye parameters used in the calculations are listed in Table1 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 cm².

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 T₀(l_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).

3.2. 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 T₀ = 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 cm² and σ_ex = (1.29 ± 0.2) × 10⁻¹⁶ cm². The molar absorption coefficients [9] are dm³∙mol⁻¹∙cm⁻¹ and dm³∙mol⁻¹∙cm⁻¹. The RetA number density of the used sample is obtained by the relation (sample length ℓ = 0.2 cm) giving N₀ = 9.1 × 10¹⁵ cm⁻³ (concentration C₀ = 1.51 × 10⁻⁵ mol∙dm⁻³).

The complete absorption cross-section spectrum σ(λ) of RetA is shown in Figure 7. It was obtained by measuring the transmission spectrum T(λ) of RetA with a spectrophotometer (Cary 50 from Varian), transferring it to the absorption coefficient spectrum α(λ) by the relation where ℓ is the sample length, and finally converting α(λ) to σ(λ) by the relation.

4. 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 N₀ 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) ≈ T₀).

Acknowledgements

The work was supported by the Deutsche Forschungsgemeinschaft (DFG, HE3824/19-1 and HE3824/29-1 to P. H.). A. P. thanks Prof. F. J. Gießibl for his kind hospitality.

References

NOTES

^*Corresponding author.