Dual-Frequency Comb Transient Absorption: Broad Dynamic Range

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Spectroscopy and Photochemistry; General Theory

Dual Frequency Comb Transient Absorption: Broad Dynamic Range Measurement of Femtosecond to Nanosecond Relaxation Processes JunWoo Kim, Byungmoon Cho, Tai Hyun Yoon, and Minhaeng Cho J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00886 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018

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The Journal of Physical Chemistry Letters

Dual Frequency Comb Transient Absorption: Broad Dynamic Range Measurement of Femtosecond to Nanosecond Relaxation Processes JunWoo Kim,† Byungmoon Cho,† Tai Hyun Yoon,*,†,‡ Minhaeng Cho*,†,§ †

Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, Republic of Korea §

‡

Department of Physics, Korea University, Seoul 02841, Republic of Korea

Department of Chemistry, Korea University, Seoul 02841, Republic of Korea *e-mail: [email protected], [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT We experimentally demonstrate a dual frequency comb based transient absorption (DFC-TA) technique, which has a 12 fs time resolution and an ultrafast scan rate. Here, the fast scan rate is achieved by employing the asynchronous optical sampling (ASOPS), which utilizes two independent mode-locked lasers with slightly detuned repetition rates. The ASOPS approach is advantageous because photo-degradation damage of optical sample during TA measurements can be minimized by a gated sampling. We show that the vibrational and electronic population relaxations of near-IR dye molecules in solution that occur in the time range from femtoseconds to nanoseconds can be resolved even with a single time-scan measurement. The phase coherent nature of our dual frequency comb lasers is shown to be the key for successful coherent averaging with femtosecond time resolution preserved over many data acquisitions. We anticipate that the present DFC-TA method without using any pump-probe time delay devices could be of use in developing ultrafast TA-based microscopy and time-resolved coherent multidimensional spectroscopy.

TOC GRAPHICS

KEYWORDS time-resolved spectroscopy, quantum beat, ultrafast dynamics, dual frequency comb, asynchronous optical sampling


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One of the most widely used time-resolved spectroscopic techniques is transient absorption (TA), which provides quantitative information on reaction dynamics of excited molecules in condensed phase. Due to its versatility, TA has been extensively applied to studying intramolecular photochemical reactions1-2 and energy-transfer dynamics in multi-chromophore system3-6 and to developing a microscopy that can visualize the energy-transfer flow in space7-8. Over the past decades, asynchronous optical sampling (ASOPS) technique utilizing two mode-locked lasers with slightly different repetition rates has been shown to be of exceptional use for fast data acquisition of TA signals.9 In ASOPS, the pump-probe time delay is scanned by slightly detuning the repetition rate of two different light sources. Therefore, in contrast to the conventional time-delay generation with mechanical stage, ASOPS does not have any problem associated with variations in time-delay dependent spatial beam quality fluctuation. This is critical in time-resolved spectroscopy of chromophores with very long population decay times. THz spectroscopy is another useful application of this ASOPS, because the electronic or vibrational coherences induced by an impulsive excitation do not require absolute phase relation between any pairs of pulses from the two mode-locked lasers.10-11 Microscopy with the transient property of the system has been demonstrated, which fully employs its fast scan rate advantage.12-13 Recently, the ASOPS has been used for TA measurements of a dye solution,9 but still it has not been widely used for studying chromophores in condensed phases.14 Unlike conventional mode-locked lasers used in all the previous ASOPS studies, optical frequency comb (OFC) has a quite distinctive feature that is the carrier-envelop-offset frequency, fceo, phase-locked to an external reference frequency.15 When fceo of a dual frequency comb (DFC) system is controlled to be zero, the carrier-envelop phase of every pulse is fixed, so that the interference between the two OFCs becomes recordable with ASOPS. The DFC technique has


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been shown to be a useful tool for gas-phase spectroscopy.15 DFC spectroscopy with its fast scan rate and precise timing accuracy provides high frequency-resolution Fourier-transformed molecular spectra.16-17 Still, DFC technique has not been actively employed for measuring electronic transitions of chromophores dissolved in solution, where typical electronic dephasing is very fast on the order of tens of femtoseconds.18-20 To achieve DFC spectroscopy of chromophores in condensed phases, both ultrashort laser pulse and ultrabroad dynamic range detection capability are simultaneously required. Recently, we reported a broadband DFC spectrometer allowing us to measure the electronic absorption and dispersion spectra of dye molecules in solution.21 In this Letter, we propose and demonstrate a novel TA technique based on a broadband DFC system (DFC-TA). The unique properties of the DFC-TA system with fs time resolution, long phase coherence time, and ASOPS capability allow us to demonstrate TA measurements with fast data acquisition rate over 1 kHz, fs-to-ns dynamic range, and coherent averaging over 10000 TA signals, which all contribute to an increase of the signal-to-noise ratio. Our proof-of-principle experiment demonstrates a novel use of DFC-TA technique developed here for studying fs-to-ns population relaxation dynamics with fast scan rate. The two OFC’s denoted as OFC1 and OFC2 in Figure 1 are considered to be pump and probe beams, respectively, in the present DFC-TA. The optical frequency f n of the nth-mode is determined by the repetition rate ( f r ) and the carrier-envelop-offset frequency ( f ceo ) as

f n = nf r + fceo . Here, the repetition frequencies of the OFC1 (pump) and OFC2 (probe) are controlled to be different by ∆f r , i.e., f r ,1 = f r + ∆f r and f r ,2 = f r , respectively. The electric field of the pulse train from OFCj is written as Ej (r, t ) = e

ik j (ωc , j )⋅r −iωc , j t

∞

∑A

n, j

e

− i 2π n f r , j t

+ c.c. ,

(1)

n =−∞


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where the magnitude of wave vector, |k j (ωc , j ) | , is µ (ωc , j )ωc , j / c with refractive index of

µ (ωc , j ) . The carrier (center) frequency of the jth OFC is defined as ωc , j = 2π (nc , j f r , j + f ceo, j ) with the mode number nc , j . The nth Fourier coefficient in Eq. (1) is related to the Fouriertransform of the temporal pulse envelop function (Supplementary note 1). The optical sample interacts with both OFC1 and OFC2 fields so that the interaction Hamiltonian is given as

Hˆ I = −µˆ E(r, t ) , where µˆ is the electric dipole operator and E(r, t ) = E1 (r, t ) + E2 (r, t ) . Then, the third-order pump-probe signal field propagating along the probe (k2) direction can be obtained by

calculating

the

corresponding

third-order

polarization,

P (3) (k 2 , t )

,

i.e.,

E (3) (k 2 , t ) ∝ i P (3) (k 2 , t ) . Using the time-dependent perturbation theory22-23 with the interaction Hamiltonian and electric field for the dual frequency combs, we obtained a theoretical derivation of the DFC-TA signal in terms of frequency-dependent nonlinear response function (see Supplementary note 1 for detailed step-by-step derivations). The DFC-TA signal, which results from the interference between the third-order pump-probe signal field, E (3) (k 2 , t ) , and the probe (OFC2) field, E2 (k 2 , t ) , is found to be (see Supplementary note 1)

 ∞  S DFC −TA (t ) ∝ 2 Re[ E2* (k 2 , t ) E (3) (k 2 , t )] ∝ 2 Im  ∑ A M e− iM ∆ωr t  ,   M =−∞

(2)

where M represents the summation integer. By considering four nonlinear transition pathways contributing to the TA signal, the complex amplitude A M of the Mth oscillating component of which frequency is M ∆ωr is defined as, for a two-level chromophore,

AM ≡

∞

∑

q , n =−∞

Cq[1]+ M ,q ,n + M , n S% (3) (ωc ,2 , M ωr ,1 , −ωc,1 ) +Cq[2]+ M ,q ,n − M ,n S% (3) (ωc ,2 , M ωr ,1 , ωc ,1 ) 


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+Cn[3]+ M ,q ,n ,q − M S% (3) (ωc ,2 , (n − q + M )ωr ,1 , −ωc ,1 ) +Cn[4]+ M ,q ,q − M ,n S% (3) (ωc ,2 , (n − q + M )ωr ,1 , ωc ,2 )  ,

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(3)

where the auxiliary constants C[px,m] ,n with integers p, m, and n are determined by the pulse spectra of the two OFC’s. S% (3) (ω3 , ω2 , ω1 ) is the frequency-dependent nonlinear response function (see Eq. (S12) for its three-dimensional Fourier-transform relation to the time-domain nonlinear response function in Supplementary note 1). To obtain the theoretical expression for the DFCTA signal in Eq. (2), we assumed that the carrier frequencies of the two comb lasers that are on the order of 100 THz are degenerate, i.e., ωc = ωc ,1 = ωc,2 and are much larger than the laser pulse repetition frequency (~100 MHz), i.e., ωc >> ωr . Furthermore, the inequality ωr ,1 >> ∆ωr was also used, because the laser pulse repetition frequency (~100 MHz) is much larger than the difference (~100 Hz) in the two repetition frequencies. Now it should be noted that the dependences of S% (3) (ω3 , ω2 , ω1 ) on the two frequencies,

ω1 and ω3 , are determined by the electronic transition frequencies (~100 THz) and the associated electronic dephasing constants. However, the dependence of S% (3) (ω3 , ω2 , ω1 ) on the remaining frequency ω2 is related to the rate of population decay of the electronically excited state, the coherent vibrational oscillations and dephasings, and ultrafast solvation dynamics. Here, it is interesting to note that the interference term, Re[ E2* (k 2 , t ) E (3) (k 2 , t )] , which is the experimentally measured DFC-TA signal in real time, has a frequency comb structure. Furthermore, the spectral amplitude of the Mth comb tooth at M ∆ωr , denoted as A M in Eq. (2), is determined by both the shape of comb laser pulse spectrum and the third-order response function of the material (optical sample or chromophore). In addition, the comb spacing in the


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frequency domain is ∆ωr , which is on the order of 100 Hz (or ms in time domain). Therefore, the DFC-TA signal whose decay times are determined by ∆ωr (~100 Hz) can be directly measured in real time with photo-detector of which response time is in the range from µs to ms – note that there is no photodetector whose response follows optical frequency. It is this frequency down-conversion effect by a factor of ∆ωr / ωr (~10-6) that is the critical aspect of dual comb spectroscopy differentiating it from the conventional pump-probe or transient absorption measurement methods with a single mode-locked laser combined with time-delay-scanning translational stage or other mechanical delay-scanning device. Although the DFC-TA signal decays on the timescale of µs in laboratory (or recording) time, its decaying pattern is determined by the excited state population decay and vibrational dephasings of vibronically excited modes, which are on the timescales around ps to ns. Therefore, the effective (or molecular relaxation) time is shorter than the laboratory (recording) time by the factor of the same down-conversion constant of ∆ωr / ωr (~10-6). Therefore, our DFC-TA technique with combining interferometric trigger system does not need many meter-long translational stage for ns pump-probe time delay scanning nor highly controllable delay stage for femtosecond timeresolution. This is experimentally demonstrated here in this Letter. Details of our dual frequency comb laser setup just for measuring the linear absorption spectrum of a dye solution were presented and described in ref. 22. Here, a detailed description of our dual OFC-TA apparatus based on two Ti:Sapphire mode-locked lasers operating at around 800 nm is presented. They have an identical bandwidth of 300 nm and pulse-width of 7 fs. We used a multichannel RF frequency synthesizer, which is phase-locked to a GPS-disciplined Rb atomic clock (Figure 1a),


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to provide multiple frequency references for the phase-locking servos to stabilize two degrees of freedom for the OFC1 and OFC2 at f r ,1 = 80.0 MHz + ∆f r and f r ,2 = 80.0 MHz, respectively. fceo was set to be zero, i.e., f ceo = 0.0 Hz, for both OFC’s. Once two frequency degrees of freedom of the OFCs are phase-locked, we can generate a linear time-delay t = n∆t , where ∆t =

∆f r / ( f r2 + f r ∆f r ) ≅ ∆f r / f r 2 , n being an integer, between each pair of the pump and probe pulses. Here, we can tune ∆f r in the range from 2.5 Hz to 1.0 kHz and the detuning range is limited by the dynamic range of the f r -servo controller. The frequency fluctuation of ∆f r is, in our DFC system, as small as or less than 0.1 mHz, which is basically limited by the residual phase error of the phase-locking servo operating at the frequency of 18 fr = 1.440 GHz. The pump and probe pulses are non-collinearly focused at the sample and the probe intensity is recorded at a photodetector (PD2). Here, the spatially separated probe beam (OFC2) propagating along the direction different from that of the pump beam (OFC1) contains the TA signal carrying information on the population dynamics and vibronic relaxations at the pumpprobe time-delay, t = n∆t . In this way, the pump-probe time-delay in our DFC-TA method, increases linearly ( ∆fr > 0 and ∆t > 0 ) from zero to the pulse-to-pulse time interval of the probe pulses given by 1/ fr (12.5 ns in the present work). For measuring TA signals, the phase coherence of the two OFCs is not needed because the TA signal is not sensitive to fceo locking. However, it should be emphasized that we introduce a new interferometric trigger scheme for repeating measurement cycles (coherent averaging). The two pulse trains from the two OFCs are combined at the beam splitter in front of a fast photodetector (PD1). When the OFC1 and OFC2 pulses overlap in time, they would produce strong interference signals with a width of 7 fs at


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every 1/ ∆f r , which can be detected by PD1 and used as a trigger source of the digitizer. This critically differs from previously reported ASOPS TA studies, where optical phase-insensitive and much broader intensity correlation (IC) signal between the two lasers was used as an optical trigger.11,14 Compared to the previous methods, our interferometric triggering system has two advantages. First, the oscillating nature of the interference provides a steep, sharp triggering signal, which minimizes the time jitter much less than 2 fs. The interference pattern recorded at the trigger line with ∆f r = 5 Hz is shown in Figure 1b. Furthermore, since the interference between two light sources is the first order interaction, comparatively small amount of energy is needed for such a triggering. In order to show the time resolution and the performance of our interferometric trigger, the intensity correlation function (ICF) between the two OFC’s was measured with a sum-frequency generation of the two OFC’s at the TA line by replacing the sample with a 20-µm BBO crystal. The full-width at half-maximum of the ICF is found to be 12 fs and the averaged ICF is not broadened at all during the averaging by time jitter (Figure 1b). See Supplementary notes 2 and 3 for more details on the experimental scheme and measurement procedure. Before we present the experimental results obtained with the interferometric trigger DFCTA method, it should be mentioned that the ASOPS-based TA have certain advantages compared with the conventional TA with a single intense fs mode-locked laser combined with time-delay scanning scheme. First of all, the AOSPS makes the spatial beam quality independent on the required time delay. In fact, the spatial beam quality varies a lot when one uses a mechanical stage based time-delay scan, which deteriorates data quality. Thus, the uniform beam quality provided by the ASOPS approach is quite useful for studying transient dynamics at very long relaxation times.24 Secondly, it should be noted that molecular systems (optical samples) are


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often damaged during a given measurement time, due to complicated photochemical and photothermal processes induced by high-energy pulses25 and intense light source, respectively. In contrast, the DFC-TA introduced here is relatively free from such photoexcitation-induced sample damages. For instance, photochemical damage is comparatively negligible in the present DFC-TA due to its low pulse energy ( a few to tens of


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picoseconds) is mostly contributed from electronic population relaxation and rotational dynamics of chromophores in solution. To extract various frequency components contributing to the short-time oscillatory features, we carried out Fourier-transformations of the DFC-TA signals observed in Figure 3a by separately considering the time zones I and II (Figure 3b). Here the noise spectrum is the Fourier transform of the background signal in the time range from − 3 ps to − 1 ps. At short times (

Dual-Frequency Comb Transient Absorption: Broad Dynamic Range

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