Design and Characterization of a Femtosecond ... - OSA Publishing

Design and Characterization of a Femtosecond Fluorescence Spectrometer Based on Optical Kerr Gating S. ARZHANTSEV and M. MARONCELLI* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802

Design and characterization of a general-purpose spectrometer for recording time-resolved emission spectra of typical fluorescent species is described. The system is based on a high repetition rate amplified Ti : sapphire system, an optical Kerr shutter for gating the emission, and a polychromator plus charge-coupled device (CCD) detection system. Using 1 mm of liquid benzene as the Kerr medium, and optics designed to provide high polarization quality, emission spectra of dilute solutions of solutes with nanosecond lifetimes can be recorded with good signal-to-noise ratios. The current spectrometer uses excitation wavelengths near 390 nm and provides spectra over the wavelength range 400–650 nm with 4 nm resolution and instrument response times of 450 fs (full width at half-maximum, FWHM). Selected applications are described to demonstrate the utility of this instrument. Index Headings: Instrument design; Time-resolved spectroscopy; Fluorescence.

INTRODUCTION Time-resolved emission is often used for characterizing the dynamics of chemical and biological systems in the picosecond and femtosecond time domains.1,2 In many applications, kinetic information recorded at one or a few selected emission wavelengths is sufficient, but for studying complex or low-barrier reactions, or for examining continuous relaxation processes such as solvation dynamics,3 complete time- and wavelength-resolved spectra are required. In the present report we describe our approach to obtaining such data with sub-picosecond time resolution using an apparatus based on optical Kerr gating. A number of methods are presently available for measuring time-resolved emission spectra (Table I). These methods can be divided into two categories depending on whether single-wavelength or multi-wavelength data are collected. In the case of single-wavelength detection, temporal emission decays are recorded at selected wavelengths and time-resolved spectra are subsequently reconstructed by an appropriate relative normalization procedure.4 The most widely used single-wavelength technique is time-correlated single-photon counting (TCSPC).5,6 When coupled to stable, high repetition rate lasers, the high sensitivity, large dynamic range, and statistical quality of the data obtained make TCSPC the method of choice in many applications where sub-nanosecond time resolution is required. Single-channel methods based on frequency-domain analysis of emission excited by modulated sources are also popular, especially among the biophysical community,1 and complement TCSPC work.7 The main disadvantage to both TCSPC and frequencydomain methods is that instrument response times cannot Received 10 August 2004; accepted 20 October 2004. * Author to whom correspondence should be sent.

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Volume 59, Number 2, 2005

be pushed beyond the tens of picoseconds range. For higher time resolution, fluorescence upconversion8–11 is the single-wavelength method most often employed. Response times of less than 200 fs can be readily achieved,12–17 making fluorescence upconversion the best option when temporal resolution is of primary importance. Offsetting this primary advantage, fluorescence upconversion requires the most exacting optical alignment of the fluorescence methods, and only low to moderate sensitivities are afforded by the technique. Finally, if details of the spectral evolution, for example, widths and especially line shapes, are of interest, then all singlewavelength methods suffer from the disadvantages of low spectral resolution (typically 10–20 wavelengths are recorded) and uncertainties in the reconstruction processes.† In such cases multichannel detection of time-resolved spectra is advantageous. The phase-matching requirements of the upconversion process render it most easily employed in a single-wavelength mode. Nevertheless, two groups have gone beyond simple spectral reconstruction using fluorescence upconversion. Gustavsson et al.19 developed an upconversion instrument capable of automated scanning over wavelengths at fixed time delays. By simultaneous computer control of the phase-matching angle of the upconversion crystal, the monochromator, and the delay stage, these workers demonstrated the ability to collect spectra with ;10 nm spectral resolution and nearly 200 fs time resolution at fixed time delays. True multichannel detection of emission was achieved using a broadband (;100 nm) upconversion approach by Ernsting and co-workers. 20 The latter experiment was noteworthy for the time resolution (;100 fs) achieved, but the limited spectral range and difficulty of the experiment probably preclude the use of broadband upconversion as a general-purpose technique, at least in the near future. Inherently better suited to multichannel collection of time-resolved emission spectra are methods based on streak camera detection. 2,21 Although streak cameras have most often been used in a single-wavelength mode, the coupling of a streak camera to a spectrograph with twodimensional detection offers the ultimate in multichannel detection: the ability to record emission intensities continuously dispersed in both the time and wavelength. 22,23 The advantages of this approach are the broad spectral coverage available and the relatively simple optical alignment required. Apart from expense, the main drawbacks to the use of streak cameras for time-resolved emission spectroscopy are the low dynamic range of these detec† It should be noted that with the high-quality results afforded by TCSPC and sophisticated methods of analysis, highly accurate spectra are possible. See for example, the work of Ref. 18.

0003-7028 / 05 / 5902-0206$2.00 / 0 q 2005 Society for Applied Spectroscopy

APPLIED SPECTROSCOPY

TABLE I. Comparison of time-resolved emission techniques.a Method TCSPC

Advantages

high sensitivity, mainly statistical noise (GHz) frequencyavailability of low cost domain fluorometry MHz variants upconversion excellent time resolution streak camera ease of use, direct 2D resolution Kerr gating

a

Disadvantages electronics-limited time resolution electronics-limited time resolution difficult alignment, limited sensitivity limited sensitivity and time resolution

complete spectra with large background siggood time resolution nals from long-lived samples

Laser characteristics pJ-nJ ;4 MHz ;10 nJ ;4 MHz 1 nJ @ 80 MHz; 1 mJ @ 4 kHz 1 nJ @ 100 MHz 10 mJ @ 1 kHz 1 mJ @ 10 Hz 200 mJ @ 1 kHz 100 nJ @ 200 kHz

Instrumental resolution

Sensitivity

Representative systems

20–30 ps

single photon

58, 59

20–30 ps

PMT current

1, 60

100–200 fs 2–10 ps 200–400 fs

limited by SFG 11–17 efficiency similar to cur26, 61–65 rent mode of PMT similar to single 37–42, this work photon

The data in this table are meant to provide only an indication of characteristics typical of the different methods, as described in the references provided in the last column. The laser characteristics listed are excitation pulse energies and repetition rates of one or more representative experiments. Instrumental resolution is the full width at half-maximum of the instrumental response function. The sensitivity column indicates sensitivities as being comparable to those achieved using a photomultiplier (PMT) in either photon counting or current mode. SFG 5 sum frequency generation.

tors and the limitations on the time resolution currently available. Although 200 fs resolution has been demonstrated with low-repetition rate signals, 24 streak-camera systems suitable for time-resolved fluorescence work have thus far only achieved 2–3 ps time resolution. 25,26 The final technique to be considered here is Kerr-gated emission spectroscopy. 2 This method offers time resolution that is beginning to rival that of fluorescence upconversion, combined with the benefits of wide spectral coverage and ease of alignment comparable to that of streakcamera-based systems. Like fluorescence upconversion, spontaneous emission excited by an ultrashort laser pulse is gated using a second, delayed pulse. In the case of the Kerr shutter, gating is effected by using the delayed pulse to create a transient birefringence in a Kerr-active medium. This birefringence enables momentary passage of fluorescence otherwise blocked by a pair of crossed polarizers. Such a Kerr shutter was first proposed for time resolving emission by Duguay and Hansen in 1969. 27,28 Using liquid CS2 as the Kerr medium, these authors demonstrated the method by measuring the picosecond lifetimes of two polymethine dyes. In the following year, Rentzepis and co-workers 29 published the first crude time-resolved emission spectrum (of rhodamine 6G in ethanol). During the two decades following this initial work, only sporadic use was made of optical Kerr gating. In 1987 Rulliere and co-workers30 reported construction of a ‘‘picosecond fluorimeter’’ based on Duguay’s design for a Kerr shutter. This work received little attention, perhaps because other techniques available at the time afforded better time resolution than the laser-limited resolution of 25 ps reported. Until very recently, optical Kerr gating for purposes of emission spectroscopy has been largely ignored. In contrast, optical Kerr shutters have become a routine tool in ultrafast spectroscopy since the introduction of frequency-resolved optical gating techniques for measuring pulse structure by Trebino and coworkers in 1993.31,32 Another noteworthy use of optical Kerr gating is for rejection of fluorescence in time-resolved resonance Raman (‘‘TR3’’) spectroscopy.33,34 Matousek et al. have shown that the temporal characteristics of a liquid CS2 optical Kerr gate are ideally suited to capturing time-resolved Raman signals while rejecting

nanosecond fluorescence background. Use of such a Kerr shutter has enabled them to obtain TR3 spectra of unprecedented quality, even for strongly fluorescent solutes.35,36 It has only been within the past few years that optical Kerr gating has re-emerged as a potentially viable alternative for collecting time-resolved emission spectra with both high spectral and temporal resolution. Two groups in Japan37–41 and one in Germany42 have recently described femtosecond fluorescence spectrometers based on optical Kerr shutters. The approaches of all three groups are similar in that they employ kHz amplified Ti : sapphire laser systems for producing excitation and gating pulses and cooled charge-coupled device (CCD) cameras for detection. The optics used by the two Japanese groups also share much in common, consisting of a pair of offaxis parabolic mirrors for fluorescence collection and focusing and thin dichroic polarizers for minimizing wavelength dispersion. The key to achieving high time resolution in these experiments is the use of optical glasses and other solid materials as Kerr media rather than the traditional liquid CS2. Kanematsu and co-workers surveyed the suitability of 17 optical glasses38 for fluorescence applications. They found that OKE efficiencies increase approximately linearly with both the refractive index and the dispersion of the material. Unfortunately, two-photon absorption, which leads to interfering emission from the gate, as well as temporal broadening of signals due to group velocity dispersion, also increase in this same direction. These authors recommended the high-index glass SFS1 as the best compromise for emission spectroscopy and demonstrated the ability to acquire broad-band spectra of several short-lived solutes with ;350 fs time resolution.37,38 They later explored several crystalline materials as Kerr media39 and improved the time resolution to 180 fs using a 50 mm thick SrTiO3 crystal for the gate material. Takeda and co-workers, who used a lower repetition rate laser (1 kHz vs. 200 kHz), employed quartz as the gate medium and achieved a comparable time resolution of ;250 fs in measurements of b-carotene.40,41 Most recently, Schmidt et al.42 used a laser system with much shorter pulses (;40 fs compared to ;150 fs in the former systems) and showed that even APPLIED SPECTROSCOPY

207

better time resolution is possible with this method. Employing Cassegranian objectives for collection and focusing, a wire grid polarizer, and 1 mm fused silica as the gate medium, Schimdt et al. demonstrated 135 fs response times for collection of time-resolved emission spectra of samples of b-carotene and an azobenzene derivative. These three groups have clearly proven that both broad spectral coverage and time resolution rivaling that of fluorescence upconversion are available using optical Kerr gating. But the applicability of the technique for measuring time-resolved emission from typical fluorescent probes is not clear from their work. The reason is that all of the demonstrations reported thus far involve only solutes with ultra-short lifetimes; the longest lived solute studied to date had a lifetime of only ;5 ps.43 If Kerr-gated emission spectroscopy is to be of general utility, it will need to be shown that it can also be used for ‘‘normal’’ fluorescent probes, i.e., those with nanosecond lifetimes. The early work of Rulliere and co-workers,30 as well as observations made by workers primarily interested in Raman applications of Kerr gating,35 suggest that high-quality emission of normal fluorophores can indeed be obtained. The only question is to what extent will it be possible to maintain high time resolution in doing so. The purpose of the present paper is to document our efforts to construct a Kerr-gated emission spectrometer that is capable of measuring spectra of nanosecond lifetime solutes while at the same time maintaining the sort of time resolution just described. Some compromises are inevitable in order to obtain the high gate efficiencies and rejection of ungated emission required to obtain highquality spectra of such solutes. Nevertheless, we find that it is possible to achieve this goal and still maintain 450 fs system response times. We show by a number of sample applications that the system described herein is well suited for studies in which such time resolution (which can probably be pushed to ;200 fs) coupled to high spectral resolution is important. The remainder of this paper is structured as follows. In the following section we present some theoretical aspects of the Kerr effect relevant to its use for fluorescence gating. Next is the Experimental Setup section. The fourth section contains a discussion of the selection of a Kerr medium and the efficiency of the gating achieved here. In the fifth section correction of spectra for temporal dispersion and the wavelength-dependent sensitivity of the instrument are discussed. Methods of data collection and analysis are described in the sixth section. Finally, in the seventh section we present data from selected applications, and we summarize the main results of this work in the eighth section.


(2)

where Dn 5 ns 2 nf is the birefringence at the wavelength l, and L is the thickness of the plate. When a retardation plate is placed between a pair of crossed polarizers, the transmission is given by T 5 sin 2(2u)sin 2(f/2)

(3)

where u denotes the angle between the slow axis of the retarder and the output polarizer direction. Note that f is only a function of the wavelength, birefringence, and plate thickness, and by choosing a proper combination of d and Dn for a particular wavelength (i.e., such that f 5 l/2), the maximum transmittance of unity can be achieved by orienting the retardation plate at u 5 458. To adapt Eq. 3 to the case of an optical Kerr shutter, the static birefringence of the retardation plate is replaced by the birefringence of a Kerr medium induced by a gating pulse with intensity profile I g(t). The phase shift of an emission signal being gated is then fem(t) 5 2pLgIg(t)/lem

(4)

In this case, u is the angle between the gate polarization and the orientation of the first polarizer. To maximize throughput, the angle u is chosen to be 458 as in the case of the retardation plate, whereupon the transmittance of the signal becomes T(t) 5 sin 2

[ ] [

]

fem (t) pgL 5 sin 2 I (t) 2 lem g

(5)

Finally, for a signal consisting of an emission transient Iem(t), the time-resolved signal detected using the optical Kerr shutter is

E

t

T(t 2 t9)Iem(t9) dt9

(6)

2`

The optical Kerr effect refers to the light-induced change in the anisotropy of the refractive index or birefringence Dn of a substance. In an isotopic medium, the lowest-order change induced by the electric field of light is quadratic in the field or proportional to the light intensity I:44

208

f 5 fs 2 ff 5 2pLDn/l

Igated(t) 5

THEORETICAL BACKGROUND

Dn 5 gI

where g is the nonlinear refractive index (intensity coefficient) of the medium. To construct an optical shutter, such a medium is placed between crossed polarizers, which, in the absence of the shutter, block passage of the signal beam of interest. A short, intense pulse of light impinging on the Kerr medium is used to produce a transient rotation of the polarization of the signal beam, allowing some portion of the signal to pass through the output polarizer, thereby gating the signal. The operation of an optical Kerr shutter is most easily analyzed by considering its static equivalent, a retardation plate. Retardation plates operate by imparting unequal phase shifts to orthogonally polarized components of an incident wave, changing its polarization. Assuming a linear birefringence, the phase shift f between light polarized along the slow and fast (s, f) axes of such a retarder is

(1)

where t is the delay between the excitation and gate pulse. As seen from Eqs. 5 and 6, the detected signal depends on the intensity of the gate pulse and the nonlinear refractive index and the thickness of the Kerr medium. It is also important to note that the gating efficiency is a nonlinear function of signal wavelength. Even in the low transmittance regime wherein the sine function can be linearized, the transmittance and thus the detected signal

are inversely proportional to the square of the signal wavelength. For purpose of later discussion, it is useful to examine what Eqs. 5 and 6 imply about the signal-to-noise (S/N) ratio expected for the signals observed in a real experimental situation. The goal is derive relationships describing how the polarizer efficiency, gate pulse width (or time resolution), and emission lifetime combine to determine the S/N achievable in a particular experiment. For simplicity, we assume the gating pulse to be a square pulse of intensity Igate and width dt, and the sample emission to be exponential, Iem(t) 5 I0exp(2t/t)

this noise arises from three sources: (1) the ÏN noise in Nopen and Nclosed , (2) variations in the gate efficiency dEg , caused by fluctuations in the gating pulse, and (3) variations in the emission intensity reaching the Kerr cell, caused by fluctuations in the excitation beam. We incorporate the latter into dN0. With these assumptions, the noise in S can be written (dS) 2 5 (dNopen ) 2 1 (dNclosed )2 5 Nopen 1 Nclosed 1

(7)

1

with dt K t. The intensity of the gated light is Igated (t) 5 C sin 2

1

2

pgL I I (t9) 5 CEg I0 e2t9/t l g em

(8)

1

2

pgL Eg [ sin I l g

C I (t9) « em

(10)

the (ideal) number of background counts integrated over the same interval will be

E

`

0

¯ 01 t Iem (t) dt 5 N « dt

2

2

]

(dN0 ) 2

(15)

1 2 dS S

2

ù [1 1 2r (t)]

1 2

1 dEg 1 S(t) Eg

1 2 dN0 N0

2

2

(16)

where ¯ N 1 1 t 1t/t r (t) [ ¯ back 5 e Ngated (t) Eg « dt

(17)

Equation 16 is the central result of this section. It shows the relative noise in the time-dependent signal to be the sum of contributions from the ÏN noise in the signal S(t), the relative noise in the gate efficiency dEg /Eg, and relative noise in the fluorescence reaching the Kerr gate dN0 /N0. The importance of these contributions is controlled by r(t), the ratio of background and gated signals, which itself is a product of three ‘‘collection efficiencies’’: the gate efficiency Eg, the polarizer extinction ratio «, and the fraction of the emission being sampled e2 t/tdt/ t. It should be kept in mind that the former two quantities are expected to be significantly dependent on emission wavelength. EXPERIMENTAL SETUP

(12)

¯ 0 5 C9I0dt is the number of photons that would where N be detected at zero delay for a perfect shutter (Eg 5 1). The desired signal from the experiment is an approxi¯ gated(t). What is actually measured, mation to N S(t) 5 Nopen(t) 2 Nclosed

]Nclosed ]N0

1 [1 1 r (t)] 2

The signals detected in our experiments are the net numbers of photons impinging on the detector integrated over some fixed time interval. If the (ideal) gated signal accumulated during this time interval for a particular delay time t is ¯ gated(t) 5 C9Eg Iem(t)dt 5 N ¯ 0Ege 2t/t N (11)

¯ back 5 C9 N «

1

(9)

is the efficiency the Kerr shutter. Unfortunately, Igated(t) is not the only light to reach the detector. Even when no gating pulse opens the shutter, some of the sample emission reaches the detector due to imperfections in the blocking polarizers. For a polarizer extinction ratio of « 5 T\ /T⊥ the intensity of emission reaching the detector in the absence of the gate pulse, i.e., for a closed shutter, is Iclosed (t) ù

2 1 2

2

2

Substituting for Nopen and Nclosed the ideal values from Eq. 14, the relative error in the signal (i.e., the inverse S/N ratio) can be written

where C accounts for the overall transmission of the remainder of the optical system and where 2

[1

]Nopen ]N0

1

]Nopen (dEg ) 2 ]Eg

(13)

is the number of photons detected when the gate is open at a delay time t, Nopen(t), minus the number detected when it is closed, Nclosed, where the latter value is determined from the signal observed at some large negative delay. The measured quantities Nopen and Nclosed relate to the ‘‘ideal’’ quantities defined in Eqs. 11 and 12 as: ¯ gated 1 N ¯ back Nopen ù N and Nclosed ù Nback (14) These relations would be equalities except for the presence of noise in the measured values. We assume that

The femtosecond Kerr-gate fluorescence spectrometer we have constructed (Fig. 1) is similar to those described in Refs. 38 and 40. The light source is a high repetition rate amplified laser system consisting of a Ti : sapphire oscillator (Coherent MIRA-900) and a regenerative amplifier (Coherent RegA-9000) with an external stretcher/compressor (Coherent). This system provides 160 fs optical pulses at 250 kHz repetition rate with energies of about 3.5 mJ, tunable over the range 775–820 nm. The output of the laser system is split into two beams in the ratio of 25 to 75. The smaller portion of the fundamental beam is doubled in a BBO crystal (0.2 mm, Inrad) and used to excite the sample, and the larger portion is used for the Kerr gate. The excitation light, at 387 nm for all of the data reported in this paper, is focused by a 225 mm focal length (f.l.) lens into a 1 mm quartz flow cell containing the sample. Solute concentrations are typically chosen so that ;30% of the excitation light is APPLIED SPECTROSCOPY

209

FIG. 1. Schematic diagram of the Kerr-gated fluorescence spectrometer. PM denotes an off-axis parabolic mirror; P1 and P2 are polarizers; F1, F2, and F3 are filters; and l/2 denotes half-wave plates (see text for details).

absorbed by the sample; however, much lower concentrations are readily measurable. Sample fluorescence is collected using a 1½-in.-diameter off-axis parabolic mirror (PM; Thermo Oriel Opticon) with an effective focal length of 4 in., redirected as a collimated beam to a steering mirror, and focused in the Kerr cell by a 100 mm f.l. lens to a spot size of ;200 mm. This mirror 1 lens combination was found preferable to the second off-axis parabolic mirror used by others38,40 due to the improved focusing it provided (see also following section). After the Kerr cell, fluorescence is transferred to the entrance slit of a 0.3 meter spectrograph (Acton, SpectraPro-300i) by two 150 mm f.l. lenses and detected by a liquid nitrogen cooled CCD camera (Princeton Instruments, LN/CCD1340/100-EB/1). The scattered light from the gate is rejected by placing a 1-in.-diameter dielectric high reflecting mirror (F2; Newport, 10B20UF.21) after the second polarizer. Scattered excitation light is blocked by a 3 mm thickness Schott OG400 glass filter (F1) placed before the first polarizer. The Kerr shutter consists of a 1 mm quartz cell of benzene placed between a pair of crossed polarizers. The first polarizer (P1) is a joined pair of metal grid polarizers (Moxtek, Proflux PPL04 on fused silica substrates) and the second polarizer (P2) a large (1½-in. aperture) Glan–Taylor prism. After a variable delay (Newport ILS250PP), the gate pulse is focused by a 500 mm f.l. lens to a spot size of roughly 300 mm into the Kerr medium. The gate is polarized at 458 relative to orientation of the first polarizer using a half wave retarder (l/2(v); CVI, QWPO-800-08-2-R10). The magic angle condition for fluorescence detection is obtained by rotating the excitation polarization using a second half waveplate (l/2(2v); CVI, QWPO-400-08-2-R10). The instrument response estimated as the full width of the Ra210


man scattering signal observed in neat solvent samples is ;450 fs. The spectral resolution is 3–4 nm using a 300 grooves per mm grating. The measured spectra are corrected for spectral sensitivity and temporal dispersion as described in the following sections. In order to account for laser fluctuations during the course of an experiment, a correction that is important when studying long-lived fluorescence probes, a reference channel is sometimes employed. This reference measures back-emitted fluorescence from the sample, which is collected by a single lens and directed to a PMT. The spectral region in which fluorescence is collected is determined by an appropriate set of optical filters, F3. (A typical example is a pair of Corning 3-71 and Schott BG39 filters.) Signal from the PMT is amplified by a factor of 10 and the output level held for a few microseconds by a home-built amplifier, digitized (National Instruments, AT-MIO-16E-1), and stored in the computer. Software for data collection was written in Visual Basic using dynamic link libraries (DLL) obtained from Princeton Instruments for acquisition of the spectra from the CCD, Newport Corporation for controlling the delay stage, and National Instruments for controlling the AT-MIO-16 A/ D board for the reference channel. SELECTION OF THE KERR MEDIUM AND GATE EFFICIENCY The choices made in selecting the components just described were based on the ultimate goal of constructing an instrument useful for as broad a range of common fluorescent probes as possible, while maintaining subpicosecond time resolution. Broad applicability implies the use of laser wavelengths near the blue end of the usable

TABLE II. Some characteristics of potential Kerr media.a Medium

g/10220 m2/W21 @ l [nm] lmin /nm

nD

CS2

390 @ 694

380

1.627

SFL6 Glass Fused Silica Benzene

18.9 @ 1060 2.7 @ 1060 35 @ 694

367 165 278

1.796 1.458 1.501

4.7 @ 530 2.8 @ 694

205 190

1.328 1.333

Methanol Water

Origin of response Electronic 42% Nuclear 58%b Electronic Electronic Electronic 85% Nuclear 15%c Electronic Electronic

g is the nonlinear refractive index (intensity coefficient) from Ref. 66. lmin is the wavelength below which the optical density of 1 cm of sample exceeds unity. Values from Ref. 67. nD is the linear refractive index at 589 nm at 25 8C (glass data from Ref. 66 and liquid data from Ref. 68.) b Ref. 45. c Ref. 47. a

Ti : sapphire range (;770 nm) and, more importantly, the ability to work with fluorophores having nanosecond lifetimes. The former criterion limits the choice of Kerr medium to ones not having significant one- or two-photon absorption in the 390–780 nm range. To enable measurement of systems having nanosecond lifetimes with good S/N requires that the gate efficiency, polarizer extinction, and system transmission be as high as possible (Eqs. 16 and 17). How these various design criteria dictated component selection is described below. We begin with the choice of Kerr medium. Characteristics of some potential Kerr media are presented in Table II. In addition to transparency, the primary criteria for choice of a Kerr medium are that it possess a large nonlinear refractive index g at the gate wavelength for high gating efficiency and that its response be rapid so as not to limit time resolution. Of the possibilities considered, carbon disulfide has the largest nonlinear refractive index and is therefore the most efficient gate material. Unfortunately, it begins to absorb near 390 nm, and, in addition, it has a relatively slow response of about 1.6 ps due to the large contribution of orientational polarizability to its nonlinear refractive index.45 Faster times are found for systems whose optical Kerr response is dominated by electronic polarizability. Optical glasses exhibit responses that are almost purely electronic in origin, and have been shown to provide gate times of 200 fs38,40 or less.42 The characteristics of two readily available glasses are shown in Table II. SFL6 has one of the largest values of g of the glasses surveyed by Kinoshita et al.38 and it was their recommendation for use in emission spectroscopy. Unfortunately, SFL6 also absorbs significantly in the 390 nm region. Fused silica, on the other hand, is completely transparent at this wavelength, but it has a 10-fold smaller nonlinear refractive index, illustrating the contrary nature of transparency and Kerr efficiency. The medium that we have found to be the best compromise for our purposes is liquid benzene. The nonlinear refractive index of benzene is roughly comparable to that of the best optical glasses, but it is much more transparent in the region of interest. Like CS2, benzene’s optical Kerr response contains both electronic and orientational contributions, which renders it slower than glasses. Nevertheless, its Kerr response is dominated by the electronic contribu-

TABLE III. Characteristics of Kerr media observed in use (lgate 5 775 nm).a Medium

NRam

Nfluor (530 nm)

Dt/fs

SFL6 Glass Fused Silica Benzene

25 1 125

250 2.5 8

750 300 450

a

All Kerr media are 1 mm thick. Liquids were contained in a quartz cuvette (1.25 mm wall thickness). NRam and Nfluor denote the relative count levels observed with a 1 mm sample of methanol. NRam measures the relative height of the methanol Raman peak (435 nm) and Nfluor gate fluorescence at 530 nm. Dt is the full width at half-maximum intensity of the Raman peak, used as a measure of the instrument response function.

tion, enabling it to provide a substantially faster response compared to CS2.46,47 Data illustrating the performance of several potential Kerr media in the present setup are provided in Figs. 2 and 3 and in Table III. Figure 2 shows spectra of a sample of neat methanol recorded using (a) benzene and (b) SFL6 as the Kerr media. Spectra at two time delays, 0 and 220 ps, are shown. The spectra at 220 ps consist of ungated background scatter and the fluorescence from the Kerr medium that results from one- and two-photon absorption of the gate beam. (Note that these spectra are not corrected for instrumental sensitivity so that the shape of the emission is not meaningful.) The spectra at zero delay time show sharp features near 435 nm not present at 220 ps due to gated Raman scatter from the methanol sample. The relative magnitudes of the Raman signals provide rough indications of the relative gating efficiencies, and the intensity at ;530 nm provides a measure of the relative amount of interfering emission of the various Kerr media. These measures are compiled in Table III.

FIG. 2. Kerr-gated spectra of a neat methanol sample using 1 mm of (a) benzene and (b) SFL6 glass as the Kerr medium. Two spectra are shown, one at zero delay and another at 220 ps delay. The latter signal is primarily fluorescence from the Kerr medium; however, the peaks at l . 620 nm are from residual scatter of the gate pulse, with oscillations in the l . 620 nm region resulting from the filter F2. The 220 ps spectra are shown with the correct vertical scale, whereas the 0 ps spectra have been vertically displaced by 1000 counts for clarity.


211

FIG. 3. Instrument response functions obtained using (a) benzene and (b) fused silica as Kerr media. Dashed lines show Gaussian fits to these functions with the full widths indicated.

Also shown here are temporal widths (FWHM) of the Raman bands, which we take to be measures of the instrumental response. Two of these response functions are also plotted in Fig. 3. Of the materials examined, CS2 and SFL6 glass show very high background emission when gating at 775 nm and for this reason were rejected as potential gate materials. In fact, we found CS2 to be completely unusable at this wavelength, because there was enough absorption of the gate to cause thermal lensing, which completely obscured the signal. Benzene and fused silica perform much better in this regard, with both materials showing negligibly small emission relative to the fluorescence signals of interest. (For sake of comparison, solute fluorescence in typical experiments is 3–10 times larger than the Raman signals shown in Fig. 2.) As expected from their relative g values (Table II), the observed gating efficiency is roughly 100 times smaller in fused silica compared to benzene. Figure 3 shows instrumental response functions obtained using benzene and fused silica as Kerr media. The response from fused silica has a symmetrical shape and a width of about 300 fs, which is close to the autocorrelation function of our laser system output (;250 fs). The response using benzene is asymmetrical in shape and has a width of about 450 fs. The extra width in the case of benzene can be ascribed to the reorientational contribution to its Kerr response.47,48 It is the price that must be paid for the much greater efficiency of benzene, essential for measuring nanosecond lifetime solutes. The origin of the asymmetry observed using benzene but not silica as the Kerr medium is not clear. We note that the 450 fs response time obtained with the present setup could undoubtedly be improved by narrowing the laser pulses used for excitation and gating, but by how much is presently unknown. Some appreciation for the effect of solute lifetime on S/N can be derived from the data in Fig. 4. Shown here are raw spectra of two solutes, C153 (coumarin 153) and 212


FIG. 4. Illustration of the relative contributions of gated and ungated emission to the spectra of (a) coumarin 153 (C153) and (b) 4-dimethylamino-49-cyanostilbene (DCS) in acetonitrile. The desired signal is the difference between the spectra recorded at 20 ps (gated) and 220 ps (ungated). The latter signal comes primarily from solute emission but the peaks near 630 and 660 nm are scattered gate light. The optical densities and accumulation times for the two samples are: C153 5 0.43, 32 s and DCS 5 0.23, 40 s.

DCS (4-dimethylamino-49-cyanostilbene), in acetonitrile. The total signal levels shown here are typical of what we observe with highly fluorescent solutes: count rates of 105 to 107 s21 for sample absorbances in the range of 0.2–0.5 OD. The difference in total signal between these two examples is due to many factors, including differences in sample concentration, solute quantum yield, etc., and is not important here. What is significant is the difference between the relative intensities of the observed spectra at 220 ps and 120 ps. The spectra at 220 ps (dashed curves) reflect primarily sample emission that leaks through the shutter, whereas the 120 ps spectra are what is observed when the shutter is opened by a gate pulse. The difference is the desired signal S(t 5 20 ps). In the case of C153, the 220 and 120 ps spectra are only slightly different and the signal is less than 10% of the background, whereas in the case of DCS the signal and background are roughly equal in magnitude. The important feature distinguishing these two solutes is their fluorescence lifetimes: 6 ns in the case of C153 and 0.6 ns in DCS. The data in Fig. 4 also enable estimates of the gating efficiency achieved here. Using Eqs. 8 and 10, and recognizing that I(20 ps) ; I0 for these solutes, the gate efficiency for any emission wavelength is given by: Eg (l) 5 5

[ [

]

Igated (l, t) 1 t Iclosed (l) «(l) dt

]

I(l, 20 ps) 2 I(l, 220 ps) 1 t I(l, 220 ps) «(l) dt

(18)

where t is the solute lifetime, dt is the width of the instrument response function, and «(l) is the polarizer ex-

tinction at the observation wavelength. For an emission wavelength of 530 nm, the extinction is about 104 as discussed below. Using the parameters dt ; 450 fs and tC153 ; 6 ns, tDCS ; 0.6 ns, both sets of data in Fig. 4 provide the same value for the efficiency, Eg(530 nm) ; 12%. The theoretical efficiency can be determined from Eq. 9. Using the values g ; 35 3 10220 m 2 W21 (Table II), L 5 1 mm, and Ig ; 2 3 1014 W m22 also yields the value Eg 5 12%. Because the value of Ig depends on the square of the diameter of the gating beam (;300 mm) the theoretical value is only a rough estimate, and the agreement between the observed and calculated values should only be taken to mean that our gate efficiencies are in the expected range. Equation 9 predicts that Eg(l ) should decrease with increasing emission wavelength (approximately as l 22) and this is roughly what is observed, with values ranging between 5 and 20% with wavelength. These efficiencies are larger than values reported in other recent applications of Kerr gated emission spectroscopy,37,38,40–42 primarily due to the choice of benzene as the Kerr medium. In addition to gating efficiency, high polarizer extinction is critical to achieving high S/N with nanosecond lifetime probes. Poor extinction was a major problem with the original components tested. Using two parabolic mirrors as received from Janos Technology, even with two high-quality (« . 105) Glan–Taylor polarizers we observed an extinction of only 500:1 for the Kerr shutter. The problem was the significant depolarization caused by the limited surface quality of these two mirrors (l/10 at 10 mm) in the visible region. Custom polishing (by Thermo Oriel Opticon) improved their quality substantially, but residual scattering remained a problem. Replacement of the second parabolic mirror by the combination of a flat mirror and a lens eliminated the problem and greatly improved the S/N achieved. Several types of polarizers were tested for use as the input polarizer (P1, Fig. 1). The superior extinction and transmission properties of Glan–Taylor polarizers would render them ideal for this purpose if it were not for the large temporal dispersion produced by the inherent thickness of such polarizers. Thin film dichroic polarizers (3.2 mm, OptoSigma WVL380-700/AP50/LO) reduced the dispersion problem, but to achieve extinction ratios greater than 103 two of these polarizers were needed, which significantly reduced the transmission of the system. The best solution found to date is the use of metallic grid polarizers, which offer comparable extinction to dichroic polarizers but with much higher transmission. A pair of ProFlux PPL04 polarizers (Moxtek) is found to provide better than 50% transmission over the spectral range of interest. Combined with a Glan–Thompson polarizer as P2, this choice of P1 provides extinction of greater than 104 at the center of the spectral window and greater than 103 at the red and blue edges. An approximate representation of «(l) is provided in Fig. 5. CORRECTIONS FOR TEMPORAL DISPERSION AND SPECTRAL SENSITIVITY Temporal Correction. A number of transmissive optics are used in the present setup, and variations in their refractive indices with wavelength cause a wavelength-

FIG. 5. Approximate extinction spectrum «(l) of the Kerr shutter. This curve was determined as the ratio of the emission detected (in the absence of the gate pulse) when polarizer P1 is rotated to provide maximal and minimal signal levels. Data from three probes (see description of spectral correction) was combined in order to cover the full spectral window.

dependent delay across the 390–675 nm emission window. As illustrated in Fig. 1, fluorescence emitted inside the sample cell passes through one cell wall, polarizer P1, the focusing lens, and some portion of the Kerr cell prior to gating. If these elements are crudely modeled as being equivalent to ;10 mm of fused silica, a delay of ;0.5 ps is estimated between the bluest and reddest wavelengths across the ;300 nm range accessible. The index dispersion of the polarizers and benzene are unknown but are expected to be much larger than that of fused silica. In addition, chromatic aberrations of the lens‡ are expected to increase the temporal dispersion somewhat. We therefore expect the actual dispersion across the emission window to be significantly greater than 0.5 ps, and this dispersion must be accounted for in order to obtain accurate spectral dynamics. We use two approaches to measuring the temporal dispersion of the instrument. The first employs a white light continuum generated in a 3 mm sapphire plate at the sample position. To produce the continuum, a portion (25%) of the fundamental beam normally used to generate second-harmonic light is focused into the sapphire plate using a combination of a 250 mm f.l. lens to prefocus the 10 mm beam and a microscope objective with numerical aperture of 0.1 and magnification of 5. The continuum light so produced traverses the same optical path as the sample emission and is time resolved by the Kerr shutter. This approach is relatively simple to employ due to the high intensity and short duration of the continuum. Unfortunately, the pulse energies available with our laser system only provide usable continuum over about ½ of the spectral range needed. For this reason we also employ a second method to access the bluer portions of the spectrum missed by the continuum. The second approach uses the emission from a set of fluorophore plus solvent combinations in which no fast spectral dynamics are expected. For this purpose, the pair of solutions C153 in cyclohexane (400–500 nm) and POPOP in benzene (400–500 nm) were found to be suitable. The spectral dynamics of C153 in cyclohexane have been studied by fluorescence upconversion and shown to be minimal for ‡ The collimating lens we use is a simple plano-convex lens (2-in. fused silica). We tested the performance of an achromatic lens (Newport, PAC073) but found that it caused considerably more temporal dispersion.


213

FIG. 6. Temporal dispersion of the instrument measured using (a) continuum light generated at the sample position and (b) samples of C153 in cyclohexane (circles) and POPOP in benzene (triangles). The curves shown on both panels are a fit of all of the data to the following function: Dt 5 a 1 b/l 1 cl 2.

times greater than ;30 fs.17 POPOP in benzene was chosen for its convenient absorption and emission wavelengths and high radiative rate.49 The fluorescence of each probe was collected separately between 23 ps and 5 ps delay times and time-zero calculated as the point of maximal first time derivative on the rising edge of the emission. Data collected using both methods are plotted in Fig. 6. The solid curves are an inverse second-order polynomial fit to all of the data. As illustrated here, the two methods are in good agreement over their range of overlap and a simple functional form accurately characterizes the temporal dispersion. The total delay measured between the bluest and reddest wavelengths is ;2 ps, which is several times larger than the estimate based on fused silica optics, as expected. The simple wavelength dependence of this dispersion renders correction relatively straightforward. For a given optical arrangement this dispersion varies little over time so that fitted data of the sort shown in Fig. 6 provide for accurate correction of spectral data. It would nevertheless be desirable to reduce or eliminate this dispersion. Apart from the Kerr cell itself, the primary source of dispersion in the system is probably the absorptive filter F1. We note that dispersion from F1 would be eliminated by repositioning it after the Kerr cell. However, placement before the Kerr cell is required to remove a coherent interaction between the residual pump and gate pulses in the Kerr cell, which distorts the spectra in cases where the sample is weakly absorbing. Spectral Correction. For quantitative work all fluorescence spectrometers require correction for the wavelength-dependent sensitivity of their detection systems. In the present case, the filters, polarizers, monochromator, CCD detector, and the Kerr medium all have wavelengthdependent properties. Determination of the spectral re214


FIG. 7. Spectral correction curves appropriate for (a) steady-state operation, determined with a standard lamp; and (b) time-resolved operation, determined with the three dye solutions indicated.

sponse is typically performed either using a calibrated lamp as an irradiance standard or using the emission of secondary fluorescence standards. We examined both methods for calibrating the present instrument. For an irradiance standard we employed an intensity-stabilized tungsten-halogen lamp in place of the sample. The broad emission from the lamp enables rapid calibration but only of the performance of the system without gating, due to the fact that the intensity of the lamp is too weak to be observed when gated. The ‘‘steady-state’’ correction curve CSS (l) (proportional to the inverse of the system responsivity) obtained in this manner is shown in Fig. 7a. Over the wavelength range of interest here the variation in CSS (l) amounts to about a factor of 3. To measure the more relevant correction for time-gated emission we used three dye 1 solvent systems as secondary standards: tetraphenylbutadiene (TPB) in cyclohexane, C153 in acetonitrile, and DCM (trans-4-dicyanomethylene-6-p-dimethylaminostyryl-4H-pyran) in methanol. These three systems were chosen because they can be readily excited at 387 nm and their collective spectra cover the range 390–670 nm with good overlap between successive spectra. In addition, their photophysics are such that their steady-state emission is expected to be equal to the emission monitored at long (;100 ps) times. The time-resolved spectral correction curve displayed in Fig. 7b results from splicing together50 the ratios of the gated emission of these systems measured at 100 ps to their steadystate emission spectra measured on a corrected fluorimeter (Spex fluorolog F212). Comparing the two panels, it is clear that the steady-state and time-resolved correction curves are quite different, as they should be. Using CSS (l) to denote the correction measured with the standard lamp and CTR(l) the correction based on gated emission of the secondary standards, we expect CSS (l) } «(l)Eg (l) CTR (l)

(19)

The much greater variation in CTR(l) with wavelength (about a factor of 10), as well as its overall shape, mainly reflect the strong wavelength dependence of «(l) shown in Fig. 5. EXPERIMENTAL PROCEDURES AND DATA ANALYSIS The primary data collected with this spectrometer are two-dimensional (2D) data sets consisting of approximately 200 spectra recorded at delays separated by several different time increments (typically 0.1, 0.5, 1.0 ps). Each spectrum consists of 1340 points evenly spaced in wavelength. Within such a data set, several background spectra are recorded at large negative delays (220 ps) and included for later subtraction. Reference intensities (one point per spectrum) are also collected and stored with the data set. In addition to the solute 1 solvent data, another data set consisting of the neat solvent is also often collected in order to obtain solvent Raman data to be used as an instrument response function and for subtraction of solvent Raman peaks from the solution spectra. Spectra at each time delay are typically accumulated for 30–40 s, and collection of an entire data set takes 1–2 hours. The analysis of spectral data involves a number of data processing steps as well as various fitting options, all of which are performed by an in-house program written in FORTRAN-95. These steps are illustrated by the data on DCS in acetonitrile shown in Fig. 8. In all cases, primary data is read in and the random spikes resulting from cosmic rays impinging on the CCD are removed.§ If reference channel data were recorded, each spectrum is normalized by a factor near unity (typically varying by only 61%) to account for variations in this reference intensity. A background spectrum, interpolated from several spectra recorded at various times throughout the data collection process, is then subtracted from the spectrum at each delay, as previously illustrated in Fig. 4. These steps result in ‘‘raw’’ (signal) spectra of the sort illustrated in Fig. 8a. If, as in this case, solvent Raman bands are prominent in the spectra near zero delay, a 2D set of solvent blank data are subtracted to remove these bands (Fig. 8b). In this subtraction, the solvent data are rescaled to account for the effects of solute absorption (a factor of 0.5– 1 is typically required) and sometimes shifted slightly in time (6.1 ps) in order to achieve the most complete removal of Raman bands as judged by visual inspection. For later use in fitting, uncertainties, based on an assumed ÏN noise in the original data, are propagated through all of the above manipulations. At this point the processed data are ready for analysis, which can be performed in several different ways. The simplest case is when the dynamics of interest are slower than the instrumental resolution. In such instances the data are interpolated and time-shifted to correct for temporal dispersion and the intensities are multiplied by a § Due to the timing of the experiments, cosmic ray spikes occurred over several adjacent wavelength channels within a spectrum at a given delay, but were uncorrelated with respect to delay time. Spikes were repetitively removed by examining the time-derivative of the data and removing points whose magnitudes were beyond some threshold value.

FIG. 8. Representative spectra of DCS in acetonitrile illustrating the various steps of data processing (a) ‘‘raw’’ spectra after background subtraction, (b) after subtracting a solvent blank, (c) after time correction, and (d) after spectral correction. Spectra are at nominal delay times of 21, 20.5, 0, 0.5, and 5 ps with negative delays indicated by dashed lines.

spectral correction file. The effects of such corrections are illustrated in Figs. 8c and 8d. Usually, a frequency representation of the data is most meaningful for comparison to theory, and the data can be converted to this format by a suitable l 2 re-weighting and subsequent interpolation to provide equal frequency spacing. In most cases, however, the dynamics of interest occur on time scales comparable to the instrumental response, and it is desirable to (partially) remove the effects of instrumental broadening from the data. Ideally, one could use an instrument response function to perform a numerical deconvolution using Fourier transform methods as is done, for example, with OHD-OKE data.16 Unfortunately, the noise inherent in these data do not allow for numerically stable deconvolution. Instead, data must be fit to a model function and an iterative reconvolution approach5 employed. We found two forms of the latter approach to be useful. In many instances, for example, in studies of barrierless processes, an important first characterization of the time-evolving spectra is provided by the time dependence of the total intensity: APPLIED SPECTROSCOPY

215

I(t) 5

E

i(n, t) dn

(20)

and average (or first moment) frequency: n¯ (t) 5

E

i(n, t)n dn/I(t)

(21)

of the spectra I(n, t) integrated over some spectral region. We calculate these characteristics using a reconvolution procedure suggested by Gustavsson et al.19 We assume that the ideal quantities I(t) and n¯ (t) can be represented by multi-exponential functions: I(t) 5 I(0)

Oa

(I) i

exp[2t/ti(I) ]

i

Oa Oa

(I) i

51

(22)

(n) i

51

(23)

i

and n¯ (t) 5 n¯ (`) 1 Dn¯

Oa

(n) i

exp[2t/ti(n) ]

i

i

where I(0), n¯ , Dn¯ , and {ai , t i}( I,n) are adjustable parameters. A time-shift between the instrument response dt and the spectral data is also included as an adjustable parameter in these fits. I(t) and the product w(t) 5 I(t)n¯ (t) are convoluted with the instrument response function R(t) and compared to the observable quantities Iobs(t) 5 # Iobs(n, t) dn and wobs(t) 5 # Iobs(n, t)n dn. The parameters in Eqs. 22 and 23 are adjusted using a Marquardt–Levenberg algorithm51 so as to minimize the sum

O {[I (t ) 2 R(t 1 dt)∗I(t )]/s } 1 O {[w (t ) 1 R(t 1 dt)∗w(t )]/s obs

j

j

(I) j

2

j

j

(w) j

}2

(24)

j

where the s j are estimated uncertainties in the data and ‘‘*’’ indicates a convolution. In the cases studied to date, three or fewer components for both I(t) and n¯ (t) have sufficed to fit such data within its estimated uncertainties. An example of data fit in this manner is provided in Fig. 9. In cases where complete deconvoluted spectra are required, individual temporal decays are fit in a manner similar to that just described. No correction for temporal dispersion is applied to the data as this correction is accounted for in the fitting procedure. To reduce the computation required, the spectral data are first thinned by averaging over five or more frequency points, leaving ;300 frequencies for fitting. (The actual resolution of the spectrometer is much lower than the pixel density of the CCD, so that the spectral resolution is not significantly affected by this averaging, which mainly serves to enhance the S/N in the remaining data.) The intensity decays iobs(n, t) at each frequency are then fit by comparing to calculated decays icalc 5 (n, t) 5 R[t 1 dt(n)]∗i(n, t)

(25)

where the ideal decays i(n, t) are represented by multiexponential functions: i(n, t) 5

O a (n)exp[2t/t (n)] i

i

(26)

i

The fitting parameters ai(n), t i(n), and dt(n) are again optimized by minimizing a sum over weighted residuals of the form 216


O {[i

obs

(n, tj ) 2 icalc (n, tj )]} 2 /s 2j

(27)

j

j

obs

FIG. 9. Illustration of a fit to the total spectral intensity and average frequency described by Eqs. 20–24. These data are for a sample of C153 in acetone. The connected points are the experimental data, the solid curves are the fit to these data, and the dashed curves are the ideal (deconvoluted) quantities. The inset to panel (b) compares the ideal n¯ (t) curve obtained in this manner (dashed curve) to what is derived from the fitted spectra of Fig. 11.

We explored a variety of approaches for choosing and linking parameters in these decay fits. In the simplest case, the parameters ai, ti, and dt are treated independently for each frequency. Three exponential components (seven adjustable parameters) are usually sufficient to describe iobs(n, t) at any frequency n. In typical cases, where spectra evolve toward the red with time, the time shifts dt on the blue side of the spectrum are well determined by unconstrained fits, however, on the red side, fast rises are often distorted by variations in dt. For this reason, fits are performed in which dt(n) is constrained to reproduce the measured temporal dispersion curve (Fig. 6) to within some overall displacement. Constraining the values of a i and t i as a function of frequency also leads to more realistic time-dependent spectra than does treating these parameters independently. Increasing the number of time constants t i from 3 to 5–8 but requiring that they be the same for all n leads to comparable quality fits for individual frequencies but better time-resolved spectra. Probably the most realistic time-dependent spectra are derived by using a smaller number of components but assuming that ai(n), t i(n), and dt(n) are inter-related by simple (firstto third-order) functions of n. Figures 10 and 11 illustrate the nature of such fitting procedures, using data on C153 in acetone as an example. Figure 10 shows fits to emission decays at three wavelengths across the emission spectrum. These fits are unconstrained fits to a triple exponential form. The residuals shown here are representative of what we typically observe. They provide a better indication of the real S/N in the experiments than instantaneous spectra (e.g., Fig. 8), because the latter do not display the effects of unaccounted for fluctuations in signal level and gating efficiency.

FIG. 11. Spectra of C153 in acetone (a) after all processing and (b) after fitting to remove the effects of instrumental broadening.

from fitting integral I(t) and w(t) data according to Eqs. 20–24. FIG. 10. Time-resolved decays of C153 in acetone at selected wavelengths (points) and 3-exponential fits to these data (smooth curves). Above each decay are shown the unweighted residuals of the fit. The vertical scale in each case shows the accumulated count (averaged over 5 wavelength points in the original data set).

The noise levels here are between 2–3% of the signals. Based on an assumption of only ÏN noise in the data, values of the xn2 fit parameter52 of ;2 are calculated for these fits. The fact that these values of xn2 are not near unity reflects the non-negligible effect of the dEg and dN0 terms in Eq. 16. Figure 11a shows processed spectra (i.e., after time correction) in a frequency representation. The rise of the intensity at negative times (dashed curves) illustrates the instrumental broadening of the signal by several hundred femtoseconds. Figure 11b shows the spectra obtained after fitting the decays using time-shifts constrained by the independently measured dispersion curve (Fig. 6) and an eight-exponential, fixed-time-constant representation with amplitudes fit to an eleventh-order polynomial in wavelength. As illustrated here, constraining the amplitudes of the individual decays in this manner serves to remove most of the high-frequency noise in the original spectra,18 but low-frequency noise is still present on the edge of the spectra where signal levels are low. Analysis of fitted spectra such as these provide results comparable to those obtained with the previous method of fitting integrated data. An example is provided on the inset to Fig. 9b where we compare the first moment frequencies of the fitted spectra of Fig. 11 (solid curve) with those obtained

REPRESENTATIVE APPLICATIONS In this section we briefly illustrate the use of the spectrometer with a few applications, mainly related to measurement of solvation dynamics in various environments. First we consider comparisons to previous results obtained using fluorescence upconversion. Figure 12 shows the time-evolution of the peak frequencies np(t) of the spectra of C153 in three room-temperature solvents, acetone (data from Fig. 11b) and two other solvents, acetonitrile (ACN) and dimethylsulfoxide (DMSO), using similar spectra and fitting methods (solid curves). The points shown here are the averaged results of np(t) data previously recorded for these same systems using the fluorescence upconversion method.17 The agreement between the two sets of data is excellent; differences are less than the uncertainties expected for the upconversion data alone. To achieve such good agreement, it was necessary to correct the Kerr-gated results slightly. Apparently, the spectral correction applied for these experiments was imperfect and resulted in a displacement of ;400 cm21 compared to the upconversion data, as shown by the dashed curve in Fig. 12b. The solid curves were obtained by ‘‘re-correcting’’ the spectra so that at long times (100 ps) they agree with steady-state spectra. We have since made improvements to the spectral response of the system, but have not rerun these particular experiments. But, as can be seen from Fig. 12b, the error in the correction file has little effect on the extent of the peak shift observed or in its time dependence. A final comment to be made from these spectra is that we capture the same dynamics, even in very rapid solvents such as acetonitrile (tsolv ; 0.26 ps), as do the upconversion exAPPLIED SPECTROSCOPY

217

FIG. 13. Spectra of DTN (4-dimethylamino-49cyanodiphenylacetylene) in DMSO. (a) The signals as recorded at times of 0.2, 0.5, 1, 2, 5, and 10 ps (left to right). (b) These same data after correction for temporal dispersion and normalization to unit peak height. The inset shows normalized intensity I(t)/I(0) and frequency n¯ (0) 2 n¯ (t)]/[n¯ (0) 2 n¯ (`)] functions.

FIG. 12. Temporal evolution of peak frequencies of C153 in three solvents: acetone, acetonitrile, and DMSO. Results obtained with the Kerrgated emission experiment are shown with solid lines, and data from prior upconversion work17 are shown as points. The Kerr data here have been ‘‘recorrected’’ using the solution spectrum at long times as described in the text. The dashed curve in panel (b) is the result prior to this recorrection.

periments. Given that the upconversion data were recorded with an instrument response of 120 fs, this comparison speaks well for the effective time resolution of the present spectrometer. As already noted, the S/N in the Kerr experiment is a strong function of the lifetime of the system being studied. Coumarin 153 is a difficult solute by virtue of its lifetime being 4–6 ns in many solvents. Figure 13 illustrates the time-resolved spectra obtained in a more favorable case, DTN (4-dimethylamino-49-cyano-diphenylacetylene) in DMSO. The lifetime of DTN is relatively short, 690 ps. In addition, unlike C153 (and DCS) DTN undergoes a barrier-less transition between a strongly emissive locally excited (LE) state and a weakly emissive charge transfer (CT) state. This transition causes a large decrease in intensity concomitant with the solvation-induced frequency shift.53 The combination of these two features results in strong signals with greatly reduced background levels compared to conventional solutes such as C153 and DCS. Compare for example the count levels shown in these spectra with Figs. 4 and 8 and their relative noise with the spectra of Fig. 11a. (Note that the latter data are additionally averaged over wavelength, whereas the data in Fig. 13 are not.) Figures 14 and 15 illustrate solvation dynamics of the 218


probe solute DCS in two atypical solvents. Figure 14 shows results in the room-temperature ionic liquid 1-butyl-4-methylimidazolium hexafluorophosphate ([bmim1][PF62]). We have previously measured solvation dynamics in this ionic liquid using the time-correlated single photon counting technique.54,55 In those experiments it was found that, despite the fact that the spectral relaxation observed is quite

FIG. 14. (a) Spectra and (b) peak frequency response of DCS in the ionic liquid [bmim1][PF62]. In both panels the solid curves denote data recorded with the Kerr-gated emission spectrometer and the dashed curves denote data obtained from spectral reconstruction of time-correlated single-photon counting data. Times illustrated in the top panel are: 0, 0.2, 0.5, 1, 2, 5, 20, 50, and 100 ps (Kerr data) and 0, 0.1, 0.2, 0.5, 1, 2, and 4 ns (TCSPC data).

average time of about 1 ps, a time comparable to that predicted by computer simulation.57 CONCLUSION

FIG. 15. Spectra of DCS in supercritical fluoroform at a density of 1.6 rc. (a) Spectra after subtraction of solvent Raman and correction for temporal dispersion. (b) Spectra derived from fitted decays using a 3exponential fit.

slow, in the nanosecond range, approximately half of the dynamics are too rapid to be measured with the ;5 ps effective resolution of the TCSPC method. The Kerr-gated emission experiment has sufficient resolution (even without deconvolution) to measure the missing portion of the dynamics. As shown in Fig. 14, the combined use of the Kerrgated emission and TCSPC techniques reveals a remarkable dispersion in time scale of the response of this ionic liquid, stretching all the way from 100 fs to 10 ns! As a final example, Fig. 15 shows time-resolved spectra of DCS in supercritical fluoroform at 1.6 times the critical density. It has long been a goal to measure solvation dynamics in supercritical solvents, but one that has until very recently been thwarted by the low sample concentrations available in supercritical fluid solvents. To our knowledge, these spectra, together with recent fluorescence upconversion data on C153 in fluoroform,56 are the first to reveal the rapid relaxation taking place in the rarefied environment of a supercritical fluid. We display these spectra mainly to highlight the sensitivity of the Kerr-gated emission technique under favorable conditions. The spectra in Fig. 15a were recorded using a sample of ,1 mM (,0.1 OD) concentration and a specially designed cell having thin quartz windows and 2 mm sample thickness. Except for subtraction of solvent Raman bands and correction for temporal dispersion, these spectra are shown as recorded (40 s accumulation time), indicating the excellent S/N obtained with such dilute samples. This high S/N is partly due to the fact that under supercritical conditions the lifetime of DCS (limited by isomerization) is only ;50 ps, which greatly reduces the contribution of ungated fluorescence to the background noise. The bottom panel shows spectra after fitting with a triple exponential representation and normalizing to unit peak height. The continuous movement of the spectrum reflects the solvation dynamics occurring with an

We have described a fluorescence spectrometer based on an optical Kerr shutter for recording time-resolved emission spectra of typical fluorophores with subpicosecond time resolution. The instrument is based on an amplified Ti : sapphire laser and features the use of benzene as the Kerr medium together with other optical components used to maintain the high polarization quality necessary to enable observation of solutes having nanosecond lifetimes with good S/N. The present system provides excitation wavelengths near 390 nm, a usable spectral window of 400–650 nm, ;4 nm spectral resolution, and an instrument response time of 450 fs (FWHM). The spectra recorded to date prove this instrument to already be a powerful tool for chemical research. However, improvements in both time resolution, spectral coverage, and S/N are certainly possible. The time resolution of the current instrument is partially limited by the laser system employed and we anticipate that ,300 fs operation could be achieved by substituting shorter excitation and gate pulses. Much higher resolution will require selection of a different Kerr medium, probably at some cost in versatility. In the present work we have used a benzene gate and optimized component selection so as to maintain access to as wide a range of solutes and conditions as possible. In contrast, previous workers have optimized for time resolution.37,38,40–42 Many intermediate optimization points could also be envisioned. Furthermore, although our focus has been on spectral dynamics, there is nothing precluding the use of Kerr gating in other types of emission measurements, for example, measurements of timedependent anisotropies\ or resonant energy transfer. For these reasons, we anticipate that further study will prove Kerr-gated emission spectroscopy to be a useful alternative to other methods for obtaining picosecond and subpicosecond fluorescence data in a variety of applications. ACKNOWLEDGMENTS The authors gratefully acknowledge Yasuo Kanematsu and June Takeda for helpful discussions in the early stages of this work and Dr. Noritsugu Kometani for enabling us to measure the supercritical spectra in Fig. 15. This work was supported by funds from the Office of Basic Energy Sciences of the U.S. Department of Energy.

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