Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection

This study demonstrates a measurement system for a non-degenerate two-photon absorption (NDTPA) spectrum. The NDTPA light sources are a white light super continuum beam (WLSC, 500 ⇠ 720 nm) and a fundamental beam (798 nm) from a Ti:Sapphire laser. A reliable broadband NDTPA spectrum is acquired in a single-shot detection procedure using a 128-channel lock-in ampliﬁer. The NDTPA spectra for several common laser dyes are measured. Two photon absorption cross section enhancements are found in the experiment and validated by theoretical calculation for all of the chromophores. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (


I. INTRODUCTION
Interest in materials that exhibit high optical nonlinearity has increased dramatically in recent years.In particular, two-photon absorption (TPA) has been exploited in several current technologies, including optical power limiting, 1 all-optical shutter, 2 two-photon fluorescence microscopy, [3][4][5] and others. 6Two-photon induced fluorescence (TPIF) [7][8][9] is the most frequently used method for measuring TPA spectra and cross sections in nonlinear materials, while the Z-scan method 10,11 is less commonly employed.However, to acquire broad information on TPA spectra, wide tunable laser sources such as an optical parametric amplifier or dye laser sources are needed. 7,12,13But, even with a tunable source, the measurement must be repeated for each selected wavelength.As it is often impossible to maintain the experimental conditions throughout the time required to perform the measurement for each wavelength across the full spectral range, experimental errors are introduced.The instability in the peak intensity of the laser pulses also inevitably induces large experimental errors into this time-consuming measurement, a problem that is further enhanced by the nonlinearity of the process.Furthermore, due to the diversification in the pulse duration during the pulse wavelength shifting, the pulse intensity changes for each measurement.In addition, these methods are indirect ways to measure the TPA spectrum, and thus may su↵er from other systematic errors related to the intermediate parameters, such as the collection e ciency of emitted fluorescence, fluorescence quantum e ciency, and so on. 7inally, the degenerate detection's intensity squared dependence on the excitation beam intensity may lead to a large error during the square calculation.Such inaccuracies may a↵ect the measurements and may explain the quite di↵erent TPA cross section values that have been reported when the same method is used to examine some well-known materials. 5,7,12,14,15n 1999, Belfield et al. reported for the first time an method for measuring the non-degenerate TPA (NDTPA) spectrum using a pump-probe two-beam configuration 16 in which the strong pump was a monochromic IR laser beam and the weak probe was a white-light super-continuum (WLSC) beam.In this setup, a broad TPA spectrum can be directly measured in a single procedure by the spectral subtraction of the absorbed probe beam from the reference beam.The pump beam intensity has a linear dependence on the TPA cross section (as discussed later), which apparently induces a lower level of error than the intensity squared degenerate detection.However, the acquired spectrum di↵erence is time dependent due to the overlapping time shift between pump and probe beams.This is due to the chirping e↵ect occurring during the WLSC generation and the group-velocity dispersion (GVD) e↵ect on the probe pulse propagation time.Kovalenko et al. proved that the chirp could be eliminated by using time-correction procedure when using a supercontinuum probe. 17However, since the publication of the work by Belfield et al., there have only been a few reports using this setup for a limited number of direct-gap semiconductors and semiconductor quantum dots. 18,19n this study, we improve this method in several ways.First, we use chirp mirror pairs to compress the WLSC pulses before propagation in the sample.A very broad WLSC is generated via complex processes that include a self-phase modulation, plasma generation, and stimulated Raman scattering.Due to the di↵erent contributions of these phenomena to the generation mechanism, the transient refractive index change is wavelength dependent in a very complicated way.Therefore, it is di cult to compress the chirp of WLSC.To minimize the chirp e↵ect in our detector, we replace the spectrometer used in Belfield's setup with a time-resolved two-dimensional induced absorption ( A) spectrum map obtained by combining a polychromater with a multi-channel lock-in amplifier (MLA). 16This A map is of vital importance for determining the pump and probe pulse overlapping position in time.The MLA not only causes a large improvement of the signal noise ratio (SNR), but also makes it possible to simultaneously and directly measure a broadband di↵erence absorption spectrum with 128 spectral points and a spectral resolution of 0.83 nm.With this high performance equipment, the TPA profiles for several laser dyes.The TPA spectra thus obtained are confronted to theoretical predictions to further validate our approach.

II. THEORY
In general, the attenuation of a light beam passing through an optical medium along an axis, designated here as the z-axis, can be expressed by the following phenomenological expression (this case includes linear and nonlinear interactions): 20 Here, I(z) is the intensity of the incident light beam propagating along the z-axis and ↵, , and are the one-, two-, and three-photon absorption coe cients of the transmitting medium, respectively.To compare the absorption induced by the two-photon process in the case of an incident laser with a negligible bandwidth to the electronic bandwidths relevant to the two-photon transition including virtual states, we have the following: The non-degenerate condition, in our situation for an intensity I 1 of the WLSC probe beam and I 2 for the pump beam, leads to: Here, the two-photon absorption coe cient is linear and proportional to the imaginary part of the third order nonlinear susceptibility as given by 21
AIP Advances 5, 127138 (2015) " i denotes the dielectric constant at the angular frequency of !i for each incident light, and c is the velocity of light.For input (before the medium) beam intensities labeled I 10 and I 20 , and considering the case where I 20 >> I 10 , Eqs. ( 3) and ( 4) can be solved as follows I 1 e 1 I 20 z I 10 . Then, 1 I 20 z = ln This condition is met in our setup as the intensities at the sample position of the pump and the probe within the spectral resolution are estimated to be 15 GW/cm 2 and 0.1 GW/cm 2 , respectively.From Eq. ( 8), it is easy to see that with an intense pump, the TPA coe cient is linear in proportion to the pump beam-induced WLSC probe beam absorbance di↵erence ( A).The relationship between the TPA cross section in cm 4 /GW) and TPA coe cient (in cm/GW) is given by 17 where N A is the Avogadro constant and c is the concentration of the sample (in M).From Eqs. ( 8) and ( 9), we can conclude that the TPA cross section is proportional to the absorbance change ( / A).As A can be directly acquired through the pump probe experiment, the TPA cross section can be calculated from experimental data without interference from other error sources (vide supra).Noteworthy, in this study, all spectra reporting TPA cross sections are based on the transformed TPA wavelength, which is the relative value calculated using (2/ TPA = 1/ pump + 1/ probe ).

III. EXPERIMENTAL PROCEDURES
We use a pulse energy of about 200 µJ from the Spitfire Ace Laser system (Spectra Physics, 1 kHz repetition rate, central wavelength at 798 nm).Total energy is divided into two using a 10% reflection beam splitter.The transmitted beam a↵ords the pump beam, while the reflected beam is used to generate the WLSC, focusing the fundamental beam on a 2-mm-thick sapphire plate.The strong fundamental part of the beam is blocked by transmitting the beam through a 720 nm short pass dichroic mirror.The WLSC spectral range is from 500 nm to 730 nm.A pair of chirp mirrors (GVD, 470⇠810 nm, -40 ± 20 fs 2 ) are used to slightly compress the WLSC beam with a triple-pass configuration.Next, the WLSC probe beam and the time-delayed pump beam are both focused using an o↵-axis parabolic mirror and overlapped at the sample point.After passing through the sample, the beams are collimated by another o↵-axis parabolic mirror.The pulse duration of the fundamental pump beam is measured as 103 fs using the SHG-FROG method. 22The spot size of the focused pump beam at the sample surface is measured with a CCD beam profiler (Thorlabs) that has x-and y-axis of 146.1 and 149.9 µm, respectively.For data collection, the WLSC probe beam is focused into a multimode fiber, which is guided to the polychrometer, where the signal is captured by a 128-channel MLA.A synchronized chopper with half of the laser repetition frequency is introduced into the fundamental beam path and provides the reference frequency signal for the MLA.The pump beam power is controlled by a wheel gradient-neutral density filter set in the pump path.

IV. RESULTS AND DISCUSSION
A typical result for our TPA spectrum measurement procedure is shown in Fig. 1.The sample is coumarin 6 dissolved in chloroform at a concentration of 23.7 mM.The time-resolved twodimensional di↵erence absorbance ( A) spectra of the probe beam (WLSC) is shown in Fig. 1(a).The large positive signal located at the center, around 560 nm, with a delay time of around zero, corresponds to the TPA e↵ect.The black solid line traces the peak of this A map; it shows the zero time position where the pump and probe pulses overlap. 17The twists in this peak-tracing line are due to residual chirp of the WLSC and its group velocity dispersion (GVD) in the solvent.The TPA cross section spectrum of coumarin 6 is shown in Fig. 1(b).It has a spectral resolution of about 10 nm, which is due to the FWHM of pump spectral shape.For coumarin 6, the results shows a TPA peak located at 652 nm with a cross section of 1015 ± 107 GM.This TPA band is in fairly good agreement with the computed NDTPA spectra (Fig. S2), given the di↵erent approximations that cannot be avoided (see Supplemental Material 30 for details).
The two-dimensional A map for rhodamine 6G dissolved in methanol (concentration: 16.2 mM) is shown in Fig. 2(a).Due to losses caused by the stationary absorption of the sample solution, the WLSC probe spectral range is limited to the lowest end at 562 nm.A large positive A signal is observed for the probe wavelength range from 562 nm to 658 nm.Noticeably, in the same spectral range, some large negative signals appear with delay times longer than 100 fs, and the intensity decreases as the wavelength increases.The comparison of this pattern with its spontaneous fluorescence spectrum, confirms that it is the result of the stimulated emission (SE) of rhodamine 6G.This SE can also be observed in the A map of coumarin 6 when the intensity scale is narrowed, although the intensity is too weak to be perceived directly in Fig. 1(a).
The TPA is one of the most common third-order nonlinear optical processes, but other third-order nonlinear e↵ects, such as stimulated Raman scattering, have already been well-studied using a similar non-degenerate pump-probe setup. 17In this work, we stress that a strong stimulated Raman loss 23 (SRL) signal is found in a blank test made of methanol solvent.The details are shown in Fig. 2(b).An inverted triangle shaped signal is located near 645 nm; its intensity distribution has a two peak structure.These two peaks are caused by the Raman shift of 3000 cm 1 and 3300 cm 1 , respectively, which correspond to the -CH 3 asymmetric stretch and the -OH stretch.Many common solvents, such as ethanol, DMSO, water and so on, have similar intense SRL signals in this spectral range.These additional signals must be rigorously accounted for in dye measurements.Carbon tetrachloride (CCl 4 ) or chloroform (CHCl 3 ) are the recommended solvents for experimental verification as they do not have a large SRL signal around 3000 cm 1 .Unfortunately, many common dyes such as xanthene dyes do not readily dissolve in such solvents.Therefore, solvents with intense Raman signals in the probe spectral range must sometimes be used, and it is necessary to account for the contribution a Raman solvent makes to the observed TPA spectrum.The comparison of Fig. 2(a) with Fig. 2(b) shows that the TPA signal of the sample is contaminated with a Raman loss signal induced in the solvent; the contamination range is marked with a circle of red dots.It is di cult to distinguish the SRL's contribution to the TPA signal when they are spectrally overlapping, as they are both two-photon processes belonging to the comparable third-order nonlinear e↵ects. 17,22The two incident beams (WLSC (! 1 ) and 800 nm (! 2 )) can interact with each other in time overlapping conditions, and both the ! 1 photons and the ! 2 photons can be absorbed during a TPA process.In the same way, when associated with the ! 1 photons, the ! 2 photons can be absorbed (scattered) by the Stokes mechanism or can be amplified by the anti-Stokes mechanism if the vibrational di↵erence level corresponding to the frequency di↵erence (! 1 ! 2 ) is populated.The latter case is not fulfilled in this experiment.Furthermore, coupling between the TPA and Raman processes may occur if the solvent levels in the sample (including at the solvent molecule level) are coherently coupled.
The vibronic states of solvent molecules do not lead to strong coupling with the solute vibronic states due to the lack of strong interaction through the hydrogen bonding.Therefore, there is no "intrinsic" interference between the electronic polarization and the solute molecule coherence in the solvent system.However, an extrinsic interference is possible.For example, interference may occur if an amplified ! 2 photon created via a stimulated Raman scattering by ! 1 photons is used in the TPA together with ! 1 .The Raman gain expected for a ! 2 photon when ! 1 photons exist can be estimated by the Raman correspondence of the solute molecule with a 24.7 M concentration.It is 5 ⇥ 10 12 photons/cm 2 sec when the number of ! 1 photons is 2 ⇥ 10 16 photons/cm 2 sec.The loss of the probe light through this process can be completely negligible, and the following equation can be used: Here, A TPA and A RS refer to the TPA and Raman e↵ect, respectively.For the solvent sample, which is a mixture of the solute and solvent, the e↵ect of both should be considered.Especially in this setup, it is expected that the TPA will not create interference, even in the neat solvents, as the absorption edge of the solvent molecules are located much higher (blue side) than the half of the shortest edge of the continuum spectrum.However, Raman scattering of the solute scarcely occurs in a relative Raman shift larger than 2000 cm 1 .Even if, due to the solute in the sample, the Raman signal makes a contribution, it is expected to have a negligibly low intensity as the concentration of the dyes molecules is lower than the concentration of solvent molecules by the factor of 10 3 .The concentrations of the solute and solvent in the experiment are calculated to be 24.7 M and 8.1⇥10 3 M, respectively.Therefore, from the right part of the Eq. ( 10), it can be concluded that A TPA is a measure of the solute only, and A RS is a measure of the solvent only.
A polymethyl methacrylate (PMMA) thin film doped with rhodamine 6G is investigated with the expectation of directly removing the solvent interference.PMMA has a large molecular weight and is transparent in the visible and near IR light range; thus, it is expected to be an appropriate matrix to investigate TPA of organic molecules.The PMMA powder and rhodamine 6G are both dissolved in chloroform and mixed with each other; then the mixture is dried and spin-coated on a glass plate.After being stripped from the slide, the film is used for the measurement.The measured A map in Fig. 2(c) shows that this sample does not have a large A peak around 645 nm (red dash circle mark), which means the Raman background e↵ect is e ciently minimized.However, it is di cult to directly determine the TPA cross section with this doped PMMA film, because it is di cult to precisely determine the film thickness and the number of dissolved molecules, as the molecules in the polymer matrix sample are inhomogeneous.This is a serious problem in any kind of spectroscopic measurement of doped molecules in a polymer film.In spite of this, the relative values of the TPA cross section recorded at di↵erent wavelengths are reliable due to the broadband measurement.This is verified with several scans.Fig. 2(b) suggests that, for the probe range 580 nm to 600 nm, the distortion e↵ect from the solvent is negligible.Then, by assuming that rhodamine 6G has the same TPA properties in methanol as in PMMA, we can reconstruct a more reliable TPA cross section spectrum by merging and scaling the result in PMMA to the methanol case.Fig. 2(d) shows that the measurement starts with the blue round line from 670 nm and transforms into the red open square line around 690 nm.The optimized TPA peak is located at 691 nm with a cross section of 596 ± 69 GM.This result is discussed in more detail in the next section.
We use a sample of rhodamine 6G in methanol to study the dependence of the TPA cross section on the pump power and sample concentration.To examine pump power dependence, the sample is fixed at a concentration of 16.2 mM.The pump power is adjusted to between 40 µW and 840 µW with a neutral density filter.For convenience, we track the A peak values at 620 nm probe wavelength on each A map acquired by di↵erent pump power; they are shown as blue triangle marks in Fig. 3.The linear fitting has a nearly zero intercept, which shows a good agreement with Eq. ( 8).As shown in Fig. 3, there is almost no visible saturation of TPA in this pump power range.For the concentration dependence measurement, the pump power is fixed at 400 µW.Several samples with di↵erent concentrations are investigated in a similar way: A peak values at 600 nm and 620 nm for each concentration are marked with black circles and red round lines in Fig. 3, respectively.The linear fitting for each group shows that the 600 nm A data has a nearly zero intercept, while the 620 nm clearly does not.This non-zero intercept evidences the above mentioned solvent's SRL interference, while zero intercept fitting lines are examples of a purely TPA phenomenon.
Having clarified all these issue, we can further investigate other dyes: rhodamine 123 (4.2 mM) dissolved in methanol and coumarin 343 (27.3 mM), Nile red (0.75 mM), and Nile blue A (0.68 mM) dissolved in chloroform.The choice for chloroform, despite its low solubility for the chosen solutes, is based on minimum SRL contribution to avoid contamination of the TPA signal.Corresponding TPA cross sections are shown in Fig. 4 (black square dotted line).The rhodamine 6G, rhodamine 123, coumarin 6, coumarin 343, Nile red and Nile blue A show e cient TPA peaks at 691 nm, 660 nm, 652 nm, 651 nm, 669 nm and 626 nm, respectively.The corresponded NDTPA cross sections are 596 GM, 776 GM, 1015 GM, 49 GM, 3270 GM and 1407 GM, respectively.In general, all of the results in this study evidence a larger TPA peak value than those reported using degenerate conditions.In fact, Table I compares the rhodamine 6G TPA cross sections obtained in this work to previously published values performed using degenerate conditions.The results all agree that the position of the TPA peak is around 690 nm.Obviously, our NDTPA values are larger than the DTPA found in other reports.Noteworthy, ns pulses are known to overestimate TPA cross sections, especially due to excited state absorption (the two-photon absorption can be non simultaneous).Some studies have reported that the NDTPA is usually enhanced as compared to DTPA. 20,25his phenomenon can be explained as an intermediate state resonance enhancement (ISRE); one of the photons can have an energy close to one of the molecular excitation energies, and will achieve intermediate state resonance.
To get theoretical confirmation of our experimental results, we have implemented quantum chemical and few states approaches for both linear and nonlinear optical responses of the chromophores of interest.We use density functional theory (DFT) and time-dependent (TD) DFT approaches, as implemented in the Gaussian 03 and 09 packages. 26,27No simplifications are made for the chemical structures.The properties of interest are related to ground state geometry: that is, geometry optimization and one-and two-photon absorption is related to the electronically excited states (ES).The polarizable continuum model (PCM) as implemented in Gaussian 09 and Gaussian 03 is used to simulate the solvent e↵ects on geometries and optical spectra, respectively.No additional local field corrections are considered. 28Optical spectra are obtained using the density matrix formalism for non-linear optical responses as proposed by Tretiak and Chernyak. 28,29Absolute TPA amplitudes are derived using expression (38) of Ref. 28 for degenerate two-photon absorption (DTPA) considering both diagonal and non-diagonal contributions.For non-degenerate TPA, the TPA cross section is related to the imaginary part of the third-order polarizability ( ! 1 ; ! 1 , ! 2 ,! 2 ) and the frequency dependent prefactor ! 2 is replaced by 2! 1 2 ! 2 /(! 1 +! 2 ) as in Ref. 24, where index 1 refers to the probe beam and index 2 refers to the pump beam.The calculated TPA spectra shown in Fig. 4 are obtained at the TD-B3LYP/6-311+G*//B3LYP/6-311+G* level of theory in conventional quantum chemical notation "single point//optimization level" including up to 20 singlet ES.Given the overall good agreement between the experimental and theoretical OPA band positions (Fig. S1), NDTPA spectra were computed for the experimental pump wavelength only (1.55 eV/800nm).The damping factor introduced to simulate the finite line width in the resonant spectra is fixed according to Table S1 in the Supplemental Material. 30The ES structure was further checked at the TD-! B97xD/6-311+G*//B3LYP/6-311+G* level.More details for the calculation are included in the Supplemental Material. 30he calculated TPA cross sections are significantly larger than the experimental results shown in Fig. 4.This may be attributed to a number of factors related to the level of theory in use.First, B3LYP, the most suitable exchange-correlation functional in Gaussian 03 for optical properties, is known to overestimate conjugation and thus reduce bond length alternation and overestimate transition dipole moments. 31For example, if the TPA cross section scales as the fourth power of dipole moment matrix elements (see expressions S1-S3 in the Supplemental Material 30 ), a 15% overestimation of the dipole moments may double the TPA cross section.Next, the choice for the finite line width, which is set the same for all ES, directly a↵ects the TPA amplitudes.In fact, when the two-photon excited state is near resonance, the TPA amplitude scales as 1/ (Fig. S2).In addition to local field corrections such as dynamic contributions, 28 other contributing factors include all of those currently considered in predictions of linear optical properties (band shape, amplitude and position) of solvated chromophores. 32Specifically, the present solvation model is limited and does not account for state specific responses, 33 or for explicit solvent molecules or counter-ions.Furthermore, vibronic contributions 34 are not simulated.Despite all of these approximations, this level of theory has already proved ecient for rationalizing experimental TPA spectra. 28,33The OPA spectra are systematically blue shifted compared to the experimental results.However, compared to the TD-B3LYP/6-31G(d)//HF/6-31G(d) level of theory in a vacuum, both the solvent and a larger basis set improve the agreement between calculated and experimental results.Given the small spectral window investigated experimentally, to be compared with the error in the calculated peak position (vide supra), these TPA spectra reveal a TPA band that is close to that experimentally observed.These bands, which have significant magnitude, are related to one (or several) higher lying excited state(s).Comparison between DTPA and NDTPA calculated spectra (Fig. 4) clearly demonstrate the intermediate state resonance enhancement experimentally observed., which depends on the excited state structure of the particular chromophore.In fact, further intuitive understanding may be gained from few states models as discussed in details in the supplementary information.Besides the larger ISRE for rhodamines as compared to coumarins, the various transition energies taken for the TPA states for Nile Red and Nile blue A (Table S2) evidence the strong influence of respective transition energies compared to pump and probe photon energies on the overall enhancement factor.

V. CONCLUSION
In this study, we improve the method for measuring non-degenerate TPA cross sections by introducing an MLA system into the detection setup.With this system, high resolution and precise chirping correction is achieved using a A map.However, this method still requires further improvement.First, many solvents, such as water and methanol, contribute a strong Raman loss signal with a Raman shift around 3000 cm 1 ⇠ 3300 cm 1 .This disturbance can be minimized by selecting an appropriate solvent and by properly correcting for the Raman e↵ect.Second, the TPA spectrum detection range is limited to between 600 and 760 nm, when using 800 nm pumps, as in this study.This problem can be solved by choosing a solvent like chloroform or by changing the pump beam wavelength to a variable range with an OPA setup.Another feasible and easily available solution is to use a much wider WLSC, such as one generated by tapped fiber or photon crystal fiber. 35his study measures the TPA spectrum for several types of the laser dyes including xanthene dyes (rhodamine 6G and rhodamine 123), coumarin dyes (coumarin 6 and coumarin 343), and oxazine dyes (Nile red and Nile blue A).By comparing the results for our analysis of rhodamine 6G to published degenerate measurements, we confirm that TPA is enhanced in non-degenerate cases.We verify this conclusion with theoretical calculations.To the best of our knowledge, this is the first report of measurements for the other laser dyes sampled here.This method makes the measurement of TPA spectrum of materials much more convenient.It contributes to the new TPA materials development, and has already been applied by our collaborators. 36

127138- 5 Xue
FIG. 2. (a) Two-dimensional absorbance change of WLSC through rhodamine 6G dissolved in methanol.(b) Background test for solvent methanol only.(c) Absorbance change of WLSC through rhodamine 6G doped in PMMA film.(d) Measured TPA cross section spectrum of rhodamine 6G in methanol and PMMA.

FIG. 3 . 7 Xue
FIG.3.Pump power dependence (blue triangle) and sample concentration dependence (red round and black circle) in rhodamine 6G TPA cross section measurement.

FIG. 4 . 8 Xue
FIG. 4. Measured and calculated TPA cross section for (a) rhodamine 6G, (b) rhodamine 123, (c) coumarin, 6 (d) coumarin 343 (e) Nile red and (f) Nile blue A. In each figure, black solid line with error bar are the measured experimental value; calculated DTPA and NDTPA spectrum (800 nm pump) are plotted in blue dash line and red solid line.

TABLE I .
Measured rhodamine 6G TPA cross section value compared with previous literature.
a NLT: nonlinear transmission.b TPIF: two photon induced fluorescence.c NWLP: nondegenerate white light probe.d Pump pulse duration.