We present a new technique for direct measurements of degenerate two-photon absorption (TPA) spectra of two-photon absorbing materials including non-fluorescent samples. This technique is based on the use of an intense single continuum-generation beam as the coherent white-light source with specially flattened spectral distribution. The different spectral components of the continuum beam are spatially dispersed and then passed through the sample material along different pathways so that nondegenerate TPA processes among different input spectral components can be avoided. By comparing the input and transmitted continuum spectral distributions, the TPA spectrum for a given sample can be obtained. As an example, the continuous TPA spectrum (from 550 to 1000 nm) is measured for a novel two-photon-absorbing compound (AF-389) which exhibits an extremely high TPA cross-section value of ~1×10-20 cm4/GW, or ~249 GM, around ~800-nm spectral range in femtosecond regime.
© 2002 Optical Society of America
Interest in seeking novel nonlinear optical materials with high capability of two-photon absorption (TPA) has been rapidly growing in the recent years. So far, a large number of new organic chromophores have been reported, which possess much higher TPA cross-section values than those commercial organic dyes [1–10]. However, the measurements of TPA cross-section values for these new compounds were mostly performed at either a single wavelength or few discrete wavelengths of laser radiation. From the viewpoint of molecular design and application considerations, it is necessary to know the cross-section value as a function of excitation wavelength in a wide spectral range. To reach this goal, a pulsed laser source with high peak power is needed and it should be tunable in a very broad spectral range in order to cover the complete TPA spectral band of a tested sample. Tunable dye laser, optical parametric generator (OPG), and Ti:sapphire laser are the common candidates for this purpose [11–13]. However, the spectral tunability for dye lasers is less than 50~70-nm without changing the dye species. The effective tunability (with a considerable output level) for Ti:sapphire is usually less than 200-nm and for OPG it is around 300~350-nm in the spectral range of 500~1000-nm without changing the pump wavelength. This method is very time-consuming because of its slow spectral tuning process and the nature of multi-points measurement. For materials exhibiting two-photon excited fluorescence, an alternative approach is to measure TPA-induced fluorescence intensity as a function of excitation wavelength [14–16]. The advantage of this technique is its higher sensitivity for detecting fluorescence signals and a much lower requirement for intensity levels of tunable laser source. The disadvantage is that the final TPA cross-section spectrum can be extracted only with the assumption that the quantum yield of TPA-induced fluorescence as a function of excitation wavelength is known. However, this information is not always available especially for new materials. Obviously, this method is not applicable to those materials that are two-photon absorptive but not fluorescent.
It is well know that in many transparent liquid and solid media, a white-light continuum-generation can be efficiently produced by using high peak-power ultrashort laser pulses of picosecond or femtosecond duration [17,18]. Even in the early stage of continuum-generation with picosecond laser pulses, this new type of coherent white light source has been employed to measure the transient linear absorption spectra of sample materials [19 ]. A major advantage of this approach is the elimination of need for spectral tunability and scanning mechanism; in other words, the entire linear absorption spectral structure can be obtained, in principle, with a single shot of continuum pulse.
The same continuum-generation technique can also be used to measure TPA spectra of various nonlinearly absorbing materials. Very recently, the continuum-generation technique has been successfully used to measure the nondegenerate TPA spectra for organic chromophore solutions [3,20,21]. In that work a pump-probe two-beam configuration was employed: a weaker white continuum light (450–750 nm) was employed as a probe beam along with a stronger 1210-nm laser beam to excite nondegenerate TPA process in the sample medium. In this case, the most critical requirement is to ensure a synchronous arrival at the sample position of the monochromatic pump pulse and the probe pulses with different spectral components. It is difficult to meet this requirement because the frequency chirping effect takes place in continuum generation .
We report here a new approach to measure the direct degenerate TPA spectra, which is based on using a single intense continuum beam only. In this approach, a powerful continuum beam is spectrally dispersed by a prism or a grating and then focused into a measured sample. Since different spectral components of the continuum beam pass through different areas of the sample, the nondegenerate TPA processes among these different spectral components can be eliminated. Furthermore, the frequency chirping effect among different spectral components of the continuum has no impact on the TPA spectral measurement.
In our experiment heavy water was chosen as the nonlinear transparent medium to provide continuum generation because of its high efficiency and stability compared with other commonly used solvents or liquids [19,22]. The pump source of this continuum generation was a focused ultra-short pulsed laser beam provided by a Ti:sapphire laser oscillator/amplifier system with following output parameters: pulse duration ~140 fs, wavelength ~790 nm, beam size ~3 mm, divergence angle ~0.3 mrad, repetition rate 1 kHz, and available average power up to ~150 mW (or pulse energy up to 150 μJ). The experimental setup for continuum generation and TPA spectrum measurement is schematically shown in Fig. 1. The ~140-fs and ~790-nm laser beam was focused by an f=20-cm lens into the center of a 10-cm long liquid cell filled with heavy water. The reason of using a long liquid cell here is to increase the energy conversion efficiency from the input pump pulses to the white-light continuum pulses, also to avoid the possible damage or continuum-generation from the cell’s windows. The output continuum light beam was collimated via an f=30-cm lens, passed through a SF10-glass prism (or alternatively reflected from a dispersion grating), and then focused via an f=10-cm lens into the center of a 1-cm-path quartz cuvette filled with either a sample solution or a pure solvent. With this particular arrangement, different spectral components of the continuum beam were spatially separated from each other at sample position and only degenerate TPA from the same spectral component could take place. The intensity distribution of the dispersed spectral image at the sample position can be further imaged through a camera lens set on the surface of a CCD array (mode ST-7E from SBIG Inc.). By comparing the recorded continuum spectrum passing through a chromophore solution sample to that passing through the pure solvent sample, the attenuation of different spectral components due to the investigated chromophore can be readily determined. Furthermore, if the linear absorption in the measured spectral range is known or negligible, the relative nonlinear absorption spectrum due to degenerate TPA can be finally obtained.
The reason to use a prism not a grating as the spectral dispersion element in our current setup is that most of the energy for different spectral components can be retained after passing through it without the zero-order energy loss occurring in grating diffraction. However, the angular dispersion of the prism is highly nonlinear and determined by the refractive-index dispersion curve of the material of which the prism is made. In our setup the prism is made of SF10 glass and the CCD array has 765×510 pixels in the x- and y-directions, with 9×9-μm size for each pixel.
Calibration of Wavelength-Channel Relationship
Four laser beams of λ 1=532 nm (from frequency-doubled Nd:YAG laser), λ 2=632.8 nm (from He-Ne laser), λ 3≈790 nm (from Ti:sapphire laser) and λ 4=1064 nm (from Nd:YAG laser) were separately used to calibrate the channel-wavelength curve that can be theoretically calculated based on the refractive-index dispersion curve of SF10 glass. By comparison, the measured apparent linewidths of these laser lines in channel scale of CCD array were Δλ 1≤2 channels, Δλ 2≈2 channels, Δλ 3≤3 channels, and Δλ 4≤3 channels, respectively. The corresponding values of spectral resolution of our system in these wavelength ranges are 1 nm (at 532 nm), 2.5 nm (at 632.8 nm), 5 nm (at 790 nm), and 20 nm (at 1064 nm).
One issue should be addressed here, which is the temporal behavior of different spectral components within the continuum spectrum. In order to measure the pulse duration of these components as a function of wavelength, we placed a narrow slit in the solution sample position shown in Fig. 1 to select a spectral component with certain wavelength. The pulse duration of such chosen spectral component could be determined by using a standard cross-correlation SHG technique in conjunction with a BBO crystal. Our results show that the measured duration values of different spectral components were basically the same, i.e. δt≈850 fs in the measured spectral range from ~650 to 900 nm, within an experimental uncertainty of ±15%. Therefore, the CCD array-recorded electronic signal intensities for different spectral channels are simply proportional to their light intensities.
Figure 2 (a) shows the relative spectral distribution curves of the continuum light from the heavy water at eight different input levels (average power from 0.4 to 35 mW or pulse energy from 0.4 to 35 μJ) of the 790-nm pump laser beam. These curves are recorded by the CCD array working within its linear response range and corrected for its spectral sensitivity curve provided by the manufacturer. It can be seen that there is an asymmetry between the Stokes-and the Anti-Stokes sides of the pump wavelength, and the relative intensity in ranges of both sides and far from the central peak position are increasing with an increase of pump power level.
Spatially Selective Attenuator for Flattening of Continuum Spectrum
As shown in Fig. 1, a set of neutral-density filters with very low transmission were placed in front of the CCD array to significantly attenuate the intensities of spectral signals arriving at the array surface. This is to guarantee that the maximum intensity of measured spectra is lower than the saturation level of the CCD-array detector that has an effective dynamic range ~3×103 with cooling the detector down to -8 °C. In Fig. 2(a) one can see that even at a higher input pump level the spectral intensity levels in 650–550-nm range are still remarkably lower than the central peak. It means that no good signal/noise ratio can be obtained in this spectral range. On the other hand, if the central spectral intensity of the continuum is too high, the saturation effect of TPA process may take place, which is undesirable for our experimental purpose. For these two reasons we have to use a spatially selective attenuator to attenuate the central part of continuum spectra while keeping other parts unattenuated. To do so we put a narrow and highly reflective silver-film strip, which was coated on a thin glass slide, in front of the sample cuvette along with the vertical (y-) direction. Choosing a suitable width for the coating strip and slightly adjusting the transverse position and the gap distance between the coated slide and the front window of the cuvette, the signal intensity at the central part of the continuum spectra can be properly attenuated. Consequently, the relative intensities over the spectral range of 650–550-nm can be increased, by reducing attenuation ratio of the neutral density filter in front of the CCD array. As an example, Fig. 2 (b) shows the modified relative spectral distribution curve of the continuum generation at a input pump level of 35 mW and after passing through a silver-coating strip attenuator. It is obvious that the relative intensity in the shorter wavelength range (550 to 650 nm) has been remarkably enhanced, which is desirable to get an improved signal/noise ratio for the CCD array response in this range.
The sample employed for our current TPA spectral measurement is the solution of a strongly two-photon absorbing organic chromophore (AF389) in tetrahydrofuran (THF). This new chromophore was synthesized at the Polymer Branch, AFRL/MLBP, Materials & Manufacturing Directorate, Air Force Research Laboratory. The chemical structure of AF389 is shown in Fig. 3. The linear absorption spectral measurement of AF389 in THF shows that the major one-photon absorption band is located at ~437nm position with a band with of ~75 nm. There is no linear absorption in the spectral range from 550 to 1000 nm for the solute for a 1-cm-long solution sample of 0.02 M concentration. The latter feature makes the TPA spectral measurement in this range much simpler and easier. In other wards, any intensity-dependent nonlinear absorption occurring in this spectral range can be readily measured using the procedure described in the following section. In addition, AF389 solution in THF is highly fluorescent upon excitation of one-photon (400–470 nm) or two-photon (~800 nm) absorption. In both cases, the fluorescence emission peak is located at ~510 nm with a spectral bandwidth of ~60 nm.
Relative TPA Spectral Curve
Figure 4(a) shows the relative spectral-intensity curves of the transmitted continuum beam after passing through a 1-cm long pure THF sample, and passing through an AF389/THF solution sample of d0=0.02 M with the same path length separately. The input pump level was 70 mW (pulse energy 70 μJ). Each curve was averaged over five measurements, and each measurement was based on a 2-second exposure for 1 kHz continuum light pulses (integrated over two thousand pulses using the program provided by SBIG Inc.). From these two curves we could immediately obtain the nonlinear transmission curve that is shown in Fig. 4(b) which is determined by equation (1):
where I THF(λ) and I AF(λ), respectively, are the transmitted spectral intensity distribution of the continuum beam after passing through the pure solvent sample and the AF solution sample separately. The reason to define the transmissivity by Eq. (1) is that the possible TPA contribution from the solvent (THF) itself can be automatically subtracted. Assuming that the degenerate TPA is the major mechanism leading to the observed intensity-dependent transmission drop, T(λ) can be theoretically described as 
Here, β is the two-photon absorption coefficient, z is the path length of the sample medium, and a uniform transverse-intensity distribution for each spectral component within a small spectral interval is assumed. From the above equation, the β value as a function of λ can be derived as
In our case both I THF(λ) and I AF(λ) are measured in relative units, then the relative β values as a function of λ. can be readily obtained according Eq. (3). Such obtained relative spectral curve of β(λ) for AF389 in THF is shown in Fig. 4(c).
TPA Spectrum in Absolute Scale
According to its definition, the TPA coefficient β is a material parameter and only dependent on the wavelength of the excitation wavelength; but it is not dependent on the input intensity provided that no saturation or reverse saturation effect occurs. It is known that the β value (in units of cm/GW) has a simple linear relation with the TPA cross-section value, σ 2(λ), described by 
Here, N A=6.023×1023 is the Avogadro number, d 0 is the chromophore concentration (in units of M) in the sample solution, and hν is one photon energy (in units of J). From these relations we know that the relative spectral curve of TPA coefficient β(λ) is equivalent to that of TPA cross-section σ2(λ). Moreover, the obtained relative spectral curve can be further transferred to a scale of absolute TPA cross-section values. Therefore we need to measure the absolute value of σ2(λ 0) at any given wavelength position using an ordinary quasi-chromatic laser beam of λ 0 in the same pulse-duration domain. Once a single absolute value of σ2 λ 0 is known at the λ position, the entire TPA cross-section spectrum curve can be simply calibrated accordingly.
In our case, it is more convenient to measure the absolute cross-section value σ2(λ 0) at ~790-nm position using a much weaker input laser beam (not shown in Fig. 1) directly from the Ti: sapphire laser system. By measuring the nonlinear transmissivity change as a function of the absolute input intensity level, the absolute value of TPA cross-section (at λ 0≈790 nm) for AF389 solution in THF is determined to be ~1×10-20 cm4/GW according to Eq. (4), or ~2.49 ×10-48 cm4sec according to Eq. (5), or ~249 GM in another unit (1 GM=10-50 cm4sec), with an experimental uncertainty of ±15%. In this case, special care should be taken to ensure that the intensity level of unbroadened laser pulses and the induced nonlinear transmissivity change are nearly the same as the case using corresponding spectral component of the continuum-generation beam.
Based on the principle and procedure we have briefly described, one may recognize that our method is straightforward in principle, relatively simple, highly efficient and much less time-consuming to execute. As we mentioned above, the whole relative TPA spectral curve from 500 to 1000-nm range for a given sample can be measured in less than several tens of seconds.
The reliability and reproducibility of this technique is essentially determined by several major factors. One is that the local spectral intensity levels in the sample material over the whole tested spectral range should be high enough so that the change in nonlinear transmissivity must be considerably large (at least > 1–3%). For the same reason the concentration of the sample solution should be as high as possible (at least >0.01 M). Otherwise much poor signal/noise ratio will result. The other factor is the profile flatness of spectral distribution of the continuum-generation input. A large difference or rapid intensity variation along the spectral distribution profile of the input continuum-generation may lead to some additional complexity related with either excited-state absorption (reverse saturable absorption) or the TPA saturation. One task for the further improvement is to be able to attenuate the central peak band more effectively and more smoothly; the other is to enhance the relative intensity levels over the short-wavelength range. Then the signal/noise ratio can be significantly improved over this spectral range.
The spectral resolution of this technique is mainly determined by the spectral dispersion element adopted. In the present case it is relatively low owing to the poor angular dispersion of the prism. However, the spectral resolution can be significantly improved by replacing the prism by a high-efficiency grating. In the latter case the final spectral resolution may also be affected by several other factors, such as the filament formation in continuum-generating medium, the diffraction effect from the edge of silver-stripe attenuator, as well as the relative ratio between the confocal parameter of the focused continuum beam and the optical path-length of the solution cell.
This work was supported by the U. S. Air Force Office of Scientific Research, Washington D.C. and the Polymer Branch, Materials & Manufacturing Directorate, U. S. Air Force Research Laboratory, Dayton, Ohio.
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