Original research articleRevisiting the temporal dispersion and broadening impact on degenerate two-photon absorption
Introduction
The white light continuum (WLC) Z-scan technology that can measure resonant and nonresonant nonlinear spectra allows extracting the nonlinear absorption coefficients at a broad spectral range in a single scan. In 2004, similar WL) Z-scan techniques were proposed by Balu et al. [1] and De Boni et al. [2] almost simultaneously and independently. Compared to the Z-scan experimental setups that use a prism or a grating to disperse spectral components spatially [3], [4], [5], WLC Z-scan technology without any spacial dispersion has the superiority of system-simplicity and a fast processing speed. However, a conventional WLC Z-scan system without any dispersion has an essential issue that cannot be ignored, that inevitable nondegenerate nonlinear absorption (NLA) impacts the measurement with the entire incident WLC pulses. According to the report by Balu et al. [1], if no dispersion is proceeded, it may lead to a bad fitting to the Z-scan traces, and the values of β extracted are larger than those extracted by “single-wavelength” (monochromatic) experiments. Therefore, to obtain degenerate absorption coefficients for various materials, considerable efforts [4], [6] have been made to develop WLC Z-scan technique since then. As reported by Balu et al. [1], it can reduce the impact of nondegenerate absorption on the effective β efficiently by increasing the chirp of incident WLC pulses. Moreover, De Boni et al. [6] applied rate equations to WLC Z-scan technique with a chirp of ∼4 ps. Using rate equations, degenerate NLA coefficients were precisely measured considering the dispersion of the chirp [6], [7]. It has been reported that the chirp of WLC pulses is sufficient to disperse spectral components temporally in works such as Refs. [6], [7], [8], [9]. Though no extra chirp were added, they obtained satisfying degenerate β for Coumarin-120 [9], YbPc2 solution [6], Chlorophyll a [7], and MEH-PPV [8]. However, in the case of ZnSe, extra chirp must be introduced to extract the degenerate TPA coefficients [1]. Therefore, it is still confusing to us whether the chirp of WLC is sufficient for any cases. For instance, Van Styland and Hagan [10] states in their book at Chapter 3.1.4 that “the entire WLC cannot be used in a single Z-scan since besides the degenerate 2PA there will be strong nondegenerate 2PA and these two processes cannot be simply separated. The simplest method to apply is to spectrally filter the WLC prior to the sample and perform a normal single frequency Z-scan.” Therefore, to better apply the WLC Z-scan technology, it is essential to explore more on how the chirp impacts the NLA process.
Additionally, ZnSe is a commonly used material to calibrate TPA coefficients in NLA field, for which the related theory and experiments are developed well. Hence, it is a suitable material for verification of our spectral-resolved Z-scan system. In the previous work [11], we have proved the feasibility of this system and extracted the 3PA coefficient of CS2 using a monochromatic source (at central wavelength of 793 nm). Based on this system and the WLC Z-scan setup [1], [2], we propose a method to calibrate the peak power spectral density (PSD) of the WLC spectra. Combining this method with WLC Z-scan system, we are able to extract degenerate TPA coefficients for continuous spectra by evaluating an adequate chirp.
Section snippets
Experimental setup
Referring to Refs. [1], [2], [9], we design a similar WLC Z-scan system to study the chirp effect on nondegenerate absorption. In contrast with the scheme that adds extra chirp with a thick chunk of ZnSe, which is the same material with the sample, for “it possesses large GVD in the visible which imposes a large temporal dispersion on the WLC [1]”, we use several thick quartz glass chunks due to the high transmittance in the visible region.
The light source is provided by a Ti-sapphire
Main procedures
The unit of collected data by spectrometers is analog-to-digital converter (ADC) counter, which is proportional to the peak PSD. Therefore, the spectral data cannot be used directly, instead, calibration is required to obtain the peak PSD. We will discuss about that later in Section 3.2 and Appendix A. Before each experiment, monochromatic Z-scans at central wavelength of 793 nm are applied. Using the β data (2.7 cm/GW) given by Tseng et al. [13] at 790 nm, the peak intensity can be calibrated
Factors that impact multi-photon absorption
As we all know, the major factors that impact multi-photon absorption (MPA) are the structure of energy states and the MPA cross-section. If there exist any intermediate states, sequential MPA (i.e., ESA) may take place besides instantaneous MPA, so that the total absorption increases. The conduction band of ZnSe is 2.7 eV higher than the valence band. Thus, broad spectral range of TPA can be observed at 500–900 nm. Most of the works about NLA process of ZnSe focus on the study of monochromatic
Conclusion
Based on the conventional WLC Z-scan system, we propose a method to obtain nonlinear absorption coefficients for continuous spectra by estimating a weighting function of nondegenerate absorption contribution then convolving it with the peak PSD. Consistent results with the previous works are obtained by adding adequate chirp. Using this method, we find that nondegenerate absorption depends on several factors, including pulse monochromaticity and the NLA absorption band corresponding to the
Funding
National Key Research and Development Program (No. 2019YFA0307701); National Natural Science Foundation of China (11974138,11674128,11504129,11704145,11674124).
Conflict of interest
None declared.
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