2.3.1. Resonant NLO properties at 800 nm
Because two derivatives possess strong linear absorption below 860 nm, it was expected that strong nonlinear absorption effect may occur within the absorption band. Then, using femtosecond pulses of 800 nm (1000 Hz, 100 fs) as an excitation light source, we measured the open aperture Z-scan data of the DMSO solutions of two derivatives with a concentration of around 1.3 × 10
-3 M (
Figure 3a). The incident light intensity was around 76.4 GW/cm
2. Under the same incident light intensity, derivatives exhibit strong saturable absorption effect, while no obvious signals were observed in the DMSO solvent.
In the open-aperture experiment, the simplified expression formula of normalized transmittance can be described as follows [
38]:
where β (in unit of cm/GW) is the nonlinear absorption coefficients. I
0 (in unit of GW/cm
2) is the light intensity at the focal point (z=0). L
eff (in unit of cm) is the effective length of the sample, which is expressed as L
eff=(1-e
-αL)/L, with the linear absorption coefficient α and the physical thickness L. z
0=kω
0/2 is the diffraction length, in which k=2π/λ is the wave number and ω
0 is the spot radius at the focal point. By fitting the experimental data with Equation (1), the nonlinear absorption coefficients (β) of BDP-1 and BDP-2 in DMSO solutions can be determined as -0.30 and -0.16 cm/GW. Considering the NLO properties of sample solutions were influenced by the concentration, it will be more objective to compare the intrinsic NLO parameters among different samples according to following equation [
39]:
in which
x (solution) is the total NLO parameters of the sample solution, including nonlinear absorption coefficient, nonlinear refractive index.
f is the volume fraction of the derivatives relative to DMSO.
x (solvent) is the NLO parameters of DMSO.
x (intrinsic) is the intrinsic NLO parameters of the derivatives. As a result, the intrinsic nonlinear coefficients of BDP-1 and BDP-2 were determined, i.e., β (intrinsic) -1.48 × 10
4 and -8.26 × 10
3 cm/GW, respectively. Considering the 4-(N, N-dimethylamino) phenyl group has weaker electron-donating ability than the 1-ethyl-1,2,3,4-tetrahydroquinoline groups, the larger β (intrinsic) of BDP-1 should be caused by its stronger absorption at 800 nm.
To determine the saturable absorption intensity (I
s) and modulation depth (A
S) of two derivatives, which are two important parameters for the Q-switching or mode-locking of fiber lasers, we measured their transmittances under different excitation intensities, as shown in
Figure 3b and
Figure 3c. It can be seen that with the increase of incident light intensity their transmittances gradually increase, indicating a saturable absorption effect, which is consistent with the Z-scan data. I
s and A
S of two derivatives were estimated,
i.e., 98 GW/cm
2 and 61.3% for BDP-1 and 106 GW/cm
2 and 52.5% for BDP-2, according to the following equation [
40]:
where I is the input intensity; A
S is the modulation depth; I
s is the saturable absorption; n
s is the nonsaturable loss. In addition, BDP-1 has larger modulation depth and smaller saturable absorption intensity, implying this derivative is more promising for the application in Q-switching or mode-locking of fiber lasers. In order to facilitate comparison, the NLO parameters at 800 nm for two derivatives were compared in
Table 1.
2.3.2. Nonresonant NLO properties at 1300 nm
Considering two derivatives have negligible absorption at 1300 nm, it is interesting to investigate their nonlinear refraction effect and 2PA. From the closed-aperture Z-scan experimental data divided by corresponding open-aperture ones, as shown in
Figure 4a, it can be seen that the solutions of two derivatives exhibit a self-defocusing effect, while the DMSO solvent exhibits a self-focusing effect. The experimental data in
Figure 4a can be theoretically fitted using following formula [
41]:
where ΔΦ
0(t)=kΔnL
eff is the nonlinear phase shift at the focal point and Δn=n
2I
0. n
2 is the nonlinear refractive index, while x=z/z
0 is the ratio of the sample position z to the diffraction length z
0. As a result, the nonlinear refractive indices of BDP-1 and BDP-2 in derivative solutions, and pure DMSO solvent were determined to as -3.36 × 10
-7, -4.48 × 10
-7 and 7.71 × 10
-7 cm
2/GW. Although the solution concentrations of two derivatives were much low, their nonlinear refractive indices were only several times smaller than that of carbon disulfide (n
2 ~ 3.0 × 10
-6 cm
2/GW). With the influence of DMSO solvent subtracted according to Equation (3), the intrinsic nonlinear refractive indices of two derivatives were estimated, i.e., n
2 (intrinsic) - 7.60 × 10
-3 cm
2/GW for BDP-1 and -7.85 × 10
-3 cm
2/GW for BDP-2, respectively. Furthermore, they are even higher than those of organic molecules reported in a lot of NLO materials, including Zn-terpyridine polymer (~ 1.1 × 10
-4 cm
2/GW at 765 nm) [
42] and crystalline nickel-p-benzenedicarboxylic acid MOF (Ni-MOF)(~ - 8.9 × 10
-7 cm
2/GW at 1550 nm) [
14].
The open aperture Z-scan data of two derivatives under the excitation of femtosecond pulses of 1300 nm (an excitation light intensity of 337 GW/cm
2) are shown in
Figure 4b. It can be seen that the signal of solvent can be ignored, and two samples have the smallest transmittances at the focal point, which is caused by 2PA. According to the Equation (1), the 2PA coefficients of BDP-1 and BDP-2 were estimated as 3.35 × 10
-3 and 4.19 × 10
-3 cm/GW, respectively. In addition, with the help of Equation (2), the intrinsic 2PA coefficients of two derivatives were determined as 165 and 213 cm GW
-1. 2PA cross-section (σ
2) that is in unit of GM, with 1 GM= 10
-50 cm
4 s
-1 photon
-1, can be determined according to the following equation [
38],
where h is the Planck's constant in unit of J·s; υ is the incident light frequency in unit of 1/s, N
A is Avogadro’s number and C
0 is concentration in unit of M/L.
As a result, 2PA cross-sections of BDP-1 and BDP-2 can be estimated as 59 and 77 GM at 800 nm, respectively, as summarized in
Table 2. It can be concluded that BDP-2 exhibits larger 2PA cross-section compared to that of BDP-1, as a result of stronger electron-donating ability of the 1-ethyl-1,2,3,4-tetrahydroquinoline groups [
43].
To realize the application in all-optical switching, the NLO materials should have strong nonlinear refraction but weak nonlinear absorption. To realize such an application, two Stegeman’s figures of merit should satisfy following conditions [
44,
45]:
Since linear absorption of two derivatives are negligible at 1300 nm, their W values are larger than 1. In addition, based on the experimental data, T is estimated as 1.06 for BDP-1 and 0.652 for BDP-2. Therefore, BDP-2 may have potential application in all-optical device applications.
Meanwhile, in order to avoid the influence of linear absorption, we measured the PL spectra of two derivatives under 1400 nm excitation, which are peaking at 1000 and 1060 nm, respectively, as shown in
Figure 5a. The spectra are similar to those under single-photon excitation, indicating that the same emission states are involved in two cases. The inset shows the relationship between the PL intensity and excitation power. The slopes around 2 for the best-fitting straight lines on logarithmic scales indicate the occurrence of 2PA. We repeated Z-scan measurements at different wavelengths and obtained their 2PA cross-sections within the range of 1200 - 1600 nm. The molecular probes with large 2PA action cross-sections (the production of a 2PA cross section and PLQY), which is also called two-photon fluorescence brightness, will be beneficial for the two-photon bioimaging. Therefore, 2PA action cross-sections of two derivatives at different wavelengths are calculated and presented in
Figure 5b. The moderate 2PA action cross-sections of BDP-2 and PL emission in NIR-II window make it to be promising in deep-tissue bioimaging.