All-optical switching (AOS) has significantly advanced signal processing speeds, pushing frequency from the traditional gigahertz level into the terahertz level. This breakthrough is paving the way for new applications in optical communications, optical computing, and quantum information processing^[1–5]. The third-order nonlinear optical effects of materials, such as the optical Kerr effect and two-photon absorption (TPA) are considered fundamental for AOS^[6–8]. Consequently, identifying materials with strong nonlinear properties is essential for the development of ultrafast AOS. Among the promising candidates, transparent conductive oxides (TCOs), which are a representative of epsilon-near-zero (ENZ) materials, have attracted attention. Due to their large nonlinear response^[9,10], sub-picosecond response time (RT)^[11], and excellent compatibility with complementary metal-oxide-semiconductor technology^[12], TCOs have become significant platforms for advancing the capabilities of AOS^[13,14]

As a representative of TCOs, zinc oxide (ZnO) has become a widely researched material because of its wide bandgap, abundant resources, and low manufacturing cost. Notably, Ga-doped ZnO (GZO) exhibits higher electrical conductivity and carrier mobility^[15–17]. Additionally, the nonlinear response of the GZO material in the near-infrared region (NIR) can be further enhanced due to the ENZ characteristics^[18–21], and the ENZ wavelength can also be tuned through defect engineering^[22,23]. This enhancement and tunability approach a major focus of current research. However, the speed of the nonlinear response at the ENZ wavelength is limited by the carrier relaxation lifetime. The nonlinear absorption associated with inter-band transitions is characterized by longer photogenerated carrier relaxation time (picoseconds to nanoseconds), which significantly limits its application in ultrafast AOS^[24]. In contrast, the bound-electron nonlinear effect has an instantaneous response with ultrafast modulation speed and can be further enhanced through band resonance effects under a non-degenerate case^[25–27]. However, the limitation of non-degenerate conditions is the stringent requirement on the wavelengths of both pump and probe beams (typically necessitating ultraviolet pump light and near-infrared or even mid-infrared probe light), which significantly restricts their development and application especially over the visible wavelength range^[28].

Gallium doping not only inhibits the formation of intrinsic defects but also can introduce Ga-related resonant energy levels into the band structure in ZnO, making it possible to enhance the transient optical nonlinearity within the visible spectrum^[29–31].

In this work, the nonlinear optical response of GZO across the entire visible spectrum is investigated using femtosecond transient absorption spectroscopy (TAS). Our findings showed the enhancement of an optical nonlinear response based on Ga-related defect energy level in a broadband wavelength, and the nonlinear modulation depth and the AOS characteristics were evaluated. Subsequent to the correction of the nonlinear response through the walk-off model, the TPA spectrum was accordingly extracted and the enhancement trend was further analyzed. Additionally, the photoluminescent properties as well as the optical nonlinear enhancement mechanisms were clarified based on the internal defect states of GZO.

The [0001]-oriented GZO crystal studied in this paper is commercially obtained from MTI Corp. The melt growth method was used to grow the crystal; the GZO crystal exhibits a low dislocation density (<4×104cm−2). The sample dimension is 10mm×10mm×0.5mm, and it is an n-type conductive material with a carrier concentration of ∼1018cm−3.

The transient nonlinear optical properties and dynamics of GZO within 1 Ps were investigated using femtosecond pulse-pumped supercontinuum spectroscopy. The excitation source consisted of a tunable laser pulse output from an optical parametric amplifier (OPA, Light Conversion ORPHEUS) pumped by a Yb:KGW femtosecond laser (PHAROS, 1030 nm), with a pulse duration of ∼190fs and a repetition frequency of 6 kHz. In the femtosecond TAS setup, supercontinuum white light (400–800 nm) was generated by focusing the probe beam on the sapphire substrate, which was then spectrally dispersed by a grating and detected by a linear array charge-coupled device, which has 256 pixels with a spectral resolution of approximately 1.2 nm. This setup allows for the simultaneous acquisition of broadband dynamic characteristics of the material at different delay time^[32]. In addition to the ultrafast time-resolved characteristics, more accurate photodynamic information can be obtained by comparing the supercontinuum spectra at different time. Optical density (OD) is defined as −lg(I0/I), where I0 and I are the intensities of the incident and transmitted beams, respectively. The OD change (ΔOD) is used to denote the transient absorption response: ΔOD=lg(TunpumpedTpumped),(1)where Tunpumped (Tpumped) is the normalized transmittance of the sample without (with) pump excitation. All experimental measurements were performed at room temperature.

The absorption dynamics under the pump wavelength of 650 nm conducted by femtosecond TAS are shown in Fig. 1(a). Upon excitation with a pump fluence of 6.62mJ/cm2, the GZO crystal exhibited a significant change in optical density (ΔmOD) over a broad spectral range (450 to 750 nm). The maximum ΔmOD can reach 700, corresponding to the modulation depth (−ΔT/T) up to ∼80%. The pump wavelength used in the experiment was 650 nm, with a photon energy of 1.91 eV, satisfying the basic condition for TPA (Eg/2<ℏω<Eg). The modulation depth induced by TPA, as a function of delay time, is depicted in Fig. 1(b); the pump pulse exhibits a Gaussian profile with a pulse width of 190 fs and the autocorrelation width of approximately 270 fs. This value aligns with the full width at half-maximum (FWHM) indicated in the revised figure. The other wavelength is shown in Fig. S1 in the Supplement 1. The RT of the optical switching is also a critical factor in evaluating AOS performance. In this study, the RT of the AOS was determined by 10% and 90% of the maximum modulation capability^[33]. The transient response of the optical switching exhibited a rise time of 130 fs (7.7 THz) and a recovery time of 150 fs (6.67 THz); the schematic diagrams of the corresponding on and off states are displayed in Fig. S2 in the Supplement 1.

In this work, the dynamic characteristics of GZO crystal across various delay time and probe wavelengths are simultaneously explored. Additionally, the TPA spectrum data at different probe wavelengths were extracted and converted into normalized transmittance. However, when probing the sample with a weak white-light continuum (WLC), the group velocity mismatch (GVM) causes the probe and pump pulses to undergo differing time intervals within the sample, ultimately resulting in a pump-probe pulse walk-off^[34,35]. The experimental manifestation of walk-off is illustrated in Fig. 1(c). In the degenerate case as shown in Fig. 1(d), there is no significant delay range in the degenerate condition, but under non-degenerate conditions, a greater wavelength difference between the probe and pump wavelengths leads to a broader range of delay for the nonlinear response. As the wavelength difference increases, the GVM phenomenon becomes more pronounced, which causes the delay time of the probe light relative to the pump light within the sample to be further prolonged^[36]. Due to the influence of walk-off (GVM) on the peak value and delay range of the TPA, the TAS at zero delay is severely affected. This deviation undermines the accurate representation of the sample’s non-degenerate TPA characteristics. The accurate non-degenerate two-photon absorption (ND-TPA) spectrum is important for understanding the origin of optical nonlinearity and the bandgap structure, so the experimental data need to be further corrected.

The TAS data obtained under 650 nm excitation wavelength were used for analysis. Without considering the influence of GVM, under the approximation of thin samples and slowly varying envelopes, the propagation equations for the pump and probe beams in the GZO sample can be expressed as^[37,38]$$\begin{gathered} dIpdz=−2βNDIeIp, \\ dIedz=−βDIe2, \end{gathered}$$(2)where βND (βD) represents the TPA coefficient of the sample under a non-degenerate (degenerate) condition. Ie and Ip denote the intensities of the pump light and probe light, respectively. Accordingly, the ND-TPA coefficient at different probe wavelengths can be initially obtained by theoretical fitting without correction, but a significant discrepancy was found between the theoretical fitting curve and the experimental curve, as shown in Fig. S3(a) in the Supplement 1. Accordingly, the aforementioned walk-off effect must be considered to correct the nonlinear response due to the delay interval. In the non-degenerate case, the normalized transmittance can be expressed as^[39]$$\begin{gathered} NTτd,ρ,βND′=exp(−2)π∫−∞+∞exp{−(τ+τd−ρ)2 \\ −βND′πρ[erf(τ)−erf(τ−ρ)]}dτ, \end{gathered}$$(3)where βND′ is the corrected TPA coefficient, and τ is defined as the normalized temporal variable characterizing the instantaneous time evolution of the probe pulse within the group velocity reference frame of the pump pulse. τd represents the normalized initial delay time, which governs the temporal overlap between the pump light and probe pulses at the sample entrance; when τd=0, the pump and probe pulses are perfectly temporally aligned at the input. This parameter ρ is defined as the normalized GVM parameter, influenced by ωp (pump pulse width), L (thickness of sample), and Δng (difference in GVM). The effects of sample thickness and laser pulse width on walk-off are analyzed in Fig. S4 in the Supplement 1. When the walk-off parameter ρ<0.5, the βND′ deviates from the βND by less than 10% (∼7%), indicating that the influence of GVM on the spectrum can be neglected in ZnO. However, when ρ>0.5 (the deviation of 10% at ρ=0.505), the influence of GVM on the spectrum must be considered. Moreover, walk-off correction is required when the ratio of pump pulse widths to sample thicknesses is lower than 2.30 ps/mm; this finding provides a convenient and efficient means for determining whether spectral correction is required (see Table S1 in the Supplement 1). Naturally, when the pump and probe wavelengths are the same, resulting in no walk-off (i.e., ρ=0), the following equation holds: NT(τd,ρ,βD′)=exp(−2)π∫−∞+∞exp[−(τ+τd)2−2βD′exp(−τ2)]dτ,(4)where βD′ denotes the corrected TPA coefficient under a degenerate condition. As shown in Fig. S3(b) in the Supplement 1, the data demonstrate that using the walk-off model to correct the spectra effectively explains the delay range phenomena caused by GVM in regions far from the pump wavelength. By applying the model correction, the corresponding walk-off parameters and corrected TPA coefficients were all obtained. It was observed that the walk-off parameter depends on the wavelength difference between the pump light and probe light. A larger walk-off parameter results in a more pronounced effect on the TPA coefficient, as shown in Table 1. The TPA coefficient at the probe wavelength of 650 nm has been calibrated by the home-built Z-scan measurement under the same conditions. The βND at 470 nm is much lower than at 650 nm, but the βND′ at 470 nm increased by 67% relative to 650 nm; this indicates the necessity of correction for analyzing the spectrum. The corrected data indicate a further enhancement of the nonlinear response in the short-wavelength region (<600nm), which is also consistent with the dispersion relation in this region.

To further analyze the impact of the walk-off parameters, TAS experiments were conducted under the same pump fluence of 1.27mJ/cm2 and the pump wavelengths of 750, 700, and 450 nm. The results of the nonlinear response, along with the trends of the corrected TPA coefficients, are illustrated in Fig. 2. The trend of the modulation depth at different wavelengths was obtained; the maximum modulation depth can reach over 25% with a peak up to 40%. This demonstrates a significant advantage compared to aluminum-doped zinc oxide (AZO) thin films^[18], metal-insulator-metal (MIM) nanocavities^[40], 6H-SiC^[41], and indium tin oxide (ITO) nanocrystals^[42], as shown in Table 2. Under the pump wavelength of 750 nm, the TPA coefficient obtained by fitting the experimental data is 1.6×10−11m/W with the probe wavelength of 710 nm; the corrected TPA coefficient reaches a maximum value of 17.58×10−11m/W at short wavelength regions, representing a nearly fourfold enhancement in the nonlinear response compared to pure ZnO^[60]. In the analysis of the corrected TPA spectrum, it was found that the ND-TPA coefficient exhibits an enhancement of nearly one order of magnitude compared to the degenerate TPA coefficient, as shown in Table S2 in the Supplement 1. Additionally, the TPA enhancement is comparable to that under extremely non-degenerate conditions, suggesting that the study can achieve an effective nonlinear enhancement while improving the stringent experimental conditions.

Based on theoretical calculations and experimental results, the enhancement observed in the non-degenerate case is attributed to the energy level resonance effect. This finding aligns with the non-degenerate enhancement model based on Keldysh tunneling theory^[43–46]. In this model, the dispersion of the ND-TPA coefficient is described by β2(x1;x2)=A×(x1+x2−1)32x1x22×(1x1+1x2)2,(5)where A is a calibration parameter, x1=ℏv1/Eg(x2=ℏv2/Eg), and x1 and x2 represent the ratios of the photon energy of the pump light and probe light to the bandgap of the material, respectively. Based on linear absorption spectroscopy and calculated using the Tauc-plot method, the material’s band gap was determined to be approximately 3.3 eV. As shown in Fig. 3, the corrected TPA spectrum is compared with the dispersion obtained through Eq. (5).

Through the analysis conducted at a pump wavelength of 650 nm, it was found that the experimental data deviate from the model by approximately 7% at a probe wavelength of 650 nm. However, at the shorter probe wavelength of 450 nm, the deviation reaches as high as 35%. The experimental findings indicate that as the excitation wavelength approaches the NIR, the discrepancy between the TPA coefficient and theoretical value widens significantly, particularly under a short probe wavelength, reaching a maximum deviation of 207%. Unlike ZnS, ZnSe, and GaAs that conform to this dispersion model as shown in Table S3 in the Supplement 1, the deviation of the TPA coefficient in GZO further suggests that the enhancement is not solely due to non-degenerate effects; the other enhancement mechanisms should contribute as well^[47,48]. Furthermore, using the Drude-Lorentz model, the effective ENZ wavelength of GZO should be above 2000 nm, thereby eliminating the probability of the enhancement attributed to ENZ properties.

This study further considers whether the enhancement in nonlinearity is associated with the defects introduced by Ga doping. The PL spectra reveal that under 340 nm excitation, the sample exhibits three main emission peaks [as shown in Fig. 4(a)]: UV emission peak at 380 nm and blue emission peaks at 407 and 478 nm. The UV emission is consistent with the bandgap and can be identified as inter-band luminescence^[28,29], while the blue emission peaks within the bandgap are attributed to the defect states. Unlike GZO crystal, the defect-related PL spectrum of intrinsic ZnO is primarily concentrated around 728 and 591 nm [as shown in the inset of Fig. 4(a)]; these may be attributed to VZn− and VZn- related intrinsic defects^[49]. Through Ga doping, the formation of the intrinsic defects in ZnO is suppressed, leading to the emergence of new defect states associated with Ga, specifically the blue emission peaks at 401 and 485 nm^[23]. Due to the high Ga concentration in the sample, the Ga-related defects are primarily GaZn, GaZn−VZn, and GaZn−Oi. However, hybrid density function calculations reveal that both GaZn−VZn and GaZn−Oi complexes act as deep acceptors, possessing thermodynamic transition levels of (0/−) at 948 and 394 nm above the valence band (VB), respectively. These charge states are inherently unstable with a high formation energy of up to 6.70 eV, making these complexes unlikely to form stably. Therefore, the defect GaZn is the major defect in GZO and should be mainly discussed^[50].

The GaZn defect serves as a donor level capable of providing a substantial number of electrons. Specifically, the zinc atoms within the ZnO crystal are substituted by gallium atoms, which behave as donors and provide additional free electrons. Typically, these defects exist in the charge states of GaZn0 and GaZn−. As the energy level of the GaZn defect (–/0) is located very close to the conduction band, only a small excitation energy (in the meV range) is required for the GaZn− defect charge state to spontaneously promote the electron into the conduction band, making the GaZn defect stabilized in the form of a GaZn0 charge state^[51,52]. As shown in Fig. 4(b), under the excitation of the pump light, the charge state of the GaZn0 defect recombined with holes in the valence band [GaZn0+h+→GaZn+, corresponding to the solid upward arrow in Fig. 4(b)], leading to an expected emission peak associated with this transition at around 2.5 eV. This aligns with the blue-cyan emission peak observed at 485 nm in the PL spectrum, which originates from the optical transition of the GaZn defect (0/+) energy level [see solid downward arrow in Fig. 4(b)]. Similarly, recombination of holes in the valence band with the GaZn− defect charge state [GaZn−+h+→GaZn0, corresponding to the solid upward arrow in Fig. 4(c)] was expected to result in an emission peak at around 414 nm. Combined with the PL spectrum, the blue emission peak at 407 nm can be attributed to optical transitions of the GaZn defect (−/0) energy level [see the solid downward arrow in Fig. 4(c)].

With the participation of defect-free energy levels, the extremely non-degenerate enhancement for TPA is achieved through the virtual energy level resonance between the pump light and the probe light; the process satisfies Fermi’s golden rule (derived from the second-order time-dependent perturbation theory) in the form of the two-photon transition rate^[53–55]: W2ND=2πℏ∑vc|∑D[(c|H2|D)(D|H1|v)EDv(k)−ℏω1+(c|H1|D)(D|H2|v)EDv(k)−ℏω2]|2⁢δ[Ecv(k)−ℏω1−ℏω2],(6)with indices 1 and 2 designating the two photons, H representing the electron-field interaction Hamiltonian, and v, c, and D representing the valence, conduction, and intermediate defect states, respectively. ECv (EDv) is the energy difference between the valence state (intermediate state) and conduction state. In previous reports, it was observed that when the wavelength of high-harmonic generation matches the energy level of a specific defect state, the harmonic intensity is further enhanced. Additionally, the phenomenon of three-photon-enhanced four-photon absorption was discovered based on exciton state resonance^[56,57]. Therefore, according to the configurational coordinate diagram of the GaZn defect state, the ND-TPA may increase remarkably when the real state [GaZn (0/+) energy level] plays the intermediate states for resonance enhancement^[58,59]. As shown in Fig. 4(b), this resonant energy level is located 1 eV (1200 nm) above the valence band, so the ND-TPA enhancement will become greater when the pump photon energy approaches 1 eV. The principle of resonance enhancement is that the denominator in Eq. (6) approaches zero [EDv(k)−ℏω1→0] or the Hamiltonian on the molecule becomes larger, thereby greatly enhancing the TPA effect. This energy level model can also effectively explain the observed phenomenon of Ga-related defect-enhanced four-photon absorption^[60].

Based on the TAS results obtained at different pump wavelengths and PL spectra, the following conclusions can be drawn: firstly, the enhancement achieved when the pump photon energy approaches the resonant energy level is greater than when the probe photon energy approaches the resonant energy level. Specifically, under excitation at 650, 700, and 750 nm, the ND-TPA coefficients measured at probe wavelengths near 500 nm are greater than those measured at 750 nm under 450 nm excitation. Secondly, the ND-TPA coefficient at 750 nm is significantly higher, by an order of magnitude, than that observed in the degenerate case. This observation is attributed to the fact that at a pump wavelength of 750 nm, the probe wavelength only needs to be between 496 and 621 nm (2 eV) to achieve the energy level resonance effect. When the probe wavelength is 496 nm, the resonance energy levels become closer to the (0/+) energy level of the GaZn defect, resulting in a better enhancement effect for non-degeneracy; this is also consistent with the experimental phenomenon described above.

In summary, this study presents research on AOS properties based on the enhanced TPA across a broad spectrum. In the GZO crystal, the modulation depth induced by TPA at a pump wavelength of 750 nm can reach 86%, accompanied by ultrafast switching RT (approximately 280 fs); compared to the Kerr effect, TPA offers a more practical pathway to achieve a high modulation depth and ultrafast response time. Through the fitting of the walk-off model, the ND-TPA coefficient at a pump wavelength of 750 nm reaches 17.58×10−11m/W, which is an order of magnitude higher than that in the degenerate case, showing a further enhanced trend towards the NIR. The ND-TPA spectra under different GVMs are further extracted in this study; it is found that the non-degenerate enhancement is not solely attributed to the non-degenerate resonance effect, but also involves auxiliary resonance enhancement due to the (0/+) energy level of the GaZn defect in GZO. The study provides a method that can be simply and effectively used to extract accurate ND-TPA spectra, and also clarifies the mechanism of nonlinear enhancement. The findings highlight the significant advantages of GZO in terms of ultrafast RT and a high modulation depth for applications of AOS.