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Abstract
GaN is a one of promising materials for nonlinear optical applications. In this work, the broadband nonlinear optical response and potential applications for all-optical switching (AOS) are evaluated in low-defect GaN. In the pump-probe experiments, the ultrafast optical switching times are consistent with pulse widths accompanied with relative weak free-carrier absorption response, and the modulation contrast can reach ∼60% by varying the polarization orientations between the pump and probe lights. In the visible region, the broadband two-photon absorption effect exhibits excellent values for the imaginary part of figure of merit (FOM), providing the possibility of AOS based on nonlinear absorption (magnitude). While in the near-infrared region and under the presence of three-photon absorption, not only the real part of FOM based on Kerr effect is evaluated, but also the maximum light intensity for the usage of AOS based on nonlinear refraction (phase) is determined. The broadband nonlinear optical and AOS features in low-defect GaN will be highly favorable for the applications in the field of integrated nonlinear photonics and photonic circuits.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
GaN is known as the third-generation semiconductor (including SiC and ZnO) because of its wide-bandgap (3.4 eV at room temperature) [1–4]. The properties of high thermal conductivity and high breakdown field enable broader commercial prospects for high-temperature and high-power electronic devices [5–7]. In addition, GaN also has great applications in optoelectronics platform, for instance blue and ultraviolet emitting diodes and photodetectors [8–14], etc. Notably, an ultrawide transparent window (ultraviolet to mid-infrared) and high electron mobility of GaN make it exceptionally suitable for ultrafast optical communication.
Materials with strong optical nonlinearity can implement control and modulate optical signals, and providing diverse performance for integrated photonic chips [15,16]. Recently, optical nonlinearity in the different wide-bandgap semiconductors have been investigated by theoretical calculation and experimental measurements. Calculations revealed that the modulation of GaP arising from optical Kerr effect and two-photon absorption (2PA) can achieve high modulation speeds in all-optical switching (AOS) applications [17,18]. ZnO and 6H-SiC materials are also demonstrated to have high potential for ultrafast AOS [19–22]. Notably, applications of the materials in ultrafast optical signal processing are limited by excitation light intensity, so it is significant to characterize the maximum light intensity of the semiconductors for AOS [23,24]. GaN has garnered attention in the realization of integrated nonlinear photonics and photonic circuits in recent years. At telecommunication wavelengths, the nonlinear refractive index of GaN is comparable with that of 4H-SiC and GaP, and about an order of magnitude larger than AlN [25–28]. Meanwhile, GaN has high-quality (Q) factor (over 2.5 million) and lower optical loss (∼0.17 dB cm-1). Therefore, GaN seems to be more advantageous in chip-level nonlinear applications, particularly for optical communication [28–33]. Although optical nonlinearities in GaN have been studied for decades, but the fruitful nonlinear optical (NLO) response is primarily limited by using single wavelength or narrow wavelength band [34–38], lacking of research in the broadband for systematically assess the application of AOS. On the other hand, the optical nonlinear response is also influenced by threading dislocations (TDs) in GaN [39]. The defect density can be greatly reduced through GaN epitaxially grown on a GaN substrate, allowing us to measure purer NLO response.
In this letter, we evaluate the broadband optical nonlinear response and AOS characteristics in GaN with low TDs. The dynamics and ultrafast switching time based on 2PA are studied by degenerate pump-probe technique in picosecond and femtosecond time domain. The wavelength dependent nonlinear coefficients are determined by both fs and ps Z-scan measurements under broadband wavelength [40–42]. Based on real and imaginary parts of the third-order nonlinear polarizabilities, the applicability of GaN for AOS is explicitly analyzed.
2. Experimental method
The [0001]-oriented GaN free-standing crystal studied in this paper is commercially obtained from Suzhou Nanowin Technology Co., Ltd. The sample grown by hydride vapor phase epitaxy (HPVE) has low density of TDs (∼5 × 105 cm-2). The single crystal sample has dimensions of 10 × 10.5 mm2 with a thickness of ∼369 µm after double polishing. The HPVE-grown GaN is n-type conductivity due to residual donor impurities such as oxygen and silicon, resulting in a resistivity below 0.5 Ω·cm at 300 K. The low-defect GaN sample analyzed in this paper is denoted as LD-GaN. To investigate the broadband optical nonlinearity and free-carrier dynamics in LD-GaN crystal, Z-scan and phase object (PO) pump-probe technique under both picosecond and femtosecond time domains are conducted [43]. The experimental setup of Z-scan and pump-probe can be found elsewhere [24,44]. All experiments in this paper were performed at room temperature.
In the picosecond time domain, the laser pulses were emitted from a mode-locked and Q-modulated solid laser (PW10641B). The output wavelength, pulse duration and repetition rate are 532 nm (2.33 eV), 18 ps, 20 Hz, respectively. The output laser beam was focused by a convex lens of 30 cm focal length to a beam waist of ∼16.9 µm. In the pump-probe experiments, the output laser beam (532 nm) was split into two parts, which was used as both pump and probe beams. The pump (probe) beam was focused by a convex lens of 400 mm (300 mm) focal length to a spot radius of ∼67.8 µm (20.3 µm). The delay time between the pump and probe beam was controlled by a motorized stage. The beam of incident light is parallel to the c-axis. θ represents the angle of the probe polarization relative to that of the pump (horizontal polarization), and the polarization direction of the probe is tuned by a half-wave plate.
In the femtosecond time domain, the excitation sources are generated from an optical parametric amplifier (Light Conversion ORPHEUS) pumped by an ytterbium-doped fiber laser (Yb: KGW, PHAROS-SP). The range of output wavelength, pulse duration and repetition rate are 490-1000 nm, 190 fs and 20 Hz, respectively. The output laser beams with different wavelengths were focused by a convex lens of 250 mm focal length to beam waists of ∼15.6-31.8 µm.
3. Results and discussions
3.1 Transient optical nonlinearity of LD-GaN crystal
The LD-GaN is totally transparent below the bandgap as shown in Fig. S1 (see Supplement 1). The optical loss is only due its reflection on the front and rear surface. Optical nonlinearity in LD-GaN crystal is firstly studied at 532 nm by picosecond Z-scan technique. Figure S2 (see Supplement 1) shows that the LD-GaN exhibits obvious reverse saturate absorption and strong self-defocusing, and the third-order nonlinear absorption coefficient and refractive index fitted by Z-scan theory are listed in Table S1 (see Supplement 1) [45]. The nonlinear absorption (NLA) coefficients exhibit almost no intensity dependence, but the nonlinear refractive index increases with the incident light intensity, indicating the existence of high-order nonlinear processes.
In order to discriminate the nonlinear effects of bound electron and free carrier, the degenerate pump-probe technique based on PO is conducted at 532 nm and 18 ps. The nonlinear absorption and refraction dynamics can be measured simultaneously through the PO pump-probe technique [44]. The photon energy of the pump is 2.33 eV (satisfies Eg/2 < ħω < Eg), which can make the valence band (VB) electrons absorb two photons simultaneously. As the light intensity of probe is very weak than pump (∼5‰), the pump beam can be seen as the only source for 2 PA to excite carriers. The carrier-generation rate can be expressed as
Figure 1 presents the dynamics curves of NLA and nonlinear refraction (NLR) in LD-GaN under different pump intensities. Figure 1(a) shows that the free-carrier absorption (FCA) effect has long lifetime in the order of hundreds of nanoseconds. The FCA response is weaker than that of 2 PA (∼5%), so that the valley in transmittance at zero delay is governed by 2 PA. Figure 1(b) also shows that the NLR exhibits no recovery subsequent to a rapid decrease, indicating that the bound electron Kerr effect is much weaker than the free-carrier refraction (FCR). The photophysical parameters in LD-GaN, obtained by fitting a transient nonlinear model based on the rate equation [Eq. (1)] and [Eq. (2)], are summarized in Table 1.
Fig. 1. Pump intensity dependent transient optical response in LD-GaN under the excitation of 532 nm and 18 ps. (a) Nonlinear absorption dynamics curves at short delay time; (b) Nonlinear refraction dynamics curves. The solid lines are the theoretical fitting.
Table 1. Photophysical parameters in LD-GaN based on the fitting of a transient nonlinear model with the rate equation
According to the analysis earlier, NLO mainly arises from 2 PA and FCR at 532 nm. The FCR has no fast-recovery with long switching time, which is not favorable for the AOS. Therefore, 2 PA may play a key role in the AOS since its ultrafast response. The NLA dynamics for probe polarization parallel (θ = 90°) and perpendicular (θ = 0°) to the pump are shown in Fig. 2(a) and (c). It can be seen that varying the polarization angles between pump and probe pulses is able to modulate the 2 PA response significantly. Moreover, the polarization dependent 2 PA coefficient and AOS modulation depth (-ΔT/T) are further analyzed, and the relevant photophysical parameters are listed in Table S2 (see Supplement 1).
Fig. 2. The transient absorption dynamics curves at (a) polarization angle of ∼90° and (c) polarization angle of ∼0° under excitation of 532 nm and 18 ps, the pump intensity is ∼0.9 GW/cm2; (b) The degenerate 2 PA coefficient and modulation depth at different angles under excitation of 532 nm and 18 ps, the pump intensity is ∼3.8 GW/cm2. (d) The transient absorption dynamics curves under excitation of 720 nm and 190 fs. The solid lines are the theoretical fitting.
The light-intensity independence of the 2 PA exhibits a linear relationship with the effective third-order nonlinear susceptibility $\chi _{\textrm{eff}}^{(\textrm{3} )}$ [45]. The illustrated dependence of 2 PA coefficients on the angle can be well described by the equation: $\chi _{\textrm{eff}}^{(\textrm{3} )}(\theta )= \chi _{\textrm{xxxx}}^{(\textrm{3} )}{\cos ^2}(\theta )+ \chi _{\textrm{xxyy}}^{(\textrm{3} )}{\sin ^2}(\theta )$, as shown in Fig. 2(b). The maximum value of 2 PA coefficient occurs at θ = 0° ($\chi _{\textrm{xxxx}}^{(\textrm{3} )}$ is probed) with β// = 4.60 cm/GW and the minimum value occurs at θ ≈ 90° ($\chi _{\textrm{xxyy}}^{(\textrm{3} )}$ is probed) with β⊥ = 1.35 cm/GW. The 2 PA coefficient exhibits an oscillation of 180° period and the anisotropy ratio S ($\chi _{\textrm{xxxx}}^{(\textrm{3} )}$/$\chi _{\textrm{xxyy}}^{(\textrm{3} )}$) is approximately to be 3.4. In addition, as shown in Fig. 2(c), the full width at half-maximum (FWHM) value near the zero delay is 27 ps, which is consistent with the picosecond autocorrelation width (∼26 ps). The switching time based on 2 PA can be further shortened under femtosecond excitation, as shown in Fig. 2(d). The FWHM of 288 fs remains equally to the autocorrelation width of femtosecond pulse (∼280 fs), corresponding to the AOS modulation speed up to ∼3 THz. Furthermore, the transient absorption exhibits even lower FCA response at femtosecond time domain. Compared with 6H-SiC and GaP, larger modulation depths (∼25%-60%) under different polarization angles [see Fig. 2(b)] can be obtained in LD-GaN at a lower light intensity of ∼3.8 GW/cm2 (1-3 orders of magnitude lower) [22,17] . The ultrafast switching time and large modulation depth based on transmission (magnitude) imply that the LD-GaN will be satisfactory for the AOS applications.
3.2 Spectral dependence of NLO in LD-GaN
Figure 3 shows the open-aperture (OA) and closed-aperture (CA) Z-scan curves of LD-GaN crystal at 700 nm (visible region) and 760 nm (near-infrared region) under femtosecond excitation. The incident photon energy of 700 nm (1.78 eV) satisfies Eg/2 < Ephoton < Eg, the OA should be accordingly fitted by 2 PA model [see Fig. 3(a)(b)]. While the photon energy of 760 nm (1.64 eV) satisfies Eg/3 < Ephoton < Eg/2, and three-photon absorption (3 PA) model should be used [see Fig. 3(c)(d)]. Under 700 nm, the 2 PA coefficient β2 is ∼1.8 cm/GW and the nonlinear refractive index γ is ∼2.0 × 10−4 cm2/GW, and under 760 nm, the 3 PA coefficient β3 is ∼1.8 × 10−3 cm3/GW2 and the nonlinear refractive index γ is ∼1.25 × 10−4 cm2/GW. The third-order NLO Kerr coefficients for NLR are independent on the incident light intensity, excluding higher-order of the NLR effects.
Fig. 3. The NLO response in LD-GaN crystal at different incident light intensities. (a) OA and (b) CA Z-scan curves under wavelength of 700 nm; (c) OA and (d) CA Z-scan curves under wavelength of 760 nm. The solid lines are the theoretical fitting.
For the NLR response under femtosecond, the Kerr nonlinearity is the dominant origin, which is completely different from that under picosecond. Since the bound electron effect is extremely dependent on the excitation wavelengths, it is crucial to investigate the broadband bound electron effects in LD-GaN from visible to near-infrared. The NLA coefficients obtained from femtosecond Z-scan under wavelength are listed in Tables S3 and S4 (see Supplement 1).
Using theoretical model based in a two-band and a perturbation theory, we can obtain the relative dispersion relation based on the multiphoton absorption (MPA) coefficients [46]:
Fig. 4. Dispersion of (a) 2 PA, (b) 3 PA and (c) Kerr coefficients as a function of Eptoton/Eg for LD-GaN crystal. The solid lines are the theoretical fitting.
3.3 AOS features in LD-GaN crystal
In the visible region, ultrafast switching times, large modulation depths and even weaker free-carrier response are demonstrated to be able to accomplish AOS based on 2 PA (magnitude). Herein, linear absorption (optical losses) must be taken into consideration for the practical AOS applications. The third-order nonlinear susceptibility and figure of merit (FOM) for the imaginary part of the third-order optical nonlinearity can be deduced [47,48]:
Table 2. NLO parameters and FOMIm values in LD-GaN crystal, SnO2-x film, WSe2 films and Ga2O3 crystal
While in the near-infrared region, the loss is dramatically reduced due to the absent of 2 PA, and Kerr refraction exhibits an instantons response time (consistent with the femtosecond pulse duration) according to the results of PO pump-probe (see Fig. S3 in Supplement 1). Therefore, the Kerr refraction can be used to realize optical switching, but the 3 PA becomes the primary loss limiting the quality of AOS. In this situation, the real part of FOM under the presence of 3 PA (FOMRe) need to be analyzed emphatically. FOMRe is defined as |n2/λβ3Is| [50], where β3 is the 3 PA coefficient, Is is the starting light intensity, corresponding to the difference between a peak and valley transmittance ΔTPV of ∼0.1 in CA Z-scan. There is also literature to measure the superiority of the material by defining the maximum light intensity, that can be calculated through the equation [24]: Imax =|n2/λβ3|, where Imax is the threshold light intensity to evaluate the maximum light intensity of the material for the AOS. The calculated results related to the AOS features are shown in Table 3. LD-GaN exhibits extremely large quality factors (greater than unit) throughout the measured near-infrared region. Moreover, Imax for the usage of AOS based on NLR (phase) is as excellent as that for β-Ga2O3 [24], inferring that LD-GaN also presents great potential for applications in the field of integrated nonlinear photonics devices in the near-infrared.
Table 3. NLO parameters, FOMRe, and Imax values in LD-GaN crystal in the near-infrared region
4. Conclusion
In summary, the broadband optical nonlinearity and AOS features in LD-GaN crystal were systematically studied under picosecond and femtosecond excitations. Pump-probe measurements show that varying the polarization orientations is able to significantly modulate the instantaneous bound electron effect. A large modulation depth (∼60%) induced by 2 PA was accomplished under a low light intensity. Moreover, the weaker FCA response (only 5% of the 2 PA) provide the possibility for optical switching based on 2 PA. Remarkably, the switching time (∼280 fs) under femtosecond excitation are almost consistent with the pulse duration, which suggests a modulation speed performance of ∼3 THz. The broadband real and imaginary parts of the third-order susceptibility were both evaluated for the potential AOS applications. In the visible region, because of the long recovery time for FCR and weak Kerr effect, the AOS applications can be achieved based on NLA (magnitude) accompanied with excellent values of FOMIm. While in the near-infrared region, the Kerr refraction (phase) can realize the AOS due to weaker 3 PA compared to the 2 PA. The LD-GaN not only has superior values of FOMRe, but also possesses excellent threshold light intensity for the AOS. Our results indicate that the pristine GaN material is promising for applications in the field of ultrafast optoelectronic and integrated nonlinear photonic devices.
Funding
National Natural Science Foundation of China (11704273, 12374300); Natural Science Foundation of Jiangsu Province (BK20221384); Jiangsu Key Disciplines of the Fourteenth Five-Year Plan (2021135); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22_3267); Qinglan Project of Jiangsu Province of China (SZ2022002); Science and Technology Innovation Team of Guizhou Education Department ([2023]094); Science and Technology Foundation of Guizhou Province (ZK [2021]031).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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