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Abstract
Second harmonic generation plays a vital role in frequency conversion which mutually promotes the laser technology and allows the wavebands extension of new coherent source. The monolithic crystals are supposed to be a superior choice for harmonic generation due to long interaction distance, however, the phase-mismatch brought a sharp reduction in the conversion efficiency. Although birefringent phase-matching and quasi-phase-matching techniques are commonly utilized to fill the phase gap in monolithic crystals, these techniques are limited by the natural refractive index of crystal and the domain engineering, respectively. In recent years, subwavelength structures evolve as a flexible scheme to realize phase matching by engineering the geometry features of crystals. Here, structured nanogratings are designed and fabricated on a monolithic PMN-39PT (Pb(Mg1/3Nb2/3)O3-0.39PbTiO3) substrate, a novel ferroelectric crystal with promising optical prospect, for enhancing second harmonic generation, where birefringent or quasi phase-matching is hard to achieve. The nanograting-assisted second harmonic generation enhancement is observed which is not limited by the availability of thin crystalline films. Meanwhile, a boost in the second harmonic signal synchronously promotes the cascading third harmonic generation. This method may provide an alternative solution for enhanced harmonic generation on monolithic substrates and develop potential nonlinear optical materials for frequency conversion.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nonlinear optical harmonic generation is utilized as a significant approach for manipulating the optical field frequency, which stimulates the thriving optical materials and laser technology [1,2]. Harmonic generation offers a preferable solution for exploiting coherent light sources with new spectra, regardless of the energy level limitation of gain medium. Second harmonic generation (SHG), as the milestone in the birth of nonlinear optics [3], has been widely applied in developing light sources and biomedical imaging [4–6]. Due to the weak inherent second-order nonlinear response of the medium, the SHG often requires the nonlinear crystal to extend the light-matter interaction length [7]. However, since dispersion occurs when light propagates in a monolithic crystal, the momentum conservation condition is difficult to be satisfied directly. The SHG conversion efficiency was drastically reduced which can be attributed to the phase-mismatch Δk = k2ω−2kω between fundamental and harmonic wave vectors. Thus, the birefringence phase matching (BPM) and the quasi-phase-matching (QPM) are introduced for improving SHG efficiency [7–9]. BPM relies on the inherent refractive index of crystal along with strict incident conditions of pump laser. Contrarily, QPM is often used for ferroelectric while makes a request for maturity periodically-poled domain engineering [10–12]. For example, although the quartz was the first crystal for discovering nonlinear optical response with great transmittance both in ultraviolet and visible wavebands, its birefringence is inappropriate and periodically-poled technology is hard to achieve. Hence, quartz can hardly be regarded as a preferable choice for efficient harmonic generation. These two techniques indeed improve SHG efficiency while their harsh conditions inevitably exclude a large number of nonlinear crystals and limit the optical wavelength extension. Fortunately, micro/nano optical structures offer an alternative solution to this dilemma [13,14]. The phase-matching condition can be readily satisfied due to the additional momentum provided by diffraction or scattering. Furthermore, the localized electric field in the subwavelength structures will also improve the SHG efficiency [15,16].
Herein, two nanogratings are designed and fabricated on the same monolithic Pb(Mg1/3Nb2/3)O3−0.39PbTiO3 (PMN-39PT) surface. The phase-matching condition for high-efficiency SHG is satisfied by the Bragg diffraction but not by BPM or QPM [17]. The localized optical field also supports an efficient nonlinear process. The measured spectra and the power dependence of harmonic signal match well with the theoretical values and simulation results. Additionally, benefiting from the strong SHG, the intensity of third harmonic generation (THG) also exhibits a significant enhancement related to the phase-matching angle due to the cascading effect. The proof-of-concept demonstration verifies an effective solution for harmonic generation enhancement in monolithic crystal where either BPM or QPM technique is hard to achieve. Meanwhile, the proposed approach for second-order nonlinear response on a monolithic substrate is not limited by the availability of thin crystalline films. The nanograting-assisted phase-matching method may help developing the variety of the nonlinear optical material and strengthen its nonlinear optical responses.
2. Sample fabrication and modeling
The PMN-39PT crystal, a typical ferroelectric material, is commonly studied as the piezoelectric ceramic and lacks of optical-related researches [18]. The single-domain PMN-39PT possesses tetragonal structure with 4mm points group [19]. Recently, the PMN-PT has been demonstrated with a considerable optical property while retaining its excellent piezoelectric property [18,20]. However, only a weak second harmonic signal was detected with a poor efficiency cause by phase-mismatching. On the one hand, neither a Type I (k2e ≤ 2k1o) nor Type II (k2e ≤ k1o + k1e) BPM can be satisfied in its bulk medium due to its limited refractive index [19]. Figure 1 depicts the dependency between wavelength and wave vectors in PMN-39PT single crystal within 1.2 to 1.8 µm covering the wavelength selected in subsequent demonstration. The wave vector of second harmonic signal is too small to satisfy the BPM. On the other hand, the QPM required periodical domain-reversal is hard to achieve in its present stage due to the complicate domain switching kinetics in single domain PMN-39PT single crystal [19,21]. Thus, the nanograting-assisted harmonic generation is proposed in order to achieve the enhanced second harmonic signal in monolithic PMN-39PT.
Fig. 1. The wave vectors in bulk PMN-39PT for BPM conditions at near-infrared region. k1o, o-polarized FW; k1e, e-polarized FW; k2e, e-polarized SHG.
Two essential conditions for an enhanced harmonic generation on grating structure are supposed to be satisfied, Bragg diffraction assisted phase-matching and localized filed enhancement. The Bragg diffraction assisted phase-matching can be expressed as [17]
Fig. 2. (a) Mechanism of the proposed nanograting-assisted SHG in monolithic PMN-39PT. (b) The dependence of grating period, etching depth on FW incident angle. (c) Simulated localized optical field with selected nanograting parameters. (d) Scanning electron microscope (SEM) images of the fabricated nanogratings with Au cladding.
The etching depth can be estimated by [22]
Figure 2(c) displays the FDTD simulation results for the bounded localized optical field with two different nanogratings for better verification of grating-assisted phase-matching angle concept. The FW fields were well-confined in both subwavelength structures, while the field strength of grating 2 is weaker than that of grating 1. The simulation results are possible to infer that the grating 1 works better than grating 2 in improving SHG, which is also confirmed in the subsequent experimental results in this work.
3. Experiments
In experiment, two nanogratings were fabricated on the same monolithic PMN-39PT crystal by focused ion beam (FIB, FEI Scios) with acceleration voltage of 30 kV and beam current 45 pA. A 60 nm thick Au layer was first deposited on the bare PMN-39PT surface via sputtering for the poor electrical conductivity of PMN-39PT. The Au layer was removed by dilute HNO3 solution after the FIB etching. Figure 2(d) displayed the scanning electron microscope (SEM) images of the prepared nanograting before the Au layer was erased. Based on the simulation results, the period of grating 1 and 2 were etched as Λ = 775 nm and Λ = 840 nm, respectively. Although the coupling region length for two nanogratings was similarly fixed at L1 = L2 = 40 µm, the actual FIB values were affected by the etching quality for errors about 1-2 µm. The predetermined value for the grating width is the same for the designed two gratings as L0 = 10 µm with a practical error of no more than 0.01 µm. The enlarged views of the gratings were depicted in the zoom-in SEM images in Fig. 2(d). The designed two gratings were etched parallel to the single-domain polarization direction and close to the crystal edges.
The home-built microscope optical measurement setup was shown in Fig. 3(a). A femtosecond (fs) pulsed laser was utilized with a central wavelength λFW = 1550 nm, repetition rate 80 MHz and the pulse width 100 fs. The incident power can be controlled by a set of neutral density (ND) filters. The linearly polarized FW was maintained by a Glan-Taylor prism. Fundamental wave was loosely focused on the sample via an objective lens (50×, NA = 0.4). Another objective lens was employed to collect the signal and connected to the sample stage, which can be adjusted for incident angle θ. Then a dichroic mirror (DM) was inserted before the spectrometer (Andor SR-500I-DI-R) and an enhanced charge coupled device (EMCCD, Andor DU-888) to block the FW. Power meter (PM) 1 and PM 2 were equipped to monitor the real-time power of pump laser and harmonic generation. For better comparison, the two nanogratings were fabricated on the same monolithic PMN-39PT substrate. Figure 3(b) showed the measured harmonic signals from these two gratings and the unetched monolithic PMN-39PT area. Since the refractive index of PMN-39PT cannot meet the phase-matching condition, the mismatch harmonic signals from flat region of PMN-39PT monolithic substrate were detected only if pumped with a larger FW power. However, the harmonic generation with gratings has a lower demand for pump power and higher efficiency. Meanwhile, the grating 1 illuminated at incident angle θ = 30°performed better than grating 2 with θ = 35°at the same FW power, which also confirmed the better FDTD simulation results of grating 1 (Fig. 2(c)).
Fig. 3. (a) Schematic of microscope optical measurement setup. BS, beam splitter; ND filter, neutral density filter; HWP, half-wave plate; GT, Glan–Taylor prism; OBJ, objective lens; DM, dichroic mirror; PM, power meter. Inset: schematic of grating etching direction. (b) The spectra of SHG and THG utilizing the monolithic PMN-39PT, grating 1 and grating 2, respectively.
In addition, although the initial grating design was aimed at the SHG enhancement, the THG increased simultaneously because of the cascaded effect. The peak value of the SHG/THG signals from grating 1 keeps rising with the increasing of the FW intensity. The power dependence of the SHG and THG with FW was depicted in Fig. 4(a), which satisfied the fitting correlation log(PFW) = 1.7log(PSHG) and log(PFW) = 2.8log(PTHG), respectively. The second harmonic signal is basically consistent with a square dependence on incident power with a small deviation which caused by the contaminate on the crystal surface and etching quality, and so is THG [23,24]. Similarly, the dependency between harmonic signal and FW power from grating 2 is plotted in Fig. 4(b), giving as log(PFW) = 2.0log(PSHG) and log(PFW) = 2.9log(PTHG). Since the etching quality, crystal defect, and surface contamination all affect the efficiency of harmonic generation, the fitting coefficients of the harmonic signal are fluctuated. The fitted coefficients above aim at demonstrating the approximate square and cubic relationships corresponding to second and third harmonic signals, respectively. Additionally, although the two nanogratings are etched on the same PMN-39PT surface, the grating 1 is prepared and tested before grating 2. Based on the accumulated experience of grating 1, the preparation and measurement of grating 2 are more careful, including pre-polishing of etching area and pump-power control. Thus, the measured results of grating 2 are closer to theoretical values, and the fitting coefficients are less biased than those of grating 1.
Fig. 4. (a) Dependence of SHG and THG upon FW pump intensity with grating 1. (b) Dependence of SHG and THG upon FW pump intensity with grating 2.
Figure 5(a-b) draw the collected SHG spectra of two gratings with different incident angles. As shown in Fig. 5(a), the peak value of grating 1 assisted SHG gradually increases with the incident angle varied from 26° to 30° and reach the maximum at θ = 30°. Subsequently, the incident angle continuous to increase, but the second harmonic signal attenuates, which conforms to the phase-matching condition. Although the SHG enhancement is limited with grating 2, the variation trend of SHG power is still matched with the phase-matching condition (Fig. 5(b)). For instance, the peak value of SHG signal on grating 2 keeps rising as the incident angle increases from 32.5°to 35.5°, while more than θ = 36°it attenuates. The phase-matching angle of the two designed gratings brings into correspondence with the theoretical value calculated by Bragg diffraction phase-matching condition. The phase-matching angles for two designed nanogratings are listed in the following Table 1.
Fig. 5. (a) Evolution of SHG spectra of grating 1 on incident angle. (b) Evolution of SHG spectra of grating 2 on incident angle. Inset: Simulated sinc2-dependence of its SHG on the incident angle.
Table 1. Theoretical and experimental SHG phase-matching angles for two designed nanogratings.
For grating 1 with incident angle θin1 = 30°: pump power of fundamental wave (FW) was PFW1 = 400 mW at λFW =1550 nm, and we measured the power of the second harmonic generation (SHG) to be PSHG1 = 11 µW. For grating 2 with incident angle θin2 = 36°: pump power of FW was PFW2 = 400 mW, and the corresponding SHG power was measured as PSHG2 = 8 µW. Because the unenhanced SHG signal from the bare PMN-39PT was much weaker due to its single domain structure and inherent refractive index, a higher pump power was required to make sure the SHG can be detected by the power-meter. Using an excitation power of PFW = 980 mW with θin = 0°, we measured the SHG power from the bare PMN-39PT to be PSHG = 0.23 µW (equivalent to 0.09 µW at 400 mW incident power). Therefore, the estimated SHG enhancement factors (EFs) are EF1 = 123 and EF2 = 88 for grating 1 and grating 2, respectively.
4. Conclusion
To sum up, an approach is proposed for realizing the phase-matching SHG on monolithic PMN-39PT substrate which is difficult for conventional BPM or QPM technology. The nanograting structure is introduced in single monolithic PMN-39PT substrate for providing reciprocal lattice vector by Bragg diffraction and localized field without thin crystalline films. The parameters of nanograting were optimized by simulation and well-matched with proof-of-concept demonstration results. The phase-matching angles of the two designed nanogratings are consistent with the calculated value, which also supports the nanograting-assisted phase-matching concept. This work may provide a fresh thinking for improving the harmonic generation efficiency in monolithic crystal and boost the variety of the nonlinear crystal.
Funding
Natural Science Basic Research Program of Shaanxi Province (2024JC-YBQN-0023); Fundamental Research Funds for the Central Universities (Northwestern Polytechnical University); National Natural Science Foundation of China (62305378).
Acknowledgments
Northwestern Polytechnical University Analytical & Testing Center; Instrumental Analysis Center of Xi'an Jiaotong University.
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.
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