1. Introduction

Among the various phase matching approaches, the quasi-phase-matching (QPM) technique, which is based on the periodic modulation of the nonlinearity of one-dimensional (1D) and two-dimensional (2D) crystals of LiNbO₃, LiTaO₃, and KTiOPO₄, is considered to be the standard method for fabricating nonlinear optical devices [1,2]. Fabrication of periodic grating is important to compensate for the phase mismatch caused by the difference in the group velocities of the fundamental wave and the harmonic generated wave. Moreover, in the case of 2D grating structures, the QPM conditions are more complicated than those required to fabricate 1D arrays. Berger suggested that the nonlinear photonic crystal (PhC) extends from a conventional linear grating, which maintains a constant dielectric function in space but periodically reverses the sign of nonlinear tensor at every coherent length of $l_c={\lambda }_{\omega }/4(n_{2\omega }-n_{\omega })$ [3,4]. The 2D nonlinear PhC can be applied to multiple wavelength second-harmonic generation (SHG), which can be simultaneously achieved in different directions on a plane; the mechanism of this generation is similar to that of linear diffraction in beams of several orders by diffraction grating.

Despite the drastic advancements in the development of nonlinear optics using the above mentioned bulk materials, there has been a constant demand for novel nonlinear optical crystals that can be applied to integrated optics [5]. Owing to their flexibility and affordability, thin films and nanostructures with large nonlinear optical response have attracted the attention of researchers; it is important to study the effect of the characteristics of films on nonlinear optical properties for their application in the nonlinear optical devices. There have been many efforts to fabricate the photonic crystal using the various patterning methods [6–8]; in addition, a few methods have been used to successfully realize a structure that periodically reverses the second-order susceptibility using semiconducting materials such as GaN, GaAs, and ZnO [9–11]. However, in contrast to the bulk nonlinear optical materials [12,13], the 2D periodically polarity-inverted (PPI) semiconductor structures with nanometer scale have not been extensively studied. Recently, ZnO was proposed as a potential candidate for a new nonlinear optical material, owing to its strong nonlinear susceptibilities [14].

In this work, we report the realization of a nonlinear photonic crystal with 2D PPI ZnO heterostructures, which were fabricated using previously proposed in situ polarity control methods. Suggested polarity control methods for obtaining PPI heterostructures can be used to fabricate multi-dimensional grating. In the case of ZnO heterostructure, the growth rates of Zn- and O-polar ZnO are different; as a result, the grating is formed with a step height whose magnitude depends on the growth conditions of PPI ZnO structure [11,15]. Moreover, the proposed fabrication approach can be expanded to the other wurtzite semiconductor materials with polarity characteristics.

2. Experimental

The 2D PPI ZnO structures were fabricated on c-sapphire substrate, where the growth and patterning sequences were obtained by carrying out laser holographic (LH) lithography, as illustrated in Fig. 1 . A CrN film is grown on (0001) Al₂O₃ to form the template. First, low-temperature (LT) ZnO layers are grown on a Zn-exposed CrN/Al₂O₃to protect CrN surface from oxidation [15]. Next, 2D periodic patterns are fabricated on the LT ZnO. The submicrometer-scale patterns are obtained by using LH lithography technique, whose mechanism and applications are provided elsewhere [16]. After lithography, the LT ZnO layers are completely etched by reactive-ion etching (RIE); the CrN surface, however, is only partially etched. For the formation of a Cr₂O₃ layer, the exposed CrN surface was subjected to O-plasma treatment; this led to the formation of Cr₂O₃ layers on CrN surface in patterns shown in Fig. 1(c); the formation of Cr₂O₃ is essential for the subsequent growth of O-polar ZnO film. Finally, a 1.4 µm-thck high-temperature (HT) ZnO layer was grown on the LT ZnO; this results in the growth of the Zn-polar ZnO on CrN area and the O-polar ZnO on the Cr₂O₃ layer [15]. After the fabrication of the 2D PPI ZnO structures, the behavior of second-harmonic generation (SHG) in the structures is investigated by the Maker fringe methods. A commercial Q-switched Nd:YAG laser system operating at λ = 1064 nm at a repetition rate of 10 kHz and a pulse width of τ = 8 ns was used as the fundamental input wave. The desired polarization of the fundamental beam is selected by using the half-wave plate and Glan-Thomson polarizer. The second-harmonic waves were detected by a photomultiplier at λ = 532 nm. The SHG measurement system was calibrated by means of a Y-cut α-quartz crystal to prevent the fluctuations of laser power intensity. In addition, the crystal and optical qualities of ZnO heterostructures are investigated by high resolution x-ray diffraction (XRD) and photoluminescence(PL).

 

Fig. 1 Schematic illustration of procedures for fabricating PPI ZnO structures. (a) LT ZnO grown on Zn-pre-exposed CrN buffer. (b) 2D pattern formation on LT ZnO by LH lithography. (c) O₂ plasma treatment on exposed CrN surface for formation of Cr₂O₃. (d) Re-growth of ZnO, resulting in Zn-polar film on CrN and O-polar film on ZnO on Al₂O_3.

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3. Results and discussion

In order to investigate the structural properties including the epitaxial relationship and crystallinity of PPI ZnO structures, a high resolution x-ray diffraction (HR XRD) measurement was performed. Figure 2(a) shows the XRD θ–2θ spectrum of the 2D PPI ZnO. The diffraction peaks can be indexed to (0002) ZnO, (111)CrN, and (0006) Al₂O₃, respectively. Typical full width at half maximum of rocking curves data obtained from the (0002) peak of the PPI ZnO structures were between 0.2 to 0.3 ^o as shown in inset of Fig. 2(a). In addition, as shown in Fig. 2(b), six equidistant narrow peaks of the (10-11) ZnO plane are observed in the Φ-scan range, which is indicative of the growth of good crystallinity and single-domain ZnO films in entire region. Moreover, in order to collect optical properties of the fabricated PPI ZnO, photoluminescence spectra were acquired. Strong near band edge emission in the UV range and negligible week green emission were observed (not shown here). The details of optical properties of PPI ZnO can be found out in our previous publication [17].

 

Fig. 2 X-ray diffraction (a) θ–2θ scan, (b) φ-scan spectra of (10-11) ZnO planes of the PPI ZnO structures. Inset of (a) shows the typical ω-rocking curve of the (0002) ZnO plane.

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Figure 3(a) shows the schematic diagram of the coordinate system used in this study to represent the 2D PPI ZnO structure as a nonlinear optical crystal. The Zn-polar and O-polar ZnO films are periodically and two-dimensionally arrayed on alternating CrN and Cr₂O₃ intermediate layers. The periodicity of 2D PPI-ZnO was found to be 540 ± 4 nm. To show the grating effects arising from the PPI structures with different growth rate, depending on the polarity of ZnO, we measured the transmission spectra of the film. The incident light was used as either an s- or p-polarized wave, which was obtained using a prism polarizer. The transmission spectra were measured with a Fourier-transform spectrometer over a wavelength range of approximately 450 nm to 1.1 µm at varying angles of incident light. Figure 3(b) shows the typical angular resolved transmission spectra of the 2D PPI ZnO grating, obtained with the p-polarized incident light. The plane of propagation of the incident light was aligned in the x direction (Г-X direction). The resonance features observed in the spectra correspond to the coupling of the incident beam with the resonant modes; when the incident angle (θ) increased from 0° to 30°, these resonance features clearly became dispersive. Along the x direction, the resonant modes can be selectively excited by using either the s- or p-polarized light. Corresponding to their polarization at the azimuthal angle = 0° between the in-plane wave vector and the direction perpendicular to PhC plane. The minima were selected as the wavelengths corresponding to the positions of the excited resonant modes determined by the transmission measurements. The shift of valley as a function of the azimuthal and incident angle demonstrates the typical grating effect [18].

 

Fig. 3 (a) Schematic illustration of 2D PPI-ZnO in planar geometry and coordinate system used in this study. (b) Experimental incident-angle-dependent transmission spectra measured along x axis with p-polarized light.

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The SH-signal intensity measurements were conducted on the 2D PPI ZnO structure with a frequency conversion from 1.064 µm (fundamental wave) to 532 nm (SH wave). The incident angle (θ) was changed on 2D PPI ZnO with a periodicity of 540 nm. The incident wave vector κ_in (ω) with the z axis normal to the PhC plane defines the plane of incidence. The direction of the wave vector k(ω) is specified by the angle of incidence θ between κ_in (ω) and the z axis. κ_//(ω) can be determined using κ_// (ω) = κ_in(ω) sin θ.

The four peaks of the SH signal are clearly indicated by the violet arrows in Fig. 4 . The four peak positions are 8°, 21°, 42°, and 66°, respectively. In the case of a bare sapphire substrate having the same experimental sequences, the intensity changes were not detected, indicating that the peaks do not arise from the substrate. Moreover, only one broad peak was observed in the intensity spectra of a ZnO film without the 2D grating on the surface. Therefore, it can be concluded that the four peaks observed are attributed to the PhC of the 2D PPI ZnO structure. In addition, the input power of the fundamental wave was changed using an IR-cut filter. The relatively low intensity can be attributed to the low thickness of the PPI ZnO structures.

 

Fig. 4 (a) SH signal intensity as a function of incident angle. (b) Calculated QPM conditions in 2D PPI ZnO structures from dispersion relation.

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The experimentally obtained results demonstrated the enhancement of SHG at particular incident angles, as shown in Fig. 4(a). Herein, we discuss how such discrete peaks arise from the 2D PPI ZnO structures. In order to analyze the origin of the four peaks, we consider the QPM conditions of the 2D PPI ZnO structure with a periodicity of 540 nm. In this study, we take into account the phase matching conditions by considering a simple photonic-band model [19]. Since exact computation for the 2D PPI ZnO is considerably difficult, the simple photonic-band model is used to describe the qualitative properties of SHG. An incident light of 1064 nm was generated by the Nd:YAG laser and propagated in the xy plane with p polarization, as shown in Fig. 3(a). The incident light produces the in-plane photonic modes with wavenumber κ _//in in the PhC along the x axis, which is parallel to the ΓM direction. From the conservation of the tangential component of the wavenumber at the interface, we can estimate the wavenumber of the incident light in air. The induced photonic modes are fundamental waves in the in-plane SHG. The SH waves (532 nm) were obtained, and only the SHG component parallel to the xy plane was measured. It was confirmed that the intensity of the SH wave is proportional to the square of the power of the incident light. As shown in Fig. 4(b), four QPM conditions can be suggested. The solid black lines in the figure indicate the photonic modes at periodic air-object interface, the dashed blue lines indicate the photonic modes at periodic object-substrate interface. The photonic bands are represented in normalized units with wavenumber and frequency. The photonic modes from left to right correspond to the incident angles of 2°, 23°, 53°, and 80°; the corresponding measured incident angles were 8°, 21°, 42°, and 66°, respectively. Thus, the four peaks are reproduced and show qualitative agreement with the results calculated using the simple photonic-band model.

4. Conclusion

In conclusion, we fabricated the 2D grating structures of ZnO with nanometer-scale periodicity on (0001) Al₂O₃ substrate by using the periodical polarity inversion method. The fabricated 2D PPI ZnO structures demonstrated the grating effect and SGH under QPM condition, which was achieved by controlling their periodicity and the angle of the incident light. The SHG characteristics of the 2D PPI ZnO were analyzed by using a nonlinear photonic crystal model. From the experimental and theoretical results, the fabricated 2D PPI ZnO structures can be used as a second-order nonlinear frequency conversion device by employing its SHG under QPM conditions.