Efficiently controlling and manipulating emission photons at the nanoscale level has a broad range of applications in compact optical components such as nanolasers [1,2], single photon sources [3,4], and light-emitting diodes [5,6]. Recently, extending the linear optical control to the nonlinear regime has been a novel research point. It has attracted a lot of research interest, including nonlinear volume holography [7], generation of entangled states [8], and nonlinear wavefront engineering [9]. To realize the beam steering of nonlinear sources, many approaches have been utilized, such as the phase control of effective nonlinear polarizability in nonlinear photonic metasurfaces [10–13] or by engineering the interference of multiple modes in a single particle [14–16]. However, these schemes generally require additional structural design around the nonlinear materials, which will improve the complexity of the final elements. Compared to the above nanostructures, one- or two-dimensional structures (such as nanowires or nanobelts) offer a simple and efficient manipulation degree of freedom of polarization-dependent optical response and are suitable with the waveguide system [17,18]. It is of great significance to achieve nonlinear wavefront engineering in the waveguide, which will promote the development of functionalization for nanophotonic devices [19].

Among various steering approaches, mode-selective excitation in nanostructures is considered to be a powerful means to achieve efficient and active beam steering, where the emission characters of the nano source are dependent on the type and number of the excitation modes [20,21]. To selectively excite modes into the nanostructures, different kinds of active methods are proposed such as using a spatial light modulator [21] or manipulating the phase properties of input beams [20]. Nanophotonic waveguides with high index have strong mode dispersion, which considerably minimizes intermode coupling and improves mode selectivity [22]. Directional emission has been demonstrated by selectively exciting the supported modes [17,18,23]. The excitation modes in the waveguide depend on the polarization, chirality, and phase [24,25]. The position of the excitation light will also influence the excitation modes [26]. Due to the advantage of the simple structure, easy modulation, and compatibility with the standard photonic elements, the mode-selective excitation in the waveguide will provide a feasible steering scheme for the nonlinear nano source.

Here, we demonstrate the stable beam steering of the second-harmonic generation (SHG) in a hybrid waveguide, consisting of the CdSe tapered nanobelt and the Au film. Central to our approach is the selective excitation of guided modes involved in nonlinear processes in the waveguide. We previously used a similar technique to enhance the conversion efficiency of SHG by the plasmonic grating in the waveguide [27] or modulating the types of guided modes by adjusting the diameter of the nanowires [28]. A nontrivial extension to nonlinear beam steering in one waveguide has now been realized by varying the excitation modes. In the tapered waveguide, the variety of the mode selection is outstanding and will promote the study of nonlinear beam steering. The selective excitation of different guided modes allows for influencing and directing the second-harmonic (SH) intensity distribution in the waveguide. The Fourier imaging of SHG signals confirms the interference between guided modes. The measured SH emission patterns from different excitation conditions are well in agreement with simulations. A directivity change (6.1°) for the SH emission is observed when the interference modes change from TE00 & TE01 to TE00 & TE02 at a wavelength of 800 nm. This device can potentially serve as a tunable coherent light source and promote the development of nonlinear beam engineering in integrated nanophotonics.

A schematic of the beam steering system based on the nanophotonic waveguide is shown in Fig. 1(a). It consists of a CdSe nanobelt and Au film, where nanobelts are synthesized by the chemical vapor deposition method [29], and the Au film (thickness 200 nm) is fabricated by the template stripping [30,31]. The CdSe nanobelt has a large nonlinear susceptibility, and the c axis is along the short edge as in the transmission electron microscopy (TEM) characterization in Appendix A. The Au film acts as a mirror and promotes an efficient air coupling. The distribution of SHG in the waveguide is dependent on the excitation position of the incident light. Figure 1(a) presents the situation when the beam is focused on the corner of the edge of the waveguide. Figure 1(b) shows the far-field radiation pattern of the SHG beam at the y–z cross-section view. The beam steering is a result of the change of participation modes in the SHG process. When the input beam is focused on the center of the edge of the tapered waveguide, the TE00 and TE02 modes are excited. When the illumination is at the corners of the tapered waveguide, the TE00 and TE01 modes are excited. Due to the momentum conservation, the wave vectors of the counterpropagating guided waves cancel each other and generate coherent SH signals along the direction perpendicular to the hybrid waveguide (gray area) [28,32,33]. This part of the SH beam is not steered when varying the excitation positions. The adjustable parts of the SH emission (orange line or red line) come from the interference between different counterpropagating modes [34,35].

Figure 1(c) shows the dependence of guided-mode effective refractive indices on the waveguide width W for the nanobelts of thickness 120 nm (finite element method). The wavelength of the excitation light is 800 nm. The mode refractive index increases with waveguide width growth, and the difference between the effective indices of different modes decreases with the increasing width. It is the single-mode area where only the TE00 mode is supported when the width is smaller than 0.7 μm. For widths from 0.7 to 1 μm, there are two modes (TE00 and TE01) coexisting. More modes will participate in the SHG process when the width is larger than 1 μm. Figure 1(d) shows the mode profiles of the electric field components |Ex| at z along the center of the CdSe nanobelt of W=1.2μm. The lateral electric field component Ex is dominant for the two even modes (TE00 and TE02) and one odd mode (TE01). These three modes can be excited with polarization parallel to the short axis of the nanobelt.

Next, we move to the experimental realization of the beam steering for SH emission in the waveguide, where the SHG measurement is performed at room temperature (more details in Appendix B). A collimated beam of a picosecond laser (NKT Photonics, EXB-4) was focused by a 100× objective lens (NA=0.9, Olympus) onto the end of a CdSe nanobelt, where the diameter of the spot is 1 μm and the wavelength is 800 nm. The polarization of the incident laser was controlled by inserting a polarizer and a half-wave plate in the input optical path. We used two bandpass filters (380–420 nm) to remove the fundamental light in the SHG collection path, and the SHG signal was imported into the spectrometer (iHR 320, Horiba Jobin Yvon) for the spectroscopy or CCD camera (Retiga 3000, QImaging) for the image. A set of lenses were added to the imaging collection path to map the back focal plane of the objective. To realize the diverse excitation of modes in the waveguide, we choose a tapered nanobelt where the width is wide at the upper edge and narrow at the lower edge. Figure 2(a) shows the scanning electron microscopy (SEM) image of the hybrid waveguide where the nanobelt has a length of 13.4 μm and a width of the lower edge of 0.98 μm and the upper of 1.2 μm. The thickness of this nanobelt is ∼120nm. Figure 2(b) shows the SHG spectra collected from the red boxed region in Fig. 2(d), and a clear peak at 400 nm indicates the SH characteristic. The power dependence has a slope of 2.00, proving the second-order nature of the nonlinear process. The conversion efficiency of the hybrid plasmon waveguide shown in Fig. 2(d) is estimated to be 2×10−5W−1, using a pump laser of 1 mW (Appendix C). The efficiency can be further improved by exciting two sides of the tapered waveguide simultaneously because SHG emission in our structures is mainly decided by the intensity of the reflected waveguide mode.

According to the mode analysis with widths, there are two modes (TE00 and TE01) that could be excited at the lower edge, and three modes (TE00, TE01, and TE02) are supported at the upper edge. The whole system has four cases of the mode interference. (1) When the input beam is focused on the center of the lower edge, only the TE00 mode is excited. (2) The even mode TE00 and odd mode TE01 are both excited when the input beam is moved to the right (left) corner of the lower edge. (3) At the center of the upper edge, the even modes TE00 and TE02 are both excited. (4) Three modes (TE00, TE01, and TE02) are all excited when the input light moves to the left or right corner of the upper edge. In the tapered waveguide, the mode conversion does not happen as shown in Appendix D. The excitation polarization is parallel to the short axis of the nanobelt. The Fourier image setup in Fig. 2(f) determines the direction of the SHG radiation I(θ, φ), where θ and φ are the spherical coordinates [36,37]. It enables exploration of the emission properties of the SHG photons. In Case 1, when the input beam is focused on the center of the lower edge, only the TE00 mode is excited [Figs. 2(d) and 2(g)]. The forward TE00 mode and its reflection mode will interfere with each other and generate coherent SH signals emitting in the direction perpendicular to the hybrid waveguide. This is demonstrated by the major component of the SHG emission at ky=0 in the Fourier imaging. In Case 4, three modes (TE00, TE01, and TE02) are all excited when the input light moves to the left corner of the upper edge [Figs. 2(e) and 2(h)]. These modes interfere with each other and generate the periodic SHG image, and more sidelobes appear in the Fourier imaging.

We selected the interference of two modes (Case 2 and Case 3) in the experiment to achieve the nonlinear beam steering. In Case 2, when the input beam was focused on the right corner of the lower edge, even mode TE00 and odd mode TE01 are excited [Figs. 3(a) and 3(d)]. Superposition of even and odd modes results in field enhancement on one side of a single supercell and field reduction on the other side due to constructive and destructive interference of the fields [38–40]. The zigzag pattern is due to the beating of two copropagating modes (TE00 and TE01 modes) with different propagation constants. The beating period agrees with the equation given by [28] ΛR=λn0−n1,(1)where n0 and n1 are the effective refractive indices of the TE00 and TE01 mode, respectively. The counterpropagating TE00 and TE01 modes generate tilt SHG emission at θR=±3.5°, following the equation (see Appendix E) n0−n1=2sinθ.(2)This is close to the tilt angle θR=±3.3° in the Fourier image in Fig. 3(d). In Case 3, when the incident light was focused onto the center of the upper edge of the nanobelt, TE00 and TE02 modes were excited [Figs. 3(b) and 3(e)]. The interference between TE00 and TE02 modes results in the period ΛC=2.5μm and tilt angle θC=±9.4° [Fig. 3(e)], which is also in agreement with the above equations. In Fig. 3(c), when the waveguide is illuminated on the left corner, the SHG beating pattern can be switched by half a period as compared to the SHG image in Fig. 3(a). The electric field distribution of the TE01 mode is zero on the center of the lower edge and with opposite field signs on the left and right corners as shown in Fig. 1(d). The Gaussian beam with a diameter of 1 μm only overlaps with half of the TE01 field distribution, resulting in a relative phase shift π when the waveguide is exited on opposite corners. The Fourier image in Fig. 3(f) presents the same SHG emission as Fig. 3(d), further demonstrating the involved modes (TE00 and TE01) in the SHG process. Beam steering of the SH emission is 6.1° when the interference modes change from TE00 & TE01 to TE00 & TE02.

The beam steering mechanism was further confirmed by utilizing the 3D finite-difference time-domain (FDTD) simulation method (see Appendix G). We used the mode sources and selectively inputted the specific guided modes into the tapered waveguide with a length of 13.4 μm. In Fig. 4(a), we calculated the electromagnetic power density of the SHG at a plane 500 nm above the top of the waveguide. We launch the TE00 and TE02 modes at the upper edge of the tapered waveguide. The beating periodic pattern originates from the difference between effective refractive indices of the copropagating TE00 and TE02 modes, which agrees with the experiments in Fig. 3(b) and the Eq. (1). The zero momentum of SHG along the y axis is from the cancelation between the same counterpropagating modes, just in the middle line of the Fourier image in Fig. 4(b). The signals deflected from the normal direction with an angle ±θC are from the interference between the input TE00 mode and the reflected TE02, or vice versa. When the TE00 and TE01 modes are launched into the waveguide from the lower edge, the zigzag SHG pattern and Fourier imaging are reproduced as shown in Figs. 4(c) and 4(d).

Then we studied the distribution changing of SHG emissions from the TE00 & TE01 (and TE00 & TE02) by varying the excitation wavelength (760–815 nm). The emission angles of SHG for both excitation conditions are a function of the excitation wavelength as shown in Fig. 4(e). The experiments agree well with the equation Δn(λ)=2sinθ, and Δn(λ) is the difference between the effective index of guided modes. We change the combination modes from TE00 & TE02 to TE00 & TE01, and the SHG emission angles will be steered as Δθ=θC−θR. The steering angle of SH emission Δθ increases with the wavelength. To capture and describe further the main mechanisms that govern the SHG, we further used the dipole chain model to reproduce the experimental results very well [32] (see Appendix H). In our system, the divergence angle is δθ=0.9°, and the wavelength sensitivity dθ/dλ was 0.06(°)/nm on average (see Appendix I). Further studies will aim at achieving the on-chip steering of SHG emissions by controlling the types of guided modes in the waveguide. Recently, utilizing the phase-gradient metasurface to manipulate the types of guided modes has been demonstrated in the waveguide [41,42], which will help realize the integrated steering nonlinear source.

In summary, we have demonstrated the stable and efficient beam steering of the SHG in a hybrid waveguide consisting of a CdSe nanobelt and an Au film. This was accomplished by selective excitation of three modes (TE00, TE01, and TE02) in the waveguide, and the types of excitation modes depend on the position of the incident beam on the tapered nanobelt. Our scheme uses mode-selective excitation and does not involve complex beam steering optical elements. Through Fourier imaging analysis of the SHG emission, we find that the interference between different guided mode combinations causes the SHG beam steering. We experimentally and theoretically confirmed the exact mode types involved in SHG processes, including TE00 & TE02 modes by the center excitation and TE00 & TE01 modes by the edge excitation. The beam steering angle is 6.1° when the excitation wavelength is 800 nm. This work provides new possibilities for the development of integrated nonlinear wavefront shaping photonic components.