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Abstract
We designed, fabricated and tested gallium phosphide (GaP) nano-waveguides for second harmonic generation (SHG). We demonstrate SHG in the visible range around 655 nm using modal phase matching. We observe phase matched SHG for different combinations of interacting modes by varying the widths of the waveguides and tuning the wavelength of the pump. We achieved a normalized internal SHG conversion efficiency of 0.4% W−1cm−2 for a continuous-wave pump at wavelength of 1283.5 nm, the highest reported in the literature for a GaP waveguide. We also demonstrated temperature tuning of the SHG wavelength with a slope of 0.17 nm/°C. The presented results contribute to the development of integrated photonic platforms with efficient nonlinear wave-mixing processes for classical and quantum applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Integrated photonics promises miniaturization of optical devices, leading to the development of scalable on-chip solutions [1,2]. One of the key challenges is that the most efficient detection, storage and manipulation of photons are done in the visible spectral range, whereas the most efficient transmission occurs at the telecom wavelengths. Nonlinear optical processes can be exploited to bridge this gap [3,4]. The nonlinear material for the frequency conversion process should satisfy several requirements: transparency at both the telecom and the visible wavelengths, high nonlinearity and high refractive index to provide strong light confinement for compact devices on integrated photonic platforms.
A number of integrated platforms have been developed so far based on different nonlinear materials including lithium niobate (LiNbO$_3$), gallium arsenide (GaAs), aluminium nitride (AlN) and gallium nitride (GaN) [5–17]. At present, the most promising bulk material for commercial applications is LiNbO$_3$ because of its broad transparency window, moderately high $\chi ^{(2)}$, and the possibility of periodic domain inversion [18]. Major progress has been made in the fabrication of LiNbO$_3$ nanostructures [19,20]. However, its relatively low refractive index of of $\sim$2.2 makes dense integration of nanophotonic devices difficult. Semiconductor materials like AlGaAs and GaAs have even larger nonlinear parameter $\chi ^{(2)}$ and higher refractive index [13,21,22]. However, the transparency cut-off wavelength for AlGaAs is around 900 nm [23]. Hence AlGaAs cannot be used in the visible wavelength range which is relevant to applications in imaging, quantum optics and sensing. AlN is another material which is under consideration [12]. However, AlN has relatively low refractive index and $\chi ^{(2)}$. A comparison of the material parameters is given in Table 1.
Table 1. Parameters of nonlinear materials at 1310 nm
For the above mentioned reasons, we have selected gallium phosphide (GaP) as a promising candidate for frequency-conversion. It has a high refractive index ($\sim$3.1 in the O-band), high second-order nonlinear parameter (d$_{36}$ of $\sim$50 pm/V in the O-band), good thermal conductivity for temperature tuning and broad transparency range from 550 nm to 11 um [23–41].
GaP is gaining interest in the research community [23,37], but thus far it is relatively less well studied compared to other nonlinear materials, with few articles describing $\chi ^{(2)}$ processes in nano-waveguides. As a first step in developing an integrated GaP platform for frequency conversion, we target to demonstrate second harmonic generation (SHG) in nano-waveguides. SHG remains the most studied and widely applied second-order nonlinear process among others [42], for a broad variety of applications, including lasers, pulse characterization, quantum optics, spectroscopy and imaging to name a few [43–46]. Hence, more efficient platforms for SHG are always desirable and motivates a strong interest in the community for studying nonlinear frequency mixing processes.
In this work, we first review the theory of SHG in GaP waveguides. The crystal axis orientation is of crucial importance in design and modeling of the waveguides, as it is required to calculate the overlap integrals for the mode coupling in SHG. We thus measured and confirmed the GaP crystal axis orientation of the thin film on our samples. We further elaborate on SHG in nano-waveguides by modal phase matching. We then describe the nano-waveguide fabrication process using samples of thin film GaP on SiO$_2$, on top of sapphire substrate. Finally, we report our experimental results on SHG in GaP nano-waveguides.
2. SHG in GaP waveguides
The fields excited in the waveguide at the angular frequency $\omega$ can be given as a superposition of eigenmodes [50],
We consider GaP waveguides embedded in silicon dioxide cladding. The tensor components $\chi ^{(2)}_{ijk}(x,y)=0$ when the coordinates $(x,y)$ are outside the GaP waveguide. Under the Kleinman symmetry conditions, $\chi _{ijk}^{(2)} (\omega ,2\omega ) = \chi ^{(2)}_{ijk}(\omega ,\omega ) \equiv \chi ^{(2)}_{ijk}$. Also, the zinc blende crystal structure of GaP further reduces the total number of tensor elements that need to be considered: $\chi _{xyz}^{(2)} = \chi _{xzy}^{(2)} = \chi _{yzx}^{(2)} = \chi _{yxz}^{(2)} = \chi _{zxy}^{(2)} = \chi _{zyx}^{(2)} = 2 d_{36}$ [42]. We assume $d_{36}$ = 50 pm/V in our analysis [49,51].
As the crystal axis is not necessarily the same as the waveguide axis, it is important to do the rotational transformation between the two coordinates when calculating the overlap integrals. In our case the GaP crystal axis orientation, as stated by the vendor, has to be tilted with respect to the sample surface. Confirmation of the tilt angle is needed to calculate the overlap integrals and is critical for designing of the nano-waveguides [52–54].
2.1 Measurement of the crystal axis orientation
The surface normal vector of the thin film gallium phosphide (GaP) sample is tilted at an angle $\theta = 15^\circ$ towards the [111] crystal direction. This tilt angle was chosen by the vendor because it is helpful for the nucleation in hetero-epitaxial growth with large lattice mismatch. We verify the tilt angle by measuring the SHG under normal incident pump. We rotate the GaP thin film around the normal direction and compare the experimentally measured SHG with the simulation data for various tilt angles $\theta$.
Figure 1(a) shows the schematic of the experimental setup [55]. The pump is a pulsed optical parametric oscillator (OPO) at 1310 nm, pumped by a Ti-Sapphire oscillator with the spectral width of 11 nm and repetition rate of 78 MHz. Dichroic beam splitter is used to spectrally filter the pump pulses from the OPO at 1310 nm. The light from the output of the dichroic passes through a polarizer to increase the extinction ratio of the polarized output from the OPO. The light then passes through a plano-convex lens and focusses at the thin film sample of GaP. The objective lens with an NA of 0.45 then collects the output from the thin-film. The light at the output of the thin film GaP sample contains both the pump and the SHG signal. A dichroic beam splitter and filter are used to filter the SHG from the sample at the wavelength of approximately 655 nm. The filtered SHG signal is then collected and analyzed using a spectrometer.
Fig. 1. (a) Experimental system used to analyze the crystal axis of GaP sample. MM–multi-mode, M–mirror, BS–beam splitter, L–lens, OPO–optical parametric oscillator. (b) Experimental (blue dots) and simulated normalized SHG amplitude (red lines) as a function of the rotation angle $\phi$ of the sample. $\theta = 15^\circ$ matches best with the experiment data. (c) Visualization of the relationships between the crystal axis, the sample plane and the waveguide axis.
The sample is rotated over $180^\circ$ around the normal, with normally incident pump at horizontal (H) polarization. The strength of the SHG signal is analyzed as a function of the rotation angle $\phi$, which is the angle between the pump polarization and the projection of [111] onto the sample plane. This projected vector is perpendicular to the edge of the sample and for $\phi = 0^\circ$ it is parallel to the pump polarization. Figure 1(b) shows the experiment results (blue dots). Comparing with the simulation results (red lines), $\theta = 15^\circ$ has the best match, verifying the crystal axis tilt angle. A clear signature of the tilt angle $\theta$ is the ratio of SHG powers, $\frac {P_{2\omega }(\phi =0^\circ )}{P_{2\omega }(\phi =90^\circ )}$, which decreases as $\theta$ increases.
To calculate the overlap integrals, we fix the sample frame and allow the waveguides to rotate in the sample plane. Thus, in the following section, we define $\varphi$ as the angle between the waveguide axis and the projection of [111] onto the sample plane. Figure 1(c) visualizes the relationships between the various reference frames.
2.2 Modal phase matching
For SHG in waveguides, the exact phase matching condition for the case of two interacting eigenmodes is $n_{2\omega } = n_{\omega }$. Due to material dispersion, the effective index of same order eigenmodes increases as the wavelengths decreases. On the other hand, effective index decreases with increasing mode order. As such, modal phase matching is achieved by adjusting the waveguide dimensions so that a higher order eigenmode of the second harmonic has the same effective index as a lower order eigenmode of the pump.
Figure 2(a) shows the calculated mode effective indices for a waveguide height of 220 nm and side wall angle of 70$^{\circ }$, at a pump wavelength of 1310 nm. Figure 2(b) shows the electric field component profiles for each case, calculated using a commercial eigenmode solver (Lumerical). The 1$^{st}$ mode (blue), commonly called a quasi-TE mode, has the largest components in the $x$ and $z$ direction and is excited by injecting horizontal (H) polarized pump light. The 2$^{nd}$ mode (red), commonly called a quasi-TM mode, has the largest components in the $y$ and $z$ direction and is excited by injecting vertical (V) polarized pump light. A common feature of these two pump eigenmodes is the two lobed $E_z$ fields. The second-order nonlinear susceptibility tensor of GaP enables unique modal coupling configurations for these dipolar eigenmodes [56].
Fig. 2. (a) Effective index plot versus top width of GaP waveguide, at 1310 nm. The dashed lines are the second harmonic eigenmodes and the colored lines are the two lowest order pump eigenmodes. The phase matched points are circled. The inset shows the geometry of the GaP waveguides. (b) The electric field components of the two lowest order pump eigenmodes (red and blue) and the corresponding phase matched higher order eigenmode of the second harmonic. The plots are normalized to the maximum $|E_i|$ across the three components.
We identify phase matched configurations based on the line intersections, circled in Fig. 2(a). The quasi-TE (blue) and quasi-TM (red) modes are each separately phase matched with higher order second harmonic modes. For SHG, the coupled equations become
with $\Delta \beta = 2 \beta _\omega - \beta _{2\omega }$. In general, the crystal axis $(x',y',z')$ need not coincide with the waveguide axis $(x,y,z)$. The vector components of the electric fields, originally described in the waveguide frame, have to be recast into the crystal frame prior to performing the overlap integral. After accounting for the GaP crystal symmetry, the overlap integral is now,Using the above formalism, we calculate the absolute square of the overlap integral $|\kappa |^2$ in units of W$^{-1}$cm$^{-2}$ for each of the phase matched configurations in Fig. 2(a), which we label as H and V according to the input pump polarization. The results are shown in Fig. 3, with the overlap integral being strongly dependent on $\varphi$.
Fig. 3. Calculated absolute square of overlap integral $|\kappa |^2$ versus $\varphi$ angle for each of the phase matched configurations in Fig. 2(a). We set $\theta = 15^\circ$, as in our thin film GaP sample (see Fig. 1).
3. Fabrication of the GaP nano-waveguides
We start by depositing an AlGaInP buffer layer on a GaAs substrate by metal-organic chemical vapor deposition (MOCVD). This is to reduce the lattice mismatch between GaAs and GaP. Then a crystalline GaP active layer of thickness $\sim$400 nm was grown on top. This structure is directly bonded to a 150 $\mu$m sapphire substrate after depositing $\sim$2 $\mu$m SiO$_2$ layers on the top of both bonding surfaces. The GaAs substrate is then removed by wet etching, as shown in Fig. 4. Finally, the wafer is cut into square samples. Each has a GaP layer of about 400 nm on top of few $\mu$m of SiO$_2$, which sits on top of the sapphire substrate.
Fig. 4. (a) Fabrication flow, refer to text for details. (b) SEM image of fabricated waveguide with height of 215 nm and side wall angle of 70$^{\circ }$. The deviation from the nominal dimensions is due to fabrication uncertainty.
The fabrication of the GaP nano-waveguides begins with a standard wafer cleaning procedure (using acetone, iso-propyl alcohol and deionized water in that sequence under sonication). GaP layer was thinned down to the designed thickness using inductively-coupled plasma reactive ion etching (ICP-RIE) with N$_2$ and Cl$_2$ gas. The sample was followed by O$_2$ and hexamethyl disilizane (HMDS) priming in order to increase the adhesion between GaP and subsequent spin-coated electron-beam lithography (EBL) resist of hydrogen silsesquioxane (HSQ). After spin-coating of HSQ layer with a thickness of $\sim$540 nm, EBL and development in 25$\%$ tetra-methyl ammonium hydroxide (TMAH) defines the nano-waveguide regions in HSQ. ICP-RIE is then used to transfer the HSQ patterns to GaP. Finally, $\sim$3.2 um SiO$_2$ cladding layer is deposited on top of the waveguides by ICP-CVD. The HSQ is not removed as it has a refractive index similar to SiO$_2$ and does not affect waveguiding. Devices are diced by laser cutting. Our waveguides are fabricated to have a propagation direction oriented perpendicular to the edge of the square samples cut from the wafer, i.e. $\varphi = 0^\circ$ or $90^\circ$ (see Fig. 1(c)).
4. Measurement results
4.1 Experimental setup to study SHG
Figure 5(a) shows the schematic of the experimental setup [55]. The pump light from a narrow linewidth continuous-wave tunable laser (Yenista, 1260 nm - 1360 nm, linewidth $\sim$400 kHz) is coupled into the waveguide using a tapered polarization-maintaining lensed fiber (OZ optics) designed for wavelengths around 1310 nm. An objective lens with a numerical aperture (NA) of 0.7 (Mitutoyo) is used to collect the higher order second harmonic light output from the waveguide. The output from the objective is imaged using a charged coupled device (CCD) camera (uEye), which also gives the intensity readings in counts. The CCD camera is preceded by a filter centered at 650 nm and having a bandwidth of 150 nm (Semrock). Another 10x objective lens and CCD camera are mounted above the structure to observe the interface with the fiber. A flip mirror is used to direct the SHG light into the spectrometer (Ocean Optics). The lock-in amplifier (Signal Recovery) is phase-locked to the chopper rotating at a frequency of 500 Hz, which is used for modulating the SHG signal. The amplified photo-detector (PD, Thorlabs) is used to detect the SHG signal. Since the chopper reduces the power by half, it is introduced at the output of the waveguide for SHG instead of the input pump because of the quadratic dependence between the pump power and the SHG power. SHG is studied in the waveguide for H and V pump polarizations. The polarization of the pump is set by rotating the tapered lensed fiber and measuring the fiber output through a polarizer without the waveguides in the path.
Fig. 5. (a) Experimental setup showing tapered fiber input, chip mount, output objective to collect the second harmonic light, CCD camera used to analyze the second harmonic. CCD–camera, MM–multi mode, M–mirror, PM–polarization maintaining, PD–photodetector. (b) Top view of the waveguide when pump light is coupled in, without phase matching. (c) Top view of the waveguide when pump light is coupled in, with the waveguide marked using an ellipse where the SHG generation can be observed. (d) Spectrum of SHG with the pump spectra given in the inset.
4.2 Phase matching study
We first studied the dependence of the phase matching SHG wavelengths on the waveguide top width. We fabricated arrays of waveguides having a height of 220 nm, with the top width varying from 280 nm to 420 nm in steps of 10 nm and a side wall angle of $70^\circ$. Due to the non-uniformity of the thickness of the GaP thin film ($\pm 5$ nm) across the wafer and the inevitable deviations in the fabricated waveguide width and side wall angle, there will be uncertainty in the final waveguide dimensions. The waveguides have a length of 1.5 mm excluding tapered edge couplers. The tapered edge couplers are used for coupling from the lensed fiber to the waveguide [57]. They have a length of 100 $\mu$m at both facets, with the starting top width of 220 nm. The cross-sectional scanning electron microscope (SEM) image of the waveguide is given in Fig. 4(b).
We observed the scattered SHG light from the waveguide using the CCD camera above the chip. Figure 5(b) shows the image from the top CCD camera when the pump light is tuned to a wavelength without phase matching. Figure 5(c) shows the image from the top CCD camera when pump light is at the phase matching wavelength and there is SHG scattered by the waveguide. A filter centered at 650 nm was used to remove the pump light. Figure 5(d) shows the spectrum of the SHG obtained from the spectrometer and the inset shows the optical spectrum of the pump light.
We tune the pump wavelength from 1260 nm to 1360 nm in steps of 0.1 nm and take the phase matching wavelength as the value where SHG power is maximum. Figure 6 shows the dependence of the phase matched pump wavelength on the top width of the waveguide for V (red markers) and H (blue markers) polarized input pump light. The phase matching wavelengths varies between nominally identical structures due to uncertainty in the dimensions of the fabricated structures.
Fig. 6. Experimental (markers) and simulated (lines and shaded regions) phase matched second harmonic wavelengths in waveguides for H and V polarized input pump light. Labels indicate the (side wall angle, height) used in simulation. Each shaded region represents a fixed side wall angle with continuously varying height. (Insets) CCD counts versus wavelength, showing the phase matching bandwidth.
To verify that we are observing SHG due to the interacting modes depicted in Fig. 2, we compare the experimentally measured phase matching wavelengths with simulation results. Fabrication uncertainty was accounted for by simulating waveguides with side wall angle of $65^\circ$ to $75^\circ$ and height from 210 nm to 230 nm. Each shaded region in Fig. 6 represents a fixed side wall angle with continuously varying height, as indicated by the labels. Overall, the experimental results agree well with the simulations, affirming that we have identified the correct interacting modes. The insets of Fig. 6 show the CCD counts versus the pump wavelength, giving a phase matching bandwidth of $\sim$1.2 nm (FWHM) for both H and V pump polarizations. The simulated phase matching bandwidth is $\sim$0.2 nm and we attribute the broadening to non-uniformities along the waveguide.
The observed SHG power was significantly less than is predicted by Eqs. (8) and (9). The fiber-to-waveguide coupling loss and the high propagation loss contributed to the mismatch between the experimental and theoretical conversion efficiencies. After factoring the simulated coupling losses of about $-7$ dB, we estimate the pump propagation losses to be about 2 dB/mm. We attribute the high propagation losses to the roughness at the waveguide interfaces [58]. Moreover, we expect the propagation loss at the second harmonic wavelength to be higher since roughness scattering loss $\propto 1/\lambda ^2$. To model the effects of losses, Eqs. (8) and (9) can be augmented by adding loss terms. Assuming undepleted pump and exact phase matching, we can derive an effective length of interaction,
The internal normalized conversion efficiency is then reduced by a factor $(L_{\textrm {eff}}/L)^2$. Another possible cause for the discrepancy between experiment and theory is the non-uniformity of the waveguide dimensions along its length due to fabrication imperfections. Variations in geometry causes shifts in the phase matching wavelength, as seen from Fig. 6, and disrupts the coherent build-up of the second harmonic signal.
4.3 Design and fabrication optimization
Building on the measurement results from the phase matching study, we fabricated the second set of optimized waveguides. We consider waveguide designs with height of 330 nm, top width of 240 nm and the side wall angle of $85^\circ$. The tapered edge couplers have a length of 100 $\mu$m on both facets and a starting top width of 100 nm. To extract the coupling and propagation loss, we fabricated and measured waveguide structures of different lengths. We obtained a coupling loss per facet of 2.6 dB and propagation loss of 2.6 dB/mm for the pump wavelength using H polarization, which shows improvement over the earlier batch. Top view images of the scattered light from the waveguide were captured with a CCD camera and the image brightness decay along the waveguide was analysed to obtain the propagation loss [59]. This method was verified by comparing with the results obtained using the standard method with waveguides of varying lengths. We see that both the methods agree with each other with discrepancy of $<$1 dB at the pump wavelength. With the scattered light method, we extracted the propagation loss at the second harmonic wavelength to be 28 dB/mm. From Eq. (11), the effective length of interaction $L_{\textrm {eff}}$ is thus 0.15 mm.
Figure 7(a) shows the calculated mode effective indices for this waveguide cross-section, at a pump wavelength of 1280 nm. The dashed lines are the indices of eigenmodes at the second harmonic wavelength and the red (quasi-TM) and blue (quasi-TE) colored lines are the indices of the two lowest order pump eigenmodes. Our waveguide design has phase matched SHG when injecting H polarized pump and exciting the quasi-TE mode, as indicated by the circle. Figure 7(b) shows the electric field component profiles of the pump and second harmonic modes, normalized to the maximum $|E_i|$ across the three components. The cross-section SEM image of the waveguide is given in Fig. 7(c). The conversion efficiency dependence on $\varphi$ is shown in Fig. 7(d), calculated under no propagation loss (Eqs. (8) and (9)). The maximum theoretical conversion efficiency of 596 $\%$ W$^{-1}$cm$^{-2}$ occurs at $\varphi = 0^\circ$.
Fig. 7. (a) Effective index plot versus top width of GaP waveguide, at 1280 nm wavelength. The dashed lines are the second harmonic eigenmodes and the colored lines are the two lowest order pump eigenmodes. The phase matched point for quasi-TE pump is circled. The inset shows the geometry of the GaP waveguides. (b) The normalized electric field components of the quasi-TE pump eigenmode and the corresponding phase matched higher order eigenmode of the second harmonic. (c) SEM cross-section image of the fabricated waveguide. (d) Calculated normalized conversion efficiency ($\%$ W$^{-1}$cm$^{-2}$) versus $\varphi$ angle for phase matched SHG using H polarized pump, assuming no propagation loss.
The conversion efficiency of the SHG is measured using a tunable continuous-wave laser set to the phase matching wavelength of 1283.5 nm. The dependence of the second harmonic power on the input pump power is plotted in Fig. 8(a). The blue dots (dashed line) represent the experimental data (fit). The second harmonic power dependence on the input pump power to the waveguide has a slope of approximately two in the log-scale, as expected from the theory. The inset of Fig. 8(a) shows a CCD image of the top scattered SHG light, which is much brighter than that seen in Fig. 5(d), indicating higher SHG efficiency. Since we observed SHG for H polarized pump, and the conversion efficiency for H pump at $\varphi = 90^\circ$ is nearly zero, this indicates that our waveguides are oriented with $\varphi = 0^\circ$ (see Fig. 7(d)).
Fig. 8. (a) Dependence of output second harmonic power (dots) on the input pump power into the nano-waveguide. Log-linear fit to the experimental data is given by dashed lines. (Inset) Top view CCD image of the scattered SHG light when pump light is coupled in. (b) Temperature dependence of the phase matching wavelength (dots) and linear fit (line). (Inset) Phase matching bandwidth.
For an optical pump power of 12.4 mW at the input of the waveguide of length 1.5 mm, we measure a maximum SHG power of approximately 3.4 nW before the chopper (chopper reduces the SHG power by $50\%$). This corresponds to a normalized external conversion efficiency of $\frac {P_{2\omega }}{(P_\omega \cdot L)^2} = 0.1\%$ W$^{-1}$cm$^{-2}$. Based on simulations, we estimate the collection efficiency of the SHG light from the waveguide to the detector using the objective (Mitutoyo) to be 85%. Factoring both the experimental pump coupling efficiency and the theoretical estimated second harmonic collection efficiency gives a normalized internal conversion efficiency of 0.4% W$^{-1}$cm$^{-2}$. Using the effective length of interaction and coupling losses, the theoretical estimated internal and external conversion efficiencies are $6.1\%$ W$^{-1}$cm$^{-2}$ and $1.6\%$ W$^{-1}$cm$^{-2}$, respectively. We attribute the discrepancy between experiment and theory to the fabrication non-uniformities causing deviation from exact phase matching. An ongoing design and fabrication effort is underway to further reduce losses in order to achieve higher experimental conversion efficiencies.
Next, we demonstrated the temperature tuning of the phase matching wavelength. We heat the waveguides from 22 $^{\circ }$C to 100 $^{\circ }$C. Figure 8(b) plots the variation of the phase matching wavelength as a function of the set temperature of the waveguide mount. We observe over 13 nm tuning of the phase matching wavelength. This corresponds to a slope of 0.17 nm$/^\circ$C (or equivalently $\sim$6 $^\circ$C/nm), which is comparable to the temperature slope of thin film lithium niobate nano-waveguides [60,61]. Waveguide engineering techniques can be used to further improve the temperature tunability of SHG [62]. The inset of Fig. 8(b) show the phase matching versus pump wavelength at $T = 22.3 ^\circ$C, giving a phase matching bandwidth of $\sim$1.4 nm (FWHM). We attribute the spectral broadening to non-uniformities along the waveguide.
5. Conclusion
We have presented the theory of SHG in GaP nano-waveguides, taking into account the configuration of the nonlinear susceptibility tensor. We measured and confirmed the crystal axis orientation of the GaP film, which is critical for the modeling of SHG. We designed, fabricated and tested gallium phosphide nano-waveguides for SHG by modal phase matching. The fabricated devices of different widths generated second harmonic light around 655 nm. We observed SHG interaction between different modes depending on the pump polarization, pump wavelength and waveguide width. The dependence of experimentally obtained phase matched wavelengths on the waveguide top width closely matches with the simulations. We further fabricated another optimized set of waveguides and obtained a normalized internal conversion efficiency of $0.4\%$ W$^{-1}$cm$^{-2}$ using a continuous-wave pump at 1283.5 nm. To the best of our knowledge, this is the highest reported SHG conversion efficiency achieved using modal phase matching in GaP nano-waveguides. Finally, we also presented temperature tuning of the SHG wavelength with a slope of 0.17 nm$/^\circ$C.
Given the many advantageous material properties of GaP, we are convinced that future improvements would help to overcome some of the current limitations compared to existing platforms, e.g. those based on GaAs, LiNbO$_3$. Efforts are in progress to increase experimental conversion efficiency through improved fabrication and optimized waveguide designs. The results presented in this work will be useful for the further development of nonlinear and quantum photonic platforms based on GaP.
Funding
Agency for Science, Technology and Research (A*STAR), Science and Engineering Research Council (A1685b0005).
Acknowledgments
We thank Victor Leong for his help in designing and building the experimental systems.
Disclosures
The authors declare no conflicts of interest.
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