Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency

Xiang Guo; Chang-Ling Zou; Hong X. Tang

doi:10.1364/OPTICA.3.001126

1. INTRODUCTION

Second-order nonlinearity ( $χ^{(2)}$ ) has been used for various important classical [1–3] and quantum [4–6] applications. The optical cavities [7,8] are often employed to reduce the mode volume and enhance the nonlinear interaction efficiency. In the last decade, cavity-enhanced second-harmonic generation (SHG) has been reported in various platforms, including macroscopic (millimeter-sized) whispering gallery mode resonators [9–11], on-chip microrings [12–14], microdisks [15–18], and photonic crystal cavities [19–21]. Among these demonstrations, the on-chip devices have the advantage of miniaturized footprint, excellent scalability, and potential to integrate with other on-chip functional components. The realized efficiency of SHG for on-chip devices, however, is still much lower than the state-of-the-art of the macroscopic resonator [10], mostly due to the relatively low quality factor and unoptimized coupling scheme to the resonator. On one hand, the reported quality factors of the on-chip microresonators are usually much below $1 \times 10^{5}$ (except [14,16]). On the other hand, tapered fiber, instead of the integrated waveguide, is often used to couple light in and out of the microresonators [15–18]. This non-integrated coupling scheme not only limits the devices’ functions as scalable components, but also hinders the optimization for achieving the best coupling condition simultaneously for the dual-wavelength bands involved in the SHG process. For example, a critical coupling condition for both fundamental and second-harmonic (SH) modes is required for achieving highest SHG efficiency in the low-power (non-depletion) regime (as will be illustrated below). By utilizing a single tapered fiber to couple with modes in both wavelength bands, it is hard to optimize the coupling individually for each mode and achieve critical coupling simultaneously. This non-optimized coupling reduces the achievable conversion efficiency.

In this work, we systematically study and optimize the second-harmonic generation process in an aluminum nitride (AlN) microring resonator. AlN is a newly developed material combining the two favored properties: (1) intrinsic $χ^{(2)}$ nonlinearity [14] and (2) low-loss waveguide circuits with precisely controlled nanofabrication technology [22]. Its enormous energy gap (6.2 eV) and broad transparency band (from UV to mid-IR) allow SHG in a wide range of wavelength. Here a high-quality-factor microring resonator is fabricated which is coupled to two independently engineered coupling waveguides: one for pump light in the telecom band, one for SH visible light. Combining high-quality-factor optical modes, perfectly fulfilled phase-match condition, small mode volume, and optimized coupling condition, a dual-resonant, fully integrated device with SHG efficiency as high as $η = P_{SHG} / P_{p}^{2} = 2500 % W^{- 1}$ is realized. We also carry out experiments in the high-power regime where the depletion of pump light is no longer negligible. With 27 mW pump power, we realize an absolute power conversion efficiency of $P_{SHG} / P_{p} = 12 %$ . Theoretical calculation shows that a conversion efficiency of more than 50% with similar pump power is within reach if the device fabrication process (microring’s quality factor) is further improved.

2. MODEL

The SHG process in a microring cavity involves two optical modes, one mode at the fundamental frequency ( $ω_{a}$ ) and another mode at the second-harmonic frequency ( $ω_{b} \approx 2 ω_{a}$ ). The system with the pump field near the fundamental frequency can be described by the Hamiltonian

H = ω_{a} a^{†} a + ω_{b} b^{†} b + g [{(a^{†})}^{2} b + a^{2} b^{†}] + ϵ_{p} (a e^{i ω_{p} t} + a^{†} e^{- i ω_{p} t}) .

Here, $a$ ( $b$ ) is the Bosonic operator for pump (SHG) mode in the microring and $ω_{a} (ω_{b})$ is the angular frequency of mode $a (b)$ . $ϵ_{p} = \sqrt{2 κ_{a, 1} P_{p} / ℏ ω_{p}}$ is the input pump field strength, where $P_{p}$ and $ω_{p}$ are the power and frequency of the pump laser, respectively. $κ_{a, 1}$ is the external coupling rate of the mode $a$ . The nonlinear coupling strength $g$ between the two modes reads

ℏ g = ε_{0} \int \int \int d θ r d r d z \frac{3 χ^{(2)}}{4 \sqrt{2}} (r) {[u_{a, z}^{*} (r)]}^{2} u_{b, z} (r) .

Here, $χ^{(2)} (r)$ is the second-order susceptibility of the medium and $ε_{0}$ is the vacuum permittivity. The electric fields of optical modes in the cylindrical symmetric microring can be expressed as $u_{a (b), z} (r) = u_{a (b), z} (r, z) e^{i m_{a (b)} θ}$ and satisfy the normalization condition $∭ d θ r d r d z ε_{0} ε_{r} (ω_{a (b)}, r) {| u_{a (b), z} (r) |}^{2} = ℏ ω_{a (b)}$ , where $m_{a} (m_{b})$ is the angular momentum of mode $a (b)$ . $ε_{r} (ω_{a (b)}, r)$ is the relative permittivity of dielectrics as a function of frequency and position. Introducing the effective mode-overlapping factor at the cross-section of the microring where

ζ = \frac{\iint d r d z {[u_{a, z}^{*} (r, z)]}^{2} u_{b, z} (r, z)}{\iint d r d z {| u_{a, z} (r, z) |}^{2} \sqrt{\iint d r d z {| u_{b, z} (r, z) |}^{2}}},

we obtain the coupling strength

g \approx ζ \sqrt{\frac{ℏ ω_{a}^{2} ω_{b}}{ε_{0} 2 π R}} \frac{1}{ε_{a} \sqrt{ε_{b}}} \frac{3 χ^{(2)}}{4 \sqrt{2}} \times δ (m_{b} - 2 m_{a}),

with the approximation that the radius of the microring (

R

) is much larger than the width of the ring. Due to the symmetry, the integral over the

θ

gives Kronecker delta function

δ (m_{b} - 2 m_{a})

, indicating that the

g

is non-zero only when

m_{b} - 2 m_{a} = 0

, which corresponds to the momentum-conservation condition.

For low pump power and low conversion efficiency, the non-depletion approximation can be applied to solve the efficiency of SHG analytically [see Supplement 1, Section I for the derivation]. With continuous pump, the steady-state cavity field amplitude for pump light is $α = ϵ_{p} / (δ_{a} - i κ_{a})$ , and the second-harmonic generation efficiency reads

η = \frac{P_{SHG}}{P_{p}^{2}} = g^{2} \frac{2 κ_{b, 1}}{δ_{b}^{2} + κ_{b}^{2}} {(\frac{2 κ_{a, 1}}{δ_{a}^{2} + κ_{a}^{2}})}^{2} \frac{ℏ ω_{b}}{{(ℏ ω_{p})}^{2}} .

Here, $δ_{a} = ω_{a} - ω_{p}$ ( $δ_{b} = ω_{b} - 2 ω_{p}$ ) is the angular frequency detuning for mode $a (b)$ ; $κ_{a} = κ_{a, 1} + κ_{a, 0}$ ( $κ_{b} = κ_{b, 1} + κ_{b, 0}$ ) is the total loss rate of cavity mode $a (b)$ , including external coupling rate $κ_{a (b), 1}$ and intrinsic loss rate $κ_{a (b), 0}$ . To optimize $η$ , we first need to engineer the microring geometry so that the dual resonant condition $δ_{a} = δ_{b} = 0$ is achieved, which is equivalent to the energy conservation condition $ω_{b} = 2 ω_{a}$ . Then the SHG efficiency reduces to

η = \frac{16 g^{2}}{{(\frac{κ_{b, 0}}{\sqrt{κ_{b, 1}}} + \sqrt{κ_{b, 1}})}^{2} {(\frac{κ_{a, 0}}{\sqrt{κ_{a, 1}}} + \sqrt{κ_{a, 1}})}^{4}} \frac{1}{ℏ ω_{f}} .

Further optimization of $η$ requires a critical coupling condition for both modes, i.e., $κ_{a, 1} = κ_{a, 0}$ , $κ_{b, 1} = κ_{b, 0}$ . The intrinsic loss rate $κ_{a (b), 0}$ is determined by the material property (material absorption, scattering), while the external coupling rate $κ_{a (b), 1}$ can be controlled by tuning the gap between the microring and the bus waveguide. When critical coupling condition for both modes is fulfilled, the maximum achievable conversion efficiency is

η = \frac{g^{2}}{4 κ_{b, 0} κ_{a, 0}^{2}} \frac{1}{ℏ ω_{f}} = \frac{g^{2} Q_{a, 0}^{2} Q_{b, 0}}{ℏ ω_{a}^{4}} .

Here, $Q_{a, 0} = \frac{ω_{a}}{2 κ_{a, 0}}$ ( $Q_{b, 0} = \frac{ω_{b}}{2 κ_{b, 0}}$ ) is the intrinsic quality factor for mode $a (b)$ . We finally come to the last requirement for achieving high-efficiency SHG: high intrinsic quality factors ( $Q_{a, 0}$ and $Q_{b, 0}$ ) for both optical modes.

To summarize, high-efficiency SHG under the non-depletion approximation relies on: (1) high nonlinear coupling strength $g$ , which is determined by momentum-conservation condition ( $m_{b} = 2 m_{a}$ ), microring radius $R$ , second-order susceptibility $χ^{(2)}$ , and mode overlap $ζ$ ; (2) high intrinsic quality factor ( $Q_{a, 0}$ , $Q_{b, 0}$ ); (3) critical coupling ( $κ_{a, 1} = κ_{a, 0}$ , $κ_{b, 1} = κ_{b, 0}$ ); and (4) energy-conservation condition ( $ω_{b} = 2 ω_{a}$ ).

3. EXPERIMENTAL SETUP AND DEVICE OPTIMIZATION

Shown in Fig. 1(a) is the experimental setup, where the photomicrograph of the core device is shown in the center. A 1 μm thick AlN microring resonator is coupled by two independent waveguides. The top point-contact bus waveguide is designed for the coupling of the telecom pump light, while the lower wrap-around waveguide is used for the coupling of SH light. After defining the pattern using electron beam lithography and dry etch into AlN using ${BCl}_{3} {/ Cl}_{2} / Ar$ chemistry, a layer of plasma-enhanced chemical vapor deposition (PECVD) silicon oxide is deposited onto the AlN waveguide as the top cladding, while the bottom cladding is the thermal oxide.

Fig. 1. Experimental setup and device performance. (a) An AlN microring resonator is coupled by two individual bus waveguides. Continuous-wave (CW) telecom and visible lasers are coupled to the microring through an off-chip wavelength division multiplexer (WDM) and an on-chip WDM. The telecom laser light transmission is detected by an infrared photodetector (IR PD), and visible laser light transmission or SHG are detected by a visible light photodetector (Visible PD). (b) Transmission spectrum of the telecom band resonance for pump light. A loaded $Q$ of 230 K is achieved with critical coupling. (c) Transmission spectrum of the visible band resonance for SH light. A loaded $Q$ of 116 K is achieved with an extinction around 0.75.

Download Full Size | PDF

Our experiment toward high-efficiency SHG consists of the following steps in terms of design and material optimization:

(1) Optimization for high nonlinear coupling strength. For our AlN’s polycrystalline structure, the $c$ axis (perpendicular to the wafer) is aligned while the $x$ and $y$ axes (in plane direction) are random [23], which leads to a larger $χ^{(2)}$ value for transverse magnetic (TM) modes as compared to transverse electric modes. As a result, we choose to use the fundamental TM ( ${TM}_{0}$ ) mode in the telecom band as the pump light mode. The electric field distribution of this mode is shown in the inset of Fig. 1(b). To fulfill the phase-match condition (which includes momentum conservation condition $m_{b} = 2 m_{a}$ and energy conservation condition $ω_{b} = 2 ω_{a}$ ), modal dispersion [12–14] is used to compensate for the material dispersion, which means that a higher-order mode in the SH wavelength needs to be used. To maximize the mode overlap $ζ$ , however, we need to choose a proper high-order mode with symmetric electric field distribution. Guided by this principle, the symmetric ${TM}_{2}$ mode [as shown in the inset of Fig. 1(c)], instead of the anti-symmetric ${TM}_{1}$ mode, is chosen for the SH light mode. Equation (4) also shows that the nonlinear coupling strength $g$ is inversely proportional to the microring radius. We therefore tend to use microrings with smaller radius. On the other hand, however, smaller radius will lead to an enhanced electric field on the etched surface of the AlN waveguide, which results in additional radiation and scattering loss. We finally select the radius of the microring to be 30 μm, which is big enough to avoid additional quality factor degradation but small enough to get high $g$ . Considering the polycrystalline AlN film used in our experiment [23], and also a relatively long pump wavelength of 1550 nm, we estimate that the $χ^{(2)}$ of our AlN is around 1 pm/V. Using Eqs. (3) and (4), a nonlinear coupling strength $g / 2 π \approx 0.11 MHz$ is calculated.
(2) Optimization for high intrinsic quality factor. The microring’s intrinsic quality factor is determined by both the scattering loss and the material absorption. To minimize the scattering loss, we choose to use relatively thick AlN film, which is 1 μm thick. Thick waveguide can better confine the optical mode, reducing the scattering loss in the relatively rough surface formed by the dry etch process. As compared to the 650 nm thick AlN film, the 1 μm thick (with same width) microring’s quality factor can be improved by approximately a factor of two. In order to minimize the material absorption, we anneal our device in 950°C in $N_{2}$ atmosphere for 2 h after coating with PECVD oxide. Thermal annealing reduces defect absorption in both PECVD oxide and AlN, which were initially deposited at relatively low temperature. With the thermal annealing, the optical modes’ quality factors increase by a factor of around two for $Q_{a, 0}$ and three for $Q_{b, 0}$ . Finally, the achieved intrinsic quality factors for telecom and visible optical modes are measured to be $Q_{a, 0} \approx 4.6 \times 10^{5}$ [as can be extracted from Fig. 1(b)] and $Q_{b, 0} \approx 1.5 \times 10^{5}$ [extracted from Fig. 1(c)]. Note that these quality factors are not yet materially limited, but still are dominated by the scattering loss at the sidewalls of the microring waveguide. Our microring width is limited to be around 1.12 μm, as required by the phase-match condition. With the same material system, however, a higher quality factor has been measured in a device with a bigger cross-section ( $Q_{0} \sim 1 \times 10^{6}$ , in [24]). Further optimization of the fabrication process, such as surface passivation using atomic layer deposition [25,26], can help reduce the sidewall roughness and further increase the achievable quality factors.
(3) Optimization for critical coupling. In the non-depletion regime, critical coupling ( $κ_{a, 0} = κ_{a, 1}$ , $κ_{b, 0} = κ_{b, 1}$ ) is required to maximize the SHG efficiency $η$ . In the experiment, the intrinsic loss rate $κ_{a, 0}$ and $κ_{b, 0}$ are determined by the material loss (absorption) and fabrication imperfections (scattering), while the external coupling $κ_{a, 1}$ and $κ_{b, 1}$ can be controlled by tuning the gap between the microring and bus waveguide. In fiber-coupled microresonator devices, usually one optical fiber serves as bus waveguide simultaneously for both pump and SH optical modes. Therefore, it is not easy to simultaneously achieve critical coupling condition. In our implementation, two separate bus waveguides are independently coupled to the pump and SH modes in the microring: the top point-contact bus waveguide has a width of 0.8 μm and is used to couple to the pump ${TM}_{0}$ mode (with a coupling gap of 0.6 μm), while the bottom wrap-around waveguide has a total length of 80 μm and a tapered width from 0.175 μm to 0.125 μm, and is used to couple to the SH ${TM}_{2}$ mode (with a coupling gap of 0.5 μm). Note that the existence of the top bus waveguide will not affect the quality factor of the SH ${TM}_{2}$ mode due to the short coupling length and relative large gap. When the coupling gap of the bottom wrap-around waveguide to the microring is large (e.g., $> 0.3 μm$ ), this wrap-around waveguide will not degrade the quality factor of the pump ${TM}_{0}$ mode either, because the guided pump mode in such a narrow waveguide cannot couple to the pump ${TM}_{0}$ mode of the microring. We hence can individually optimize the coupling conditions for the two optical modes by engineering the coupling gaps and the bus waveguide structures. For the device under test, the transmission spectra at both pump and SH wavelength bands are shown in Figs. 1(b) and 1(c). Pump light is almost critically coupled to the microring with a loaded $Q_{a}$ of $2.3 \times 10^{5}$ , while the SH resonance is undercoupled with an extinction of 0.75 and a loaded $Q_{b}$ of $1.16 \times 10^{5}$ . We can infer from the theory that this non-critical coupling (with an extinction of 0.75) is due to the undercoupling with $κ_{b, 1} \approx \frac{1}{3} κ_{b, 0}$ , leading to a reduced SHG efficiency by a factor of 1.33 compared to the critically coupled case.
(4) Optimization for energy-conservation condition. The energy conservation ( $ω_{b} = 2 ω_{a}$ , or equivalently $λ_{a} = 2 λ_{b}$ ) is roughly fulfilled by engineering the width of the microring to be around 1.12 μm [6]. It can be seen from Figs. 1(b) and 1(c) that the resonant wavelength of mode $a$ is roughly two times that of mode $b$ , with a small misalignment. This misalignment means that the energy conservation is not perfectly fulfilled in this case. In order to optimize SHG efficiency $η$ , we hence need to finely tune the two resonances to perfectly fulfill the energy-conservation condition. The method we use is thermal tuning. Due to the thermo-optic effect and thermal expansion [27], both pump [Fig. 2(a)] and SH [Fig. 2(b)] resonances will shift to longer wavelength with increased temperature. However, these two modes shift with different speeds, with the expression $λ_{a} (T) = λ_{a 0} + d_{a} T$ , $λ_{b} (T) = λ_{b 0} + d_{b} T$ . The value of $d_{a}$ and $d_{b}$ can be fitted in Figs. 2(a) and 2(b) as $d_{a} = 0.0209 \pm 0.0001 nm / K$ , $d_{b} = 0.0113 \pm 0.0001 nm / K$ . The wavelength mismatch reads $λ_{a} (T) - 2 λ_{b} (T) = λ_{Δ} + d_{Δ} T,$ where $λ_{Δ} = λ_{a 0} - 2 λ_{b 0}$ and $d_{Δ} = d_{a} - 2 d_{b} = - 0.0017 nm / K$ . Since $d_{Δ} \neq 0$ , the wavelength mismatch $λ_{a} - 2 λ_{b}$ can be tuned with temperature. We hence expect a temperature-dependent SHG efficiency and the optimized SHG efficiency will occur at a certain temperature when wavelength mismatch $λ_{a} - 2 λ_{b} = 0$ .

Fig. 2. Temperature dependence of resonant wavelengths for (a) pump light in the telecom band and (b) SH light in the visible band.

Download Full Size | PDF

4. RESULTS

With the carefully engineered microring device, we measure the SHG spectra in the weak pump power (non-depletion) regime by scanning the pump laser across the fundamental resonance under different temperatures, as shown in Fig. 3(a). Due to a redshift resonance with increased temperature, the SHG spectrum also shifts to the longer wavelength. And at an optimized temperature, a highest SHG efficiency of $η = 2500 % W^{- 1}$ is achieved (the detailed calibration method is shown in Supplement 1, Section II), which happens with perfectly matched mode frequencies $ω_{p} = ω_{a} = ω_{b} / 2$ . For either higher or lower temperature, the detuning will reduce the efficiency due to the frequency mismatch.

Fig. 3. SHG efficiency at different temperatures. (a) Temperature-dependent SHG spectrum. With an increased temperature, the SHG spectrum shifts to longer wavelength. (b) Temperature dependence of the maximum SHG efficiency. A Lorentzian shape with a full-width-at-half-maximum (FWHM) of 7.7°C is fitted.

Download Full Size | PDF

We further extract the maximum SHG efficiency and plot against temperature, as shown in Fig. 3(b). Using the approximation that the maximum SHG efficiency occurs when the detuning of mode $a$ vanishes ( $δ_{a} = 0$ ), the theoretical formula for temperature-dependent SHG efficiency reads

η \approx \frac{2 g^{2} κ_{b, 1} {(\frac{2 κ_{a, 1}}{κ_{a}^{2}})}^{2} \frac{ℏ ω_{b}}{{(ℏ ω_{p})}^{2}}}{{[\frac{2 π c}{λ_{a} λ_{b}} (λ_{Δ} + d_{Δ} T)]}^{2} + κ_{b}^{2}} .

From the expression, we found that temperature dependence of $η$ has a Lorentzian shape, with a full-width at half-maximum (FWHM) determined by $Δ T = \frac{κ_{b} λ_{a} λ_{b}}{π c \times_{Δ}} = \frac{λ_{a}}{Q_{b} d_{Δ}}$ . According to the previously measured value of $Q_{b}$ , $λ_{a}$ , and $d_{Δ}$ , we can calculate that $Δ T = 7.8 \pm 1.4 (° C)$ . A Lorentzian fitting of the measured data is done as the solid line in Fig. 3(b), with a fitted $Δ T = 7.7 ° C$ being consistent with the theoretical estimated value.

Finally, the power dependence of SHG is shown in Fig. 4(a). For low pump power, non-depletion approximation is valid. We plot the SHG data with weak pump power ( $< 1 mW$ ) in the inset of Fig. 4(a). A close to quadratic dependence is measured with a slope of $1.95 \pm 0.03$ , which matches the theoretical prediction of 2 reasonably well. Using Eq. (6), we can fit the experimental data with the only unknown parameter, $g$ . The best fitting of the experimental data is obtained with $g / 2 π = 0.08 MHz$ . Compared to the theoretical prediction of $g / 2 π = 0.11 MHz$ as calculated by the mode-overlapping integral in Eq. (3), the realized nonlinear coupling strength in our experiment is quite close to this theoretical value. This indicates that our systematic optimization of the AlN microring system works. The difference between the measured value and theoretical prediction may arise from the unconsidered propagation loss of the waveguide circuits.

Fig. 4. (a) Power dependence of SHG. Blue line: fitting by the model with non-depletion approximation. Red line: fitting by the model considering the pump power depletion. Inset: zoom-in of the low-pump-power regime. A close to quadratic power dependence with a slope of 1.95 is fitted. (b) Absolute power conversion efficiency ( $P_{SHG} / P_{p}$ ) against the external coupling $Q$ . In the calculation, the pump power and intrinsic quality factors for the two modes are fixed to be $P_{p} = 27 mW$ , $Q_{a, 0} = 4.6 \times 10^{5}$ , and $Q_{b, 0} = 1.5 \times 10^{5}$ , respectively. The circular and rectangular dots in the figure correspond to the used experimental parameters ( $Q_{a, 1} / Q_{a, 0} = 1$ , $Q_{b, 1} / Q_{b, 0} = 3$ ) and the optimized parameters for best conversion efficiency, respectively. (c) Calculated optimal conversion efficiency ( $P_{SHG} / P_{p}$ ) for given input pump power (0.3, 3, 30 mW) and intrinsic optical quality factors of the two modes (assuming $Q_{a, 0} = Q_{b, 0} = Q_{0}$ ).

Download Full Size | PDF

5. DISCUSSION ON DEPLETION REGIME

The experimental results in Fig. 4(a) also show the SHG for higher pump power. Although the model of non-depletion approximation predicts that the SHG power increases quadratically with the pump power, the obtained SHG deviates from this model [blue line in Fig. 4(a)] when the pump power is larger than 1 mW. The reason for this is that when the pump power is high enough—for instance, $η \times P_{p} \sim 1$ —the non-depletion approximation for the pump light is no longer valid. Here, we want to further discuss the SHG in the depletion regime and provide insights on possible experimental improvements.

In the derivation of the dynamics of cavity field in the classical limitation $a = α$ and $b = β$ (neglecting the fluctuation of optical fields), we have

\frac{d}{d t} α = [- i (ω_{a} - ω_{f}) - κ_{a}] α - i 2 g α^{*} β - i ϵ_{p} = 0 .

The effect of SHG field is included in the term $- i 2 g α^{*} β$ , which actually corresponds to the stimulated parametric down-conversion process. Due to the interference, the pump field from external driving and the down-conversion cancels, leading to a depletion of pump cavity field. At steady state, the cavity fields satisfy the nonlinear equation (see Supplement 1, Section I)

\frac{1}{4} {(\frac{4 g^{2} {| α |}^{2}}{κ_{a} κ_{b}})}^{2} κ_{a}^{2} {| α |}^{2} + (\frac{4 g^{2} {| α |}^{2}}{κ_{a} κ_{b}}) κ_{a}^{2} {| α |}^{2} + κ_{a}^{2} {| α |}^{2} - ϵ_{p}^{2} = 0

for perfect frequency matching

δ_{a} = δ_{b} = 0

and

β = \frac{i g α^{2}}{κ_{b}}

. From the nonlinear Eq. (11), we noticed that if

\frac{4 g^{2} {| α |}^{2}}{κ_{a} κ_{b}} ≪ 1

, the equation can be approximately linear and we get the results with non-depletion approximation [Eq. (5)]. Since

κ_{a} / 2 π = 0.42 GHz

and

κ_{b} / 2 π = 1.68 GHz

, then

\frac{4 g^{2} {| α |}^{2}}{κ_{b} κ_{a}} \approx 1

corresponds to

P_{p} \approx ℏ ω_{p} κ_{b} κ_{a}^{2} / (4 g^{2}) = 10 mW

. Therefore, the non-depletion approximation breakdown for

P_{p} \approx 10 mW

.

In Fig. 4(a) (red solid line), we numerically solved the nonlinear equations considering the pump power depletion, which agrees with the experimental data reasonably well. At 27 mW pump power, the SHG power is 3.3 mW, corresponding to a power conversion efficiency of $P_{SHG} / P_{p} = 12 %$ . It is not surprising that the absolute power conversion efficiency ( $P_{SHG} / P_{p}$ ) saturates at a finite value due to the intrinsic loss of pump field and SH photons. This reminds us that, in the high-pump-power regime, the optimal SHG might be realized beyond the critical coupling condition. In Fig. 4(b), we calculate the absolute power conversion efficiency ( $P_{SHG} / P_{p}$ ) under different external coupling quality factors $Q_{a 1 (b 1)}$ , where the pump power and intrinsic quality factors are fixed at $P_{p} = 27 mW$ , $Q_{a 0} = 4.6 \times 10^{5}$ , and $Q_{b 0} = 1.5 \times 10^{5}$ , respectively. For our experimental parameters [ $Q_{a 1} / Q_{a, 0} = 1$ , $Q_{b 1} / Q_{b 0} = 3$ , as illustrated by the circular dot in Fig. 4(b)], the achievable conversion efficiency is only 12%. However, this value can be improved to 26% by using over-coupled device [as illustrated by the rectangle dot in Fig. 4(b)]. Therefore, for given intrinsic $Q$ s and the pump power, the SHG can be optimized by designing the external coupling $Q$ s, which is feasible for our experimental design with two independent couplers for two wavelengths. In Fig. 4(c), we compare the maximum conversion efficiency $P_{SHG} / P_{p}$ against the intrinsic $Q$ for given pump power of 0.3, 3, and 30 mW. If we can realize the material limited $Q_{0} \sim 10^{6}$ in AlN, the SHG with 30 mW pump can be as high as 70%.

6. CONCLUSION

In conclusion, we have designed an AlN microring structure and experimentally demonstrated the SHG (on chip, device footprint around $60 μm \times 60 μm$ ) that converts 1550 nm light to 775 nm light with an efficiency of $η = P_{SHG} / P_{p}^{2} = 2500 % W^{- 1}$ in the lower pump power (non-depletion) regime, which is an over 65-fold improvement of the state-of-the-art value obtained in an integrated device ( $38 % W^{- 1}$ , [18]). Regarding the absolute power-conversion efficiency $P_{SHG} / P_{p}$ , a maximum efficiency of 12% is realized for 27 mW pump power. This absolute conversion efficiency is much higher than other integrated devices, comparable with state-of-the-art millimeter-size disk resonators [9,10]. Our experiment with high pump power actually shows the effect of depletion, suggesting the possibility for further improvement by optimizing the external coupling strength and increasing the intrinsic quality factors. For our device, 70% conversion efficiency is possible for 30 mW pump light for the material limited $Q_{a (b), 0} (\sim 10^{6})$ .

Funding

Defense Advanced Research Projects Agency (DARPA); David and Lucile Packard Foundation.

Acknowledgment

Facilities used for device fabrication were supported by Yale SEAS cleanroom and Yale Institute for Nanoscience and Quantum Engineering. The authors thank Michael Power and Dr. Michael Rooks for assistance in device fabrication.

See Supplement 1 for supporting content.

REFERENCES

1. Y. R. Shen, “Surface properties probed by second-harmonic and sum-frequency generation,” Nature 337, 519–525 (1989).

2. M. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997). [CrossRef]

3. K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y. S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006). [CrossRef]

4. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995). [CrossRef]

5. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).

6. X. Guo, C. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon pair source on a nanophotonic chip,” arXiv:1603.03726v1 (2016).

7. Z. Yang, P. Chak, A. D. Bristow, H. M. van Driel, R. Iyer, J. S. Aitchison, A. L. Smirl, and J. E. Sipe, “Enhanced second-harmonic generation in AlGaAs microring resonators,” Opt. Lett. 32, 826–828 (2007). [CrossRef]

8. Z. Lin, X. Liang, M. Loncar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).

9. V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004). [CrossRef]

10. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010). [CrossRef]

11. G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103, 181107 (2013). [CrossRef]

12. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415–11421 (2011). [CrossRef]

13. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19, 10462–10470 (2011). [CrossRef]

14. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012). [CrossRef]

15. P. S. Kuo, J. Bravo-Abad, and G. S. Solomon, “Second-harmonic generation using 4-quasi-phasematching in a GaAs whispering-gallery-mode microcavity,” Nat. Commun. 5, 3109 (2014).

16. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Lončar, “Integrated high quality factor lithium niobate microdisk resonators,” Opt. Express 22, 30924–30933 (2014). [CrossRef]

17. S. Mariani, A. Andronico, A. Lemaître, I. Favero, S. Ducci, and G. Leo, “Second-harmonic generation in AlGaAs microdisks in the telecom range,” Opt. Lett. 39, 3062–3065 (2014). [CrossRef]

18. D. P. Lake, M. Mitchell, H. Jayakumar, L. F. Dos Santos, D. Curic, and P. E. Barclay, “Efficient telecom to visible wavelength conversion in doubly resonant gallium phosphide microdisks,” Appl. Phys. Lett. 108, 031109 (2016). [CrossRef]

19. M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frédérick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).

20. K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vucković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009). [CrossRef]

21. S. Buckley, M. Radulaski, K. Biermann, and J. Vucković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103, 211117 (2013). [CrossRef]

22. C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012). [CrossRef]

23. C. Xiong, W. H. P. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. 12, 3562–3568 (2012). [CrossRef]

24. H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013). [CrossRef]

25. J. Schmidt, A. Merkle, B. Hoex, M. C. M. van de Sanden, W. M. M. Kessels, and R. Brendel, “Atomic-layer-deposited aluminum oxide for the surface passivation of high-efficiency silicon solar cells,” in 33rd IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2008).

26. B. Guha, F. Marsault, F. Cadiz, L. Morgenroth, V. Ulin, V. Berkovitz, A. Lemaître, C. Gomez, A. Amo, S. Combrié, B. Gérard, G. Leo, and I. Favero, “Surface-enhanced gallium arsenide photonic resonator with a quality factor of six million,” arXiv:1605.00477 (2016).

27. T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004). [CrossRef]

Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency

Abstract

1. INTRODUCTION

2. MODEL

3. EXPERIMENTAL SETUP AND DEVICE OPTIMIZATION

4. RESULTS

5. DISCUSSION ON DEPLETION REGIME

6. CONCLUSION

Funding

Acknowledgment

REFERENCES

Supplementary Material (1)

Cited By

Figures (4)

Equations (11)

Optica