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On-Chip Χ Microring Optical Parametric Oscillator Research Article Vol. X, No. X / April 2016 / Optica 1 On-chip c(2) microring optical parametric oscillator ALEXANDER W. BRUCH1,X IANWEN LIU1,J OSHUA B. SURYA1,C HANG-LING ZOU2, AND HONG X. TANG1, * 1Department of Electrical Engineering, Yale University, New Haven, CT 06511, USA 2Department of Optics and Optics Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China *Corresponding author: [email protected] Compiled September 18, 2019 Optical parametric oscillators (OPOs) have been widely used for decades as tunable, narrow linewidth, and coherent light sources for reaching long wavelengths and are attractive for appli- cations such as quantum random number generation and Ising machines. To date, waveguide- based OPOs have suffered from relatively high thresholds on the order of hundreds of mil- liwatts. With the advance in integrated photonic techniques demonstrated by high-efficiency second harmonic generation in aluminum nitride (AlN) photonic microring resonators, highly compact and nanophotonic implementation of parametric oscillation is feasible. Here, we em- ploy phase-matched AlN microring resonators to demonstrate low-threshold parametric oscil- lation in the telecom infrared band with an on-chip efficiency up to 17% and milliwatt-level output power. A broad phase-matching window is observed, enabling tunable generation of signal and idler pairs over a 180 nm bandwidth across the C band. This result establishes an important milestone in integrated nonlinear optics and paves the way towards chip-based quan- tum light sources and tunable, coherent radiation for spectroscopy and chemical sensing. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement http://dx.doi.org/10.1364/optica.XX.XXXXXX 1. INTRODUCTION threshold that is demanding on both the optical loss and modal phase-matching of the device [19]. The first demonstration of For decades, optical parametric oscillators (OPOs) have been microcavity-based OPO was achieved in a bulk lithium niobate a source for coherent radiation for reaching long wavelengths whispering gallery resonator (WGR), producing signal and idler (2) [1–3]. Traditional OPOs rely on a c material inserted in an pairs near 1100 nm from a 532 nm pump [20]. The very high opti- optical cavity that is resonant for the pump wavelength as well cal quality (Q) factors of 107 − 108 afforded by the WGR system, as the generated signal and/or idler wavelengths [4, 5]. The gen- enabled an OPO threshold of 6 mW [20]. Radially or linearly pol- erated signal and idler waves can then be tuned by controlling ing these devices further enabled tunable quasi-phase-matching arXiv:1909.07422v1 [physics.optics] 16 Sep 2019 the phase-matching via a myriad of techniques, such as tuning beyond 2 mm wavelengths with in-resonator OPO conversion (2) the temperature or angle of the c crystal [6], engineering a efficiencies near 50% [21–25]. Recent work has employed OPOs fan-out grating of the crystal poling [7], rotation of a diffraction for high resolution spectroscopy in the mid-infrared regime grating [8], electro-optic shaping of the parametric gain spec- [26, 27] and has extended the wavelength of the idler waves be- trum [9], or tuning of the pump wavelength [10]. Meanwhile, yond 8 mm using novel materials such as AgGaSe2 and CdSiP2 mirrorless OPOs without cavity enhancement were reported [28, 29]. through careful engineering of counter-propagating waves in a periodically-poled crystal [11]. Beyond long-wavelength co- Despite progresses in bulk WGRs, low-threshold OPOs have herent radiation, there has been interest in OPOs for generating proven to be quite challenging in planar photonic platforms. optical squeezed states [12], correlated photon pair sources [13– A milliwatt-level OPO threshold was observed in a planar 17], and quantum random number generation [18]. periodically-poled Ti:LiNbO3 waveguide, requiring a relatively Unlike second harmonic generation (SHG), OPO has a power long crystal length of 80 mm [30]. Monolithic semiconductor Research Article Vol. X, No. X / April 2016 / Optica 2 OPOs were later realized in orientation patterened GaAs [31] b and g0 is the nonlinear coupling strength between modes a as well as GaAs/AlGaAs [32] ridge waveguides by employing and b. We then apply an external pump laser near mode b at a dielectric coatings on the chip facets. However, these devices frequency wp with the strength suffered from relatively large OPO thresholds of 5.7 W and 210 p s 2kb,1 Pp mW, respectively. Recently, epitaxial aluminum nitride (AlN) b = (2) has emerged as a compelling photonic platform with the achieve- −i(wb − wp) − kb h¯ wp ment of high-Q microring resonators from the ultraviolet to near- where P is the pump power and k = k + k is the infrared wavelengths [33, 34] and the demonstration of efficient p a(b) a(b),0 a(b),1 total amplitude decay rate of mode a(b), with subscripts 0,1 c(2) and c(3) nonlinear processes [35–37]. A recent demonstra- denoting the intrinsic and external coupling losses, respectively. tion of a record-high SHG conversion efficiency of 17,000 %/W Applying a mean field approximation in the rotating frame of [38] further poses AlN as a serious contender to traditional c(2) wa, the effective Hamiltonian at infrared probe mode a becomes materials such as lithium niobate (LN). While the intrinsic Pock- † † 2 2 els coefficient of AlN (∼6 pm/V [38]) is less than that of lithium He f f /¯h = daa a + g0b((a ) + a ) (3) niobate (∼30 pm/V [39]), it is free of photo-refractive effects and where da = wa − wp/2 represents the angular frequency detun- is less susceptible to two-photon absorption losses, making it a ing of the signal (idler) from the down-converted pump. promising material platform for low-threshold, chip-integrated We note that the term g0b in Eq. (3) denotes the nonlinear optical parametric oscillation. gain of photons at mode a when driven by the pump mode b. In this paper, we present the first demonstration of optical The mode a will begin to oscillate when the nonlinear gain g0b parametric oscillation in a waveguide-integrated AlN microring is greater than its total cavity loss given by resonator. By optimizing the modal phase-matching and dual- 2k P resonance condition between the near-visible (780 nm) and the k2 ≤ g2b2 = g2 b,1 th . (4) a 0 0 2 2 hw telecom infrared (IR) band (1560 nm), we achieve a low OPO (wb − wp) + kb ¯ p threshold of 12 mW as well as 21% SHG and 17% OPO power A full derivation of the parametric oscillation condition can be conversion efficiencies. We show that the phase-matching condi- wa(b) found in the Supplementary Information. Using ka(b) = tion can be well controlled via an external heater, which allows 2Qa(b) the signal and idler pair to be tuned across a bandwidth of 180 and assuming critical coupling (ka(b),1 = ka(b),0 = ka(b)/2) and nm (23 THz) including the final transition from non-degenerate the external pump on resonance with mode b (wp = wb), the to degenerate OPO. Our approach can be extended to achieve OPO threshold power can be derived as chip-based, narrow-linewidth light sources at other wavelengths h¯ w4 important for a variety of potential applications including molec- h¯ wb 2 b 1 Pth = k kb,0 = (5) ( ) 2 a,0 2 2 ular spectroscopy and chemical sensing, as well as in other c 2 g0 32g0 Qa,0Qb,0 materials such as LiNbO3 on insulator [39, 40]. Here, Qa(b),0 is intrinsic intrinsic quality factor of mode a(b). Compared with the SHG efficiency hSHG below [38, 45] 2. MODELING OF THE OPO THRESHOLD AND PARA- 2 2 2 P g 1 g Q Qb,0 METRIC OSCILLATION BEHAVIOR = b = = 0 a,0 hSHG 2 2 4 (6) Pa 4k kb,0 h¯ wa h¯ wa Figure1 (a) schematically illustrates the parametric oscillation a,0 we find that P = 2 after assuming w = 2w , suggesting a process, where the system under study can be idealized as two th hSHG b a coupled cavities. A visible pump laser at an angular frequency lower OPO threshold for a device with a higher SHG efficiency. wb pumps the device, producing a signal and idler pair at fre- Above the OPO threshold, we solve Eq. (3) in the steady-state ˙ quencies ws and wi (blue and red, respectively) which satisfies (a˙ = b = 0) to find the energy matching condition ws + wi = wb. For the degenerate p s 2 2kb,1 Pb kakb OPO process (ws = wi = wb/2), a single frequency oscillation jaj = − . (7) g h 2 is realized at half the frequency (twice the wavelength) of the 0 ¯ wb 2g0 pump. In the non-degenerate case, ws 6= wi and parametric Defining the single-photon cooperativity oscillation is realized at two distinct resonances centered about 2 the pump. g0 1 C0 = = (8) P 8kb In contrast to the derivation from Refs. [19, 41], we derive kakb th ,1 1 h¯ w k k the OPO threshold via a bosonic coupled-mode model, which b b a p (2) we can simplify Eq. (7) to jaj2 = 1 ( P /P − 1). The total is also applicable for other c processes such as spontaneous C0 b th parametric down-conversion (SPDC) and on-chip strong cou- OPO output power then reads pling [16, 42, 43]. A similar Hamiltonian approach for modeling OPO in a WGR can be found in Ref. [44]. To gain insights in 2 Ps+i = 2ka,1h¯ wajaj (9) the OPO process and a comparison to SHG, here we focus the ka,1 kb,1 p derivation on degenerate OPO.
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