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Nonlinear Nanophotonic Devices in The Nanophotonics 2020; 9(12): 3781–3804 Review Jinghan He, Hong Chen, Jin Hu, Jingan Zhou, Yingmu Zhang, Andre Kovach, Constantine Sideris, Mark C. Harrison, Yuji Zhao and Andrea M. Armani* Nonlinear nanophotonic devices in the ultraviolet to visible wavelength range https://doi.org/10.1515/nanoph-2020-0231 1 Introduction Received April 7, 2020; accepted June 12, 2020; published online July 4, 2020 The past several decades has witnessed the convergence of novel nonlinear materials with nanofabrication methods, Abstract: Although the first lasers invented operated in enabling a plethora of new nonlinear optical (NLO) devices the visible, the first on-chip devices were optimized for [1–4]. Originally, the focus was on developing devices near-infrared (IR) performance driven by demand in tele- operating in the telecommunications wavelength band to communications. However, as the applications of inte- improve communications. One example of an initial suc- grated photonics has broadened, the wavelength demand cess is on-chip modulators and add-drop filters for has as well, and we are now returning to the visible (Vis) switching and isolating of optical wavelengths. While and pushing into the ultraviolet (UV). This shift has initial devices were fabricated from crystalline materials required innovations in device design and in materials as [5–7], the highest performing devices were made from well as leveraging nonlinear behavior to reach these organic polymers [8–16]. As nanofabrication processes wavelengths. This review discusses the key nonlinear improved, higher performance integrated devices were phenomena that can be used as well as presents several developed, such as high quality factor optical resonant emerging material systems and devices that have reached cavities, and higher order nonlinear behaviors became the UV–Vis wavelength range. accessible. This technology enabled on-chip frequency Keywords: inverse design; nanophotonics; nonlinear combs [2, 17, 18], stokes and anti-stokes lasers [19–21], and optics; optical materials; organic materials. super continuum sources [22]. While these devices can be used in many fields, one clear application of these devices is in quantum optics. While many quantum phenomena can be investigated using near-infrared (IR) lasers, atomic clocks based on Rb and Ce transition lines require visible lasers as excitation *Corresponding author: Andrea M. Armani, Dept. of Chemistry, sources. Initial work developing proof of concept systems University of Southern California, Los Angeles, CA, 90089, USA; Ming relied on large optical lasers. More recently, the focus Hsieh Dept. of Electrical and Computer Engineering, University of shifted to “clocks on a chip” [23–26]. Because the transition Southern California, Los Angeles, CA, 90089, USA; and Mork Family lines are in the visible, the development of an ultra-narrow Dept. of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, 90089, USA, linewidth and stable visible laser source at a complemen- E-mail: [email protected]. https://orcid.org/0000-0001-9890-5104 tary wavelength was a key stepping stone. Similarly, over Jinghan He: Dept. of Chemistry, University of Southern California, Los the past few years, a plethora of novel quantum emitters Angeles, CA, 90089, USA. https://orcid.org/0000-0001-7713-1226 have been discovered [27]. However, the majority are Hong Chen, Jingan Zhou and Yuji Zhao: School of Electrical, Computer, excited in the visible. In order to realize integrated devices and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA based on these new materials, it is necessary to have an Jin Hu and Constantine Sideris: Ming Hsieh Dept. of Electrical and integrated source with sufficient power. Computer Engineering, University of Southern California, Los Angeles, Visible sources also play a key role in biotechnology, CA, 90089, USA namely, the miniaturization of diagnostics and imaging Yingmu Zhang and Andre Kovach: Mork Family Dept. of Chemical systems. Tissue and biosamples absorb strongly in the Engineering and Materials Science, University of Southern California, near-IR wavelength range. This absorbance will degrade Los Angeles, CA, 90089, USA Mark C. Harrison: Fowler School of Engineering, Chapman University, the performance of many diagnostic techniques, and it can Orange, CA, 92866, USA result in scattering and signal degradation in imaging Open Access. © 2020 Jinghan He et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 3782 J. He et al.: Nonlinear nanophotonic devices [28–30]. In addition, many imaging methods require fluo- dA(ω) ω ( ) − j P NL (ω)e jkz (5) rescent probes. The majority of light emitting bio-labels are dz 2nϵ0c excited in the ultraviolet (UV) to visible wavelength range In other words, the amplitude of the field as a function (∼300–∼700 nm) [31–33]. Therefore, to support this rapidly of frequency will vary depending on the nonlinear po- emerging field, there is a growing effort to develop com- larization density, which is medium dependent. The plementary integrated sources. particular form of the nonlinear component of polariza- This review will introduce the key theoretical mecha- tion will depend on the nonlinear process generated in the nisms that underpin nonlinear interactions in integrated material, but in general the polarization density can be photonic devices. These act as design rules for both the expanded in a power series. The first term represents the devices discussed here as well as devices in general. Then, a linear part, and all subsequent terms represent the discussion of several new crystalline and organic materials nonlinear part: and devices being actively used to achieve ultraviolet (UV)- (1) (2) 2 (3) 3 visible (Vis) emission with be reviewed. Lastly, a discussion P ϵ0χ E + ϵ0χ E + ϵ0χ E + ... (6) of possible new research directions will be presented. The χ terms represent different orders of nonlinear susceptibility, and each is a tensor with terms to mix the x, 2 Basics of nonlinear optics y, and z components of the electric field. Additionally, Eq. (6) is only valid in the frequency domain or for ultrafast 2.1 Background nonlinearities in non-dispersive materials. In other in- stances in the time domain, overlap integrals with the Maxwell’s equations form the basis for describing electric response time are required, but for our simple analysis, Eq. fi fi and magnetic fields at a macroscopic level. Combining (6) will suf ce. We will explore speci c components of them, one can obtain the wave equation which is the nonlinear polarization in the following sections and discus foundation for electromagnetic radiation, also known as how they can be leveraged to generate frequencies in the – light. Two of Maxwell’s equations for electric displacement UV Vis range. (D) and magnetic field (H) are given below: ∇⋅ ρ χ(2) D f (1) 2.2 effects: second harmonic generation and three wave mixing ∂D ∇ ñH j + (2) f ∂t In this section, we focus on the second-order terms, which ρ (2) where f is the free charge density, and jf is the free current correspond to the χ expansion term, and are thus often density. Furthermore, D and H can be obtained through the referred to as χ(2) effects. The χ(2) coefficient is often repre- constitutive relationships. We will focus on D, because sented mathematically with the d coefficient d 1 χ(2). most materials (and the materials discussed herein) are 2 nonmagnetic, so H is directly related to B via µ0. The Since both of these quantities tensors, they include terms to electric displacement, D, is related to the electric field, E, mix the x, y, and z components. The χ(2) effects collectively via the permittivity (ε0) and the polarization density (P): include several 3-wave mixing effects: second-harmonic generation (SHG or frequency doubling), difference- D ϵ E + P (3) 0 frequency generation, and sum-frequency generation to Furthermore, the polarization can be represented by a name a few. For simplicity, we treat these effects together. sum of its linear and nonlinear parts: For χ(2) effects, we first consider three frequencies of light traveling through a crystal (Figure 1a) such that P P(L) + P(NL) (4) ω3 = ω1 + ω2. Now we examine the coupled wave equations Assuming a plane-wave propagating in the z direction that result from nonlinear polarization density being a with amplitude A, angular frequency ω, and propagation tensor and consider only the frequencies that satisfy the ω ω + ω vector k,weusethewaveequationtorelatethefield enforced constraint 3 = 1 2. The resulting coupled amplitude to nonlinear polarization. Applying the slowly- wave equations are: varying approximation (the field varies slowly with d μ ∗ − ( − − ) ( ) − ω 0 j k3 k2 k1 z propagation distance), which applies in most nonlinear E1 z j 1 dE3E2 e (7) dz ϵ1 materials, and assuming negligible loss we arrive at: J. He et al.: Nonlinear nanophotonic devices 3783 3 μ 2()ω 2 Δ 0 dL 2 2 kL ω() 2 sinc (12) I2 L 2 Iω ϵ0 nωnω 2 In order to let the intensity of ω3 grow beyond what is limited by the sinc function (that is, beyond the maximum allowed by the periodic variation over distance), we must get Δk = 0, and the way to achieve that is to match the phase of the mixed waves. This is conventionally done by taking advantage of the anisotropic nature of most nonlinear optical materials, but in nanophotonics in ω ω ω Figure 1: (a) Three waves with frequencies 1, 2, and 3 mix in a particular, it can also be done via modal phase matching or χ(2) nonlinear optical crystal exhibiting second-order ( ) effects, dispersion engineering. The anisotropic nature means that propagating in the z-direction. (b) For second-harmonic generation (SHG), two photons at the pump frequency are destroyed while the permittivity, refractive index, and therefore propaga- interacting with the material to produce a single photon at double tion vector k are tensors and will be a function of the po- the pump frequency (half the wavelength).
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