From Nonlinear Integrated Optics to Microresonator Frequency Combs

Perhaps one of the most spectacular current applications of nonlinear integrated optics, a field which was pioneered by George Stegeman more than thirty years ago [1], is that of nonlinear microresonator based optical frequency comb light sources. Optical frequency comb sources are characterized by a spectrum comprising many equally spaced components [2], and have a wide range of scientific and technological applications. Although commercial comb generators are based on mode-locked lasers and fiber supercontinuum generation, nonlinear integrated optics provides a low-cost and chip-scale alternative, based on a low-power cw laser coupled into a high-Q microresonator [3]. So far microresonator frequency combs have exploited the third order “Kerr” nonlinearity, which permits to generate successive comb lines with a spacing equal to the resonator free-spectral range via cascaded four-wave mixing [4-5]. Modeling of microresonator frequency combs can be greatly simplified by a single partial differential equation approach [4-6], analogous to the case of other coherently driven Kerr spatially diffractive [7] or temporally dispersive [8-9] nonlinear cavities. In order to lower the threshold power and extend the spectral range of frequency comb generation, for example into the visible or mid-infrared, while still using near-infrared cw laser pumps, quadratic nonlinear cavities can be exploited [10]. These quadratic microresonator frequency comb sources operate close to the phase-matching condition for the underlying quadratic processes, and not in the cascading regime that reduces the dynamics to the Kerr case [11]. Quite remarkably, a single time domain partial differential equation with an effective delayed third-order nonlinearity was derived to describe with excellent accuracy the dynamics of quadratic frequency comb generation [12-13]. In situations where multiple processes are present, and the frequency combs generated around the interacting waves over multiple octaves overlap, we carried out numerical modeling based on a single envelope equation approach [14]. References [1] G.I. Stegeman, E.M. Wright, N. Finlayson, R. Zanoni, and C.T. Seaton, J. Lightwave Technology 6, 953 (1988). [2] T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002). [3] P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007). [4] S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013). [5] T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013). [6] T. Hansson, D. Modotto, and S.Wabnitz, Opt. Comm. 312, 134 (2014). [7] L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987). [8] M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992). [9] F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, Nature Photon. 4, 471 (2010). [10] I. Ricciardi, S. Mosca, M. Parisi, P. Maddaloni, L. Santamaria, P. De Natale, and M. De Rosa, Phys. Rev. A 91, 063839 (2015). [11] G. I. Stegeman, D. J. Hagan, and L. Torner, Optical and Quantum Electronics 28, 1691 (1996). [12] F. Leo, T. Hansson, I. Ricciardi, M. De Rosa, S. Coen, S. Wabnitz, and M. Erkintalo, Phys. Rev. Lett. 116, 033901 (2016). [13] F. Leo, T. Hansson, I. Ricciardi, M. De Rosa, S. Coen, S. Wabnitz, and M. Erkintalo, Phys. Rev. A 93 (2016). [14] T. Hansson, F. Leo, M. Erkintalo, J. Anthony, S. Coen, I. Ricciardi, M. De Rosa, and S. Wabnitz, J. Opt. Soc. Am. B 33, 1207 (2016).