J. Eur. Opt. Society-Rapid Publ. 21, 23( 2025) 227
Figure
3. Optical frequency comb generation dynamics. In( a) we report the laser cavity detuning, while in( b) the intra-cavity energy of the FF( blue) and SH( red) fields. In the bottom part of the figure, we report the snapshots for different spectral( c, e, g, i) and temporal( d, f, h, j) OFC regimes:( c, d) OPO,( e, f) modulation instability,( g, h) chaos and( i, j) a FF CS coupled to a SH dispersive wave.
dispersion around x 0( b 2, FF < 0) sustains the soliton propagation. On the other hand, normal dispersion at 2x 0( b 2, SH > 0) does not allow for temporal confinement of the spectral components in the SH domain. As a consequence, all the power converted at 2x 0 by the FF CS is rapidly dispersed by the system.
Therefore, the generation of bicolor CSs [ 12 ] in the AlGaAs-on-insulator( AlGaAs-OI) platform at telecom wavelengths is intrinsically limited by the normal dispersion profile at shorter wavelengths( i. e. around 2x 0). This is a direct consequence of the absorption peak close to the SH wavelength k SH = 0.775lm. Notably, a pumping scheme k P 1.95 lm for a SHG assisted supercontinuum generation has been recently proposed [ 57 ]. In this specific case, supposing that a phase matching condition for the process x 0 ยก 2x 0 is satisfied, the dispersion profile is optimal at both x 0 and 2x 0, seeFigure 2f. As a consequence, the generation of bicolor CSs is not just possible, but it also represents a strong dynamical attractor.
In a telecom pumping scheme, a suitable solution consists in engineering the chromatic dispersion, for instance by a proper longitudinal modification of the waveguide profile [ 40, 41 ], which introduces local mirroring effects and frequency splittings that are exploitable for dispersion management. Recently, some prototypes of rings [ 42, 58 ] or Fabry-Perot [ 59, 60 ] resonators of this sort have been reported.
An alternative approach could involve decoupling the nonlinear problem v( 2) + v( 2), by designing two separate photonic devices, which should be eventually integrated in a single circuit. An example can be a pure Kerr microring with a SHG optical feedback. With this solution in mind, let us proceed to describe an optimal AlGaAs waveguide design for efficient frequency doubling.
4 U-shaped AlGaAs waveguide design for efficient frequency doubling
If we aim at narrow-band SHG without caring about dispersive effects, we can target the PM condition between the TE 00 and TM 00 modes [ 22 ] with no further constraints on the waveguide cross-section. This approach enhances the nonlinear process thanks to the larger overlap integral between fundamental modes. This process can be generalized by letting the waveguide turn and be wrapped in a snaky fashion [ 47 ]. The scheme of the problem is depicted in Figure 4a, where we show a U-shaped waveguide with aTE 00 mode excited at k 0 = 1.55lm and phase-matched to the TM 00 mode at its SH. The design must optimize SHG all along the waveguide. For this reason, the waveguide width w 0 in the straight section differs from the the width w 1 of the curved section, so as to preserve the modal-PM and 4-QPM conditions, respectively. Specifically, type-I modal PM arises whenever the difference of the effective indices Dn eff corresponding to the interacting modes is null, i. e. Dn eff = 0. In a curved section, the