Dual-Comb Generation in III-V Semiconductor Laser: Transverse Modes Versus Modeless Cavities

Dual frequency-combs have been relevant for applications such as spectroscopy [1], Many methods are used to generate dual-combs like polarization multiplexing [2] or wavelength/space multiplexing [3], [4]. We demonstrated two passively mode-locked dual-comb configurations in a single Vertical External-Cavity Surface-Emitting Laser (VECSEL) using a InGaAs/GaAs based optically-pumped gain mirror (1/2-VCSEL) and a fast Semiconductor Saturable Absorber Mirror (SESAM) for an emission at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.06\mu \mathrm{m}$</tex> with a pulse width of 5ps at 1GHz repetition rate. Fig. 1 a) shows the cavity design where two lenses are used to control the beam ratio on the gain mirror and the SESAM for a stable mode-locking state, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{1,2}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d_{1,2,3}$</tex> are chosen in order to get a stable Laguerre-Gauss (LG) transverse modes oscillations with one optical axis and two transverse states as shown in Fig. 1 b) (up), or a modeless self-imaging cavity with two optical axes as shown in Fig. 1 b) (down). Fig. 1 c) shows the temporal evolution of the dual-comb where the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{LG}_{00}$</tex> comb's repetition rate is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{rep}=1/T$</tex> and the LG03 comb's one is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{rep}+\Delta f$</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T$</tex> is the roundtrip time of 1 ns and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta f\approx 100\text{kHz}$</tex>.