Fig. 1. Schematic structure of the MRW device structure and principle：（a）Cross-section of the MRW； （b）Design principle of mode coupling

Fig. 2. The propagation constant real part of TM modes in QCL as a function of ridge width

Fig. 3. The number of modes in the laser at different trench etching depthes（The geometric parameters are W_M = 10 μm， W_L = 4.9 μm， W_R = 6.5 μm， respectively.）

Fig. 4. Effect of the ridge width on the coupling results：（a）Loss margin of modes as a function of the left ridge width； （b）Loss margin of modes as a function of the left ridge width

Fig. 5. Effect of different parameters on loss margin of modes in MRW structure：（a）Loss margin of modes as a function of trench etch depth； （b）Loss margin of modes as a function of etch side depth； （c）Loss margin of modes as a function of trench etch depth

Fig. 6. Field strength distribution of the fundamental modes in the laser：（a）Field strength component of the fundamental mode supported by the 10 μm independent single ridge laser； （b）Field strength component of the fundamental mode supported by the 6.1 μm independent single ridge laser； （c）Field strength component of the fundamental mode in the main waveguide of MRW laser； （d）Field strength component of the fundamental mode in right auxiliary waveguide of MRW laser

Fig. 7. Field strength distribution of high-order mode in the laser：（a）Field strength component of 1st order mode supported by the 10 μm independent single ridge laser； （b）Field strength component of the fundamental mode supported by the 4.4 μm independent single ridge laser； （c）Field strength component of the first order supermode in main waveguide of MRW laser； （d）Field strength component of first order supermode in the left auxiliary waveguide of MRW laser

Fig. 8. Field strength distribution of high-order mode in the laser：（a）Field strength component of 2nd order mode supported by the 10 μm independent single ridge laser； （b）Field strength component of 1st order mode supported by the 6.1 μm independent single ridge laser； （c）Field strength component of the second order supermode in the main waveguide of MRW laser； （d）Field strength component of second order supermode in the right auxiliary waveguide of MRW laser

Fig. 9. Mode discrimination of MRW-QCL（red circles）and conventional QCL（black triangles）