**3.3 DBR design**

The DBRs should provide a reflectivity above 95% at both signal and idler wavelengths (see **Figure 3**) and nearly null reflectivity at pump wavelength. As mentioned earlier, this has already been demonstrated with dielectric stacks deposited on the waveguide facets [6]. While the outer mirror can be fabricated in this fashion, the inner one needs to be etched at an interface. Let us estimate now the DBR coupling constants in the approximation of weak perturbations. For a DBR length of 100 μm, the coupling constant should be 220 cm<sup>−</sup><sup>1</sup> in order to achieve 95% reflectivity. **Table 4** presents the coupling constants of the fundamental TE and TM modes at 2 μm for a grating depth of 200 nm. The grating is supposed to be perfectly rectangular, with a filling factor of one-half. Whether the grating is formed by etching the top interface (air/GaAs) or by etching the underlying cladding and restarting epitaxy (GaAs/Al0.8Ga0.2As interface), an etch depth of at least 200 nm is necessary to achieve reflectivity over 95% with a DBR smaller than 100 μm.


## **Table 4.**

*Coupling constants for fundamental TE and TM modes at 2 μm, given a rectangular grating of depth 200 nm and duty cycle 50%.*

**117**

one transfer length.

**4.2 3D simulations**

*Widely Tunable Quantum-Well Laser: OPO Diode Around 2 μm Based on a Coupled Waveguide…*

We show in **Figure 7** the tunability curves of the waveguide at temperatures 20 and 40°C. Outside of degeneracy, a signal/idler wavelength range of 300 nm is

A transverse view of the structure is shown in **Figure 8**. The two waveguides are separated by 300 nm of Al0.3Ga0.7As. **Figure 9** presents a simulation of light propagation along the structure by a beam propagation method (BPM), which has been carried out with the commercial software RSoft. To reduce calculation time and quickly converge on an intuitive model, we first make a 2D effective-index approximation, whose validity will be checked in the next section. The injected mode, visible on the right-end side of **Figure 9a**, is the eigenmode presenting the highest overlap with the active region. As is visible from **Figure 9b**, 90% of the guided power is contained in the laser core layer at Z = 0, that is, before the taper. Thus, modal gain is expected to not suffer from the presence of the underlying GaAs layer. From Z = 0 to Z = 300 μm, the two top layer widths are reduced from 4 μm to 0. From Z = 300 μm to Z = 500 μm, the separation layer (Al0.3Ga0.7As) width is reduced in the same way. Over 95% of the power is transferred to the GaAs waveguide. To estimate the robustness of the design to a limited resolution in lithography, we simulate the same transfer with widths ending at 0.4 μm instead of 0: the transfer of power to the underlying waveguide is 85%. While a more detailed set of tests would be necessary to account for fabrication-

In order to find out if the power in the slab is in the desired TE2 mode, we calculate the overlap of the BPM-simulated field with the GaAs waveguide eigenmodes. The result, reported in **Figure 10**, is that 97% of the power is in the TE2 mode after

In the 2D-effective index approximation made in the previous section, we assumed single-mode behavior in the lateral direction. The geometry chosen in 3D

accessible for a pump wavelength variation of a few nm.

*Tunability curves of the waveguide supporting frequency conversion.*

**4.1 2D approximation for the effective index**

induced deviations, these results are encouraging.

*DOI: http://dx.doi.org/ 10.5772/intechopen.80517*

**3.4 Tunability**

**Figure 7.**

**4. Waveguide coupling**

*Widely Tunable Quantum-Well Laser: OPO Diode Around 2 μm Based on a Coupled Waveguide… DOI: http://dx.doi.org/ 10.5772/intechopen.80517*

**Figure 7.** *Tunability curves of the waveguide supporting frequency conversion.*
