**3.4 Tunability**

*Nonlinear Optics - Novel Results in Theory and Applications*

*(left) and 1010 nm (right). Temperature is 20°C in both cases.*

single-mode DFB laser.

wavelength.

**Figure 6.**

**3.3 DBR design**

smaller than 100 μm.

Grating depth (nm)

*and duty cycle 50%.*

**Figure 6** presents the normalized spontaneous down-conversion (SPDC) efficiency as a function of ridge width and thickness, at pump wavelengths of 990 and 1010 nm. A wavelength shift of + − 10 nm can compensate for a variation of 40 nm of the waveguide core thickness. This variation is typically accessible to a

*Normalized SPDC efficiency as a function of ridge width and thickness, for pump wavelengths of 990 nm* 

As a conclusion, while efficient parametric down-conversion is only encoun-

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.

in order

κTM (cm<sup>−</sup><sup>1</sup> )

**Grating at the lower interface (GaAs/ Al0.8Ga0.2As)**

κTE (cm<sup>−</sup><sup>1</sup> )

For a DBR length of 100 μm, the coupling constant should be 220 cm<sup>−</sup><sup>1</sup>

**Grating at the top interface (air/ GaAs)**

> κTE (cm<sup>−</sup><sup>1</sup> )

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

> κTM (cm<sup>−</sup><sup>1</sup> )

200 214.5 242.5 277 180.9

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

tered in a narrow window of parameters, it can realistically be achieved by compensating variations in fabrication with a shift in temperature and pump

**116**

**Table 4.**

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 accessible for a pump wavelength variation of a few nm.
