**3.2 Tolerances**

**Figure 4** shows the SPDC normalized efficiency as a function of ridge width and thickness. The FWHM of efficiency is 200 nm for a variation in width, a value compatible with the current state of fabrication technology. The FWHM for a variation in thickness is much smaller, around 3 nm. The typical precision of thickness achieved by molecular beam epitaxy is approximately 2%, corresponding to a variation of 2 nm in a 0.95 μm waveguide. Depending on growth systems, this value can be further increased by inhomogeneities along the wafer.


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transfer).

**Figure 5.**

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

*OPO pump power threshold for a ridge width of 4 μm (left) and 2 μm (right) as a function of length and* 

Fortunately, two tools allow us to shift the efficiency curve: temperature and pump wavelength. **Figure 5** shows the normalized SPDC efficiency as a function of ridge width and thickness, for waveguide temperatures of 20 and 50°C. A temperature shift of 30°C can compensate for a 10-nm variation of the waveguide core thickness. We stress here that the temperatures of laser and parametric conversion regions can be set separately and that an increase of 30°C in the SPDC area has a negligible impact on the laser temperature, assuming that the two regions are separated by 300 μm (a typical distance for adiabatic

*Normalized SPDC efficiency as a function of ridge width and thickness, for a waveguide temperature of 20°C* 

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

*signal/idler reflectivity. Guide thickness is 0.95 μm.*

*Normalized SPDC efficiency as a function of ridge width and thickness.*

*(left) and 50°C (left). Pump wavelength is 1 μm in both cases.*

**Figure 3.**

**Figure 4.**

**Table 3.**

*SPDC efficiency vs. ridge width in a 0.95-μm-thick waveguide surrounded by Al0.8Ga0.2As and air.*

*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 3.**

*Nonlinear Optics - Novel Results in Theory and Applications*

tage: it eliminates the uncertainty on the Al fraction.

**3.1 Conversion efficiency and OPO threshold**

threshold pump power lies in the 10–100 mW range.

can be further increased by inhomogeneities along the wafer.

**Ridge width (μm) Conversion efficiency**

*SPDC efficiency vs. ridge width in a 0.95-μm-thick waveguide surrounded by Al0.8Ga0.2As and air.*

2 600 3 380 4 230

**(W<sup>−</sup><sup>1</sup> cm<sup>−</sup><sup>2</sup> )**

**3. Nonlinear characteristics**

**3.2 Tolerances**

**Figure 2.**

The waveguide core should hold as little aluminum as possible in order to increase its nonlinear susceptibility. We set the exact Al fraction by comparing the effective index of guided modes in the upper waveguide to the effective index of the lower waveguide as taper width is reduced (**Figure 2**). For 10% Al composition, the laser mode index crosses the index of TE1 in the buried waveguide. We can thus expect the mode to couple to TE1. Using pure GaAs, the laser mode crosses only the TE2 index, which is the desired configuration. Absorption in GaAs at 1 μm is expected to be negligible [14]. Setting a pure GaAs waveguide has another advan-

*or GaAs (right) surrounded by Al0.3Ga0.7As on one side and Al0.8Ga0.2As on the other.*

*Effective indices of guided modes in the structure. (Red) Index of the laser mode as a function of guide width. (Orange) Indices of guided modes in the buried waveguide, assuming a planar waveguide of Al0.1Ga0.9As (left)* 

We calculate conversion efficiencies with a code developed in the team, based on the work presented in [15]. **Table 3** shows the nonlinear conversion efficiency at several ridge widths for a waveguide of thickness 0.95 μm surrounded by

Al0.8Ga0.2As and air. The corresponding pump powers necessary for an OPO threshold are presented in **Figure 3**. Propagation losses are assumed to be 0.1 cm<sup>−</sup><sup>1</sup>

**Figure 4** shows the SPDC normalized efficiency as a function of ridge width and thickness. The FWHM of efficiency is 200 nm for a variation in width, a value compatible with the current state of fabrication technology. The FWHM for a variation in thickness is much smaller, around 3 nm. The typical precision of thickness achieved by molecular beam epitaxy is approximately 2%, corresponding to a variation of 2 nm in a 0.95 μm waveguide. Depending on growth systems, this value

. The

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**Table 3.**

*OPO pump power threshold for a ridge width of 4 μm (left) and 2 μm (right) as a function of length and signal/idler reflectivity. Guide thickness is 0.95 μm.*

**Figure 4.**

*Normalized SPDC efficiency as a function of ridge width and thickness.*

**Figure 5.**

*Normalized SPDC efficiency as a function of ridge width and thickness, for a waveguide temperature of 20°C (left) and 50°C (left). Pump wavelength is 1 μm in both cases.*

Fortunately, two tools allow us to shift the efficiency curve: temperature and pump wavelength. **Figure 5** shows the normalized SPDC efficiency as a function of ridge width and thickness, for waveguide temperatures of 20 and 50°C. A temperature shift of 30°C can compensate for a 10-nm variation of the waveguide core thickness. We stress here that the temperatures of laser and parametric conversion regions can be set separately and that an increase of 30°C in the SPDC area has a negligible impact on the laser temperature, assuming that the two regions are separated by 300 μm (a typical distance for adiabatic transfer).

**Figure 6.**

*Normalized SPDC efficiency as a function of ridge width and thickness, for pump wavelengths of 990 nm (left) and 1010 nm (right). Temperature is 20°C in both cases.*

**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 single-mode DFB laser.

As a conclusion, while efficient parametric down-conversion is only encountered in a narrow window of parameters, it can realistically be achieved by compensating variations in fabrication with a shift in temperature and pump wavelength.
