Laser Slope Efficiency and Curve Fitting

Introduction

I have spent much of my summer dealing with issues related to the high temperature characteristics of lasers. These issues have stirred within me an interest in laser slope efficiency . Slope efficiency, also known as SE, is simply the slope of the laser's output power versus drive current curve. It varies from part-to-part and with temperature.

I am interested in how SE changes at temperatures above room temperature, which I will define here as 25 °C. I have drive current versus optical power and temperature data, and I need slope efficiency versus optical power at various temperature levels. This means more hammering of data into the form that I need for presentation.

This post will assume some knowledge of the electrical characteristics of a laser, which I covered in this post.

Background

If I had my choice, I would make SE a constant. Unfortunately, nature has not been that kind. As with most things electronic, things degrade rapidly with increasing temperature. In order to plot SE versus optical power at various temperatures, we need to precisely define what SE is. Equation 1 presents the formal definition.

Eq. 1

where

• P_Output is the laser output power, which is a function of drive current and temperature
• T is the ambient temperature that is varying over a range from 30 °C to 80 °C
• I_Drive, the drive current into the laser.

Note that Equation 1 shows SE as a function of I_Drive and temperature. However, I need to relate SE (the derivative of P_Output) to P_Output. All I need to do is to plot SE versus P_Output by using I_Drive as a parameter.

Analysis

My Data

Figure 1 shows a plot of the data I have. The data always comes to me in the form of an Excel worksheet, and it shows P_Output versus I_Drive at various temperatures. What I need is SE versus P_Output at various temperatures.

Figure 1: Drive Current Versus Optical Power and Temperature

Approach

Here is my approach for analyzing this data:

• I insert an Excel component into Mathcad, and I then insert the data into the Excel component.
• I perform a two-dimensional curve-fit using cubic splines to generate P_Output(I_Drive,T).
• I compute SE by taking a derivative of P_Output with respect to I_Drive.
• Compute P_Output versus the same I_Drive values that I used to compute SE.
• I now plot my SE versus P_Output for the same values of I_Drive at various temperatures.

Interpolation

Figure 2 shows a screenshot from Mathcad of my data and interpolation approach. I used a Mathcad program to actually process the data. I find the programs simple to develop and easy to use.

Figure 2: Test Data Component and Interpolation Programs.

Slope Efficiency Versus Optical Power at Various Temperatures

Figure 3 shows the final result of my work. Note how SE degrades with temperature.

Figure 3: Slope Efficiency Versus Optical Power at Various Temperatures.

Figure 3: Laser Tracking Error Versus Temperature.

Conclusion

I thought this was a good, practical example illustrating two-dimensional interpolation applied in an actual application. I often need to present data in a way that differs from how the data was originally gathered. Interpolation allows me to obtain the data I need with minimal effort.