PHTN9120: Fundamentals of Lasers and Light Sources
Mathematical Model of a Semiconductor Laser and Thermal Issues (2014F)

Introduction

The threshold of pump power for a semiconductor is determined using a mathematical model and then compared to experimental results from a real diode laser. Using results of this first experiment a mathematical model predicting the buildup of laser power (based on gain saturation) is developed using a spreadsheet and compared to the Rigrod approach. Finally, the effect of temperature on diode performance is investigated.

Prelab

Experiment:

Part 1: Determining Laser Diode Parameters

Diode Laser Setup
The complete laser diode setup. The diode itself is mounted inside an ILX LDM-4412 test fixture which features twin powerful Peltier-effect thermoelectric cooler modules as well as a TS-510 calibrated thermistor.

A US-Lasers 808-5 diode is installed in the test fixture. Turn on the ILX LDT-5910B Temperature Controller and set the temperature to 20C. Install a fiber such that radiation from the laser diode can be analyzed using the Agilent 86142B OSA (the fiber should be blue - swing it upwards such that the apeture intercepts the infrared beam from the diode).

Agilent 86142B OSA With the room interlock system enabled, turn ON the ILX LDX-3412 precision current source and increase the current to approximately 30mA. Using an infrared viewer card, align the fiber so that it intercepts the diode output and then align manually such that output appears on the OSA. The laser diode output should appear on the OSA around 808nm and multiple modes may well be visible.

The OSA is seen in this photo along with a sample output from the laser diode. See chapter 13 of Csele to get an idea of where the modes originate. This will allow you to compute the length of the cavity and hence the gain medium, a parameter not found on the data sheet for the diode.

Part 2: Determining Performance Experimentally

Part 3: Thermal Effects

Repeat the experiment above (Part 2) at various temperatures (10C, 20C, 30C, and 40C), determining the L/I graph at each temperature. This data is required in order to determine the characteristic temperature of the device (see the prelab for details).

Analysis:

You might need a few numbers to get started:
Cross section σ0 = 1 * 10-19 m2
ULL Lifetime τ = 1 * 10-9 s
Index of refraction of AlGaInP = 3.7
Attenuation γ = 25 cm-1

Now, knowing the gain of the device (both threshold gain and gain at a particular drive current) and physical parameters (e.g. length) we may now generate a model to show how power develops in the laser. This model will predict not only output power but also response time, an important consideration when using a laser diode in a communications system.

Develop a spreadsheet model for this diode similar to that demonstrated in class for the HeNe laser. The model must predict the intra-cavity power on each pass through the gain medium (a 'pass' considered in each direction - a round-trip is two passes). Further refinement is required by subdividing the gain medium into smaller lengths (x/2 or x/3, as required ... this will be discussed in lectures). To do this you will need a starting gain (g0): choose a drive current which corresponds to maximum diode output ("Typical drive current" from the datasheet) and determine the gain by scaling ΔN according to the threshold determined in the lab. If, for example, theoretical drive current is twice that of the threshold current, then the inversion is presumed to be twice that of the threshold inversion already determined. From there g0 may be determined.

Several parameters must be computed now, including Psat, and several have already been computed or referenced including attenuation, length, and optics parameters.

When the simulation is complete, graph gain and power output vs. pass on the same graph. Determine the time for the laser to reach 90% of the CW output level - this is the risetime of the device for practical purposes.

Assignment

Hand In a WORD PROCESSED (not handwritten) lab assignment as follows. Put each question on a new page and ensure each page has a title "Question 1", "Question 2", etc. Also, please ensure the lab report is in a folder for submission (no loose pages).

To be done individually ...

    Threshold:
  1. Hand-in a graph of Poptical vs. drive current for the laser diode as observed in the lab for various temperatures.
  2. Show, on the graph above, the threshold current for the device and explain in a paragraph how it was determined (i.e. summarize the method from the ILX application note that you used)
  3. Calculate the slope efficiency of the diode (you might have to research this). Include a Power IN:OUT plot and show how slope efficiency was computed. Remember that electrical power is calculated as current times voltage (outline where you obtained any constants required such as device voltage).
  4. Calculate the threshold gain of the diode (In the same manner as problem 5, chapter 5 of Csele, but using the device parameters found experimentally in this lab).
  5. Calculate the theoretical threshold current for the diode (show all calculations and formulae used) and compare to the experimentally-determined value. This question is worth considerably more marks than others in the lab and a large degree of detail is required to show how you developed the model. Show all intermediate steps and equations.
  6. Calculate the characteristic temperature (T0) of the diode using the method outlined in the prelab reading (from ILX). Show all calculations required (e.g. ln(Jth)) as well as the graph (for which the slope of that graph is T0).


  7. Power Development (spreadsheet-based model):
  8. Show how parameters used in the simulation model were developed (including Psat and g0 at the rated drive current).
  9. Hand-in a screen shot of the spreadsheet model showing at least the first ten rows of the simulation as well an any anchored parameters at the top. All columns must be shown (this may require more than one screen-shot) and cell references ("ABC" columns and "123" rows) must be visible. The simulation must be on a "per section through the amplifier" basis (with ΔX smaller than the amplifier length), not "round trip" as we have done in class since both the gain, and loss at each cavity mirror, is very large (The entire process will be outlined in lectures before the lab). Calculation of gsat also requires some forethought since it depends on the intra-cavity beam travelling in both directions - this was/will be discussed in lectures (In the simple simulation provided this was done by multiplying the unidirectional intra-cavity power by two ... this cannot be done here). As well, show ALL CALCULATIONS by outlining EACH FORMULA from EACH CELL in the first four rows (simply show these as, for example, "AA6=+AC6*exp($C$7*C6)" on a separate page). This question is worth considerably more marks than others in the lab and a large degree of detail is required to show how you developed the model. Show all spreadsheet formulae.
  10. Hand-in a graph (output from the spreadsheet model) showing the dependence of both intra-cavity power and gain with respect to pass # (preferably on the same graph using primary and secondary axes, as per the example simulation provided).
  11. From the simulation determine the time for the device to reach 90% output levels (i.e. the rise-time of the device)
  12. Outline (showing key mathematical steps) the prediction of output power using the Rigrod model remembering to factor-in attenuation as described in lectures.
  13. A comparison of output power at optimal drive current as predicted by (i) the pass-by-pass model in this lab, (ii) predictions from the Rigrod model, and (iii) predictions from the simple model to that stated in the datasheet. Explain why the discrepancy might exist.