PHTN1500 Advanced Laser Theory

Lab #2 - Mathematical Model of a Semiconductor Laser

Introduction

The threshold of pump power for a semiconductor is determined and mathematical model for the laser developed.


Prelab:

Experiment:

Analysis:

You might need a few numbers to get started:
Cross section σ0 = 1 * 10-19 m2
ULL Lifetime τ = 1 * 10-9 s
The rest of the numbers can be found in the pre-lab references. Please state assumptions for all constants used (e.g. absorption, etc) and a reference if available.

Now, knowing the gain of the device (both threshold and 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). To do this you will need a starting gain: choose a drive current which corresponds to maximum diode output (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:

To be done individually ...

    Threshold:
  1. Hand-in a graph of Poptical vs. drive current for the laser diode.
  2. Describe, in a paragraph, what happens at the threshold of lasing. Be specific and reference physical parameters of the medium such as gain and loss in the system.
  3. Calculate the gain of the diode (In the same manner as problem 5, chapter 5 of Csele).
  4. 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.


  5. Power Development:
  6. Hand-in a graph showing the dependence of intra-cavity power and gain with respect to pass # and outline the following:
    1. Show how parameters used in the simulation model were developed (including Psat and g0 at the rated drive current).
    2. The time for the device to reach 90% output levels
    3. A comparison of expected (from the model) output power at optimal drive current and that stated in the datasheet.

    Physical Parameters and Effects:
  7. Show a diagram of the elliptical beam shape from a laser diode and explain why divergence is higher in one dimension than the other. Specifically, explain how the beam path in each dimension (x and y) creates the elliptical pattern - a diagram would be very useful here! (Hint: Explain how the cavity dimensions involved bring about the optical characteristics of the laser. The dimension of the laser diode's cavity corresponding to the largest dimension of the output beam is counter-intuitive ... explain this)
  8. Explain why the wavelength of the diode shifts as current is increased. Specifically, describe what was observed (which way the wavelength shifted - higher or lower λ as current increases) and explain why this is or isn't expected.
  9. Calculate the slope efficiency of the diode. Include a Power IN:OUT plot and show how slope efficiency was computed.
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