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:
- Install a diode, mounted in an 'FC' bulkhead connector, onto the Agilent 86142B OSA input using a fiber cable (black ends).
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.
- Connect the diode to the output from an ILX precision current source. The anode and cathode of the diode connect to the terminals on the rear of the current source and the DB-9 connector must be installed to complete the interlock.
The diode is seen here mounted on a bulkhead connector. Plug the diode into the socket making sure the pinout matches and connect the banana jacks to the output terminals on the rear of the ILX current source. Observe normal static-sensitive precautions. The DB-9 interlock jumper must also be installed on the rear of the current source.
- Turn on the supply and set the current LIMIT of the supply to the maximum specified on the data sheet.
The current source, seen here, must be set for maximum current first. Set the MODE switch to LIMIT DISPLAY then rotate the LIMIT control to set the maximum current. Now switch the MODE switch back to CONST I to meter diode current.
- Set the meter selector to monitor diode current.
- Set the OSA for a center wavelength of 800nm and a span of 10nm to start
- Turn on the output from the ILX current source. Starting at zero mA, increase the current slowly and observe the output of the diode on the OSA. Specifically record the mode spacing (required to determine the length of the diode) at low currents (< 25mA), the threshold current (where a single mode becomes dominant), and the drift of the center wavelength as current increases from threshold to maximum.
- Determine the spacing of the modes - this gives the length of the cavity. The width and depth of the active volume of the diode can be found in the datasheet.
- Reduce the current to zero, disconnect the fiber-optic cable from the diode, and point the diode at the sensor of the Ophir Nova power meter
- Set the power meter for 808nm (MENU button, twice, then select LASER for 808nm)
- Increase laser diode current until output is detected and collect (light, current) data points. At least fifteen points are required between the point at which output begins and maximum current.
- Plot a L/I graph for the diode in the same manner as the application note of the prelab and determine the threshold using several different methods.
- Knowing the typical voltage across the diode (from the datasheet) and the current, plot Power IN versus Power OUT and determine the slope efficiency of the diode (Power IN being electrical power, Power OUT being optical power).
Analysis:
- Knowing the reflectivity of the mirrors (from n of the material - use Fresnel equations from chapter 4 of Csele), the absorption of the AlGaInP material (research this), and the length of the cavity (computed from the measured FSR), compute threshold gain (gth)of the laser. Use the threshold gain formula to do this.
- From gain, compute threshold inversion ΔN (chapter 5). Cross-section of the material is required (use the pre-lab references). Be mindful of the units for ΔN.
- Knowing ΔN, and the lifetime of the ULL, compute the recombination rate, dNULL/dt = ΔN/τ. The actual units will be in terms of "electrons per second, per unit volume" (i.e. /m3*s).
- Energy in equals Energy Out, so the recombination rate must equal the pumping rate (J/qt) where t is thickness of the recombination layer. Compute current density J (in A/m2) by assuming that each transition of dNULL/dt represents the energy of one electron charge (1.602*10-19J) , and finally (knowing the emitter size from the datasheet and from the mode spacing) threshold current. Pay attention to units to ensure the final threshold current is really in terms of Amperes, and expect a logical answer of between 10mA and 40mA. Compare to the experimentally-determined value in the lab and describe, using a logical argument, why the experimental threshold might be larger than the experimental. What assumption(s) about the behaviour of semiconductors were made in the above theoretical computations which can possibly lead to a low theoretical threshold current?
- From the Power plot, compute slope efficiency of the laser diode.
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:
- Hand-in a graph of Poptical vs. drive current for the laser diode.
- 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.
- Calculate the gain of the diode (In the same manner as problem 5, chapter 5 of Csele).
- 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.
Power Development:
- Hand-in a graph showing the dependence of intra-cavity power and gain with respect to pass # and outline the following:
- Show how parameters used in the simulation model were developed (including Psat and g0 at the rated drive current).
- The time for the device to reach 90% output levels
- A comparison of expected (from the model) output power at optimal drive current and that stated in the datasheet.
Physical Parameters and Effects:
- 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)
- 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.
- Calculate the slope efficiency of the diode. Include a Power IN:OUT plot and show how slope efficiency was computed.
Copyright (C) Niagara College, Canada, 2009
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