PHTN1500: Advanced Laser Theory
Modeling Q-Switched Lasers (2014F)


Following section 6.8 in Laser Modeling, a numerical model will be developed for the time-domain dependency of the inversion/gain of a real solid-state YAG laser (a Quantel 660) to predict the optimal point at which a Q-switch should be opened. In addition, the use of passive Q-Switches will be investigated.

The key concepts covered in this lab hence include:

Prelab (To be done prior to the lab, due upon entry)

For submission ...


This is a class-IV laser with EXTREMELY high peak powers capable of ocular damage with only one pulse. The particular danger here is the Q-switched infrared output at 1064nm since hazards presented by specular reflections are not obvious. Ensure the 1064nm output shutter is closed when the beam is not required. When the beam is required, ensure it is intercepted as close as possible to the laser and pay attention to spurious refections from optical elements in the beam path.

SAFETY GLASSES MANDATORY - DO NOT REMOVE THEM WHEN THE LASER IS OPERATING ... Q-Switched YAG lasers are responsible for more eye injuries than any other types of laser combined!

The Experiment

Part A: Determining the Shape of the Pumping Pulse

In this part of the experiment data will be gathered on the intensity of the pumping pulse which will then be used as the kernel for the convolution model to determine the optimal Q-switch firing point.

YAG Laser

The Quantel 660 YAG laser is seen firing. Light from the flashlamp is also seen flooding from around the pump reflector. This light - which represents the intensity of the pumping radiation - is monitored by a photocell as part of this experiment.


Connect a TDS oscilloscope with channel 1 on the flashlamp monitor cell and channel 2 on the system trigger (the input to the delay generator via a BNC 'Tee' connection). Set the scope to trigger on a falling edge of channel 2 - the signal will normally be logic-high (+24V in this case) and will drop to ground when triggering occurs. Output from the laser is monitored via a Newport 818-SL sensor protected by an attenuator which uses a ceramic plate to scatter the intense pulse before it passes to the sensitive silicon detector. Put the Newport meter on the 2mW full-scale setting and readings will now be in watts (2 W full scale). The energy of each pulse is simply the power (in watts) divided by the firing rate (in pulses-per-second). The sensor must NEVER be exposed to the 'raw' laser pulse which will damage it in only one pulse! When aligning the optical path be sure that any anticipated reflections fall onto a beam absorber or a power meter.

Alternative Setup:

Connect a TDS2002B oscilloscope with channel 1 on the flashlamp monitor cell, channel 2 from the GenTec joulemeter, and the system trigger (the input to the delay generator via a BNC 'Tee' connection) to the external trigger input. Set the scope to trigger on the EXT input (level approx. 776mV). When the laser triggers, the trace will start with channel 1 showing the pumping pulse amplitude in time and channel 2 the output pulse energy (note that the attenuator is used). For each set of measurements the timebase must be changed to about 100μs to determine the pulse energy and to about 50μs to determine the actual Q-Switch delay (see below). The QE-50 joulemeter is calibrated at 1064nm for 3.43V/J (Volts being PEAK volts) and the QEA-50 attenuator is installed which reduces the intensity to 20% of the true reading.

Alternative Setup - Time Domain Experiment

As per the SOP, ensure cooling water is turned ON and start the laser. Set the power supply voltage to 1.2kV.

First, set the delay to maximum (>9.0 on the control) and record the shape of the flashlamp pumping pulse on channel 1 of the oscilloscope (the laser will produce NO output at this setting). The oscilloscopes feature a front-panel USB connector allowing a screenshot as well as time/energy data for the pumping pulse to be saved to a USB key simply by pressing the Print button. The scopes only work with USB keys of 2GB or less. This data (pumping intensity with time) will be used for the model of the laser.

Set the power supply voltage to 1.7kV and repeat the data collection procedure. You will now have two pump pulses captured: one at low energies and one at twice this energy (since capacitor energy is proportional to V2).

Part B: Comparing the Model to Experimental Results

In this part of the experiment experimental data correlating pulse energy to Q-switch time delay will be collected.

Set the delay to 300μs and fire the laser at 10 pps. Note that as the DELAY is varied, the pulse energy also varies. Set the delay to be so early that the output is zero. Now, increase the delay at periodic increments of about 10μs to 20μs and note the power output. For each delay, read the EXACT delay (from the start of the trigger pulse) using the cursors on the oscilloscope (The control on the delay generator is NOT calibrated).

YAG Laser Pumping Intensity

The output of the experiment as seen on the scope. Channel 2 is the trigger pulse which defines T=0 (at point A). Channel 1 shows the intensity of the flashlamp pulse as it builds from zero at about 80μs to a maximum at about 160μs. The Q-switch fires at point B and regardless of whether the laser actually produces output or not, a 'glitch' will be seen on the scope which is generated by electrical interference of the switch firing (it is an EO Q-switch and uses high voltage). This 'glitch' allows determination of the delay by using the CURSORS on the scope - set one cursor to the trigger point and the other to the switch firing point.

Experimental results, then, will consist of a table showing time delay (μs) and laser output (mJ per pulse as measured via the meter). Laser output will only occur over a small range of timing delays.

Verifying Threshold Conditions

Set the Q-switch delay to the optimal position as determined above. Now, set the power supply voltage to 700 Volts. Meter power from the 1064nm output (shutter #3) - it should be absent since the laser is well below threshold. Monitoring the laser output, slowly increase the capacitor voltage until output is found. Now, record the 1064nm output at that voltage. Increase the voltage by 50 volts, and repeat the measurements. Stop when a maximum voltage of 1.7kV is reached.

Convert each voltage into pump energy using the equation E = 0.5 * C * V2 where E is the energy stored in the capacitor bank in Joules, C the capacitance in Farads, and V the voltage across the bank in Volts. The main capacitor is rated at 2μF. Plot optical pulse energy (J) on the y axis, against pump energy (J) on the x axis.

Verify: (a) the laser threshold condition (Csele, section 4.8) and (b) the linearity of laser output after threshold is reached. Also research, then compute, slope efficiency of this laser.

Plot both the theoretical output power available at any time t (which is proportional to ΔN) from Part A and the experimental curve together on the same graph. Normalize the theoretical output so that the peak matches that of the experimental results allowing easy comparison (W is in arbitrary units - keep a common "W" term as a single cell in the spreadsheet allowing easy scaling of results, example $B$5).

Identify the thresholds of lasing (both sides of the pump curve) on the graph.

Finally, knowing the optical parameters of the laser (6*115mm YAG rod, 100%HR, and 90%OC), compute gth, then g0 based on the maximum value for inversion as determined by the model (since gain is proportional to ΔN). Calibrate the entire vertical axis of the model from Part A (originally in arbitrary units) as GAIN in units of m-1.

Developing the Convolution Model

Develop a convolution model similar to that outlines in Laser Modeling which computes the gain (ΔN) as a function of time. From theory, we know that two factors affect the population of the upper-level, input from optical pumping (WNGND) and output due to decay (-AijNULL).

Write a spreadsheet to perform a numerical integration assuming a Δt of at least 10μs. Each successive term contains the current pumping input as well as multiple decay terms from each of the previous terms. Consider the example shown in which the following data was collected:

T=0 (start of pulse) Pumping_Intensity=0
T=25                 Pumping_Intensity=75
T=50                 Pumping_Intensity=280

In this example Δt = 25μs and we compute the population of the upper-lasing level (NULL) at any discrete time by adding the current population input (from pumping) with the decayed populations of each previous interval - in other words at T=25μs the population is simply W*75 (Where W is the pumping efficiency factor and is quite arbitrary in this analysis). At T=50μs the population is W*280 (the input term) plus the decay of the previous T=25 term at 25μs decay. At T=75μs the population is the input of the current term (pumping) plus decay of the T=25μs term at 50μs and the decay of the T=50μs term at 25μs.

We can compute NULL at any time T by solving the rate equation for spontaneous emission (see Chapter 4 and 5 of Fundamentals of Light Sources and Lasers by Csele) to yield N(t)=N0e-t/τ where τ is simply 1/A32 for the transition involved (FLL section 5.10).

The finer the granularity (smaller Δt) the closer the simulation approaches a continuum however the addition of each successive term means a larger spreadsheet. At an infinitely narrow Δt, the solution becomes that of the calculus approach (i.e. an integration of the pump pulse). It will be shown in the lectures how to utilize a granularity of 0.2μs - the granularity provided by the oscilloscope.

... and be sure to read chapter 6 as it contains a simplification to the basic model that will make formulating the spreadsheet very easy!

Lab Report

Hand in the following ...

    For EACH value of capacitor energy (low and high) ...
  1. A shot of the oscilloscope output annotated to show calibrated axes (time in units of seconds) with origins (0,0) identified
  2. A printout of the first few lines of the spreadsheet showing terms at the beginning of the flashlamp pumping pulse (as the pulse builds in intensity, not "zero" as the first few time intervals will clearly show). Cell references ("ABC" columns and "123" rows) must be visible on the printout. Columns must be labelled, with one column "ΔN / Gain" and another "Pumping Intensity" with both columns visible in the printout (as well as the column labels). In a nutshell: your output must show at least a few columns which demonstrate the exponential decay nature of the atomic populations. On a separate page, detail the formulae used in the first few rows of one of the shown columns (just cut and paste formulae from three or four consecutive rows to show how the exponential decay is calculated ... cell references and all). The formula for the "@sum" column must also be shown. Since the first few rows will be zero, you may omit these in the printout and just print the portion of the spreadsheet of interest showing where the pumping pulse is active.

    The model requires a MINIMUM granularity of 10μs.

  3. A graph of the predicted output from the spreadsheet showing ΔN (in arbitrary units) vs. time (in μs). On the SAME graph (on a secondary axis) plot the flashlamp pump pulse (the maxima of the flashlamp pulse will NOT coincide with the model output). Ensure the time axis is calibrated, and identify the time value where the maximum value of ΔN occurs.
  4. A second graph of the predicted inversion (ΔN) and the actual output energy (from experimental data of laser output in Joules/pulse vs. time delay) superimposed. Pulse output energy is an indication of available ΔN at the moment of Q-switch opening and so can be compared to theoretical ΔN computed using the model. Remember that for real output ΔN must exceed threshold levels for output so the two graphs will not look the same.
  5. Determine the threshold inversion on the graph of ΔN (where lasing begins and power output occurs) and calibrate the entire vertical axis the model in terms of gain (as outlined in the lab). Show all calculations required to do this calibration.
  6. Determine what is meant by "slope efficiency" and calculate it for this laser. Ensure units on both axes are the same (i.e. Joules:Joules)

Need a source of error to explain discrepancies between the model and the experiment? Consider that the detector used to monitor flashlamp intensity is a silicon photovoltaic cell in which photocurrent is a non-linear function of incident light intensity (to some extent).