BATP9401 Laser Systems - Time-Domain Modelling Lab

BATP9401 Laser Systems

Modelling a Q-Switched Flashlamp-Pumped Laser

Introduction

In this lab, a model will be developed for the time-domain dependency of the gain of a solid-state YAG laser - a Quantel 660 laser as used for this experiment. The flashlamp is fired and inversion allowed to build until the Q-switch is opened at some time later - the energy of the resulting pulse is an indication of the inversion at that point. The flashlamp pulse varies in time and so inversion builds at a variable rate ... inversion is also lost over time due to natural decay of the ULL t. It is expected that the inversion builds to a maximum then decays (as the pump intesity does as well) - firing the Q-switch at this maximum value of DN will result in an optimized pulse energy from the laser. Were this a CW arc-lamp or diode pumped YAG laser, one would expect the inversion to build (exponentially, and asymptotically) towards a maximum value then stabilize at that value until the Q-switch is fired - this model is also part of the lab.

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.

PreLab

Read chapter 12 in Fundamentals of Light and Lasers by Csele on Solid-state lasers
Read the SOP for the Quantel 660 YAG laser on this site.
Read through this lab

The Experiment

DANGER: 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!

Setup:

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 mounted in a special 1000:1 attenuator. The attenuator uses a ceramic plate to scatter the intense pulse before it passes to the sensitive silicon detector. Put the meter on the 2mW full-scale setting and readings will now be in watts (2 W full scale). 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 pyrometer, 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 100ms to determine the pulse energy and to about 50ms to determine the actual Q-Switch delay (see below).

As per the SOP, ensure cooling water is turned ON and start the laser. Set the power supply voltage to 1.2kV. Operate the laser in MANUAL mode pressing the CHARGE and FIRE buttons sequentially to fire the laser manually and ensure the output beam strikes the power meter.

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 new oscilloscopes feature a front-panel USB connector allowing a screenshot to be saved to a USB key simply by pressing the Print button. This data (pumping intensity with time) will be used for the model of the laser.

Now, set the delay to 300ms and fire the laser at 10 pps (the pulse energy is hence the power output, in watts, divided by ten). Note that as the DELAY is varied, the power output also varies. Set the delay to be so early that the output is zero. Now, increase the delay at periodic increments of about 25ms 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).

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 80ms to a maximum at about 160ms. 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 (ms), laser output (mJ per pulse as measured via the power meter), and pumping intensity (mV used as an arbitrary unit). Laser output will only occur over a small range of timing delays.

Part B: 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 fromm 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 1.3kV 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 2mF. 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.

The Model

Develop a model for comparison which computes the gain (DN) as a function of time. From theory, we know that two factors affect the population of the upper-level, input from pumping (WN₁) and output due to decay (-A_ijN_ULL).

Write a spreadsheet to perform a numerical integration assuming a dt of at least 20ms. 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 Dt = 25ms and we compute the population of the upper-lasing level (N_ULL) 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=25ms the population is simply W*75 (Where W is the pumping efficiency factor and is quite arbitrary in this analysis). At T=50ms the population is W*280 (the input term) plus the decay of the previous T=25 term at 25ms decay. At T=75ms the population is the input of the current term (pumping) plus decay of the T=25ms term at 50ms and the decay of the T=50ms term at 25ms.

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

The finer the granularity (smaller Dt) the closer the simulation approaches a continuum however the addition of each successive term means a larger spreadsheet.

Plot both the theoretical output power available at any time t (which is proportional to DN) 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 threshold of lasing on the graph.

Lab Report

Hand in the following ...

A shot of the oscilloscope output annotated to show calibrated axes (time and pumping intensity) with origins identified
A table of the raw flashlamp intensity data (time, pumping intensity)
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). Columns must be labelled, with one column "DN / Gain".
A graph of both the predicted output (from the spreadsheet, DN vs. time) and the actual output energy (from experimental data of laser output in Joules/pulse vs. time) superimposed
Modify your model for a CW laser - assume a 'square' pumping pulse which rises from zero to some arbitrary power instantly and stays at that power. Using the same W factor as the experiment, determine the constant pumping power required to reach threshold - compare this to the threshold found experimentally.
Show the data collected for the threshold condition experiment and results (a graph) which verify the relationships in the text. Show any calculations required (and explain why/how they are used).
Determine what is meant by "slope efficiency" and calculate it for this laser.

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).