Chapter 6 Notes

Section 6.7 outlines the characterization of a resonator based on a model in which losses are distributed throughout the length of the cavity. In chapter 4 we analyzed the gain of a ruby laser (employing an EO modulator for a Q-switch) using a simple "sum of losses" method. We revisit this laser performing the analysis using the method outlined in this section.

There are two ways to look at distributed loss: one can simply consider the loss to be distributed across the length of the rod (easiest) and one can consider the loss to be distributed across the entire cavity. For computations involving the lifetime of the photon, the later is required but for simple gain computations, consider the gain and loss as being restricted to the length of the rod alone (ref: Verdeyen, Laser Electronics {ch 9}, Prentice-Hall).

The loss from the HR is again zero, however the loss from the OC, occurring at a single point in the cavity, is distributed across the length of the rod so that:
g_OC = ln(1/0.85) / (2*7.5) = 0.0108cm^-1

Similarly, for the loss from the EO (counted TWICE during the round-trip):
g_EO = ln(1/0.772) / (2*7.5) = 0.0348cm^-1

Now, simply summing the losses results in:
g_TOTAL = g_HR + g_OC + g_ABSORPTION + g_EO = 0.0656 cm^-1

We could also have arrived at this result more directly using
g_TH = g_ABSORPTION + ln(1/(1*0.85*0.772²) / (2*7.5)

And what of compensation for the n of the rod and distribution across the entire cavity? This _is_ required for models looking at photon lifetime but not required for gain computation.

For example, the average lifetime of a photon in our laser would be:
t = 2*l_rodn_rod/c + 2*l_air/c = 5ns

Chapter 6 is concerned with laser resonators. Section 6.13 is concerned with practical resonator alignment techniques. One of the most popular techniques, used with gas lasers, is to align one optic using an autocollimator then use a rock-and-search motion to align the second optic.

An animated view through the autocollimator's beamsplitter. Visible is the plasma tube window as well as the mount for the tube itself. As the rear optic is aligned a bright spot appears in the bore of the tube (examine the center of the bore carefully in the photo) - this is the image of the lamp filament travelling through the beamsplitter and through the plasma tube, bouncing off the aligned rear optic back through the tube and reflecting off the beamsplitter to the viewer.

VIDEO: Mirror Alignment a 3.7 MB video showing the entire process of cavity mirror alignment as described in the text. An output beam in evident at the right side of the frame as the cavity is aligned.

VIDEO: Rocking the mirror a 2.1 MB video detailing the process of rocking the mirror as described in the text. The mirror is first swept in the horizontal direction then, when a flash of laser light is seen, the vertical adjustment screw is set for stable laser output (at 6 seconds into the video) at which point a beam in evident at the mirror.

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