Chapter 4 Notes

Chapter 4 is concerned with the fundamental principles of laser action including the stimulated emission process, basic rate equations (which are revisited in chapter 5 in a more thorough manner) and gain and loss in a laser. Gain may be measured through a variety of methods, two are presented here. Bear in mind that the gain figure will be a single-pass gain and, depending on probe beam power levels, may either represent an unsaturated or a saturated gain (see section 5.9 for details on saturation effects).

The same experimental setup above may be used to determine saturation parameters of the medium. By measuring the gain of the amplifier at various probe beam powers, saturated gain may be computed (see chapter 5 for details).

The second method of determining gain involved the insertion of a variable loss as seen below in which the intra-cavity beam is made visible using fog. The rotating stage under the slide is calibrated in degrees and allows precise determination of angle with respect the the laser's axis which in turn allows determination of loss using Fresnel equations. One problem with this arrangement is that an angular displacement (a translation) occurs as the slide is rotated which serves to change the optical alignment of the cavity. It is impossible in this simple experiment to isolate the effects of such a translation from the effects of the inserted loss - we simply assume that such effects are negligible. To overcome this and hence yield more precise results, Siegman (in Lasers, University Science Books) suggests the use of two contra-rotating A/R coated plates.

Remember that the results of this experiment yield the small-signal (unsaturated) gain of the amplifier, which, in an operating laser, will saturate down to the level where gain equals total losses in the system. "Excess" gain is manifested as output from the laser.

Download a Calculator (in XLS format) for the insertion loss from a glass slide. This spreadsheet allows the user to enter the value of n (index of refraction) for the glass slide and calculates both R_p and R_s. Remember to multiply the reflection by two to find total loss since the intra-cavity beam passes through two surfaces

An Undergrad laboratory in which students build a helium-neon laser with external optics and easure the gain of the laser using an inserted glass slide.

In addition to producing high-power pulses for holographic use, the Apollo-22HD dual-pulse ruby laser is also useful for demonstrating gain and loss in a laser. This laser employs an EO modulator which, unlike AO modulators, can be turned-on to any varying degree by changing the voltage applied to the device (Chapter 7: example 7.5.1). In this mode of operation they may be used as a variable intra-cavity loss in a manner similar to that outlined in chapter 4 as employed with the HeNe gas laser. In this photograph, the cover of the laser is removed and the room fogged to reveal the intra-cavity beam in the laser itself as well as the intense flash from the pumping lamps. The laser is housed in a class-10000 cleanroom facility.

The output pulse is monitored by a high-speed pin detector connected to a digital oscilloscope as the laser is fired. Scope output can be captured on a PC (as seen below) where the trigger point is set 200ms left of the display screen as seen here. This is a dual-pulse laser so the Q-switch is opened fully for the second pulse which appears in all output oscillographs at 1ms. In the test output shown below the oscillator lamp is fired at 350ms and the amplifier at 600ms. The pulses seen at those two locations are not light output but rather electrical interference created by the electronics of the laser itself when two ignitrons fire to ignite the lamp. At each of those 'lamp fire' times two pulses are evident - an initial pulse which triggers the ignitron switches and a main pulse which fires the lamp. When the ignitron switches fire, current rises rapidly with the Fourier transform of an almost vertical rise being broadband RF which is readily induced into the detector circuitry. Once the amplifier lamp has fired, the ambient light level (spontaneous emission from the rod as well as scattered light from the pumping lamp) emitted from the laser is seen to rise gently. The amplifier lamp is close to the detector and so has a great effect on it. Two pulses are also evident here where the Q-switch fires, one at 900ms and one at 1000ms corresponding to the Pockel's cell EO modulator (covered in chapter 7) opening twice during a single pumping pulse. The first pulse is a misfire and produces no laser output while the second pulse produces a sizable pulse which saturates the detector and causes a massive increase in optical output power.

The operational principles of this laser as well as an explanation of the optical layout of the laser can be found in the Standard Operating Procedures page for this laser.

In the actual experiment, the Q-switch is slowly opened from fully-closed to optimally-opened (by varying the voltage applied to the Q-switch for the first pulse) and the laser fired at various stages. The threshold gain of the rod may hence be determined by summing losses (including the loss due to the EO modulator according to equation 7.5.5).

For the sake of analysis, let us assume that laser is set as follows:

1. The master synchronizing pulse is generated at t=0
2. The oscillator lamp fires at t=240ms
3. The amplifier lamp fires at t=340ms
4. The Q-Switch opens for the first pulse at t=750ms
5. The Q-Switch opens for the second pulse at t=1000ms

In order to determine the gain of this laser using the method outlined in this chapter (in chapter 6 we shall consider another method, namely the distribution of losses), consider various losses in the laser:

• The HR
• The OC
• Scattering and absorption in the rod
• Loss at the EO modulator

Summing all losses is done by considering a round-trip through the laser. The OC and HR are counted once in a round-trip, absorption loss and the EO are counted twice (since, on a round-trip, the intra-cavity beam passed through the rod twice and through the EO modulator twice). The sum of all losses is hence (0 + 0.15 + 0.15*2 + 0.23*2) yielding a total loss of 0.91. In a single-pass through the rod, then, the gain must be half this value or 0.455. Since the rod is 7.5cm in length the gain of the rod is hence 0.061cm^-1.

It is now important to realize that 6kV is indeed below threshold, and the laser is not oscillating at this point, the laser does, however, oscillate at 7kV and so a similar computation of gain at that Q-switch voltage yields a gain of 0.046cm^-1. What we _can_ say for sure is that the actual gain of the laser is somewhere between 0.061cm^-1 and 0.046cm^-1.

This gain is considerably lower than the 'accepted' gain of 0.2cm^-1 however one will note that the gain was measured at a point only 400ms after the oscillator lamp had fired. Had one determined the gain at a later time, the rod would presumably have stored more energy and the gain figure would be considerably higher. Indeed, when a gain measurement is performed a few hundred ms later the gain is found to be in excess of 0.1cm^-1 (The exact number will not be revealed here since this laser is used for an undergraduate laboratory in which students measure the gain of the laser).

In chapter 6 the same laser will be analyzed using an alternative mathematical methodology (outlined in the chaper) in which losses are treated as if distributed across the entire laser cavity.

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