Measuring Frequency Stability

The accepted method of measuring long-term frequency stability is to heterodyne the laser to be tested with another laser of equal or greater stability. By observing the variation of the resulting beat frequencies, the combined drift of the two lasers can be measured. The results will be no better than the sum of the two instabilities and will, therefore, provide a conservative measure of frequency drift.
In the charts below, a Melles Griot frequency-stabilized HeNe was hetrodyned with the output from a Zeeman-stabilized laser. The charts show the performance over one minute and over an eight-hour typical workday. The laser can be cycled over a 20°C temperature range without mode hopping. 

METHODS FOR SUPPRESSING AMPLITUDE NOISE AND DRIFT

Two primary methods are used to stabilize amplitude fluctua- tions in commercial lasers: automatic current control (ACC), also known as current regulation, and automatic power control (APC), also known as light regulation. In ACC, the current driving the pumping process passes through a stable sensing resistor, as shown in figure 36.13, and the voltage across this resistor is monitored. If the current through the resistor increases, the voltage drop across the resistor increases proportionately. Sensing circuitry compares this voltage to a reference and generates an error signal that causes the power supply to reduce the output current appropriately. If the current decreases, the inverse process occurs. ACC is an effective way to reduce noise generated by the power supply, including line rip- ple and fluctuations.

With APC, instead of monitoring the voltage across a sens- ing resistor, a small portion of the output power in the beam is diverted to a photodetector, as shown in figure 36.14, and the voltage generated by the detector circuitry is compared to a refer- ence. As output power fluctuates, the sensing circuitry generates an error signal that is used to make the appropriate corrections to maintain constant output.

Automatic current control effectively reduces amplitude fluc- tuations caused by the driving electronics, but it has no effect on amplitude fluctuations caused by vibration or misalignment. Auto- matic power control can effectively reduce power fluctuations from all sources. Neither of these control mechanisms has a large impact on frequency stability.

Not all continuous-wave lasers are amenable to APC as described above. For the technique to be effective, there must be a monoto- nic relationship between output power and a controllable para- meter (typically current or voltage). For example, throughout the typical operating range of a gas-ion laser, an increase in current will increase the output power and vice versa. This is not the case for some lasers. The output of a helium neon laser is very insensi- tive to discharge current, and an increase in current may increase or decrease laser output. In a helium cadmium laser, where elec- trophoresis determines the density and uniformity of cadmium ions throughout the discharge, a slight change in discharge current in either direction can effectively kill lasing action.

If traditional means of APC are not suitable, the same result can be obtained by placing an acousto-optic modulator inside the laser cavity and using the error signal to control the amount of cir- culating power ejected from the cavity.

 One consideration that is often overlooked in an APC system is the geometry of the light pickoff mechanism itself. One’s first instinct is to insert the pickoff optic into the main beam at a 45-degree angle, so that the reference beam exits at a 90-degree angle. How- ever, as shown in figure 36.15, for uncoated glass, there is almost a 10-percent difference in reflectivity for s and p polarization.

In a randomly polarized laser, the ratio of the s and p compo- nents is not necessarily stable, and using a 90-degree reference beam can actually increase amplitude fluctuations. This is of much less concern in a laser with a high degree of linear polarization (e.g., 500:1 or better), but even then there is a slight presence of the orthogonal polarization. Good practice dictates that the pickoff ele- ment be inserted at an angle of 25 degrees or less. 

 

Frequency and Amplitude Fluctuations

The output of a freely oscillating laser will fluctuate in both amplitude and frequency. Fluctuations of less than 0.1 Hz are com- monly referred to as “drift”; faster fluctuations are termed “noise” or, when talking about sudden frequency shifts, “jitter.”
The major sources of noise in a laser are fluctuations in the pumping source and changes in length or alignment caused by vibration, stress, and changes in temperature. For example, unfil- tered line ripple can cause output fluctuations of 5 to 10 percent or more.
Likewise, a 10-mrad change in alignment can cause a 10-percent variation in output power, and, depending upon the laser, a 1-mm change in length can cause amplitude fluctuations of up to 50 percent (or more) and frequency fluctuations of sev- eral gigahertz.

High-frequency noise (>1 MHz) is caused primarily by “mode beating.” Transverse Laguerre-Gaussian modes of adjacent order are separated by a calculable fraction of the longitudinal mode spacing, typically ~17 MHz in a 1-m resonator with long radius mir- rors. If multiple transverse modes oscillate simultaneously, hetero- dyne interference effects, or “beats,” will be observed at the difference frequencies. Likewise, mode beating can occur between longitudi- nal modes at frequencies of Mode beating can cause peak-to-peak power fluctuations of several percent. The only way to eliminate this noise component is to limit the laser output to a single transverse and single longitu- dinal mode.

Finally, when all other sources of noise have been eliminated, we are left with quantum noise, the noise generated by the sponta- neous emission of photons from the upper laser level in the lasing medium. In most applications, this is inconsequential. 

FREQUENCY STABILIZATION

The frequency output of a single-longitudinal-mode laser is sta- bilized by precisely controlling the laser cavity length. This can be accomplished passively by building an athermalized resonator structure and carefully controlling the laser environment to elimi- nate expansion, contraction, and vibration, or actively by using a mechanism to determine the frequency (either relatively or absolutely) and quickly adjusting the laser cavity length to main- tain the frequency within the desired parameters.

A typical stabilization scheme is shown in figure 36.11. A por- tion of the laser output beam is directed into a low-finesse Fabry-Perot etalon and tuned to the side of the transmission band. The throughput is compared to a reference beam, as shown in the figure. If the laser frequency increases, the ratio of attenuated power to reference power increases. If the laser frequency decreases, the ratio decreases. In other words, the etalon is used to create a fre- quency discriminant that converts changes in frequency to changes in power. By “locking” the discriminant ratio at a specific value (e.g., 50 percent) and providing negative feedback to the device used to control cavity length, output frequency can be controlled. If the frequency increases from the preset value, the length of the laser cavity is increased to drive the frequency back to the set point. If the frequency decreases, the cavity length is decreased. The response time of the control electronics is determined by the char- acteristics of the laser system being stabilized.

Other techniques can be used to provide a discriminant. One common method used to provide an ultrastable, long-term refer- ence is to replace the etalon with an absorption cell and stabilize the system to the saturated center of an appropriate transition. Another method, shown in figure 36.12, is used with commercial helium neon lasers. It takes advantage of the fact that, for an internal mir- ror tube, the adjacent modes are orthogonally polarized. The cav- ity length is designed so that two modes can oscillate under the gain curve. The two modes are separated outside the laser by a polarization-sensitive beamsplitter. Stabilizing the relative ampli- tude of the two beams stabilizes the frequency of both beams.

The cavity length changes needed to stabilize the laser cavity are very small. In principle, the maximum adjustment needed is that required to sweep the frequency through one free spectral range of the laser cavity (the cavity mode spacing). For the helium neon laser cavity described earlier, the required change is only 320 nm, well within the capability of piezoelectric actuators.

Commercially available systems can stabilize frequency output to 1 MHz or less. Laboratory systems that stabilize the frequency to a few kilohertz have been developed. 

The Ring Laser

The Ring Laser: The discussions above are limited to two- mirror standing-wave cavities. Some lasers operate naturally in a single longitudinal mode. For example, a ring laser cavity, (used in many dye and Ti:Sapphire lasers as well as in gyroscopic lasers) that has been constrained to oscillate in only one direction pro- duces a traveling wave without the fixed nodes of the standing-wave laser. The traveling wave sweeps through the laser gain, utilizing all of the available energy and preventing the buildup of adjacent modes. Other lasers are “homogeneously broadened” allowing vir- tually instantaneous transfer of energy from one portion of the gain curve to another. 

SELECTING A SINGLE LONGITUDINAL MODE

A laser that operates with a single longitudinal mode is called a single-frequency laser. There are two ways to force a conventional two-mirror laser to operate with a single longitudinal mode. The first is to design the laser with a short enough cavity that only a single mode can be sustained. For example, in the helium neon laser described above, a 10-cm cavity would allow only one mode to oscillate. This is not a practical approach for most gas lasers because, with the cavity short enough to suppress additional modes, there may be insufficient energy in the lasing medium to sustain any las- ing action at all, and if there is lasing, the output will be very low.
The second method is to introduce a frequency-control ele- ment, typically a low-finesse Fabry-Perot etalon, into the laser cav- ity. The free spectral range of the etalon should be several times the width of the gain curve, and the reflectivity of the surfaces should be sufficient to provide 10 percent or greater loss at fre- quencies half a longitudinal mode spacing away from the etalon peak. The etalon is mounted at a slight angle to the optical axis of the laser to prevent parasitic oscillations between the etalon surfaces and the laser cavity.
Once the mode is selected, the challenge is to optimize and main- tain its output power. Since the laser mode moves if the cavity length changes slightly, and the etalon pass band shifts if the etalon spac- ing varies slightly, it important that both be stabilized. Various mechanisms are used. Etalons can be passively stabilized by using zero-expansion spacers and thermally stabilized designs, or they can be thermally stabilized by placing the etalon in a precisely con- trolled oven. Likewise, the overall laser cavity can be passively sta- bilized, or, alternatively, the laser cavity can be actively stabilized by providing a servomechanism to control cavity length, as dis- cussed in Frequency Stabilization. 

THEORY OF LONGITUDINAL MODES

In a laser cavity, the requirement that the field exactly reproduce itself in relative amplitude and phase each round-trip means that the only allowable laser wavelengths or frequencies are given by 

where l is the laser wavelength, n is the laser frequency, c is the speed of light in a vacuum, N is an integer whose value is deter- mined by the lasing wavelength, and P is the effective perimeter optical path length of the beam as it makes one round-trip, taking into account the effects of the index of refraction. For a conventional two-mirror cavity in which the mirrors are separated by optical length L, these formulas revert to the familiar

These allowable frequencies are referred to as longitudinal modes. The frequency spacing between adjacent longitudinal modes is given by

As can be seen from equation 36.22, the shorter the laser cav- ity is, the greater the mode spacing will be. By differentiating the expression for n with respect to P we arrive at

Consequently, for a helium neon laser operating at 632.8 nm, with a cavity length of 25 cm, the mode spacing is approximately 600 MHz, and a 100-nm change in cavity length will cause a given longitudinal mode to shift by approximately 190 MHz. 

The number of longitudinal laser modes that are present in a laser depends primarily on two factors: the length of the laser cavity and the width of the gain envelope of the lasing medium. For exam- ple, the gain of the red helium neon laser is centered at 632.8 nm and has a full width at half maximum (FWHM) of approximately 1.4 GHz, meaning that, with a 25-cm laser cavity, only two or three longitudinal modes can be present simultaneously, and a change in cavity length of less than one micron will cause a given mode to “sweep” completely through the gain. Doubling the cavity length doubles the number of oscillating longitudinal modes that can fit under the gain curve doubles.
The gain of a gas-ion laser (e.g., argon or krypton) is approxi- mately five times broader than that of a helium neon laser, and the cavity spacing is typically much greater, allowing many more modes to oscillate simultaneously.

A mode oscillating at a frequency near the peak of the gain will extract more energy from the gain medium than one oscillating at the fringes. This has a significant impact on the performance of a laser system because, as vibration and temperature changes cause small changes in the cavity length, modes sweep back and forth through the gain. A laser operating with only two or three longi- tudinal modes can experience power fluctuations of 10% or more, whereas a laser with ten or more longitudinal modes will see mode-sweeping fluctuations of 2 percent or less.