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.
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
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.
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.
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