详情见英文版

Acronym: SHB

Definition: a distortion of the gain shape in a laser medium (or the loss spectrum in a saturable absorber medium), caused by saturation effects of a standing wave

When two counterpropagating quasi-monochromatic light waves are superimposed, they form a so-called standing-wave interference pattern, the period of which is half the wavelength. When that happens with laser light in a laser gain medium, that has two effects:

• The gain is saturated preferentially in the antinodes of the pattern. There, stimulated emission keeps the excitation of laser-active ions at a lower level. So the excitation forms a pattern with a periodic modulation.
• The resulting amplification for light with a certain wavelength (possibly deviating from the laser wavelength) depends on how its own standing-wave pattern fits to the modulated excitation of the gain medium. The total (single or double pass) gain is most strongly saturated at the laser wavelength itself, where the light has its nodes exactly in the most strongly saturated regions. Light at other wavelength experiences less gain saturation.

This can lead to a deformation of the spectral shape of the gain, i.e., a kind of inhomogeneous gain saturation.

Figure 1: Illustration of spatial hole burning in a laser crystal. A strong beam with the blue standing-wave intensity pattern saturates the gain (red curve). It experiences a more strongly reduced gain than a weaker beam with slightly longer wavelength, indicated by the green curve.

Similarly, the loss spectrum of a saturable absorber medium can obtain a dip due to spatial hole burning. That can occur e.g. in a rare-earth-doped fiber and is the basis for, e.g., the construction of an automatic tracking filter, as is sometimes used in the context of single-frequency fiber lasers.

Spatial hole burning can have various consequences for the operation of lasers:

• The effect can make it difficult to achieve single-frequency operation with standing-wave laser resonators, because the lasing mode experiences stronger gain saturation than competing non-lasing modes.
• The optical bandwidth of a free-running laser (with excitation of multiple axial modes) may be much larger when the gain medium is near an end of the laser resonator, rather than e.g. in the middle. This is because resonator modes with similar optical frequencies have strongly overlapping intensity patterns near the resonator ends, but not in the middle of the resonator. The spatial variation of the interference contrast can be easily calculated when assuming a Gaussian optical spectrum [9].
• The effective broadening of the gain spectrum (increased gain bandwidth) may allow for shorter pulses in mode-locked lasers [9].
• When spatial hole burning occurs in a saturable absorber section e.g. of a fiber laser, this effect tends to stabilize single-frequency operation [7].
• Spatial hole burning can reduce the laser efficiency, when the excitation in the nodes can not be utilized. This effect may be avoided, however, if energy migration via inter-ion energy transfer occurs.

Note that ring resonators often allow counterpropagating waves in the laser medium to be avoided and thus spatial hole burning to be eliminated. Even in standing-wave (linear) resonators, spatial hole burning can be suppressed by the use of special polarization states (→ twisted-mode technique). Also note that the hole burning effect is suppressed for lasing with a sufficiently large bandwidth. This is often the case in, e.g., mode-locked lasers; here it is obvious already in the time domain that a circulating pulse cannot overlap (interfere) with itself in the gain medium, unless the time for traveling from the gain medium to an end mirror and back again is comparable to or shorter than the pulse duration.

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