# Lamb Dip

An interesting phenomenon that occurs in Doppler-broadened lasers (as many gas lasers are) is the Lamb Dip, which I’ll discuss in this section.

Recall that the Doppler shift is a change in the measured wavelength (frequency) due to the relative velocity of the source and the observer.  The sign of the wavelength shift depends on the sign of the relative velocity: the wavelength is shortened if the source is approaching the observer, and lengthened if the source is receding from the observer.  But the light of a laser cavity mode travels forwards and backwards between the mirror, which we’ll call the +z and -z directions.  The light source is an atom undergoing stimulated emission, and the light’s ‘observer’ is the optical cavity itself, because the optical cavity sets the optical modes (resonances).  Suppose the Fabry-Perot cavity consists of mirrors facing each other at z = 0 and z = L.  For light traveling in the +z direction, the ‘observer’ is the mirror at z = L.  For light traveling in the -z direction, the ‘observer’ is the mirror at z = 0.

The atoms of the gas within the cavity which provide the stimulated emission are moving randomly in all directions.  We are only concerned with the component of their velocity in the z direction, $v_z$, because this component will determine the Doppler shift of the light emission relative to the cavity.  The probability distribution representing the relative probability of various $v_z$ values will be centered on $v_z = 0$, which is the most likely value.  Accordingly, the peak of the Doppler-broadened lineshape $g(\nu)$ will correspond to $v_z = 0$.  Therefore, if we tune a cavity mode wavelength to the peak of the lineshape, that mode will be amplified only by a group of atoms in a very small range of velocities around $v_z = 0$.  However, if we tune a cavity mode to a wavelength slightly shorter than the peak wavelength of the gain spectrum, that mode will be amplified by two groups of atoms.  The mode’s light propagating in the +z direction (whose observer is the mirror at z = L) will be amplified by a group of atoms moving in the +z direction.  The mode’s light propagating in the -z direction (whose observer is the mirror at z = 0) will be amplified by a group of atoms moving in the -z direction.  Thus, this detuned mode will receive amplification from two groups of atoms, compared to the single group of atoms which would amplify a mode tuned to the peak.  The slightly detuned cavity has a larger fraction of the total population of atoms providing amplification to the mode.

What is the impact of this?  It effectively makes the pump more efficient, since the pump is not selective: it is pumping all of the atoms, regardless of velocity, and we have just increased the fraction of those atoms providing gain to our mode.  Therefore, it reduces the threshold pump rate $R_{th}$, since a lower pump rate is required to achieve the (fixed) threshold inversion and gain.  If we operate both a ‘perfectly tuned’ and a detuned cavity at the same pump rate, the detuned cavity will be farther above threshold, and will have higher intensity output.

The dip in output intensity when the cavity is perfectly tuned to the center frequency of the lineshape is called the Lamb Dip.  Slightly detuning in either direction (shorter or longer wavelength) increases the output intensity.  This detuning is so sensitive that it can be achieved simply by changing the temperature of the cavity.  The Lamb Dip can be used to provide feedback and frequency-stabilize the cavity.