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As far as I understood, different laser modes correspond to different transversal distributions of the electromagnetic field. Therefore, different modes must have different frequencies.

Why is it, that a laser can produce different modes? I take the HeNe-Laser as an example. The main wavelength stabilized and amplified is at $632.8\ \mathrm{nm}$. This originates simply from the neon emission.

If I would speak of different modes of the HeNe-laser, would that mean, that there occur other wavelenghts next to $632.8\ \mathrm{nm}$ ? How is this possible? I only understand what a mode is in an optical cavity: It is simply an allowed resonance frequency of the cavity, e.g. a standing wave.

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  • $\begingroup$ The cavity may support one or more allowed modes at 632.8 nm. Some other modes may occur at other frequencies. But, you must keep separate the allowed transitions (and their width) of the lasing medium from the allowed (propagating) optical modes of the cavity. $\endgroup$ – Jon Custer Sep 6 '16 at 15:24
  • $\begingroup$ I might have misunderstood this connection pointed out by you. How can I calculate or find out the allowed modes at a certain wavelength? The modes are only a function of the lenght of the cavity. $\endgroup$ – EpsilonDelta Sep 6 '16 at 15:39
  • $\begingroup$ @EpsilonDelta what do you mean "at a certain wavelength"? The wavelengths will be different, of course, as will the frequencies. Your description of what a mode is is accurate. A laser is an optical cavity with a couple extra bells and whistles. $\endgroup$ – hobbs Sep 6 '16 at 17:48
  • $\begingroup$ All of the above seems to be related to longitudal modes. But there are also transverse modes. $\endgroup$ – Jarosław Komar Sep 7 '16 at 15:29
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The key point that I think you may have missed is that the emission line of the transition used to generate photons in any laser has a finite width. In the case of a helium neon laser, 632.8nm refers to the wavelength where the emission is brightest, but it doesn't mean that all the light comes at exactly that wavelength. There's a spectrum with a peak at that wavelength, but the peak has some width meaning that some light is emitted in a band of wavelengths to either side of 632.8nm.

On top of that spectrum, you have the optical cavity modes which act like a filter. The spacing of the longitudinal modes depends on the length of the cavity, and the spectrum of those modes looks like a comb. The peaks of that comb spectrum will generally be narrower than the laser emission peak, and the result is that where the peaks of the comb overlap with the laser emission peak, light at that wavelength will be allowed through.

Depending on the wavelength of a particular laser and the length of the cavity, it's possible to design lasers with multiple cavity modes falling within the emission peak, resulting in light with several distinct frequencies, or you can have lasers with only a single cavity mode falling within the emission peak. These "single mode" lasers are useful in some circumstance because they emit light in a narrow band of wavelengths, and the exact wavelength can even be tuned by varying the propertied of the cavity slightly so as to shift the cavity mode within the emission peak. This can be done either by carefully designing and manufacturing a cavity with a particular length, or for some types of laser it can be done dynamically by heating the laser material to change the length and/or refractive index.

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  • $\begingroup$ That helped a lot, thanks. So is the frequency emitted always the one of the longitudal mode, if the emission peak overlaps with it? Or does the emitted frequency solely depend on the gain medium, e.g. the frequency of the transition in the medium? Let's, to clarify, suppose the longitudinal mode lies within the emission peak, but those two peaks are slightly shifted, will then the frequency of the longitudinal mode be emitted? $\endgroup$ – EpsilonDelta Sep 8 '16 at 12:24
  • $\begingroup$ I think an example would help. According to Wikipedia, the bandwidth of a HeNe laser is 0.002nm, so if the peak is at 632.8nm, that means that, if we ignore the effect of the cavity modes, it emits in a narrow range of wavelengths between 632.799nm and 632.801nm. Now, suppose there happens to be a cavity mode with a peak at 632.8005nm. The cavity mode will also have a bandwidth of its own, but lets say it's very narrow so I can ignore its width. What will happen is that the cavity mode will only allow through the light at 632.8005nm. $\endgroup$ – MarkH Sep 8 '16 at 15:05
  • $\begingroup$ So, inside the laser gain medium, you have the full spectrum from 632.799nm to 632.801nm. But only the part of that which overlaps with a cavity mode is allowed to escape. $\endgroup$ – MarkH Sep 8 '16 at 15:07

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