# laser spectral width vs. linewidth

I have been racking my brains over the differences between laser spectral width and something called the linewidth. The linewidth was written about in detail by Henry in 1982. The spectral width is the width at -20dB down from peak of the wavelength spectrum of the laser. I am looking at some laser data right now that is saying that laser x has 10 kHz linewidth and 60 pm spectral width. You can convert spectral width from frequency to wavelength as in this article and I have done that calculation. By that calculation, a laser with a linewidth of 10kHz should have a wavelength width of about 1x10^-6 nm, not 0.06 nm. Linewidth is often measured with self-heterodyne technique, not a spectrum analyzer. What am I missing?

• link us to the data sheet – user2963 Dec 2 '11 at 0:46

I assume you are looking at a diode laser (LD) data sheet. In practical terms, spectral width is a measure of tunability of the LD as you vary injection current and temperature. This is quite useful in experiments (say atomic physics with alkali atoms).

The linewidth is related to the phase noise of laser. It is very complicated to derive the linewidth from first principles. Agarwal is a standard reference if you wish to know more.

A practical semi-conductor LD has a typical free running linewidth of 40Mhz. This means, the uncertainty in the frequency is 40MHz. However, this entire frequency band can shift with changes in temperature and fluctuations in injection current.

This rather broad linewidth can be narrowed by optical feedback to obtain the so called external/extended cavity diode laser (ECDL). Check out this seminal paper by Weimann and Hollberg (pdf) for more information. I have built many ECDL systems from the ground up with sub-MHz linewidths. It can be quite a tricky endeavor.

Measuring the linewidth can be quite tricky. The usual direct technique is to beat the unknown laser with a known standard reference and study the beat signal. The equipment necessary is very expensive. However, you can make rough estimates from say a simple saturation spectroscopy based frequency locking setup by studying the amplitude fluctuations of the "error signal". Granted that it is crude and limited to the natural linewidth of your atomic system, but it does not need super expensive equipment or complicated electronics. There are other ways to use atomic physics (EIT, CPT resonances etc) to make reasonable estimates of laser linewidth and it all depends on what your goal is.

• Yes, the data I am looking at is for an ECDL and it is a datasheet. Thanks for the great answer! I have looked at the spectral plots for the laser (on datasheet) and the width 20 dB down from peak (power vs lambda) is indeed around 60 pm so I don't think that spectral width refers to tunability. Another point is that "reach" or "distance limit" quoted by manufacturer corresponds to a spectral width of 60 pm and that spectral width is sigmaL in equation 1 here – Ben Sprott Dec 2 '11 at 14:45
• I don't think the blog you linked to is applicable to a semi-conductor diode laser. Your link seems to be about light propagation in an optical fiber, which is a different problem altogether, unless you are referring to a fiber laser (most likely a Raman fiber laser). In a Raman laser the scattering is inelastic and hence bandwidth of such sources are very large. Coherence is built up from spontaneous emission. Check Raymer's group for papers from the 80's (6 onwards). – Antillar Maximus Dec 2 '11 at 19:04
• I am still a bit lost, though. In this paper, Agrawal defines data error rates in terms of the "spectral width"link – Ben Sprott Dec 2 '11 at 21:56
You have to convert center wavelength to frequency, then add and subtract the line width (Hz), then convert those frequencies back to wavelength, and then find the difference of the two wavelengths. This is $\Delta \nu$, or simple line width.