# Laser linewidth measurement

January 05, 2017

Coherent detection relies on interferences between a probe laser beam and a local oscillator. Phase instabilities in the laser beam are responsible for the blurring of the interferences fringes, thus limiting the performance of coherent measurement.

## Laser linewidth

When interfering two beams split from a laser source, the fringes disappears if the delay $\tau$ between the two beams is too large. The delay $\tau = \tau_{c}$ beyond which the fringes are blurred corresponds to the typical phase stability timescale of the laser and is called the coherence time. The related distance $L_{c} = c \tau_{c}$ is the coherence length. Finally, the value $\Delta f = 1 / \tau_{c}$ is called the laser linewidth and it is used to characterize the coherence of a laser source.

Many phenomena alter the phase stability of the laser, for example the spontaneous emission which is not synchronized with stimulated emission, or noise in the DFB current driver.

## Linewidth measurement methods

Linewidth measurement methods rely on a delay introduced between the arms of an interferometer. They can be classified into short and long delays (compared to the laser coherence time) setups.

### Short delay

The following self-heterodyne setup can be used:

A short-delay is placed in one arm of a Mach-Zehnder interferometer and an acousto-optic modulator (AOM) in the other one. After demodulation of the detection interferometer output, it is possible to track the phase of the laser. This provides full information on the laser phase, from which we can derive its linewidth. This method is very precise but it requires an AOM and the signal processing is quite involved.

### Long delay

Here is a method using a long delay in a self-homodyne setup:

This method is easy to implement since no modulator is required. Also the laser phase-noise is directly visible on the spectrum analyzer.

Note that if the laser under test has a significant low-frequency relative intensity noise (RIN), a self-heterodyne technique with long delay can be used placing an AOM in an interferometer arm. The laser line shape will then be observed around a carrier at the AOM modulation frequency.

### Pros and cons

For a laser with a fairly large linewidth, a Lorentzian profile and a low RIN, the long delay method is a good choice since it is easy to setup and the results are quite straightforward to interpret.

For narrow linewidth lasers the required delay might become very long (hundreds of kilometers) and absorption in the fiber becomes a limitation (especially for non telecom wavelengths). Moreover, narrow linewidth laser often have a complex line shape (such as a Voigt profile instead of a Lorentzian) and interpretation of the power spectrum becomes difficult [1]. In this case, using the short delay technique will probably be beneficial.

## DFB linewidth measurement

Here we characterize the Koheron LD100 laser. We expect the laser to have a Lorentzian line shape and a linewidth of a few MHz. We use the following long delay self-homodyne interferometer:

A laser with a 1 MHz linewidth has a coherence length of 300 m so a 10 km delay is well above the expected laser coherence length. Though the LD100 laser integrates a 30 dB optical isolator, we add an isolation stage to ensure no disturbance. A Koheron PD100 photodetector is used at the interferometer output and the detection result feeds a spectrum analyzer.

Here are the measured spectra for various currents driving the DFB:

We are actually observing the autocorrelation of the laser line shape with itself so that the measured signal has twice the laser linewidth. In other words, the linewidth defined as the full width at half maximum of the laser line shape corresponds to the half width at half maximum of the spectrum analyzer signal. Here, when driving the laser with 50 mA the linewidth is 2.4 MHz. We also observe that the laser linewidth decreases when the current increases.

[1]: Chen X. Ultra-Narrow Laser Linewidth Measurement. PhD Thesis. Faculty of the Virginia, Polytechnic Institute and State University. Virginia, 2007.