The linewidth of a laser, especially a single-frequency laser, refers to the width of its spectrum (typically full width at half maximum, FWHM). More precisely, it is the width of the radiated electric field power spectral density, expressed in terms of frequency, wavenumber, or wavelength. The linewidth of a laser is closely related to temporal coherence and is characterized by coherence time and coherence length. If the phase undergoes an unbounded shift, phase noise contributes to the linewidth; this is the case with free oscillators. (Phase fluctuations confined to a very small phase interval produce zero linewidth and some noise sidebands.) Shifts in the resonant cavity length also contribute to the linewidth and make it dependent on the measurement time. This indicates that the linewidth alone, or even a desirable spectral shape (lineform), cannot provide the full information about the laser spectrum.
II. Laser Linewidth Measurement
Many techniques can be used to measure laser linewidth:
1. When the linewidth is relatively large (>10 GHz, when multiple modes oscillate in multiple laser resonant cavities), it can be measured using a traditional spectrometer employing a diffraction grating. However, it is difficult to obtain high frequency resolution using this method.
2. Another method is to use a frequency discriminator to convert frequency fluctuations into intensity fluctuations. The discriminator can be an unbalanced interferometer or a high-precision reference cavity. This measurement method also has limited resolution.
3. Single-frequency lasers typically use a self-heterodyne method, which records the beat between the laser output and its own frequency after offset and delay.
4. For linewidths of several hundred hertz, traditional self-heterodyne techniques are impractical because they require a large delay length. A cyclic fiber loop and a built-in fiber amplifier can be used to extend this length.
5. Very high resolution can be achieved by recording the beats of two independent lasers, where the noise of the reference laser is much lower than that of the test laser, or their performance specifications are similar. A phase-locked loop or calculation of the instantaneous frequency difference based on mathematical records can be used. This method is very simple and stable, but requires another laser (operating near the test laser's frequency). If the measured linewidth requires a wide spectral range, a frequency comb is very convenient.
Optical frequency measurements often require a specific frequency (or time) reference at some point. For narrow-linewidth lasers, only a single reference beam is needed to provide a sufficiently accurate reference. Self-heterodyne techniques obtain a frequency reference by applying a sufficiently long time delay to the test setup itself, ideally avoiding temporal coherence between the initial beam and its own delayed beam. Therefore, long optical fibers are typically used. However, due to stable fluctuations and acoustic effects, long fibers introduce additional phase noise.
When 1/f frequency noise is present, linewidth alone cannot fully describe the phase error. A better approach is to measure the Fourier spectrum of the phase or instantaneous frequency fluctuations and then characterize it using the power spectral density; noise performance indicators can be referenced. 1/f noise (or the noise spectrum of other low-frequency noise) can cause some measurement problems.
III. Minimizing Laser Linewidth
Laser linewidth is directly related to the laser type. It can be minimized by optimizing the laser design and suppressing external noise influences. The first step is to determine whether quantum noise or classical noise is dominant, as this will affect subsequent measurements.
When the intracavity power is high, the resonant cavity loss is low, and the resonant cavity round-trip time is long, the quantum noise (mainly spontaneous emission noise) of the laser has a small impact. Classical noise can be caused by mechanical fluctuations, which can be mitigated by using a compact, short laser resonator. However, length fluctuations can sometimes have a stronger effect in even shorter resonators. Proper mechanical design can reduce coupling between the laser resonator and external radiations, and also minimize thermal drift effects. Thermal fluctuations also exist in the gain medium, caused by pump power fluctuations. For better noise performance, other active stabilization devices are needed, but initially, practical passive methods are preferable. The linewidths of single-frequency solid-state lasers and fiber lasers are in the 1-2 Hz range, sometimes even below 1 kHz. Active stabilization methods can achieve linewidths below 1 kHz. The linewidths of laser diodes are typically in the MHz range, but can be reduced to kHz, for example, in external cavity diode lasers, especially those with optical feedback and high-precision reference cavities.
IV. Problems Arising from Narrow Linewidths
In some cases, a very narrow beamwidth from the laser source is not necessary:
1. When the coherence length is long, coherence effects (due to weak parasitic reflections) can distort the beam shape. 1. In laser projection displays, speckle effects can interfere with surface quality.
2. When light propagates in active or passive optical fibers, narrow linewidths can cause problems due to stimulated Brillouin scattering. In such cases, it is necessary to increase the linewidth, for example, by rapidly dithering the transient frequency of a laser diode or optical modulator using current modulation. Linewidth is also used to describe the width of optical transitions (e.g., laser transitions or some absorption characteristics). In the transitions of a stationary single atom or ion, the linewidth is related to the lifetime of the upper energy state (more precisely, the lifetime between the upper and lower energy states), and is called the natural linewidth. The motion (see Doppler broadening) or interaction of atoms or ions can broaden the linewidth, such as pressure broadening in gases or phonon interactions in solid media. If different atoms or ions are affected differently, non-uniform broadening can occur.