The term "line width" refers to the width of the laser's spectral line in the frequency domain. This width is usually quantified by the full width at half maximum (FWHM) of the spectrum, as shown in the figure.

　　Schematic diagram of laser line width (full width at half maximum)

　　The generation of line width is mainly affected by external factors such as spontaneous radiation of excited atoms or ions in the laser, phase noise, mechanical vibration of the resonant cavity, and temperature jitter. The smaller the line width value, the higher the purity of the spectrum, that is, the better the monochromaticity of the laser. Lasers with such characteristics usually have extremely small phase or frequency noise and very small relative intensity noise. At the same time, the smaller the line width value of the laser, the stronger the corresponding coherence, which is manifested as an extremely long coherence length.

　　The so-called narrow linewidth laser is to limit the number of longitudinal modes that start in the gain spectrum through wavelength selectors such as tunable filters, F-B filters, and Bragg gratings, so that only a few longitudinal modes that meet specific conditions, or even only one longitudinal mode, can oscillate. The output light of narrow linewidth fiber lasers has extremely high temporal coherence and extremely low phase noise, making them important applications in high-resolution interferometers, coherent communications, fiber optic sensing, and laser radar.

　　For example, the output linewidth of an Nd:YAG laser without longitudinal mode selection is usually in the order of hundreds of GHz, and its coherence length is only a few millimeters; through longitudinal mode selection, it is relatively easy to achieve a narrow linewidth output of hundreds of MHz, and the coherence length can be increased to the order of meters. Nowadays, people have obtained extremely narrow linewidth output of sub-Hz level through Brillouin lasers, and its theoretical coherence length has reached an astonishing hundreds of thousands of kilometers. Therefore, the above advantages make narrow linewidth lasers very popular in scientific research and many application fields.

　　Narrow linewidth laser implementation and application

　　Limited by the inherent gain linewidth of the laser working material, it is almost impossible to directly achieve the output of narrow linewidth lasers by relying on traditional oscillators themselves. In order to achieve narrow linewidth laser operation, it is usually necessary to use filters, gratings and other devices to limit or select the number of longitudinal modes in the gain spectrum, increase the net gain difference between the longitudinal modes, and finally have a few or even only one longitudinal mode oscillation in the laser resonant cavity. In this process, it is often necessary to control the impact of noise on laser output, and minimize the spectral line broadening caused by vibration and temperature changes in the external environment; at the same time, it is also possible to combine the analysis of the phase or frequency noise spectral density to understand the source of noise and optimize the design of the laser, so as to achieve stable narrow linewidth laser output.

　　Next, let's take a look at the implementation methods of narrow linewidth operation of several different types of lasers.

　　1) Semiconductor lasers

　　Semiconductor lasers have the advantages of compact size, high efficiency, long life and economical affordability.

　　The Fabry-Perot (F-P) optical resonator used in traditional semiconductor lasers generally has multi-longitudinal mode oscillation, and the output linewidth is relatively wide. In order to obtain narrow linewidth output, it is necessary to increase optical feedback.

　　Distributed feedback (DFB) and distributed Bragg reflection (DBR) are two typical internal optical feedback semiconductor lasers. Their structures and output spectra are shown in Figure 5. Since the grating has a small pitch and good selectivity for wavelength, it is easy to achieve stable single-frequency narrow linewidth output. The main difference between the two structures lies in the position of the grating: the DFB structure usually distributes the periodic Bragg grating throughout the resonant cavity, and the DBR resonant cavity is usually composed of a reflective grating structure integrated on the end face and a gain region. In addition, DFB lasers use buried gratings with low refractive index contrast and low reflectivity, while DBR lasers use surface gratings with high refractive index contrast and high reflectivity. Both structures have a large free spectral range and can perform wavelength tuning without mode hopping within a few nanometers. Compared with DFB lasers, DBR lasers have a wider tuning range.

Different structures of semiconductor lasers

In addition, the external cavity optical feedback technology that uses external optical elements to feedback and select the frequency of the output light of the semiconductor laser chip can also achieve narrow linewidth operation of semiconductor lasers.

　　2) Fiber lasers

　　Fiber lasers have high pump conversion efficiency, good beam quality, and high coupling efficiency. They are a hot topic in the current laser field. In the context of the information age, fiber lasers are compatible with the current fiber communication systems on the market. Single-frequency fiber lasers with narrow linewidth, low noise, and good coherence have become one of the important directions of their development.

　　Realizing single longitudinal mode operation is the core of fiber lasers to achieve narrow linewidth output. Single-frequency fiber lasers can usually be divided into DFB type, DBR type, and ring cavity type according to the structure of the resonant cavity. Among them, the working principles of DFB and DBR single-frequency fiber lasers are similar to those of DFB and DBR semiconductor lasers.

　　As shown in the figure above, DFB fiber laser writes distributed Bragg grating into the optical fiber. Since the working wavelength of the oscillator is affected by the fiber period, the longitudinal mode selection can be achieved through the distributed feedback of the grating; DBR laser usually forms a laser resonant cavity with a pair of fiber Bragg gratings, and the selection of its single longitudinal mode is mainly performed by a narrow-band low-reflectivity fiber Bragg grating. However, the ring cavity structure is prone to mode hopping due to its usually long resonant cavity, complex structure, and lack of effective frequency discrimination mechanism, making it difficult to work stably and for a long time under a constant longitudinal mode.

　　Two typical linear structures of single-frequency fiber lasers

　　3) Solid-state lasers

　　The world's first ruby ​​laser in 1960 was a solid-state laser, which is characterized by high output energy and a wide wavelength coverage range. The unique spatial structure characteristics of solid-state lasers make it more flexible in the design of narrow linewidth output. The current implementation methods mainly include short cavity method, unidirectional ring cavity method, intracavity standard tool method, torsion pendulum cavity method, volume Bragg grating method and seed injection method.

　　Several typical methods for achieving single longitudinal mode operation of solid-state lasers

　　The above figure shows the structures of several typical single longitudinal mode solid-state lasers. (a) is the working principle of single longitudinal mode selection based on intracavity FP etalon, that is, using the narrow linewidth transmission spectrum of the etalon to increase the loss of other longitudinal modes, so that other longitudinal modes are filtered out in the mode competition process due to their low transmittance, thereby achieving single longitudinal mode operation. In addition, by changing the longitudinal mode interval by controlling the angle and temperature of the FP etalon, a certain range of wavelength tuning output can be obtained. (b) and (c) are non-planar ring oscillator (NPRO) and torsion wiggling cavity method for obtaining single longitudinal mode output. Their working principle is to make the light beam propagate in a single direction in the resonant cavity, effectively eliminating the uneven spatial distribution of the inversion particle number in the ordinary standing wave cavity, thereby avoiding the influence of the spatial hole burning effect and achieving single longitudinal mode output. The mode selection principle of the volume Bragg grating (VBG) method is similar to the semiconductor and fiber narrow linewidth lasers mentioned above, that is, by using VBG as a filter element, based on its good spectral selectivity and angle selectivity, the oscillator can oscillate at a specific wavelength or band to achieve the effect of longitudinal mode selection, as shown in (d).

　　At the same time, people can combine several longitudinal mode selection methods as needed to improve the longitudinal mode selection accuracy, further narrow the linewidth, or increase the mode competition intensity by introducing nonlinear frequency conversion and other means, so as to expand the output wavelength of the laser while obtaining narrow linewidth operation, which is difficult for semiconductor and fiber lasers to do.

　　4) Brillouin laser

　　Brillouin laser is a technology based on stimulated Brillouin scattering (SBS) effect to obtain low noise and narrow linewidth output. Its principle is to generate Stokes photons with a certain frequency shift through the interaction between photons and the acoustic wave field inside the material, and continuously amplify them within the gain bandwidth.

　　The figure below shows the energy level diagram of SBS conversion and the basic structure of Brillouin laser. Due to the low vibration frequency of the acoustic wave field, the Brillouin frequency shift of the material is usually only 0.1-2 cm-1. Therefore, when using 1064 nm laser as pump light, the wavelength of the Stokes light generated is often only about 1064.01 nm, but this also means that its quantum conversion efficiency is extremely high (theoretically up to 99.99% or more). In addition, since the Brillouin gain linewidth of the medium is usually only in the MHz-GHz range (the Brillouin gain linewidth of some solid media is only about 10 MHz), which is much smaller than the gain linewidth of the laser working material in the hundreds of GHz range, the Stokes light excited in the Brillouin laser can show obvious spectral narrowing after multiple amplifications in the cavity, and its output linewidth can be several orders of magnitude narrower than the pump linewidth. At present, Brillouin lasers have become a hot topic in the field of photonics research, and there have been many reports on extremely narrow linewidth outputs in the Hz and sub-Hz range.

　　SBS and Brillouin laser working principle

　　In recent years, Brillouin devices with waveguide structures have emerged in fields such as microwave photonics, and have developed rapidly in the direction of miniaturization, high integration and higher resolution. In addition, space-operated Brillouin lasers based on new crystal materials such as diamond have also entered people's field of vision in the past two years. They have innovatively broken through the power and cascade SBS bottlenecks of waveguide structures, increasing the power of Brillouin lasers to 10 W, laying the foundation for expanding their applications.

　　As humans continue to explore cutting-edge knowledge, narrow-linewidth lasers have become an indispensable key tool in scientific research with their excellent performance. For example, the laser interferometer LIGO for gravitational wave detection uses a single-frequency narrow-linewidth laser with a wavelength of 1064 nm as a seed source, and the linewidth of its seed light is within 5 kHz. In addition, narrow-linewidth lasers with tunable wavelength and no mode hopping also show great application potential, especially in coherent communications. They can perfectly meet the wavelength (or frequency) tunability requirements of wavelength division multiplexing (WDM) or frequency division multiplexing (FDM), and are expected to become the core components of the next generation of mobile communication technology.

　　In the future, the innovation of laser materials and processing technology will further promote the compression of laser linewidth, the improvement of frequency stability, the expansion of wavelength range and the increase of power, paving the way for human exploration of the unknown world.