Chirped pulse amplification technology can be broken down into a combination of the dispersion management technology of broadband pulses and the amplification technology of stretched pulses. Laser amplification technology has been thoroughly studied when the laser was invented. Its principle is not essentially different from that of laser oscillators. The use of dispersion to broaden and match the compression of pulses is the soul of CPA technology. [Note: Dispersion management here refers to temporal dispersion, not spatial dispersion. 】
Take the pioneering work of G. Mourou and D. Strickland in Optics Communications [1] as an example: The pulse output from the mode-locked laser is stretched to 300ps through a 1.4-kilometer-long optical fiber. After regeneration and amplification, it enters the grating to compress the optical system. The fiber material itself provides positive dispersion (long wave speed is faster than short wave speed) to broaden the broadband pulse, and the grating pair structure provides matching negative dispersion (long wave speed is faster than short wave speed) to compress the pulse.
Figure 1: Optical path design in the original reference document of CPA technology[1]
In the CPA laser system, the so-called dispersion management technology is to ensure that the sub-unit that provides positive dispersion and the sub-unit that provides negative dispersion can be completely matched, so as to obtain the narrowest pulse width and optimized pulse time quality at the end of the laser system. It is indeed admirable that Mr. Mourou could come up with a great CPA idea at that time and have it verified experimentally. However, if you still insist on adopting this specific dispersion management method today, you will be criticized because it has a big flaw: the third-order dispersion of the optical fiber material and the third-order dispersion of the grating compressor have the same sign and cannot cancel each other. If the final compressed pulse is carefully considered, its time quality will definitely be unsatisfactory.
This article is based on the principle of technical introduction and avoids entering into cumbersome mathematical formulas. First, several basic principles are given:
1. Under the condition of zero dispersion, the wider the spectrum, the narrower the pulse;
2. Under certain conditions of dispersion, the wider the spectrum, the wider the pulse is stretched;
3. Under the condition that the spectral width is constant, the greater the dispersion amount, the wider the pulse is stretched;
4. When the bandwidth (spectral range) is constant and the phases of each wavelength component are consistent, the corresponding pulse becomes the Fourier transform limit pulse. This is the ultimate goal pursued by dispersion management of ultrafast laser systems.
The spectral phase can be expanded by Taylor series:
In this series expansion, φ’’ (w0) is called group velocity dispersion GVD, or directly called second-order dispersion, φ’’’ (w0) is called third-order dispersion, and the same can be said for other orders of dispersion. CPA system dispersion management needs to at least ensure that the final second-order and third-order net dispersion are zero.
The following will introduce several typical dispersion management technologies and give corresponding commercial lasers.
1. Combination of dispersion block material and prism pair
Figure 2: Dispersion compensation using dispersive materials and prism pairs
Different wavelengths pass through optical materials, and due to their different refractive indexes, the speed is also different, thus forming a dispersion effect. Broadband femtosecond pulses have a broadening effect in time. In the near-infrared band, most optical materials have positive dispersion characteristics, that is, the speed of long wavelengths is faster. In general, the amount of dispersion produced by optical materials is relatively small. Taking fused quartz as an example, the second-order dispersion provided by a length of 10mm is 360fs2, and the third-order dispersion is 275fs3.
The dispersion compensation device paired with the optical material is generally a prism pair [2]. After the broadband light passes through the first prism pair, spatial angular dispersion is generated. Different wavelength components have different propagation distances in the second prism. The long wave speed is slow and the short wave speed is fast. Therefore, it conforms to the characteristics of destructive dispersion of each order of the material. By designing the material, spacing, insertion amount and other parameters of the prism, the purpose of compensating the positive dispersion of the material is achieved.
Before the invention of chirped mirrors, commercial Ti:sapphire femtosecond lasers all used this dispersion compensation combination, and later Femtolasers' Ti:sapphire amplifiers also adopted this method. This combination is only suitable for systems with small dispersion. For stretching amounts above 10ps, the entire system will be very large, affecting stability.
2.Material + chirped mirror
Figure 3: Dispersion compensation using dispersive materials and chirped mirrors
If the residual dispersion generated by the system is relatively small, in addition to the prism pair, a chirped mirror can be used for dispersion compensation. The principle of the chirped mirror was also introduced in the previous official article. For review, please refer to the article [Principles and Applications of Chirped Mirrors].
Chirped mirror[3] pairs are often used in ultrafast oscillators to accurately compensate for small intra-cavity material dispersions (it can be combined with a prism pair or a wedge pair). Chirped mirrors are also commonly used in the supercontinuum generation process based on ultrafast lasers. After ultrashort laser pulses pass through the supercontinuum material, the spectrum broadens, and chirped mirrors need to be used to compress the pulses to a shorter pulse width.
A commercial laser that uses this dispersion compensation scheme is the Femtolasers (now part of Spectra Physics) Ti:sapphire laser oscillator.
3.Martinez stretcher + grating pair
Figure 4: Dispersion compensation using Martinez-type stretchers and grating pairs
If the energy of the femtosecond laser system is to be further increased, from the perspective of suppressing nonlinear effects and preventing damage, higher requirements are placed on the pulse broadening. For example, the pulse broadening of mJ-level systems generally requires at least tens of picoseconds, and the pulse width of hundreds of picoseconds is better, because a wider pulse width corresponds to a higher damage threshold.
The most commonly used one at present is the Martinez type stretcher [4]. Its structure is shown in Figure
3. It uses a grating as a dispersion element, cooperates with an imaging system and a beam climber, and finally forms a system that provides positive dispersion. Through appropriate design, the pulse can be broadened to the order of hundreds of picoseconds.
The combination of a grating pair and a climber [5] can provide an equal amount of negative dispersion, ultimately compressing the pulse back to the femtosecond scale.
Taking advantage of the powerful light splitting ability of the grating, both the Martinez stretcher and the grating pair compressor can provide dispersion amounts of ~106fs2.
Typical commercial laser systems using this dispersion management combination are Ti:sapphire laser amplifiers from Coherent and Spectrum Physics.
4.Offner expander + grating pair
Figure 5: Dispersion compensation using Offner stretcher and grating pair
In the Martinez stretcher, a concave mirror is used for imaging. Since the beam is spatially expanded by a grating into a strip, aberration is inevitable. The Frenchman G. Cheriaux introduced the Offner telescope system [6], which is a combination of concave mirrors and convex mirrors, which reduces the aberration. At the same time, under the same size conditions, the Offner stretcher can provide a larger amount of dispersion, thereby broadening the pulse to the ns level, and is suitable for dispersion management of terawatt and petawatt systems.
The dispersion management method of the grating pair is also used to complete the pulse compression function.
Typical commercial laser systems using this dispersion management combination are titanium sapphire laser amplification systems from Amplitude and Thales.
5.CFBG+CVBG [7,8]
Figure 6: Dispersion compensation using CFBG and VBG
Due to its direct semiconductor pumping characteristics and extremely excellent thermal properties, Yb laser has become a new favorite in scientific research and industrial applications. Compared with titanium sapphire lasers, its bandwidth is narrower, so it can be broadened using a chirped fiber Bragg grating (CFBG) with a simpler structure and more complex process. Currently, the most mature product is the Canadian Teraxion company, which can customize and fine-tune various levels of dispersion according to specific application scenarios. The corresponding simplest dispersion matching unit is the chirped volume Bragg grating (CVBG), which has an extremely compact structure and a centimeter-level size that can greatly reduce the size of the system.
However, it should be noted that the degree of freedom of dispersion adjustment of this combination is almost zero, so designers need to accurately control the dispersion of each order of the system, otherwise the pulse will be incompressible.
The commercial laser corresponding to this combination is the YLPF series of femtosecond fiber laser systems recently launched by IPG.
6.CFBG+ grating pair
Figure 7: Dispersion compensation using CFBG and transmission grating pairs
Although the above-mentioned CFBG+CVBG combination is compact, it loses the flexibility of adjustment. Optigrate, the manufacturer of CVBG, was acquired by IPG, which basically limits the procurement channels for industrial femtosecond lasers.
One way to solve the problem of flexibility and procurement constraints is to use a combination of CFBG and transmission grating pairs, using the two degrees of freedom of the grating's pitch and angle to fine-tune the pulse width.
In fiber lasers, in order to avoid nonlinear effects, the pulse width needs to be broadened to the ns level, which requires a huge increase in the distance between grating pairs, resulting in a huge volume. This can explain that general high-power femtosecond fiber lasers are not as compact as we imagine.
According to preliminary understanding, ultrafast lasers from TRUMPF, Amphos, Amplitude and other companies use this dispersion compensation combination, but the accuracy needs to be verified.
7. Material + prism pair[9]
Figure 8: Dispersion compensation using dispersive materials and prism pairs
At the beginning of this article, it was mentioned that the third-order dispersion between the optical fiber and the grating pair is mismatched. If you still want to use compact dispersion materials for broadening, you can use the technology of the grating pair for dispersion compensation. The so-called prism pair, as the name suggests, is a combination of a grating and a prism. By controlling the optical and physical parameters of the grating and the prism, a combination of negative second-order dispersion and negative third-order dispersion can be achieved to perfectly match the material dispersion.
Commercial laser systems using this dispersion combination are several amplifiers from KMLabs in the United States. The French company Faslite holds a patent for transmissive prism pairs and provides customized dispersion compensation solutions.
[Conclusion] In the CPA laser system, there will always be imperfect dispersion management. The system will have some high-order dispersion remaining. At this time, a dispersion compensation artifact is needed. This is the acousto-optical programmable dispersion filter DAZZLER from the French company Faslite. This artifact cooperates with the pulse measurement Wizzler to form a feedback control system, which can obtain perfect Fourier transform limit pulses. The principle of Dazzler has been introduced in detail in the previous article of this official account and will not be repeated here.
Figure 9: Fastlite Dazzler+Wizzler combination achieves perfect pulse quality
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References
[1] Optics Communications, Volume 56, Issue 3, 1 December 1985, Pages 219-221
[2] R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett. 9, 150-152 (1984)
[3] "Chirped multilayer coatings for broadband dispersion control in femtosecond lasers" by R. Szipocs, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 19, 201-203 (1994)
[4] O. Martinez, IEEE J. Quantum Electron. 23, 59–64 (1987)
[5] E. Treacy, IEEE J. Quantum Electron. 5, 454–458 (1969)
[6] G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, Barry Walker, and L. F. Dimauro, "Aberration-free stretcher design for ultrashort-pulse amplification," Opt. Lett. 21, 414-416 (1996)
[7]https://www.teraxion.com/en/products/ultrafast-laser/tunable-pulse-stretcher-ultrafast-lasers-vbg/
[8]https://www.teraxion.com/en/news-events/teraxion-offers-tunable-pulse-stretcher-vbg-compressor-pair-ultrafast-laser-systems/
[9] Forget, N., Crozatier, V. & Tournois, P. Appl. Phys. B (2012) 109: 121. https://doi.org/10.1007/s00340-012-5126-2