What Is Chirp?
Chirp refers to the property of a light pulse in which its instantaneous frequency varies with time. When a laser pulse propagates through a transparent medium, chirp is generated due to the effects of dispersion and nonlinearity. The magnitude of chirp is typically quantified by GDD (Group Delay Dispersion), commonly expressed in units of fs². When a laser pulse has no chirp, it possesses the minimum possible pulse duration. Conversely, once chirp is present, the pulse width becomes broadened — an issue that must be addressed in the ultrafast field where the shortest possible pulses are pursued. Chirped mirrors are designed precisely to compensate for the chirp generated in laser pulses.
What Is a Chirped Mirror?
A chirped mirror, also known as a dispersion-compensating mirror, is primarily used in femtosecond lasers. Each reflection introduces a fixed amount of dispersion, which can correct the pulse broadening that occurs when ultrashort pulses pass through an optical system — making it highly suitable as a dispersion management tool (for example, for pre-compensation). The fundamental design principle of a chirped mirror is that the Bragg wavelength is not constant but varies spatially within the structure. This is mainly achieved through multilayer coatings: light of different wavelengths penetrates to different depths within the mirror structure, and therefore experiences different group delays.
Classification of Chirped Mirrors
Dispersion-Compensating Chirped Mirror Pairs — Dispersion-compensating pairs are designed specifically to address the issue of dispersion ripple. They consist of two different mirrors whose GDD curves oscillate with the same trend but are shifted by half a period relative to each other, thereby minimizing the residual GDD ripple. For compensating pairs with a bandwidth of less than one octave, this design is relatively easy to realize.
Dual-Angle Chirped Mirrors — Two identical mirrors are used in combination at different angles of incidence. Compared with compensating mirror pairs, this configuration offers the following advantages: 1. higher stability and lower manufacturing tolerance; 2. no need for two different coatings, resulting in lower cost.
Single-Angle / Brewster-Angle Chirped Mirrors — The beam is allowed to be incident at only one angle. If the angle is designed for Brewster-angle incidence, the Fresnel reflection is relatively low, enabling ripple-free GDD. The Brewster angle is typically ~56°, which makes it easier to apply outside the cavity; inside the cavity, however, such a large reflection angle is difficult to achieve, so it is not suitable there. Further subdivisions include high-dispersion compensating mirrors and positive-dispersion compensating mirrors.
GDD Curves of Several Typical Chirped Mirrors from Ultrafast Innovations
Chirped Mirror Pair PC147/Dual-Angle Chirped Mirror PC70/Single-Angle Chirped Mirror HD120
The design of chirped mirrors must take into account bandwidth, dispersion compensation amount, dispersion oscillation, and reflectivity characteristics. From an application standpoint, broader bandwidth and higher dispersion compensation are more versatile. From a design standpoint, however, bandwidth and dispersion compensation are inversely related, while dispersion compensation and dispersion oscillation are directly proportional. Therefore, in practice, a balance must be sought. For Ti:sapphire lasers, dispersion introduction is typically on the order of tens of fs², whereas Yb lasers generally employ high-dispersion compensating mirrors.
Application Scenarios for Chirped Mirrors
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Few-Cycle Pulse Compressors — To obtain few-cycle pulse durations, hollow-core fibers or thin-plate assemblies are typically used to broaden the spectrum, after which chirped mirrors compress the pulse width down to the few-cycle regime.
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Compensating Material Dispersion Introduced by Transmission — In ultrafast laser application systems, complex optical paths inevitably introduce positive dispersion, which broadens the initial pulse duration. To recover a near-Fourier-transform-limited pulse width, chirped mirrors can be used to compensate for negative dispersion.
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Resonator Cavity Mirrors — When designing a laser resonator, the cavity mirrors can be designed as mirrors or output couplers with a certain amount of negative dispersion, directly compensating for the negative dispersion introduced by optical components inside the cavity.