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Chirped Mirrors

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Definition: Bragg-type dispersive mirrors with a spatial variation of the Bragg wavelength

Categories: article belongs to category general optics general optics, article belongs to category photonic devices photonic devices, article belongs to category light pulses light pulses

DOI: 10.61835/yth Cite the article: BibTex plain text HTML Link to this page! LinkedIn

A chirped mirror is a kind of dielectric dispersive mirror with a spatial variation of the layer thickness values. Such mirrors are used for dispersion compensation in mode-locked lasers, for example. Another interesting feature of such mirrors is that they make it possible to achieve a broader reflection bandwidth than ordinary Bragg mirrors. Due to the many dimensions of possible optimization, chirped mirrors are often sold as custom optics.

Principles of Dispersive Chirped Mirrors

The basic idea of chirped mirror designs [1] is that the Bragg wavelength is not constant but varies within the structure (along the propagation direction), so that light at different wavelengths penetrates to a different extent into the mirror structure and thus experiences a different group delay.

However, a naïve design directly based on this idea would not work: it would exhibit strong oscillations of the group delay and even more so of the group delay dispersion. This disturbing effect can to some extent be mitigated by numerical optimization of the layer structure, but this is difficult because the optimization has to be done in a multi-dimensional space (resulting from the large number of layers) where a huge number of local optima exist, most of which do not correspond to satisfactory designs.

double-chirped mirror — Figure 1: Operation principle of a chirped mirror.

Light with a long wavelength penetrates deeper into the mirror structure and thus experiences a larger group delay. This leads to anomalous chromatic dispersion.

It was found [5] that the disturbing oscillations have two origins:

There is a Fresnel reflection at the front face (the interface to air), which leads to strong additional dispersion as in a Gires–Tournois interferometer.
The sudden “switching” of the coupling of counterpropagating waves from zero in air to a finite value in the structure causes a kind of impedance mismatch.

Both problems can be eliminated with a double-chirped design, which has two additional features:

The coupling of counterpropagating waves is turned on smoothly by also varying the duty cycle, i.e., the ratio of optical thickness of high and low index layers. (For a duty cycle above or below 50%, the effective reflectance of a layer pair is reduced.)
The Fresnel reflection is removed with an additional anti-reflection structure on top of the double-chirped section (not shown in Figure 1).

Even without numerical optimization, double-chirped designs can have a dispersion profile which relatively nicely matches the design goal. Further refinement is then achieved with numerical optimization, i.e., with fine tuning of the layer thickness values.

numerically optimized dispersive chirped mirror — Figure 2: Reflection and dispersion properties of a numerically optimized chirped mirror design, developed with the software RP Coating. The dashed curve shows the target dispersion, which is fairly precisely matched in a broad wavelength range. Even broader wavelength ranges are possible, when a larger number of layers is used.

field penetration into dispersive mirror — Figure 3: Field penetration into the chirped mirror of Figure 2. It is apparent that within the wavelength range 1000–1200 nm, the field penetrates more deeply into the structure for longer wavelengths. The larger group delay for longer wavelengths corresponds to anomalous dispersion.

Remaining oscillations in the group to latest version can be further reduced by using suitable pairs of dispersive mirrors, or alternatively by using the same kinds of mirrors with slightly different incidence angles [15].

Designing Chirped Mirrors

For designing dispersive mirror coatings, a flexible simulation and design software is indispensable. The RP Coating software is an ideal tool for such work, as it is particularly flexible. For example, you can define an initial design with a limited number of parameters and numerically optimize only those (rather than each individual layer thickness separately), which is far more efficient. Thereafter, you may still apply a local optimization of all layer thickness values.

Application in Mode-locked Lasers

For mode-locked lasers with an ultrabroad bandwidth, as required for operation in the few-cycle regime, it is challenging to design mirrors with the corresponding ultrabroad reflection bandwidth, combined with proper chromatic dispersion over the most of that range. The factor limiting the bandwidth achievable is in most cases the difficulty of making anti-reflection structures with very small residual reflectance over a large bandwidth. This problem can be solved with so-called backside coated (BASIC) chirped mirrors [11]. The key idea of such a design is to interface the chirped mirror structure with a glass substrate rather than with air; the air–glass interface is then at a different location, and the effects of the residual reflectance of that (also AR-coated) surface can be eliminated by using a wedge shape for that glass piece.

Double-chirped mirrors (DCMs) are often used for dispersion compensation in mode-locked lasers, particularly for those with pulse durations below ≈ 20 fs. They are typically designed not only to compensate a constant group delay dispersion, but also to correct higher-order dispersion. However, there are limits concerning how much dispersion (and in particular higher-order dispersion) can be compensated with a double-chirped mirror. Possible solutions are to use a suitable combination of several mirrors, where the dispersion errors from different mirrors partially cancel each other, and to combine chirped mirrors with a prism pair. Another challenge arises from the tight fabrication tolerances; at least some of the layers typically have to be fabricated with a precision of the thickness of a few nanometers. The remaining wiggles in the group delay versus wavelength can be further reduced by using appropriate combinations of mirrors where the wiggles at least partially cancel each other.

Chirped Semiconductor Mirrors

It has been shown [10] that double-chirped mirror designs can also be used with semiconductor mirrors. Such mirrors can generate a much higher amount of dispersion, although in a much smaller bandwidth. They can be used for compensating the dispersion in a mode-locked laser with a single compact device even when e.g. a long pulse duration requires a high amount of anomalous dispersion for soliton mode locking.

More to Learn

chromatic dispersion dispersion compensation dispersive mirrors dielectric mirrors laser mirrors

Bibliography

[1]	R. Szipöcs et al., “Chirped multilayer coatings for broad-band dispersion control in femtosecond lasers”, Opt. Lett. 19 (3), 201 (1994); https://doi.org/10.1364/OL.19.000201
[2]	A. Stingl et al., “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser”, Opt. Lett. 20 (6), 602 (1995); https://doi.org/10.1364/OL.20.000602
[3]	R. Szipöcs and A. Koházi-Kis, “Theory and design of chirped dielectric mirrors”, Appl. Phys. B 65, 115 (1997); https://doi.org/10.1007/s003400050258
[4]	E. J. Mayer et al., “Ultrabroadband chirped mirrors for femtosecond lasers”, Opt. Lett. 22 (8), 528 (1997); https://doi.org/10.1364/OL.22.000528
[5]	F. X. Kärtner et al., “Design and fabrication of double-chirped mirrors”, Opt. Lett. 22 (11), 831 (1997); https://doi.org/10.1364/OL.22.000831
[6]	N. Matuschek et al., “Theory of double-chirped mirrors”, IEEE J. Quantum Electron. 33 (2), 295 (1998); https://doi.org/10.1109/2944.686724
[7]	G. Tempea et al., “Dispersion control over 150 THz with chirped dielectric mirrors”, JSTQE 4 (2), 193 (1998); https://doi.org/10.1109/2944.686723
[8]	N. Matuschek et al., “Theory of double-chirped mirrors”, JSTQE 4 (2), 197 (1998); https://doi.org/10.1109/2944.686724
[9]	N. Matuschek et al., “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics”, IEEE J. Quantum Electron. 35 (2), 129 (1999); https://doi.org/10.1109/3.740733
[10]	R. Paschotta et al., “Double-chirped semiconductor mirror for dispersion compensation in femtosecond lasers”, Appl. Phys. Lett. 75 (15), 2166 (1999); https://doi.org/10.1063/1.124953
[11]	N. Matuschek et al., “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics”, Appl. Phys. B 71, 509 (2000); https://doi.org/10.1007/s003400000426
[12]	F. X. Kärtner et al., “Ultrabroadband double-chirped mirror pairs for generation of octave spectra”, J. Opt. Soc. Am. B 18 (6), 882 (2001); https://doi.org/10.1364/JOSAB.18.000882
[13]	G. Tempea et al., “Tilted-front-interface chirped mirrors”, J. Opt. Soc. Am. B 18 (11), 1747 (2001); https://doi.org/10.1364/JOSAB.18.001747
[14]	V. Pervak et al., “Dispersion control over the ultraviolet–visible–near-infrared spectral range with HfO₂/SiO₂-chirped dielectric multilayers”, Opt. Lett. 32 (9), 1183 (2007); https://doi.org/10.1364/OL.32.001183
[15]	V. Pervak et al., “Double-angle multilayer mirrors with smooth dispersion characteristics”, Opt. Express 17 (10), 7943 (2009); https://doi.org/10.1364/OE.17.007943
[16]	V. Pervak et al., “High-dispersive mirrors for femtosecond lasers”, Opt. Express 16 (14), 10220 (2008); https://doi.org/10.1364/OE.16.010220

(Suggest additional literature!)

This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics AG. How about a tailored training course from this distinguished expert at your location? Contact RP Photonics to find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, training) and software could become very valuable for your business!

Suppliers

The RP Photonics Buyer's Guide contains 17 suppliers for chirped mirrors. Among them:

Edmund Optics

Edmund Optics offers various kinds of mirrors for ultrafast laser technology, including highly dispersive chirped mirrors for different spectral regions such as 0.8 μm, 1 μm and 2 μm, but also UV and other infrared versions.

OPTOMAN

OPTOMAN can guide you through the features of chirped mirror designs and manufacture optimal dispersive mirrors for your laser system. Our dispersive mirrors feature predefined and spectrally uniform GDD. GTI mirrors can be designed for any specific GDD requirement from slightly negative (−20 fs²) up to ±10000 fs².

Matching chirped mirror pairs are also available and can give a dispersion compensation effect.

Standard GTI mirrors can be found in OPTOSHOP.

Shalom EO

Hangzhou Shalom EO offers custom chirped mirrors optimized for dispersion compensation of ultrashort pulses of ultrafast lasers. Shalom EO's chirped mirrors feature low negative group delay dispersion (GDD), minimized phase distortion and third-order distortion, and high reflectance. In our factory, Shalom EO utilizes accurate and up-to-date GDD metrological instruments to ensure the precise dispersion characteristics of our optical components which guarantees that our products meet the highest standards for pulse compression, dispersion compensation, and other ultrafast optical requirements.

In addition, Shalom EO supplies ultrafast chirped mirror pairs consisting of two matched complementary chirped mirrors. Shalom EO is also a professional supplier of a series of femtoline laser optics, like femtoline low GDD mirrors, ultrafast-enhanced silver mirrors, etc. You might visit our website to learn more.

UltraFast Innovations

UltraFast Innovations (UFI®) provides a variety of ultra-broadband compression mirror sets in several configurations. For example, mirror sets for pulse compression in chirped-pulse titanium:sapphire amplifier systems, broadband oscillators, and other applications cover the wavelength range of 400–1200 nm, i.e., up to 1.5 octaves. Our customers have reached pulse durations around 3 fs after spectral broadening in hollow-core fibers and gas cells in combination with our mirrors.

Such mirrors are not only optimized for a broad reflection bandwidth, but also for a precise chromatic dispersion profile with low group delay dispersion (GDD) fluctuations. In some cases, we use two mirrors with different angles of incidence to further reduce the oscillations (double-angle technology).

Thorlabs

Thorlabs manufactures a wide range of ultrafast optics specifically designed for ultrafast applications, including mirrors with a specialized coating optimized for use with femtosecond Ti:sapphire lasers, low-GDD beamsplitters and mirrors, nonlinear crystals, and chirped mirrors. To precisely characterize the dispersion of ultrafast optics over the 500 – 1650 nm range, consider Thorlabs’ Chromatis™ dispersion measurement system with the InGaAs detector add-on option.

LASEROPTIK

LASEROPTIK designs and produces various kinds of dispersive coatings, including chirped mirrors and matched pairs of chirped mirrors, also all other kinds of coated optics for dispersion management like GTI mirrors. We use Ion Beam Sputtering (IBS) for highest quality and widely ranging dispersion measurement setups for precise characterization.

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