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Double-angle multilayer mirrors with smooth dispersion characteristics

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz

Open Access Open Access

Abstract

We report the feasibility of precision broadband dispersion control with multilayer mirrors produced in a single coating run. Inherent fluctuations of the group-delay dispersion (GDD) are suppressed by using the mirrors at two different angles of incidence. With a specialized version of the needle optimization algorithm, we have designed the multilayer structure to yield a complementary pair with a resultant GDD substantially free from spectral oscillations characteristic of broadband chirped multilayers. Since the mirrors employed at two different incidence angles are produced in a single deposition run, their overall dispersion is more robust to errors in layer thicknesses than that of previous complementary mirror pairs manufactured in two different steps. This offers the potential for improving production yield and quality of femtosecond dispersion control. We have successfully used the first “double-angle” mirrors for compressing pulses to a duration of 4.3 fs.

©2009 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Schematic of a double-angle DM compressor. The four mirrors employed have been produced in the same coating run with their multilayer structure optimized for mutual cancellations of GDD oscillations at the two different angles of incidence chosen: α=20° and β=5°.

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Fig. 2.
Fig. 2. Characteristics of a DM designed with the double angle approach. Red and blue curves correspond to angles of incidence of 5 and 20 degrees, respectively. Green curves show the effective GDD and reflectance, see definitions in text. Dashed curve and curve in the inset of the figure is the target GDD.

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Fig. 3.
Fig. 3. Physical thicknesses of layers in our prototypical double-angle DM design. Layers are numbered starting from the substrate. Green and red bars correspond to low and high refractive index materials, SiO2 and Nb2O5, respectively.

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Fig. 4.
Fig. 4. Spectrum of femtosecond pulses originating from our gas-filled hollow fiber. With constant or linearly-varying spectral phase, it allows the generation of 4.2-fs transform-limited pulses.

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Fig. 5.
Fig. 5. 4.2-fs Fourier-limited pulse before (dashed line) and after (full line) propagation through dispersive material and our double-angle DM compressor sketched in Fig. 1.

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Fig. 6.
Fig. 6. Error analysis of our prototypical double-angle DM. Top panel (a) represents the hypothetical case of independent thickness errors in the two complementary DMs. Bottom panel (b) shows the case of identical thickness errors in the both DMs of the pair. Blue curves represent theoretical spectral dependence of GDD, green areas represent the probable range of GDD values, for details, see text.

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Fig. 7.
Fig. 7. Measured GDD and reflectance of our prototypical double-angle DM for an angle of incidence of 5 and 20 degrees (full lines). GDD and reflectance of the theoretical design are shown by dashed lines. Red and blue curves correspond to angles of incidence of 5 and 20 degrees, respectively. Dark green and dark blue curves show the effective measured GDD and reflectance, see definitions in text.

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Fig. 8.
Fig. 8. Dashed line: theoretical interferometric autocorrelation of a pulse with the frequency spectrum shown in Fig. 4 in the absence of spectral phase modulation. This Fourier-limited pulse has a duration (FWHM) of 4.2 fs. Full line: measured interferometric autocorrelation function of the pulses compressed with our prototypical double-angle DM compressor, indicating a pulse duration of ~ 4.3 fs.

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