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Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidths exceeding one optical octave

G. Steinmeyer

Open Access Open Access

Abstract

A novel design approach for dispersion-compensating chirped mirrors with greater-than-octave bandwidth is proposed. The commonly encountered problem of dispersion ripple is overcome by impedance matching via Brewster incidence in respect to the top-layer coating material. This approach totally suppresses undesired reflections off the interface to the ambient medium without any need for complicated matching sections. It is shown that Brewster-angled chirped mirrors can deliver ultrabroadband dispersion compensation over a much wider bandwidth than conventional double-chirped mirrors and without the mechanical complexity of back-deposition approaches. Due to their relatively simple structure, the sensitivity of the dispersion of the Brewster-angled designs towards growth errors is greatly reduced. Therefore, this new generation of chirped mirrors appears ideal for compression of continuum pulses with a potential of pulse durations in the single-cycle regime.

©2003 Optical Society of America

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Supplementary Material (2)

Media 1: GIF (675 KB)     
Media 2: GIF (698 KB)     

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Figures (8)
Fig. 1.
Fig. 1. Dependence of the Brewster angle on wavelength for the coating materials (low-index material: blue, high-index material red) assumed in the simulations [17]. For the wavelength range shown, the low-index material only shows minimal dispersion of the Brewster-angle of 0.2–0.4 degrees for an optical octave.

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Fig. 2.
Fig. 2. Beam path inside a chirped mirror structure oriented at Brewster’s angle relative to the incident beam. The optical path length ABC ¯ − A ′ C ¯ for a ray reflected at the interface between the (i-1)th and ith layer is shown as a blue line.

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Fig. 3.
Fig. 3. Coating designs for Brewster incidence. (a) Mechanical layer thickness of the unoptimized design. Unshaded bars refer to low-index layers, red-shaded layers to high-index layers. The layer sequence is directly calculated with the procedure outlined in Eqs. (1)–(6). (b) The sequence after computer-optimization. (c) The layer pair symmetry κ. (d) The Bragg wavelength λ B. Blue curves in (c) and (d) refer to the unoptimized design; red curves to the optimized one.

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Fig. 4.
Fig. 4. Reflective amplitude and phase properties of the design of Fig. 3 for Brewster incidence. Blue curves refer to the unoptimized design, red curves to the optimized one. (a) Group delay. (b) Group delay dispersion. (c) Power reflectivity.

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Fig. 5.
Fig. 5. Movie Sequence. Simulation of the group delay dispersion of the optimized coating structure from Fig. 3 for different incidence angles (ϑ in=50–60°). The orientation of the mirror is shown in the upper left corner. The pink line indicates the average GDD; the error bar on the left indicates the rms value of the dispersion ripple. [Media 1]

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Fig. 6.
Fig. 6. Coating properties vs. incident angle. (a) Reflectivity. (b) rms value of the GDD dispersion ripple. (c) Full width at half maximum (FWHM) pulse width after 10 reflections off the chirped mirror. Ideal recompression of the pulse would yield a 3.2 fs pulse duration, as indicated by the solid horizontal black line. Only the range of a meaningful FWHM-duration is shown. (d) rms width. Values for the unoptimized design are shown as a blue line, values for the computer-optimized design as a red line. The dotted vertical black line indicates Brewster’s angle.

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Fig. 7.
Fig. 7. Movie Sequence. Simulation of the shape of a compressed pulse, having encountered 10 bounces off the optimized chirped mirror structure, for varying angle of incidence. The mirror orientation is shown in the upper left. The error bar on top indicates the rms width of the pulse (compare Fig. 6). [Media 2]

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Fig. 8.
Fig. 8. Simulated deposition error tolerances of the GDD of the coating vs. wavelength. Color shades indicate the spread of dispersion oscillations for a given average growth error. The plot is based on 10000 simulations with random errors in all layers. These errors were weighted with the average monitorability of the individual layers in the 300–1100 nm range. Current state-of-the-art growth control should allow confinement of the GDD into the light blue zone shown.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

GDD ( ω ) = 2 d 2 d ω 2 ω l ( ω ) c ,
λ B = 2 π c ω = 2 ( t i − 1 n i − 1 cos ⁡ ϑ i − 1 + t i n i cos ⁡ ϑ i ) .
κ = t hi n hi cos ⁡ ϑ hi − t 1 o n 1 o cos ⁡ ϑ 1 o t hi n hi cos ⁡ ϑ hi + t 1 o n 1 o cos ⁡ ϑ 1 o .
l c ( ω ) = c GDD ( ω − ω 1 ) ( ω − ω 2 ) 4 ω − l max ( ω 1 − ω ) ω 2 ( ω 1 − ω 2 ) ω .
λ B ( l ) = 2 π c ω ( l ) ,
t 0 = 0 ; t i = λ B ( ∑ j = 0 i − 1 t j n j cos ⁡ ϑ j ) 4 n i cos ⁡ ϑ i .
r = n hi cos ⁡ ϑ 1 o − n 1 o cos ⁡ ϑ hi n hi cos ⁡ ϑ 1 o + n 1 o cos ⁡ ϑ hi .
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