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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 19 — Sep. 22, 2003
  • pp: 2385–2396
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Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidths exceeding one optical octave

G. Steinmeyer  »View Author Affiliations


Optics Express, Vol. 11, Issue 19, pp. 2385-2396 (2003)
http://dx.doi.org/10.1364/OE.11.002385


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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

1. Introduction

In the last few years, ultrafast pulse generation schemes have progressed well into the sub-5-fs regime. Pulses of only two optical cycles or even slightly less have been demonstrated [1

1. A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipőcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997). [CrossRef]

, 2

2. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633, (1999). [CrossRef]

, 3

3. F. X. Kärtner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882–885, (2001). [CrossRef]

]. This breakthrough has been made possible by sophisticated dispersion compensation schemes, which allow for wider bandwidths than pure bulk-optical approaches based on prisms or gratings. These advanced dispersion compensation schemes mostly involved chirped mirrors. Apart from chirped mirrors nearly octave-spanning dispersion compensation has also been achieved with liquid-crystal phase modulators in a zero dispersion delay line [4

4. L. Xu, L. Liming, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Phot. Technol. Lett. 12, 1540–1542, (2000). [CrossRef]

, 5

5. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, to be published, Oct. 15, (2003). [CrossRef] [PubMed]

]. Raman sideband generation appears to be another pulse compression method that may be pushed towards the optical octave and close to single-cycle pulse duration [6

6. N. Zhavoronkov and G. Korn, “Generation of single intense short optical pulses by ultrafast molecular phase modulation,” Phys. Rev. Lett. 88, 203901 (2002). [CrossRef] [PubMed]

, 7

7. V. Kalosha and J. Herrmann, “Ultrabroadband phase-amplitude modulation and compression of extremely short uv and vuv pulses by Raman-active molecular modulators,” Phys. Rev. A 67, 031801 (2003). [CrossRef]

]. However, even with demonstrated pulse durations of about 4 fs, dispersion compensation beyond one optical octave has neither been achieved with chirped mirrors nor any other method. Grating-based concepts encounter serious problems when orders start to overlap, i.e. at one optical octave. Design and manufacturing of chirped mirrors already becomes problematic when the bandwidth exceeds 0.6 optical octaves. Similar to chromatic correction in imaging systems, dispersion compensation becomes a challenging task when the bandwidth approaches the optical octave. In this Letter, we will explore a novel route towards pulse compression with single-cycle pulse duration based on a new generation of chirped mirrors.

2. Generations of chirped mirrors

The fundamental barrier to further extension of useful bandwidth of a chirped mirror can be tracked down to parasitic Gires-Tournois interferometer (GTI, [8

8. F. Gires and P. Tournois, “Interféromètre utilisable pour la compression d’impulsions lumineuses modulées en fréquence,” C. R. Acad. Sci. Paris 258, 6112, (1964).

]) effects, mainly arising at the interface between the chirped mirror stack and the ambient medium. Together with a reflection inside the mirror stack, the parasitic top reflection forms a variable-path GTI, which causes a modulation of the group delay dispersion vs. wavelength. This dispersion ripple overlays the desired dispersion characteristics of a chirped mirror and creates satellite pulses, which merge into a broad temporal pedestal upon multiple bounces off chirped mirrors [9

9. G. Steinmeyer, “Dispersion oscillations in ultrafast phase correction devices,” IEEE J. Quantum Electron. , 39, 1027–1034, (2003). [CrossRef]

]. Generally, a tradeoff between bandwidth and suppression of dispersion ripple can be seen and limits the usefulness of chirped mirrors to much less than an optical octave.

After the initial demonstration of chirped mirrors [10

10. R. Szipőcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broad-band dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203, (1994). [CrossRef]

], the ambient interface had been sub-sequently recognized as the main cause for dispersion ripple. The most straightforward way to suppress this effect is deposition of an antireflection coating on top of the high-reflecting mirror stack. It has been controversially discussed, whether to match from air to an average index of refraction of the layer pair [11

11. R. Szipőcs and A. Kőházi-Kis, “Theory and desing of chirped dielectric mirrors,” Appl. Phys. B 65, 115–135, (1997). [CrossRef]

] or to better match from air to one of the layer materials. The latter method has lead to the double-chirped mirror (DCM [12

12. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833, (1997). [CrossRef] [PubMed]

, 13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

]) design approach. Here a duty-cycle modulation between high and low index materials is used to additionally match the impedance adiabatically inside the mirror stack. These AR based strategies work very well up to approximately 300 nm bandwidth in the Ti:sapphire wavelength range, but are ultimately limited by the bandwidth of broadband AR coatings. For the typically used materials SiO2 and TiO2, e.g., a 300-nm bandwidth (0.6 optical octaves) results in a residual reflectivity of an AR coating of approximately 10-4 [14

14. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658, (1996). [CrossRef] [PubMed]

]. Such coatings are very challenging in terms of growth error control. Provided total absence of growth errors, only 10-3 residual reflectivity can be reached for the full octave, regardless of the number of layers used in the AR section. A 10-3 suppression of GTI satellites, however, is insufficient in terms of dispersion ripple [9

9. G. Steinmeyer, “Dispersion oscillations in ultrafast phase correction devices,” IEEE J. Quantum Electron. , 39, 1027–1034, (2003). [CrossRef]

]. Therefore, alternative approaches for impedance matching between ambient medium and mirror stack are required for octave-spanning dispersion compensation with chirped mirrors.

3. Brewster-angled chirped mirrors

Figure 1 shows the Brewster angle vs. wavelength, calculated from measured data of sputtered coating materials [17

17. K. Starke, D. Ristau, and Laserzentrum Hannover, private communication, (2002).

]. This calculation clearly reveals, that for the low-index material the Brewster angle only varies by 0.2–0.4° for an octave. The high-index material, however, shows much stronger Brewster-angle dispersion and is therefore much less suited as the cover material. A schematic drawing of a Brewster-angled chirped mirror and one representative optical path in this structure are depicted in Fig. 2.

As Brewster-angle orientation removes the prevalent source of multiple path interference, we can use a simple approach for designing an initial layer sequence from a given group delay dispersion -GDD(ω) to be compensated. Our approach is a simplified and adapted version of the WKB approach introduced in [13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

]. We ignore the interference of multiples paths for one wavelength, i.e. assume that a well-defined classical turning point exists for each and every wavelength in the coating. Then the dispersion properties of the coating can be simply mapped by a frequency-dependent path length l(ω). The group delay dispersion resulting from such a path l(ω) is then written as

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.
Fig. 2. Beam path inside a chirped mirror structure oriented at Brewster’s angle relative to the incident beam. The optical path length ABC¯AC¯ for a ray reflected at the interface between the (i-1)th and ith layer is shown as a blue line.
GDD(ω)=2d2dω2ωl(ω)c,
(1)

where c is the speed of light and the factor 2 accounts for passage back and forth through the mirror structure. From the known dependence l(ω), one can track the optical path through the mirror stack ( AB¯ in Fig. 2) to find the layer pair (t i-1, ti) with matching Bragg wavelength

λB=2πcω=2(ti1ni1cosϑi1+tinicosϑi).
(2)

Equation 2 relates optical path lengths in the angled stack to physical thicknesses ti of the individual layers. For symmetric Bragg layers t i-1 n i-1cosϑ i-1=tinicosϑi=λB/4. Impedance matching is achieved by variation of the duty cycle of the layer pairs [13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

]. This method is called double-chirping. For the angled stack in Fig. 2, we define the double-chirp coefficient

κ=thinhicosϑhit1on1ocosϑ1othinhicosϑhi+t1on1ocosϑ1o.
(3)

For κ=-1, e.g., a low-index λ B/2 layer is deposited and the high-index layer has zero thickness. κ=0 refers to symmetric λ B/4 layers. Finally, κ=1 corresponds to the situation of a 100% high-index duty cycle. Typically, a slow ramp from κ=-1 to 0 is used in the topmost 10 to 20 layers of a chirped mirror coating.

Solution of the differential equation (1) requires two boundary conditions, which are given in the form l(ω 1)=0 and l(ω 2)=l max and define the bandwidth of the coating Δω=|ω 2-ω 1|. The maximum available path length l max is typically dictated by manufacturing constraints. For the simplest case of a constant GDD, a solution lc is readily obtained

lc(ω)=cGDD(ωω1)(ωω2)4ωlmax(ω1ω)ω2(ω1ω2)ω.
(4)

Once differential equation (1) is solved, one can directly compute the Bragg wavelength as a function of optical path length

λB(l)=2πcω(l),
(5)

where ω(l) is the inverse function of the solution l(ω) of Eq. (1). For simplicity, let us ignore double chirping of the coating in the calculation of the initial layer sequence. Then the ti’s are readily determined from the chirp law Eq. (5) using the recurrence

t0=0;ti=λB(j=0i1tjnjcosϑj)4nicosϑi.
(6)
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.

The index i numbers physical layer thicknesses ti starting from the interface to air, i.e. opposite to typical numbering conventions of coating manufacturers. In this paper, we have always surmised that the index of the top layer i=1 is low, as this simplifies the design procedure and also yields a wider bandwidth. Odd indices i therefore identify low-index layers, even indices high-index materials.

Equations (16) are a straightforward extension of the procedure outlined in [13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

] and can be applied to arbitrary incidence angles. Apart from the different chirp law required to design a chirped mirror at non-normal incidence the reflectivity is also modified. Assuming p-polarization, the Fresnel reflectivity r at an interface between materials with index n lo and n hi is now written as

r=nhicosϑ1on1ocosϑhinhicosϑ1o+n1ocosϑhi.
(7)

A reduction of r requires an increase of the number of layers if the same reflectivity and bandwidth of the coating are to be achieved. With layer material data from [17

17. K. Starke, D. Ristau, and Laserzentrum Hannover, private communication, (2002).

], one calculates a change from r 0=0.23 at normal incidence to r Brewster=0.17 at Brewster’s angle, i.e. a 35% decrease of reflectivity per interface in the stack. On the other hand, however, Brewster-angled mirrors do not require AR matching sections, which in some broadband mirror designs require more than 15 layers [2

2. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633, (1999). [CrossRef]

]. In typical broadband DCM coatings, the chirped mirror stack (without AR coating) consisted of 50 layers. Assuming that the decrease of reflectivity has to be compensated by a similar increase of the number of layers, one arrives at an estimate of about 70 layers for the Brewster-angled coating. The decrease of the Fresnel reflectivity is therefore widely compensated by the absence of matching sections. However, when Brewster-angled chirped mirrors are used to cover a wider bandwidth, then one also has to increase the number of layers. In the following we use 120 layers to cover 1.2 octaves rather than 70 layers for 0.7 octaves. These numbers may serve as a rough estimation for the numbers of layers to be expected for octave-spanning mirror coatings. An initial design computed with the procedure outlined in this section is shown in Fig. 3.

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.

4. A coating design example for Brewster-angled chirped mirrors

Figure 3 shows a simple layer structure suitable for compensation of 40 fs2 dispersion per bounce (see Fig. 4). One bounce therefore compensates the second-order dispersion of a 1-mm path length in an optical glass. The layer thickness sequence follows a simple relationship with an added double-chirp section in the first 10 layer pairs designed according to [13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

]. Doublechirping was found essential for the Brewster approach to work. The stack has a total thickness of 10 microns and consists of 120 layers. In the following, an incident angle of ϑB=56.2° was assumed (compare Fig. 1). The resulting spectral reflectivity, group delay (GD) and group delay dispersion (GDD) characteristics at Brewster incidence are depicted in Fig. 4. Even without computer-optimization, the coating already exhibits a high reflectivity over more than one octave together with a reasonably smooth GDD. The GDD ripple amounts to about 50 fs2 (rms) for the octave from 400–800 nm. The GD exhibits similar oscillations with an rms value of 2.5 fs. Tuning the incident angle away from Brewster’s angle dramatically increases these values. To further reduce the dispersion ripple at Brewster’s angle, an attempt was made to improve coating properties by computer optimization. The optimized coating and its properties are also shown in Figs. 3 and 4. By comparing with the unoptimized design, one can see that the coating now extends all the way up to 1000 nm, both with smooth dispersion and reasonably high reflectivity. Some bandwidth at 400–430 nm is lost during the optimization process. Still, the resulting coating exhibits an average reflectivity of 99.5%, a GD ripple of 0.5 fs (rms), and a GDD ripple of only 8 fs2 in an 1.2 octave bandwidth. This coating therefore covers the entire bandwidth from 430–1000 nm, i.e. nearly double the bandwidth of the broadest DCMs demonstrated to date.

Most remarkably, the basic structure of the layer sequence remains conserved during the optimization process. Close to the interface to air, the main effect in the optimization process seems to be a modification of the double-chirp section. The simple linear chirp in the duty-cycle is replaced by a more complex function with a strong oscillatory component in the first 40 layers close to the interface to air. This corrugated double-chirping serves to further suppress the dispersion oscillations. Additionally, changes at the bottom of the layer structure greatly increase the reflectivity of the coating beyond 800 nm.

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]

The behavior of the GDD for varying angle of incidence (ϑ in = 50°–60°) is shown in the movie sequence Fig. 5. The calculated rms spread of the dispersion oscillations is also shown close to the left axis as an error bar. It can be clearly seen that even in this relatively small angular interval the reduction of dispersion oscillations is already dramatic. In addition, Fig. 6 contains a summary of a simulation over an even wider range of input angles. At normal incidence, the GDD ripple amounts to more than 1000 fs2. This value is reduced to 8 fs2 at Brewster incidence. At angles larger than Brewster’s angle, dispersion ripple starts to increase again.

Figure 7 further illustrates the concept of Brewster-angled chirped mirrors. Based on the simulations already discussed, we illustrate the effect of the dispersion ripple on shaping of an ultrashort optical pulse as a function of incident angle. For this purpose, we assume that an unchirped Gaussian-shaped pulse with a 140-THz bandwidth encountered a dispersion of +400 fs2, i.e. the equivalent of 1 cm of a light optical glass. Ideal recompression of such a pulse should yield the original pulse duration of about 3 fs. The mirror structure compensates for this material dispersion in 10 bounces. Dispersion oscillations cause imperfections of the recompression, which mainly manifest themselves as a broad pedestal structure but also widen the pulse at its half maximum. This is most dramatically seen far away from Brewster incidence, where the pulse extends over nearly a picosecond and exhibits many uncoordinated satellite pulses. The peak intensity is reduced to about 10% of the optimum value. Towards higher angles of incidence, the continuum structure appears more and more compressed until, at about 45° incidence, two GTI satellite pulses show up, located at ±60 fs delay from the center of gravity of the pulse. At 50° incidence, secondary GTI satellites become visible. In the vicinity of Brewster’s angle all satellite pulses are strongly suppressed and nearly the entire pulse energy is confined into a single pulse. Directly at Brewster’s angle, satellites are suppressed to below 10-4 of the main pulse. Finally, going to higher incident angles than Brewster’s angle, the isolated pulse rapidly decays into the temporal continuum structure, traversing the scenes already described in reverse order.

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.

The characteristics of the pulse in Fig. 7 are also summarized in Fig. 6. From the simulations, one can conclude that a severe degradation of pulse quality sets in at about 5 degrees deviation from the nominal Brewster’s angle. At below 52° and above 58° incidence, the pulse is compressed to 5 fs rather than the optimum 3.5 fs at Brewster incidence. This is a surprisingly large window for the operation of Brewster-angled mirrors, which makes it clear that slight errors in the angular alignment on the order of one degree can easily be tolerated in this design approach.

5. Robustness of the method

Dispersion control with chirped mirrors generally requires very precise control of layer deposition accuracies. From previously reported examples, one can conclude that the demand on deposition accuracies is growing dramatically in the vicinity of an optical octave bandwidth [3

3. F. X. Kärtner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882–885, (2001). [CrossRef]

, 13

13. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

]. For conventional chirped mirrors, a strong increase of the sensitivity to growth errors has been found for the top layers of a coating, i.e. those layers that form the matching section. As the mirror stack has already reached a very high reflectivity during deposition of the last few layers, growth errors in these layers only cause tiny changes of the coating’s transmission. The increased sensitivity of the top layers is often accompanied by the presence of very thin layers. These thin layers are very difficult to monitor via the coating transmission. The simultaneous occurrence of poor monitoring conditions and an enhanced sensitivity of the top layers is the dilemma in manufacturing chirped mirrors.

In the following, we want to convince ourselves of the utility of the Brewster-angle design approach. For this purpose, we check the sensitivity of the coating parameters to random deposition errors. For a realistic estimation of the feasibility of such a coating, we account for difficulties in optically monitoring individual layers. For deposition of each and every layer of the optimized coating sequence in Fig. 3, the average transmission change per nm deviation from the nominal layer thickness is calculated. Averaging is carried out for the wavelength range from 300–1100 nm, i.e. the range covered by silicon photo detectors. These values are used as weights for computing otherwise randomly distributed growth errors. This means that the difficult-to-monitor top layers are varied more strongly in the simulations than the bottom layers of the coating.

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]

Statistical deviations of the coating GDD from the designed value are shown in Fig. 8 for a wide spread of growth errors (0.01–1 nm). The picture is based on about 10000 calculations of the GDD of the optimized coating in Fig. 3. The coating GDD is relatively immune towards growth errors in the wavelength region below 500 nm. Generally, the sensitivity of the GDD increases with growing wavelength. Average growth errors of a few 0.01 nm would be required to exploit the full potential of the approach in terms of suppression of dispersion oscillations, but this is well out of reach even with the most advanced manufacturing capabilities. Average growth errors on the order of 0.1 nm or 0.2 nm appear to be at the verge of current state-of-the-art manufacturing capabilities [2

2. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633, (1999). [CrossRef]

, 15

15. N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522, (2000). [CrossRef]

]. This deposition accuracy relates to the light blue shade in Fig. 8. The overall GDD of the mirror would still be well in the negative dispersion region, an indication for the practicality of this approach, which would even allow for slightly increased deposition errors.

Compared to back deposition approaches, the full dispersion of the coating can be used to compensate for material dispersion, as no cover slide has to be compensated. Rotating the mirror from Brewster’s angle to normal incidence, the spectral characteristics of the mirror are shifted to longer wavelengths as the path length scales with the cosine of the internal angle, compare Eq. (2). At normal incidence the high-reflectivity regions of the coating appear shifted towards longer wavelengths. This opens an additional window for monitoring coatings that extend well into the blue spectral range. Monitoring Brewster coatings at normal incidence is another decisive advantage of the new coating design approach.

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.

6. Conclusion

The Brewster-angle approach may not be the universal solution to intracavity dispersion compensation, but it is excellently suited for extra-cavity compression of white-light continua. This compression is currently the most demanding application in terms of bandwidth and probably the only one that currently demands far greater than octave dispersion compensation. The layer sequences in the Brewster-angle design approach are structurally relatively simple, which results in a robustness of the approach towards growth errors. No complicated matching sections are required. Given current growth monitoring capabilities, reliable manufacturing of such mirrors appears promising.

Slightly modified designs can also be useful for the design of wideband dielectric mirrors at 45° incidence. Compared to normal incidence, the demands on an AR matching section would be strongly reduced for 45° incidence and p-polarization. A hybrid DCM-Brewster design may then serve to provide a broadband reflectivity with very smooth dispersion. Such mirror structures would be useful to extend the bandwidth of high power mirror designs, as they are used in Ti:sapphire amplifier chains. Quite generally, going to non-normal angles of incidence appears to be a promising new route and opens up new application areas of chirped mirrors.

Acknowledgements

The original coating design computer code, on which the simulations are based, was developed by N. Matuschek at ETH Zürich. The author further acknowledges G. Arisholm, U. Griebner, and N. Matuschek for carefully proof-reading the manuscript and their suggestions for some clarifications.

References and links

1.

A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipőcs, “All-solid-state cavity-dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997). [CrossRef]

2.

D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633, (1999). [CrossRef]

3.

F. X. Kärtner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882–885, (2001). [CrossRef]

4.

L. Xu, L. Liming, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Phot. Technol. Lett. 12, 1540–1542, (2000). [CrossRef]

5.

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, to be published, Oct. 15, (2003). [CrossRef] [PubMed]

6.

N. Zhavoronkov and G. Korn, “Generation of single intense short optical pulses by ultrafast molecular phase modulation,” Phys. Rev. Lett. 88, 203901 (2002). [CrossRef] [PubMed]

7.

V. Kalosha and J. Herrmann, “Ultrabroadband phase-amplitude modulation and compression of extremely short uv and vuv pulses by Raman-active molecular modulators,” Phys. Rev. A 67, 031801 (2003). [CrossRef]

8.

F. Gires and P. Tournois, “Interféromètre utilisable pour la compression d’impulsions lumineuses modulées en fréquence,” C. R. Acad. Sci. Paris 258, 6112, (1964).

9.

G. Steinmeyer, “Dispersion oscillations in ultrafast phase correction devices,” IEEE J. Quantum Electron. , 39, 1027–1034, (2003). [CrossRef]

10.

R. Szipőcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broad-band dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203, (1994). [CrossRef]

11.

R. Szipőcs and A. Kőházi-Kis, “Theory and desing of chirped dielectric mirrors,” Appl. Phys. B 65, 115–135, (1997). [CrossRef]

12.

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833, (1997). [CrossRef] [PubMed]

13.

N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137, (1999). [CrossRef]

14.

J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658, (1996). [CrossRef] [PubMed]

15.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522, (2000). [CrossRef]

16.

G. Tempea, V. Yakovlev, B. Bacovic, F. Krausz, and K. Ferencz, “Tilted-front-interface chirped mirrors,” J. Opt. Soc. Am. B 18, 1747–1750, (2001). [CrossRef]

17.

K. Starke, D. Ristau, and Laserzentrum Hannover, private communication, (2002).

OCIS Codes
(310.6860) Thin films : Thin films, optical properties
(320.5520) Ultrafast optics : Pulse compression

ToC Category:
Research Papers

History
Original Manuscript: July 9, 2003
Revised Manuscript: September 5, 2003
Published: September 22, 2003

Citation
G. Steinmeyer, "Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidths exceeding one optical octave," Opt. Express 11, 2385-2396 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-19-2385


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References

  1. A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, R. Szip�?cs, �??All-solid-state cavity-dumped sub-5-fs laser,�?? Appl. Phys. B 65, 175�??188 (1997). [CrossRef]
  2. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, T. Tschudi, �??Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,�?? Opt. Lett. 24, 631�??633, (1999). [CrossRef]
  3. F. X. Kärtner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, �??Ultrabroadband double-chirped mirror pairs for generation of octave spectra,�?? J. Opt. Soc. Am. B 18, 882�??885, (2001). [CrossRef]
  4. L. Xu, L. Liming, N. Nakagawa, R. Morita, M. Yamashita, �??Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,�?? IEEE Phot. Technol. Lett. 12, 1540�??1542, (2000). [CrossRef]
  5. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, O. Svelto �??Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,�?? Opt. Lett. 28, to be published, Oct. 15, (2003). [CrossRef] [PubMed]
  6. N. Zhavoronkov, G. Korn, �??Generation of single intense short optical pulses by ultrafast molecular phase modulation,�?? Phys. Rev. Lett. 88, 203901 (2002). [CrossRef] [PubMed]
  7. V. Kalosha, J. Herrmann, �??Ultrabroadband phase-amplitude modulation and compression of extremely short uv and vuv pulses by Raman-active molecular modulators,�?? Phys. Rev. A 67, 031801 (2003). [CrossRef]
  8. F. Gires, P. Tournois, �??Interféromètre utilisable pour la compression d�??impulsions lumineuses modulées en fréquence,�?? C. R. Acad. Sci. Paris 258, 6112, (1964).
  9. G. Steinmeyer, �??Dispersion oscillations in ultrafast phase correction devices,�?? IEEE J. Quantum Electron., 39, 1027�??1034, (2003). [CrossRef]
  10. R. Szip�?cs, K. Ferencz, C. Spielmann, F. Krausz, �??Chirped multilayer coatings for broad-band dispersion control in femtosecond lasers,�?? Opt. Lett. 19, 201�??203, (1994). [CrossRef]
  11. R. Szip�?cs and A. K�?házi-Kis, �??Theory and desing of chirped dielectric mirrors,�?? Appl. Phys. B 65, 115�??135, (1997). [CrossRef]
  12. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, T. Tschudi, �??Design and fabrication of double-chirped mirrors,�?? Opt. Lett. 22, 831�??833, (1997). [CrossRef] [PubMed]
  13. N. Matuschek, F. X. Kärtner, U. Keller, �??Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,�?? IEEE J. Quantum Electron. 35, 129�??137, (1999). [CrossRef]
  14. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, �??Optimal single-band normal-incidence antireflection coatings,�?? Appl. Opt. 35, 644�??658, (1996). [CrossRef] [PubMed]
  15. N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, U. Keller �??Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,�?? Appl. Phys. B 71, 509-522, (2000). [CrossRef]
  16. G. Tempea, V. Yakovlev, B. Bacovic, F. Krausz, K. Ferencz, �??Tilted-front-interface chirped mirrors,�?? J. Opt. Soc. Am. B 18, 1747�??1750, (2001). [CrossRef]
  17. K. Starke, D. Ristau, Laserzentrum Hannover, private communication, (2002).

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