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Large-scale (180 × 60 × 1 mm3) transmission gratings with groove densities of 1250 and 1740 lines/mm have been developed, resulting in diffraction efficiencies above 95%. The throughput of a folded pulse compressor with two large-scale transmission gratings was approximately 80% in a 20-fs Ti:sapphire chirped-pulse amplification (CPA) laser. The parabolic bending of the transmission grating due to anti-reflection (AR) coating was minimized to 2.9 λ at 633 nm by improving the evaporation process. By a simple analysis, we explain why this level of bending does not induce a wavefront distortion through the transmission grating near the Littrow condition while the wavefront from a reflection grating is distorted to nearly twice the bending of the grating. The calculation based on the measured bending shows that both the group delay difference relative to the ideally flat grating from 750 to 850 nm and the spatial pulse front distortion over a 60-mm-diameter input beam are negligible, even when the dispersive beam covers ~140 mm on the grating. The spatial pulse front distortion measured after the compressor was less than the measurement limit (1.5 fs) for a 20-mm-diameter beam, where the beam size in the dispersive direction on the grating was 85 mm.
© 2014 Optical Society of America
1. Introduction
For the generation and application of high-order harmonics in the soft X-ray region and attosecond pulses [1–4], high-peak-power, ultrashort-pulse lasers with a high repetition rate are required [5,6]. Gratings are one of the key components to achieve a high output power and high efficiency from chirped-pulse amplification (CPA) systems. Typical compressors and stretchers for terawatt (TW)-class Ti:sapphire lasers are composed of large-scale, Au-coated diffraction gratings (e.g., from Horiba Jobin Yvon [7]). The throughput of the compressor would drop gradually from 70% to about 50% after several months of operation [8,9] due to high thermal loading, although there is a method to recover its efficiency [10]. Gratings with a higher efficiency and longer lifetime are necessary to achieve a higher throughput constantly in high-peak-power Ti:sapphire laser systems. To achieve this, there are two alternatives. One is the multilayer dielectric diffraction grating [11,12], in which the efficiency and damage fluence are quite high. However, this kind of gratings was designed for high-energy glass lasers or high-average-power fiber lasers [13,14], and the bandwidth may not be broad enough for the Ti:sapphire laser system with a pulse duration of ~20 fs or less.
Transmission gratings can be another choice [15]. They are already frequently used in high-average-power fiber-based CPA systems. Because of the relatively narrow bandwidth and long pulse duration of fiber-based CPA laser systems [16–19], the size of the transmission grating is not large, for example 60 × 10 mm2 [17]. However, for high-peak-power Ti:sapphire CPA laser systems with an output energy of ~10 mJ, and a peak power of ~TW at 1 kHz, the size for the transmission grating should be larger. Furthermore, large-scale transmission gratings are also required in fiber lasers for further scaling of the output energies by stretching the pulses in the CPA systems [20].
Here, we developed new transmission gratings with a size of 180 × 60 × 1 mm3 and groove densities of 1740 and 1250 lines/mm by using optical lithography [21]. Both gratings showed diffraction efficiencies above 95% and a folded compressor with two gratings (four-pass) throughput up to 80%. The threshold of white-light continuum generation due to self-phase modulation becomes higher as decreasing the thickness of the substrate. However, a thin substrate would cause the bending of the gratings due to AR coating, resulting in wavefront distortion through the pulse compressor. We therefore characterized the bending of a grating due to the substrate itself and AR coating by measuring the wavefronts of the reflected beams from the substrate surface. By improving the evaporation process, the bending due to AR coating was minimized to 2.9 λ, which is almost comparable with that of the substrate itself.
There still remains a spatial bending of the transmission grating. However, we found that the spatial bending does not induce a wavefront distortion through the transmission grating in the Littrow condition of a monochromatic beam, while the wavefront distortion is approximately two times the spatial bending in the case of a reflection grating. Although femtosecond pulses contain a broad spectrum, this fact explains why a pulse compressor with transmission gratings is considerably less sensitive to the bending than that of reflection gratings.
Ray tracing calculation based on the measured bending shows that the group delay between 750 and 850 nm can be compensated within the spatial variation of <0.3 fs in a folded compressor and <0.003 fs in a four-grating compressor using 1250-lines/mm gratings for a 60-mm-diameter beam with a bandwidth of 100 nm. We measured the spatial pulse front distortion in a TW-class Ti:sapphire laser in which the beam size in the dispersive direction was 85 mm on a grating. However, we did not observe an apparent distortion for a 20-mm-diameter beam within a detection limit lower than 1.5 fs. This is consistent with the ray tracing of a pulse compressor with curved gratings.
2. Design and diffraction efficiencies of transmission gratings
Figure 1(a) shows the calculated efficiency of a conventional rectangular surface-relief transmission grating for 800 nm with an incident angle of 44° in the case of 1740 lines/mm. The calculation was done by the rigorous coupled-wave analysis (RCWA). The horizontal and vertical axes are the duty cycle and the depth of grooves, respectively. Since there is a broad area with a high efficiency over 95%, it is possible to obtain highly efficient diffraction by optimizing the duty cycle and the depth. Maximum efficiency is expected to be 97.2% with a duty cycle of 0.42 and a depth of 1.2 μm.
Fig. 1 (a) Calculated contour map of the efficiencies at 800 nm for the grating with 1740 lines/mm at an incident angle of 44°. (b) and (c) Scanning electronic microscopy (SEM) images of the grating in the scales of 1 μm and 2 μm, respectively. The red bars show the corresponding scales.
Figures 1(b) and 1(c) show the scanning electron microscopy (SEM) images of the fabricated grooves in the scales of 1 μm and 2 μm, respectively. We used a conventional projection system for semiconductor lithography to fabricate the transmission gratings. The original pattern was exposed to a resist on a 1-mm-thick fused quartz substrate with a diameter of 200 mm by a 4 × reduction lens system, and the size of one grating unit was 10 × 10 mm2. The 180 mm × 60 mm grating is made by continuously connecting the 18 × 6 matrices of one unit to form a single grating with an accuracy of 5 nm. There is no periodic placement between 10 × 10 mm2 units and the grooves across the neighboring units are connected with a constant pitch horizontally and are connected continuously vertically. The alignment accuracy of 5 nm may be less than the distribution of the groove width. Then we have not observed an apparent effect like a spectrum slip. The grooves are notched by etching the pattern on a fused quartz substrate. The back side of the grooves is AR coated.
Figure 2(a) shows the angle dependence of the diffraction efficiency of a 1740-lines/mm grating measured with broadband femtosecond pulses from the pulse stretcher ranging from 750 to 850 nm. The inset shows the spectrum used in the measurement. The incident angles were altered from 34° to 54°, and the maximum efficiency appeared at 44°. The peak efficiency was over 94% for TE polarization (along the grooves of the grating). From 40° to 48°, the diffraction efficiencies were over 90%, which can be applied in the stretcher or compressor for the fine adjustment of dispersions. The wavelength dependence of the diffraction efficiencies at an incident angle of 44° is shown in Fig. 2(b). The wavelength was scanned by a slit in the stretcher from 750 nm to 850 nm. The inset shows a typical spectrum at 800 nm with a bandwidth of 17.5 nm. As shown in Fig. 2(b), the spectral response was nearly flat during the whole range while keeping efficiency over 90%. The maximum efficiency was over 95% at 800 nm.
Fig. 2 (a) Dependence of the diffraction efficiencies on the incident angles for the TE polarization for a 1740-lines/mm grating. Maximum efficiency over 94% appears at the angle of 44°. The inset shows the normalized spectrum of the probe pulse for the measurement. (b) Dependences of the diffraction efficiency on the wavelength for the TE polarization in 1740- (red) and 1250- (black) lines/mm gratings at incidence angles of 44° and 30° respectively. The inset shows a typical spectrum of the probe centered at 800 nm.
The transmission grating with a higher groove density of 1740 lines/mm can be applied in a stretcher close to the Littrow configuration to broaden the pulse width and in a compressor to provide a high throughput. In a previous paper, a high diffraction efficiency (~93%) of the transmission grating with a groove density of 1250 lines/mm was already demonstrated [21]. In this paper, the improved version of 1250-lines/mm gratings was developed, resulting in a higher efficiency near 97% at 800 nm as shown in Fig. 2(b) and a compression throughput above 80% for 20 fs pulses by finely optimizing the groove depth, duty cycle and the groove shape during the fabrication process. The maximum efficiency of 98% is expected by the calculation with a duty cycle of 0.49 and a depth of 1.38 μm [21]. At the same time, the transmission grating with a groove density of 1250 lines/mm was developed at a wavelength of 1 μm, and applied for a high-average-power fiber laser system to stretch the pulses to 500 ps and to compress after amplification with a throughput of 80% [20].
Generally speaking, the 1250-lines/mm grating is suitable to ultrashort (i.e., broadband) Ti:sapphire lasers because of its low dispersion, while the 1740-lines/mm grating is useful to stretch pulses broader in a relatively narrow-band fiber lasers.
3. Measurement of the threshold for white-light continuum generation
The upper limit of the intensity on the transmission grating was not determined by the damage but by the generation of white-light continuum in the 1-mm-thick fused quartz substrate with a pulse width below 100 fs. The gratings were not destroyed by white-light generation. The threshold of white-light continuum generation and corresponding B integral are shown in Figs. 3(a) and 3(b) for a 1250-lines/mm grating. With a pulse width of 40 fs, the threshold intensity for the white-light generation reaches up to 400 GW/cm2. The intensity and B integral are increased as the pulse duration decreases. To confirm the origin of white-light generation, we sent the same laser beam to a wedged fused quartz plate without AR coating and observed similar white-light generation, showing that the grating substrate is the source. The threshold drops significantly when using 4- to 5-mm-thick fused quartz wedges. The thinner grating is obviously advantageous to suppress white-light generation or self-focusing by Kerr effect, although bending is inevitable in a thin grating.
Fig. 3 Threshold for white-light continuum generation in the transmission grating with 1250 lines/mm. (a) Threshold intensity as a function of the pulse width. (b) B integral versus pulse width.
4. Spatial distortion of transmission grating
Spatial distortion was measured directly in gratings with a dimension of 180 × 60 × 1 mm3. The grating is held at the four corners where it is pressed to polished flat planes (1 × 1 mm2) by elastic plates. Indeed, this scheme reduced the wavefront distortion considerably compared with the initial scheme with three-point contact. Spatial distortion from the ideal flat plane (i.e., bending) may occur due to the thin substrate and/or AR coating. To determine the deformation of the transmission gratings, we measured the wavefront of the beam reflected from a transmission grating by a Zygo interferometer equipped with a He–Ne laser (633 nm). The two-dimensional (2-D) wavefront distortion W(x, y) is expressed as
where x and y are the axes across and along the groove direction, respectively, and is the spatial distortion of the grating. For simplicity, we define W(x) as the average of W(x, y) from y = 27.5 to 32.5 mm and H(x) represents the one-dimensional (1-D) distortion.First we measured the distortion of 5 grating samples without AR coating. Peak to valley (PV) values over the total area are spread from 1 to 6.2 λ. This difference does not depend on the groove density but may come from the substrate itself or holding to the frame. Next, we measured the distortion after the ion-assisted deposition (IAD) of AR coating, which is commonly used by the manufacturer (Sigma Koki Co. Ltd.). Figure 4(a) shows a 2-D wavefront map of W(x, y) of a 1250-lines/mm grating with AR coating, and Fig. 4(b) shows the profile in the central region W(x). The PV value becomes 88 λ in W(x, y) and 44 λ in H(x, y). The positive directions of W(x, y) and H(x, y) are defined in the direction from the groove side to the AR side. Among the 5 samples with 1250- and 1740-lines/mm groove densities, the PV values of H(x, y) are distributed from 44 to 52 λ. These values are one order of magnitude larger than those without AR coating, and the bending does not depend on the groove density.
Fig. 4 (a) Reflected wavefront map (W(x, y)) of the transmission grating (1250 lines/mm with AR coating) at 633 nm (double pass). (b) Profile in the center region (averaged from y = 27.5–32.5 mm).
This large bending is obviously induced by AR coating. In general, the bending due to multi-layer coating is parabolic and is inversely proportional to the square of the substrate thickness and proportional to the thickness of the AR coating [22], although the bending is fitted to the 3rd-order polynomial in Fig. 4(b). In addition, the magnitude of the bending significantly depends on the coating materials and deposition processes. Some processes cause negative bending (i.e., the AR side becomes a concave surface) that are opposite to those depicted in Fig. 4. To compensate the bending due to the AR coating, we evaporated a SiO2 single layer by IAD that gives a negative bending under the AR coating. Furthermore, AR coating was made by an e-beam deposition to reduce a positive bending rather than IAD. The transmittance of AR coating was maintained to the maximum value.
Finally, the bending was further compensated by balancing positive and negative bending during the deposition process. Figures 5(a) and 5(b) show a 2-D wavefront map of W(x, y) and a profile in the central region W(x), respectively. The bending is considerably reduced to PV = 2.9 λ in H(x) [PV = 5.8 λ in W(x)]. In this case the shape of the wavefront is still parabolic. However, negative bending and non-parabolic distortion can be seen when the PV values decrease. This residual distortion may be due to the bending of the substrates and/or the holding to the frame because, as mentioned above, (i) it does not depend on the groove density and (ii) the amounts of the distortion are on the same order as those observed in the grating substrates without the AR coating. Therefore, the bending was more generally fitted to the 3rd-order polynomial in Fig. 5(b). In Fig. 5(a), a slight variation of wavefront along y axis would distort the beam profile. However we think this effect is small at a level of PV = 2.9 λ. We thus used a 1-D profile H(x) in the following analysis. The nano-textured surface may be an alternative for AR coating without bending, although we did not try it in this paper.
Fig. 5 (a) Reflected wavefront map of a grating with a groove density of 1250 lines/mm at 633 nm after optimizing the AR coating (double pass). (b) Wavefront profile (red solid line) averaged from y = 27.5–32.5 mm and fitted to a 3rd-order polynomial curve (green dash line). The blue line is the deviation from the fitted curve.
5. Wavefront of the diffracted beam induced by the spatial distortion of the gratings
We compared the wavefronts of the diffracted beam double-passed through a transmission grating [Fig. 6(a)] and of the diffracted beam reflected from a transmission grating [Fig. 6(b)] by a Zygo interferometer equipped with a He–Ne laser. As shown in Fig. 6(c), there is a striking difference between the two cases. The wavefront of the diffracted beam double-passed through the transmission grating was almost flat in the nearly Littrow condition (23.3°, the green short-dashed line in Fig. 6(c)), while a large distortion remained for the reflected diffraction beam in the Littrow condition (23.3°, the blue dash-dotted line in Fig. 6(c)). The wavefront through the transmission grating depends on incident angle and changes the sign. These observations posed a question on the relation between the observed wavefronts of the diffracted beam and the bending of the transmission grating.
Fig. 6 Wavefront measurement of (a) the diffracted beam double-passed through a transmission grating and (b) diffracted beam reflected from a transmission grating. (c) Wavefront error in λ at 633 nm versus grating position along the dispersive direction. At the Littrow angle (23.3°), the wavefront is flat through the transmission grating (the green short-dashed line), while highly parabolic in the reflection grating (the blue dash-dotted line). The incidence angles are shown in parentheses. At the off Littrow angles, the wavefront through the transmission grating depends on incident angle and changes the sign. PV = 52 λ in H(x).
To explain these results, we tried a simple 2-D analysis. The diffraction schemes of transmission and reflection are shown in Fig. 7(a) and 7(b), respectively. The observed wavefront distortion is given by W(x'), while the 1-D distortion of a grating is given by H(x). The values of α0 and β0 are the incident and diffraction angles to the ideally flat grating, respectively. The tangential angle to the grating surface Δα(x) at x (the change of the incidence angle with respect to the case with an ideally flat grating) is expressed as
The incidence angle α(x) at x is then given byHere we ignored the substrate. However the output angle from the substrate is identical to β, if the substrate is completely parallel. The slope of the substrate is quite small (10 µm/250 mm, 50 µrad). Then we go to the next. The corresponding diffraction angle β(x) iswhere λ is the wavelength, Λ is the groove pitch, m is the diffraction order, and . The diffraction angle β(x) is approximated by the Taylor expansion of sin−1 as follows,This approximation is justified because the maximum Δβ = 0.6 mrad is much less than β0 = 0.4 rad in the condition of Fig. 4(b) and at α0 = β0. Let us consider the observed wavefront along the x' axis (W(x')) where x' = x cosβ0. The total deviation of the diffraction angle Δγ(x) from β0 isas seen in Fig. 8(a). The observed wavefront isBy the projection of W(x') from the x' to x axes, we defined the wavefront on the grating W(x), which was already used in Section 3. In the measurement, the conversion from x' to x can be done easily by scaling the x-axis with the grating size. The wavefront after the double-pass cannot be said straightforwardly twice that after the single pass, but it is verified after a careful analysis to be approximated by twice that after the single pass. Then the observed wavefront and the grating distortion are related asIt should be noted that no cancellation occur for any incident angle by the double pass. This is a striking result. In the case of transmission gratings, the wavefront W(x) becomes zero (flat) at the Littrow condition (i.e., α0 = β0) as shown in Fig. 6(c). The wavefronts through the transmission grating were observed by changing α0 (and then β0) off from the Littrow angle as shown in Fig. 6(c). All the data are in good agreement with Eq. (8).Fig. 7 Notations for the wavefront analysis. (a) Diffraction by a transmission grating; (b) diffraction by a reflection grating. H(x) is distorted grating surface measured by the deviation from the ideally flat surface, where x is the distance along the dispersive direction. W(x') is the distorted wavefront after diffraction. α0 and β0 are the incidence and diffraction angles, respectively. Δα and Δβ are the changes of incidence and diffraction angles due to the distortion of the grating, respectively.
Fig. 8 Notation for the ray-tracing analysis. Pin: input plane, Gi: i-th grating, Pout: reference plane. Note that the curvatures of gratings are illustrated as positive for G1 and G2, and negative for G3 and G4, respectively.
On the other hand, in the case of reflection gratings, the diffracted beam ray [Fig. 7(b)] satisfies the condition:
Then the wavefront is given byIn this case, the wavefront W(x) is directly distorted by H(x) for any condition. The measured PV value of H(x) in the sample of Fig. 6(c) was 52 λ, as shown in Fig. 4. The PV value for the reflected diffraction curve W(x) is calculated from Eq. (10) to be 96 λ, in fairly good agreement with the measured value of 100 λ reported in Fig. 6(c).This fact clearly proves that the distortion of the wavefront and pulse front through a pulse compressor with transmission gratings is much less sensitive to the bending of gratings than that with reflection gratings. The above experiment and analysis are valid for monochromatic lights such as a He–Ne laser. However, femtosecond pulses contain broadband spectra and the incidence angles differ slightly from the Littrow angles at the edge of the spectrum, even though a pulse compressor is set to the Littrow condition at the center wavelength.
In the next section, the influence of the bended grating on the wave (pulse) front of broadband pulses through a pulse compressor is numerically analyzed by a 2-D ray-tracing method.
6. Ray tracing analysis of a grating-pair pulse compressor with quadratic distortion
As discussed in Section 5, the wavefront distortion is minimized at a monochromatic beam when it is diffracted by a transmission grating at the Littrow angle. In the case of grating pulse compressors, however, the incident beam has a finite bandwidth. The rays that are not at the spatial center of the beam or at the center of the spectrum are slightly displaced by the distortion of the gratings. Such displacement of the rays will induce broadening of the output pulse duration. Here, we analyzed the spatial dependences of the dispersion through a pulse compressor by using a 2-D ray-tracing method.
Figure 8 shows the schematic of the ray-tracing simulation. The grating distortion is assumed to be quadratic for simplicity and given by . The curvature parameter is assumed to be a = 2.26 × 10−7 mm−1, which corresponds to the measured grating distortion of PV = 2.9 λ at 633 nm as shown in Fig. 5. The grating thickness is neglected for simplicity. The path length is calculated from the initial reference plane Pin to the last reference plane Pout as a function of the wavelength λ, the grating curvatures ai, and the position x of the incident beam. The path length L(λ;ai,x) is then converted to a group delay τg by τg = L / c. We used the group delay difference Δτg with respect to a reference ray that passes through ideal flat gratings, as given by
The solid curves in Fig. 9(a) show the group delay differences for a typical pulse compressor using 1250-lines/mm transmission gratings at three different beam positions (x = −30, 0, + 30 mm). The position dependence of the dispersion induces spatial inhomogeneity of the pulse shape across the beam as well as the spatial distortion of the pulse front. The separations of the grating pairs (G1, G2) and (G3, G4) are set at 440 mm along the ray at 800 nm, which corresponds to a dispersion to stretch a transform-limited 30-fs Gaussian pulse to 150 ps. The beam sizes in the dispersed direction on the second and third gratings (G2 and G3) are ~143 mm, assuming a spectral range from 750 to 850 nm and an input beam diameter of 60 mm. The directions of the grating curvatures are chosen as , as shown in the inset. This pulse compressor can be constructed by two gratings with a folded geometry. The group delay differences are <1.8 fs within a bandwidth from 750 to 850 nm at x = 0 mm. The spatial variation of the group delays is <0.3 fs for the input beam of 60 mm in diameter, or ~λ/10 at 800 nm. The largest group delay difference thus becomes 1.9 fs. The group delay difference can be further minimized by optimizing the incident angle and the separation of the gratings, which will remove the residual third-order dispersion. The dotted curves in Fig. 9(a) show the residual group delay difference after subtracting the third-order dispersion, in which the largest group delay difference becomes 0.7 fs. The output rays are well collimated after the compressor. The rays are transversally displaced up to 30 μm in the 100-nm bandwidth at the reference plane P4, which is placed 1 m away from the last grating G4. This displacement is negligible compared with typical beam sizes.
Fig. 9 Group delay differences with respect to the flat grating pairs for three different beam positions (red: x = 30 mm; black; x = 0 mm; blue: x = −30 mm). The solid curves show the relative group delays directly obtained by ray-tracing, while the dotted curves show those after subtracting the third-order dispersion. The upper panels (a, b) and lower ones (c, d) are for the cases with 1250- and 1740- lines/mm gratings, respectively. The insets illustrate the directions of the grating curvature.
The group delay differences can be drastically reduced by changing the directions of the grating curvatures. Figure 9(b) shows the group delay differences with the grating curvatures chosen as (i = 1, 2, 3, 4), as shown in the inset. Although this configuration cannot be folded, the largest group delay difference becomes 0.003 fs. This is because the distortion-induced group delays are canceled each other due to the diffractions at the second and third gratings.
The ray-tracing simulations for a pulse compressor using 1740-lines/mm gratings were also performed with the same quadratic distortion. The separations of the grating pairs (G1, G2) and (G3, G4) are set at 260 mm along the ray at 800 nm, which corresponds to a dispersion to stretch a transform-limited 50-fs Gaussian pulse to 150 ps. The beam sizes in the dispersed direction on the second and third gratings (G2, G3) are ~137 mm, assuming a spectral range from 770 to 830 nm and a beam diameter of 60 mm. Figure 9(c) shows the group delay differences with the curvatures of . The largest group delay differences are 2.9 fs and 1.2 fs with and without the compensation of third-order dispersion, respectively. Similar to the cases with 1250-lines/mm grating, the group delay differences can be further improved by choosing the proper directions of the curvature. Figure 9(d) shows the case with the curvatures of , in which the largest group delay difference becomes 0.005 fs.
7. Measurement of the spatial pulse front distortion through a folded compressor
To confirm the simulated results in Section 6, we measured the spatial pulse front distortion in the output from a Ti:sapphire CPA laser [21]. Figure 10 shows the schematic of a folded compressor with two gratings (four-pass) in the Ti:sapphire CPA laser. Two transmission gratings with a size of 40 × 60 × 1 mm3 and 180 × 60 × 1 mm3 are placed inside the compressor. The possible maximum size of the input beam is less than 30 mm in diameter in this configuration. The incident angle and the grating separation were 29.5° and 350 mm, respectively. The incident beams with a spectral range from 750 to 850 nm are dispersed to about 65 mm on the second grating. The total beam size in the dispersive direction is 85 mm on the second grating when considering an input beam size of 20 mm. We optimized the distance and angles of the transmission gratings in the compressor to reduce the second- and third- order dispersions to achieve the shortest pulse duration. The obtained pulse duration was 20 fs, and there were small residual high-order dispersions.
Fig. 10 Schematic of the folded compressor with two gratings in a Ti:sapphire CPA laser with two transmission gratings (1250 lines/mm). Sizes are 40 × 60 × 1 mm3 and 180 × 60 × 1 mm3, respectively. The input beam size is about 20 mm, and the dispersive length on the transmission grating 2 is about 85 mm.
Schematic of the spatial pulse front distortion measurement is shown in Fig. 11. The center of the beam is selected by pinholes A (1.5-mm in diameter) and A' to use as a reference. The beam through the pinhole B corresponds to a sampled point in the whole input beam by translating the stage X. The relative delay between the two beams through the pinholes A, A' and B is measured by translating the flat mirror to maximize the second harmonic generated in a 300-μm-thick LBO (Lithium Triborate, LiB3O5) crystal [23,24].
Fig. 11 Schematic of the spatial pulse front distortion measurement. PD: photo detector. X and Y: translation directions.
The measured results are shown in Fig. 12(a) in the horizontal direction and Fig. 12(b) in the vertical direction. The slope due to the inclination of the roof mirror is corrected from the raw data as reported in [23]. The calculated root mean square (RMS) errors were 0.44 μm (horizontal) and 0.53 μm (vertical), corresponding to the time delay of 1.5 fs and 1.8 fs, respectively. There were no obvious parabolic tendencies in the two plots because the measurement precisions are limited by the fluctuation of the laser system. We therefore concluded that the spatial pulse front distortion was nearly negligible within the measurement limit of 1.5 fs, across the output beam size of 20 mm, which was diverged to 85 mm on the second grating. This result is also consistent with the ray-tracing analysis conducted in Section 6.
Fig. 12 Results of the spatial pulse front distortion in the horizontal (a) and vertical direction (b). The RMS errors were 0.44 μm (horizontal) and 0.53 μm (vertical). The path difference mainly originates from the noise of the laser system.
8. Summary
We presented the performances of newly designed, large-scale, high-efficiency transmission gratings. The groove densities of the fabricated gratings were 1250 and 1740 lines/mm. The aperture was as large as 180 × 60 mm2, with a thickness of 1 mm. The diffraction efficiency was measured to be more than 95% at 800 nm, resulting in a high throughput of a pulse compressor over 80% for a 20-fs Ti:sapphire CPA laser. The operational intensity is limited by the white-light continuum generation that occurs at 400 GW/cm2 with 40-fs pulses. Such a high operational intensity is achieved by using an extremely thin (1 mm) fused quartz substrate.
Moreover, we measured the effect of bending, which is inevitable in a thin substrate. The bending was improved from 44 to 2.9 λ (at 633 nm) over the total area (180 mm × 60 mm) by optimizing the evaporation process for the AR coating. We explained by a simple model that the residual distortion of the grating did not induce the wavefront distortion near the Littrow condition in the case of transmission gratings, while the wavefront was distorted by nearly twice the residual distortion in the case of reflection gratings. The ray-tracing calculation based on the measured wavefront distortion showed that the spatial variation of the group delay across a 60-mm diameter beam is <0.3 fs in a folded compressor and <0.003 fs in a four-grating compressor using 1250-lines/mm gratings.
The spatial pulse front distortion through a pulse compressor was measured to be less than 1.5 fs when the dispersive length on the grating was 85 mm, which was within the measurement limit and consistent with the ray-tracing simulations. Thinner gratings are desirable especially for the last grating in a compressor to increase the available intensity. It is possible to fabricate a 0.5-mm-thick grating by using the established production process. Optical lithography allows us to fabricate gratings up to 300–450 mm, for which such large fused quartz wafers are already available. This type of transmission gratings can be used not only in high-throughput pulse compressors, but also in high-resolution multi-pass spectrometers [25].
Acknowledgments
The authors would like to thank Dr. Takashi Onose for helpful discussions, and Mr. Kiyoshi Suda for supplying various AR coatings. This work was partially supported by Grant-in-Aid for Scientific Research (A) Grant Number 24246022 by Japan Society for the Promotion of Science.
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