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Abstract
An entirely reflective slit spatial filter is proposed to provide spatial filtering, gain isolation, and ASE mitigation for high-energy laser systems. The traditional circular pinhole is replaced by two orthogonal slits, which lowers the intensity at the spatial filter plane by up to two orders of magnitude, and by using reflective optics we reduce spatial dispersion and eliminate B-integral effects. A ray trace model of the spatial filter shows excellent transmitted wavefront, but also indicates aberrations at the foci from using cylindrical optics at 45°. It is expected that the use of off-axis parabolic mirrors would mitigate this issue but comes at the cost of more complicated, expensive optics and more complex alignment. We created a numerical model based on Fourier optics to explain this effect and guide design requirements to mitigate it. High-quality imaging and filtering capabilities are demonstrated experimentally.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Low-pass, spatial filtering, by using a small aperture pinhole in a relay telescope, is a critical element to improve the beam quality, as well as minimize the risk of parasitics and longitudinal ASE, of high-energy laser systems. As the beam propagates through the amplifier cavity, high-spatial frequency intensity fluctuations develop from gain non-uniformity or the accumulation of nonlinear phase distortions, significantly degrading beam quality [1]. By placing a pinhole aperture at the focus of a relay telescope, these high-frequency components of the spatial Fourier-mode spectrum are blocked, allowing only the low-frequency components to pass [2]. This resets high-frequency spatial B-integral effects and provides gain isolation from unwanted parasitic beams, which results in an improved far-field beam quality and mitigates damage to optics. However, high-intensity laser pulses generate a plasma when interacting with pinhole aperture material, which expands into the beam path preventing any further beam propagation through the aperture past the closure time—an effect called pinhole closure [3]. Pinhole geometry and material have a major impact on not just damage threshold but also the dynamics of pinhole closure. Design refinements have led to the use of a long, conical pinhole structure; this allows the pinhole to reflect or refract light rather than absorb it and spreads the beam intensity over a larger area, which produces a cooler, slower expanding plasma extending the time to closure [4]. Additionally, studies have shown that use of a high Z material reduces the rate of pinhole closure [5]. During the process of pinhole closure the aperture material is ablated; this deposits aperture material throughout the chamber where the pinhole aperture is located, and results in the gradual disappearance of the aperture as a filter and gain isolator. In order to reduce system maintenance costs and downtime it is important that the spatial filter has a lifetime that is a significant fraction of the overall laser system’s by operating well below the damage threshold to minimize aperture loss. Since the filter lifetime is directly determined by the number of shots per unit time, this effect becomes much more consequential as high-energy laser systems move into the high-repetition rate, high-average power regime and drives the need for a new functional solution.
One method to address this problem is to focus the beam into two longitudinally-displaced, orthogonal line foci using two nested cylindrical relay telescopes shown in Fig. 1 [6,7]. The beam intensity at each line focus is approximately two orders of magnitude lower than that of a single circular focus in a traditional pinhole filter, potentially lowering irradiance and fluence to below the plasma production threshold of the aperture material. The relative displacement of the two cylindrical relay telescopes does not affect the relay image but does separate the foci, allowing each axis to be filtered independently. This system uses slits instead of circular pinholes to filter the beam, and since each slit is at the far-field in one axis the filter response is equivalent to a square pinhole [8].
Fig. 1. Diagram of the cylindrical lens spatial filter patented by Erlandson. Here, f1 is the focal length of the first cylindrical telescope producing a horizontal line focus, f2 is the focal length of the second cylindrical telescope producing a vertical line focus, and g is the slit spacing set by the offset of the two telescopes [6,7].
The cylindrical lens slit spatial filter was implemented on the High-repetition-rate Advanced Petawatt Laser System (HAPLS) to enable high-average power beam transport [9]. Here, the two cylindrical relay telescopes utilized cylindrical lenses, operating at ∼f/20, and were offset by ∼20 cm from one another. One lens from each telescope was mounted fixed at either end of the spatial filter vacuum tube, while the other lens was attached to a translation stage for precise alignment. The filter itself is created by using materials at grazing incidence to keep the fluence on the optic below the damage threshold. This means that no plasma is ever created and thus the pinhole will endure under high average power loading. Fused silica has been proven to be the current leader in handling high laser fluence largely due to its strength and purity of materials in fabrication. The use of surface preparation techniques developed for the National Ignition Facility (NIF) called Acid Mitigation Process (AMP) produces surfaces cable of withstanding extremely high laser fluence ∼ 60-80 J/cm2 for a 1053 nm, 4.5-5 ns FWHM pulse normal to surface [10,11]. At grazing incidence, the damage threshold grows to > 300 J/cm2 where samples have undergone long term testing (100000 shots) [8,10]. This transmissive slit spatial filter was incorporated in the HAPLS Nd:Glass pump laser beamline, which is designed to deliver up to 200 J in a 20 ns pulse at a 10 Hz repetition rate [9]. The HAPLS laser system has been commissioned and installed now at ELI-Beamlines in the Czech Republic where the pump laser system, which employs the cylindrical filter, routinely produces > 100 J at 3.3 Hz. This demonstration has confirmed that the filter is stable and produces no plasma during operation.
Recently, several studies have looked at design variations of the cylindrical lens slit spatial filter proposed by Erlandson and their performance for lasers that operate around the long-pulse parameter space [12–14]; however, as laser systems move to the high-energy, short-pulse regime, it becomes important to reduce dispersion from transmissive optics. To enable industrial applications of PW-class lasers [15–19], new system architecture designs have been developed, such as the Big Aperture Thulium (BAT) laser [20,21], allowing high-intensity lasers to operate at kW average power and beyond. This has motivated the development of an entirely reflective slit spatial filter for use in high-energy, short-pulse laser systems; here, the four cylindrical lenses are replaced by four cylindrical mirrors. An all-reflective design will reduce spatial dispersion, minimize B-integral effects, and eliminate all ghost reflections and ghost foci associated with transmissive lenses [22]. This paper presents a conceptual design and ray trace model of an entirely reflective slit spatial filter and explores the theoretical basis of the optical aberrations seen in the ray trace model using Fourier analysis to confirm design constraints. Finally, we report on a proof-of-concept experimental demonstration that details the imaging and far-field qualities of the spatial filter.
2. Design and simulations of the entirely reflective slit spatial filter
The four cylindrical mirrors each have a 45-degree angle of incidence to the beam path by rotating them about their cylindrical axis, and an additional flat mirror is used to direct the output beam parallel to the optical table—a conceptual layout is seen in Fig. 2. The separation of the vertical and horizontal foci is determined by the vertical separation of the first two cylindrical mirrors. The use of 45-degree AOI makes the incoming polarization always simple with respect to the optical surface (i.e. all S or all P polarization) and maintains the polarization purity of the beam. Departing from this angle would make the design sensitive to the difference in the reflected phase of S and P polarized light off of the mirror’s multilayer dielectric coating. Thus, this configuration does not add additional constraints on coating design with respect to the other mirrors in the system, except in the case of small f-number where a large range of complex incidence angles are present on the inner two cylindrical mirrors.
Fig. 2. Conceptual layout of an entirely reflective slit spatial filter, implemented by replacing the cylindrical lenses in Fig. 1 with highly reflective cylindrical mirrors.
The primary design concern is an expected line focus distortion, caused by using cylindrical optics at 45-degrees, which can be minimized by constraining the f-number of the cylindrical mirrors to greater than ∼25-30; it is worth noting that the 45-degree angle of incidence reduces the effective focal length of each mirror by a factor of $\sqrt 2 $. Additionally, the use of a of a reflective rather than transmissive optic adds an additional degree of freedom in the non-power axis of the cylindrical mirror making the overall alignment sensitivity slightly greater than the transmissive case. The configuration demonstrated in this study constitutes a worst-case scenario since it is expected that this aberration can be largely mitigated using parabolic mirrors at the cost of increased fabrication costs and further alignment complexity.
2.1 Ray trace analysis
This conceptual design was modeled in Zemax to better understand the irradiance distribution of the line foci as well as the wavefront at the image plane. The input beam has a Gaussian spatial profile with 12.7 mm 1/e2 diameter at a wavelength of 1053 nm to match the source used in the experimental demonstration. The two offset cylindrical telescopes were composed of 25.4 mm x 25.4 mm cylindrical mirrors, each with a 400 mm focal length. With the beam incident at 45-degrees the effective focal length of each mirror is 283 mm, giving an f-number of ∼22.
The ray trace model revealed line focus distortions caused by using cylindrical optics at a 45-degree angle of incidence. Most prominent is a one-sided fringe pattern that occurs at each line focus, seen in Fig. 3 for a horizontal line focus, which cannot be completely compensated without a more complex mirror surface. It is expected that use of a higher-order super-Gaussian beam profile, used in high-energy laser systems, will enhance this fringe distortion in the far-field energy distribution due to a greater fraction of the beam energy residing in the outer portion of the beam. While these aberrations are at a spatial frequency that are well within the cutoff frequency of the spatial filter, which is filtering high-frequency components that lie tens of transform limited focal spots away from the line focus, this does emphasize the higher f-number design point discussed earlier. The theoretical wavefront output of the system is excellent, with a peak-to-valley of ∼ λ/200 waves and RMS of ∼ λ/1000 waves at the image plane. This wavefront error is insignificant when compared to thermal wavefront errors expected from any high-average power, high-energy laser system that this type of slit filter is envisioned for.
Fig. 3. Zemax simulation of a f/22 entirely reflective slit spatial filter with a Gaussian beam input a) 2-D plot of coherent irradiance at the horizontal line focus b) cross-section taken at x = 0 of log scale coherent irradiance at horizontal line focus c) wavefront of beam at the output image plane.
2.2 Numerical simulation of far-field
To better understand the intensity distribution at the slit plane, we developed a numerical model that can be compared to experimental results. This allows us to approximate the magnitude and spatial extent of the fringe pattern and, thus, determine the extent one can spatial filter without removing appreciable beam power. The dominant effect causing the fringe pattern is attributed to a third-order spatial effect from the mirror surface when examining the problem using Fourier optics. Given the symmetry of the beam profile, we consider the intensity distribution in only one of the transverse axes, reducing this from a 2D to a 1D problem, and model the input beam incident at 45-degrees on the first cylindrical mirror to solve for the intensity distribution in the focal plane. We take the input electric field to be a plane wave with a Gaussian spatial distribution in the axis transverse to propagation,
Here, z is the spatial coordinate of the beam propagation direction, x is the spatial coordinate transverse to the beam propagation, w is the width of our input Gaussian beam, and kz is the wavevector of the input beam. We then define the surface of the cylindrical mirror in the x-z plane, see Fig. 4, a circle with radius R and center at ($\frac{R}{{\sqrt 2 }}$,$\frac{{ - R}}{{\sqrt 2 }}$) to appropriately set our origin. The equation of our mirror surface is then,which, under Taylor expansion to the third-order about x equal to zero, produces,
Removing the first-order $z = x$ component, the reflection that transforms the propagation direction 90-degrees, the rest of the Taylor expansion is inserted into a phase term, which when combined with the 1-D beam profile is our input spatial function at z equal to zero:Taking the fast Fourier Transform (FFT) of this input spatial function, then propagating a distance equal to the focal length of our mirror using the free-space transfer function, we arrive at the focal plane. Performing an inverse-FFT converts this back into a spatial function allowing us to plot the spatial distribution in the focal plane. Here, f is the effective focal length of our mirror and kz is our set of spatial frequencies in the z-axis. Thus, the spatial distribution at the focal plane is given by,
Figure 5 contains the spatial intensity distribution at the focal plane for four different input beam diameters, and thus f-numbers. The strength of the fringe pattern decreases with increasing f-number; for a system of f/20, the fringes contain 25% of the total energy, while a system of f/30 has 8% of the total energy contained within the fringes. Additionally, the width of the main peak increases as the f-number increases; this width can be compared to the diffraction limited line width focus of 0.0316 mm and 0.0632 mm for the f/15 and f/30 case respectively. Reduced energy in the fringe pattern allows for tighter slit filtering, higher beam fluence, and improved performance of the optical spatial filter system.Fig. 5. Spatial distribution of beam irradiance at the focal plane of the cylindrical mirror, x-axis is transverse to the direction of propagation, for different f-numbers by varying the input beam diameter. Curves are normalized to total energy and percent energy found in the fringes for each f-number is included in the legend.
3. Experiment
A proof-of-principle demonstration was constructed using four one-inch diameter, 400 mm focal length cylindrical mirrors and two adjustable mechanical slits. A 1053 nm fiber laser attached to a triplet collimator, with a 1/e2 beam diameter of ∼4 mm, was used as the source beam. To test the spatial filter near its f-number limits the beam was expanded to a 1/e2 beam diameter of ∼12.7 mm. The two cylindrical relay telescopes were offset from each other by ∼5 cm and, as noted above, their effective focal lengths are reduced to 283 mm when used at 45-degree angle-of-incidence (AOI), yielding an initial effective f-number of approximately 22.
The imaging and filtering capabilities were quantified by inserting a USAF 1951 resolution test target before the cylindrical relay telescopes and placing a CCD camera at the image plane. The two cylindrical mirror relay telescopes showed excellent imaging quality with a measured resolution of 11.3 line pairs per millimeter (lp/mm) on the USAF 1951 resolution test target. Filtering was performed by incrementally closing each of the adjustable mechanical slits, that are separated the same distance as the telescope offset, to the point just before the beam becomes clipped. Figures 6(a)–6(d) below shows the unfiltered and filtered CCD image along with their corresponding computed fast Fourier Transform. The spatial filter was very effective in removing the higher frequency spatial components from the substantially modulated beam, and the filtered image retained 92% of the original image intensity despite the narrow slit width.
Fig. 6. (a) Non-filtered USAF 1951 resolution test target with (b) corresponding 2D FFT. (c) Filtered USAF 1951 resolution test target with (d) corresponding 2D FFT. The spatial frequencies in (b) and (d) are normalized to the cutoff frequency determined by the laser wavelength and cylindrical telescope f-number.
Images of the vertical and horizontal foci were taken with two different beam diameters to verify the dependence of the far-field irradiance pattern on the f-number of the system. Figures 7(a)–7(d) shows the images of the vertical and horizontal foci, with f-numbers 22 and 31 respectively, along with their cross-sections to highlight the fringe pattern. As summarized in Table 1, the change in irradiance distribution with f-number followed what is observed in the numerical model, namely that with increased f-number the side fringes decrease in intensity and the main peak broadens in width. Plotted along with the foci cross sections are the corresponding numerical simulations as detailed previously. For the f-number 22 vertical focus, the experimental 1/e2 main peak width is 2% larger than the numerical simulation and the peak spacing is 9% smaller. While for the f-number 31 vertical focus, the experimental 1/e2 main peak width is 12% larger and the peak spacing is 1% smaller than the corresponding numerical simulation. The discrepancy between the vertical and horizontal foci of similar f-number, as well as the difference in the numerical model to the experimental images, is attributed to imperfections of the optics used. Applying a random wavefront perturbation of λ at 633 nm, a magnitude comparable to that present on the demonstration optics, yields an improved match between measurement and simulation.
Fig. 7. Vertical and horizontal line foci of the experimental demonstration with the numerical simulation overlaid. (a) Vertical line focus for f/22 setup (b) Horizontal line focus for f/22 setup (c) Vertical line focus for f/31 setup (d) Horizontal line focus of f/31 setup.
Table 1. Experimental far-field intensity distribution characteristics of the two f-number cases.
4. Discussion
The design of this entirely reflective intense slit spatial filter was motivated by the need for novel high-energy, short-pulse laser systems operating at high-average power to drive secondary-source applications. As these high-intensity lasers move into the high-average power regime it becomes even more imperative to filter out any high-frequency spatial components that can result in self-focusing and damage to optics. Furthermore, the accumulation of spatial frequency modulations negatively affects the beam quality and shot-to-shot reproducibility, which is paramount for secondary-source applications. In the case of laser wakefield acceleration, it has been shown that the laser pulse energy outside of the main focal spot affects the self-injection process causing a broad and irregular transverse distribution of electrons [23].
While HAPLS was able to incorporate the cylindrical lens slit spatial filter into the pump laser beamline, it was not used in the primary Ti:Sapphire short-pulse laser beamline to avoid the non-linear effects and dispersion from the transmissive optics. The entirely reflective slit spatial filter should fill the gap needed for high-energy laser systems. The main concern with this design was the spatial extent of the fringe pattern in the focal plane, from using off-axis cylindrical optics, which could clip the slit aperture. However, the numerical model shows that at a distance of 13 times the diffraction limited focus, the fluence of the fringes drops to 10−4 times the peak fluence for a system with f-number ∼30; this is much smaller than the HAPLS slit width design point of 100 times the diffraction limited focus. Given the HAPLS slit filter demonstration at ∼100 J transmitted by the slits, this entirely reflective slit spatial filter is more than capable of supporting secondary source applications without exceeding the damage threshold of the slit filter material.
5. Conclusion
High-energy lasers are poised to break into the high-average power regime needed for industrial and scientific applications. This demands new laser technology capable of operating in this unique parameter space; here, we presented a novel spatial filter. A brief overview of the cylindrical lens slit spatial filter used on the pump laser beamline of HAPLS was described, introducing the concept of the slit filter. To further evolve this design we have proposed the idea of an entirely reflective slit spatial filter. By replacing the four cylindrical lenses with mirrors, we can avoid dispersion effects that prohibited use of a cylindrical lens spatial filter on the short-pulse beamline of HAPLS.
A ray trace model of the entirely reflective slit spatial filter revealed a one-sided fringe pattern at each of the line foci due to spherical aberrations of the mirror surfaces. With excellent wavefront performance predicted by the model, this aberration in the far field irradiance distribution was a primary design concern. Numerical simulations showed this to be a third-order effect that can be nearly eliminated by keeping the f-number of the system greater than 30 or utilizing parabolic optical surfaces. Finally, an experimental implementation demonstrated the effect that the f-number of the system has on the spatial distribution of the line foci seen in the numerical simulation. The two cylindrical lens telescopes were measured to have a resolution of 11.3 lp/mm and capable of filtering a heavily modulated input beam. Using cylindrical optics constitutes a worst-case scenario for aberrations; here, both the numerical model and experimental data indicate minimal degradation of performance with proper f-number selection. Extrapolating the power handling capabilities of the HAPLS transmissive slit spatial filter suggests that the entirely reflective slit spatial filter will be capable of supporting high-average power, high-energy laser systems for secondary-source applications.
Funding
Lawrence Livermore National Laboratory (17-ERD-033, DE-AC52-07NA27344).
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