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Abstract
We conducted a study on the thermal effects in chirped volume Bragg gratings (CVBGs) used as optical compressors in high-power lasers. A simulation code was developed to predict the distortion of the pulses by the thermal effects. The types and significance of the thermal distortion were analyzed using an Yb:YAG laser with an average power of 250 W. The temperature distribution in the CVBG, the thermal lens effect, the beam propagation path changes due to the thermal lens, and the compression efficiency decrease due to the phase delay were analyzed. As a result, we predict that the peak power decreases to 63.9% due to the thermal effects under the operating conditions of 250 W. We also suggest new designs for the CVBG mount that minimize the peak power loss. We expect the peak power loss to be reduced only by 1.1% when using our new mount design for the CVBG.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. INTRODUCTION
Chirped pulse amplification (CPA)-based high-power lasers have given rise to useful tools for many scientific and industrial applications [1–3]. Several advanced applications, such as material processing, nonlinear microscopy and spectroscopy, and UV and x-ray sources, require ultrashort laser pulses with high peak power and high repetition rate [4–8]. For these applications, the stability and durability of the high-power lasers must be considered. A diffraction grating-based compressor can give a large dispersion, but this significant advantage is negated by the loss in compactness, robustness, and sensitiveness. Therefore, the use of the chirped volume Bragg grating (CVBG) as an optical compressor for high-power lasers is becoming more popular, and related research is being widely conducted [9,10]. CVBGs are made of photo-thermo-refractive (PTR) glass [10]. A change in refractive index inside the CVBG is imprinted with changing period in the beam propagating direction. Since the reflected wavelength is determined according to the period of the refractive index modulations, it can be used as an optical stretcher or compressor [9–12]. The CVBG compressor is relatively insensitive to mechanical vibrations and optical misalignments. Due to its small size, there is also a significant advantage for the miniaturization of the system.
For these reasons, the CVBG compressor has been widely used in both high-power lasers and ultra-fast lasers. A laser system with an average power over 100 W at 1064 nm [9,13], a system operating at 1 kHz repetition rate at a peak power of 4.4 GW in the 2 µm region [14], and a compact ultrafast laser with 104 µJ pulse energy at 200 kHz repetition rate in the wavelength of 1030 nm have been reported [15]. A system capable of producing peak power of up to 10 GW in the mid-IR region with a pulse energy of 1 mJ [16] and an optical parametric CPA (OPCPA) tabletop system with a pump pulse energy of 260 mJ have been developed [17]. The Perla C laser at the HiLASE Centre, whose parameters are used in the simulation model of this paper, is designed for operating at 500 W and 92 kHz in the wavelength of 1030 nm. However, the actual operation is limited to 250 W because of the deterioration of the beam quality due to thermal effects of the CVBG compressor [4,18,19].
Fig. 1. Assumptions for simulation: (a) schematic of a CVBG compressor; (b) spatial shape of the beam; (c) temporal and spectral shape of the stretched beam before being compressed.
As the average power of lasers using the CVBG compressor reaches several hundred watts, research on thermal effects has begun to emerge [4,20]. The thermal effects in the CVBG need to be resolved in order to raise the average power to more than a few hundreds of watts. Thermally induced distortions without proper compensation can cause the peak power to decrease and degrade the spatial beam quality [21,22]. In order to compensate the thermally induced distortions, an analysis of the thermal effects should be carried out in advance [23–25].
In this paper, we study the thermal effects in a CVBG for high-power lasers. The heat source in the CVBG is the partial absorption of energy from the interacting chirped pulse, similar to the heat source in general optical elements. However, because the reflecting depth in the CVBG varies with the wavelength [Fig. 1(a)], the heat source distribution is somewhat different from that of general optical elements. We assume a spatiotemporal Gaussian pulse in Figs. 1(b) and 1(c) and show how to calculate the temperature distribution and introduce the thermally induced optical path difference, spectral delay, and lens effect. Using the numerical model, we discuss the anticipated thermal distortion effects and compensation methods in the Perla C laser at the HiLASE center.
2. NUMERICAL MODEL OF THERMAL EFFECTS
The CVBG compressor in the Perla C laser at the HiLASE Centre, which is also used in other high-power lasers, was modeled and analyzed. Perla C is a 500 W Yb:YAG thin-disk laser system with a repetition rate of 92 kHz [4,18]. However, the thermal effect at an average power of 250 W will be mainly presented in this work because of the severe degradation by the thermal effect of the CVBG compressor when the power is higher than 250 W [4,18,19]. The specifications of the laser used for the thermal effect simulation were assumed to be as follows: a pulse energy of 2.8 mJ at 92 kHz repetition rate, a center wavelength of 1030 nm, a Gaussian spectrum with a wavelength bandwidth of 3.2 nm at $1/{e^2}$ of the maximum, and a Gaussian beam with a $1/{e^2}$ diameter of 4.5 mm. The aperture of the CVBG compressor is a 10 mm square, and its length is 75.6 mm. The other specifications of the CVBG compressor were assumed as follows: a stretching factor of 204 ps/nm, negative dispersion, an average refractive index of 1.5, a thermal conductivity of 0.01 W/cm K, and an absorption coefficient of $0.001 \;{\rm{c}}{{\rm{m}}^{- 1}}$ [10,20,26].
Fig. 2. Simulation results at 250 W operation: (a) temperature profile inside the CVBG compressor; (b) temperature along the beam propagating axis; (c) temperature map on the front of the CVBG compressor; (d) temperature map in the middle of the CVBG compressor; (e) temperature map on the end of the CVBG compressor.
The heating of the CVBG compressor is based on the energy absorbed from the incident beam [10]. The depth at which a portion of the beam is reflected inside the CVBG is determined by its wavelength. The shape of the heat distribution map hence differs from a simple exponential curve [10,20,25]. The heat distribution, $H(x,y,z)$, inside the CVBG can be expressed as
In Eq. (1), $P(x,y,\lambda)$ is the spectral intensity of the amplified chirped pulse, and also its power is shown in Fig. 1(c). Since the wavelength determines the depth of reflection inside the CVBG, we used the spectral intensity in Eq. (1), not the power. Equation (1) assumes the beam’s incidence in a state with no thermal distortion in the CVBG. This may be somewhat inexact, considering that the beam’s path that creates the thermal distortion effect on the CVBG is different. It can be corrected by calculating iteratively, but this effect is negligible. In our condition, when we iteratively calculate, the beam diameter decreased by up to 0.5%. Based on the above assumptions, the input spatiotemporal beam shape in the form of a spatiotemporal Gaussian pulse is shown in Fig. 1, and the heat distribution in the CVBG is represented by Eq. (1). With the heat distribution, Eq. (4) gives the temperature distribution shown in Fig. 2. For the boundary conditions in the solution of Eq. (4), it was assumed that the four sides of the CVBG are joined to heat sinks with high thermal conductivity so that the temperature of the heat sink contact surfaces is kept at steady temperature [21,23],
Thermal distortion effects are divided into spatial and temporal effects. The spatial distortion effect is a thermal lens effect. As the refractive index at the center increases, CVBG interacts with the beam like a convex lens. Temporal distortion refers to the lowering of the compression quality due to the change of spectral delay. In an ideal situation where thermal effects are negligible, a CVBG provides different optical paths depending on the wavelength of the incident beam. These differences cause the beam to be compressed in time. However, the thermal effects result in the pulse to be compressed experiencing a slightly increased path length than originally intended. Without proper compensation for these thermal effects, the width of the pulse increases, and the peak power decreases [27].
3. RESULTS
Figure 3(a) shows the path of the ray inside the CVBG. To calculate the propagating path along the CVBG compressor for a given wavelength, the CVBG is modeled as a set of 92 segments, and the interaction of each segment with the beam is represented by an ABCD matrix. In the ideal case, there is no thermal effect, and the beam propagates without any change in its diameter. However, with the thermal lens effect, the beam converges and exits the CVBG after temporal compression. The severity of this thermal lens effect is affected by the average power. That is, even if the energy of the beam does not increase, but the repetition rate increases, the thermal lens effect worsens [21,23]. Figures 3(a) and 3(b), respectively, show the variation of the beam radius and focal length with the wavelength in the CVBG when 2.8 mJ pulses are repeated at 92 kHz. The dotted brown line in Fig. 3(a) is the second derivative of the on-axis temperature with respect to position. The thermal lens is proportional to the second derivative of the temperature distribution. At the end of the CVBG, the beam radius decreases almost linearly. The reason is that the thermal lens effect is relatively small since there is little heat generation at the end of the CVBG, cf. Fig. 2. Obviously, the most fundamental solution to mitigate the thermal effects is to eliminate the heat sources. Because the heat sources are related to the absorption coefficient, it can be lowered by improving the glass purity. Figure 4 shows the change in the focal length and group delay dispersion (GDD) as the absorption coefficient decreases. If the CVBG absorption coefficient is reduced to 1/10 of its original value (green line), the focal length of more than 10 m is obtained.
Fig. 3. Simulation results of the thermal effects: (a) incident (solid line) and reflected (dashed line) ray propagation tracing at the position of the beam radius ($1/{e^2}$) inside the CVBG compressor according to their wavelength. The brown dotted line shows the second derivative of the temperature distribution along the longitudinal axis of the CVBG compressor; (b) focal length induced by the thermal lens effect of the CVBG compressor.
Fig. 4. Mitigating thermal distortion by decreasing absorption coefficient (${\rm{c}}{{\rm{m}}^{- 1}}$) of CVBG: (a) focal length of thermal lens; (b) thermally induced group delay dispersion (GDD) at the center of the CVBG compressor.
The thermally induced GDD change for the beam’s central ray is shown in Fig. 4(b). These GDDs are only induced by the thermal effect. Ultrashort pulses with a broad spectrum require additional considerations such as spatiotemporal couplings (STCs) [28,29]. However, in our conditions, STCs are negligible compared to the thermal effect, so we only considered thermal effects. The thermally induced GDD reduces compression efficiency, added to the dispersion of the CVBG optimized for pulse compression. We can use this GDD to predict temporal shape of the pulse after compression. We used only the beam’s central ray to calculate the pulse’s temporal shape, and because the GDD change is the highest here, the blue lines are the compressed pulse shapes without any effects [Fourier transform-limited (FTL) pulse], the orange lines are the compressed pulse shapes expected when the thermal distortion is considered, and the green lines are the compressed pulse shapes that can be obtained by compensating up to the second order of the expected thermally induced phase delay. The dashed lines are in the shapes of compressed pulses with lower absorption coefficients. Compared to the ideal compression result, the peak output is lowered to 63.9% [Fig. 5(a)]. The results so far have been obtained assuming a Gaussian shape of the beam incident on the CVBG. The spectrum of the actual Perla C operating at the same condition of 250 W and the expected distortion effect are shown in Fig. 5(b). The peak output is lowered to 72.7% [Fig. 5(b)] in the Perla C spectrum.
Fig. 5. Pulse compression simulation results of (a) the Gaussian spectrum and (b) Perla C spectrum at 250 W operation.
Thermal distortion in the CVBG is relatively challenging to compensate because of the wavelength dependence of the distortion and the high peak power of the pulse after compression. The most realistic compensation method is to perform the compensation during the generation of the chirped pulses while the pulses are being stretched. It should be possible to anticipate the thermal distortion at the target power in advance for a laser system operating at a fixed power and repetition rate. If we can compensate the thermally induced phase up to the second-order term in the stretcher or front-end of the system, the results shown in Fig. 5 are expected (green lines). The pulses with a such compensated phase are close to the Fourier limited pulses. As a thermal distortion compensation method, temperature gradient applied to the chirped fiber Bragg grating (CFBG) can be used, and an acousto-optic programmable dispersive filter or liquid crystal based filters can be used [18,27,30,31]. However, there is a hassle of finding the optimal value according to the operating power.
4. DISCUSSION
In order to compensate the pulse shape deterioration due to the thermal effect in the compressor, it is possible and effective to generate an arbitrary phase delay according to the wavelength of the seed beam. The problem is that it is challenging to build equipment to precisely generate the phase delay, especially for lasers in industrial applications. Consequently, we propose new designs for the CVBG mount as a relatively simple alternative that can be used more widely (Figs. 6–8). The new designs improve the uniformity of the CVBG compressor temperature distribution.
Fig. 6. Case 1, ramp temperature profile: (a) temperature of the mount; (b) temperature of CVBG at the center; (c) temperature map of CVBG; (d) pulse compression simulation result.
Our first mount model for achieving a more uniform temperature distribution is a temperature gradient on the surfaces that face the CVBG. This temperature ramp gives a relatively large cooling effect in the front half of the CVBG compressor, contributing to the overall temperature uniformity. The temperature gradient of the mount surfaces may be controlled by using Peltier components. When the ramp temperature profile is imposed as shown in Fig. 6(a), the temperature variation range is reduced to less than 5 degrees at the center of the CVBG as shown in Fig. 6(b). It is reduced by over 60% compared to the result of Fig. 2(b). With this mount model, we expect to reduce the peak power loss to 9.9%. Considering the loss of 36.1% in a typical mount, this can be considered a significant improvement.
We next tried a simpler mount model. Figure 7 shows the simulation results when the surface temperatures in the front and rear halves of the CVBG are different. This is achieved simply by enhancing the cooling in the front half of CVBG, which has the advantage of being easier to implement than the ramp temperature profile. Unlike Fig. 6(b), it can be seen from Fig. 7(b) that the temperature at the front half of the CVBG is low even though more heat energy is absorbed. Using this mount, we found that the peak power degradation due to the thermal effect is almost compensated. The simulation result shows that the peak power loss is 1.1% that of the FTL peak power.
Fig. 7. Case 2, step temperature profile: (a) temperature of the mount; (b) temperature of CVBG at the center; (c) temperature map of CVBG; (d) pulse compression simulation result.
Furthermore, Fig. 8 shows the case where the rear half of the CVBG is not cooled; that is, a half-cover type mount is simulated, in which the mount wraps only the front half of the CVBG compressor. This model cools only the front half of the CVBG while the rear half is insulated. In this case, there is a 1.5% loss of the peak power as shown in Fig. 8. This is a slightly higher loss than the previous model, but appears to be a much more practical design for the mount fabrication.
Fig. 8. Case 3, partially cooled scheme: (a) temperature of the mount; (b) temperature of CVBG at the center; (c) temperature map of CVBG; (d) pulse compression simulation result.
Each of the above three mount designs shows efficient thermal effect compensation, but the effect is limited because only the temperature distribution in the beam propagating direction is homogenized, not the transversal plane. That is, the new mount designs can adequately improve the peak power but have little effect on the converging propagation in the CVBG. We cannot reduce the thermal lens effect with our proposed model. This is because the CVBG used as a high-power laser compressor is so bulky that it is difficult to make the temperature map transversally uniform even by changing the mount design. Because of this limitation, to lower the thermal lens effect of the bulky CVBG to be used as a compressor of high-power lasers, the improvement of the physical properties of CVBG, namely the reduction of the absorption, will work more effectively than other compensation methods.
5. CONCLUSION
This study presents the numerical analysis and results of the thermal effects in a CVBG used as a compressor in a high-power laser. The higher the laser output, the higher the thermal energy accumulated in the optical compressor. As the purpose of compressing chirped pulses is to obtain high peak output, the reduction of compression efficiency due to thermal distortion is an important problem. The Perla system at HiLASE achieves 76.03% of its intended peak power when operated at an average power of 250 W. Because the thermal distortion is undoubtedly influenced by the compensation design, the analysis method introduced in this paper will be useful for predicting an appropriate compensation method and the degree of compensation in various operational processes. We found that it is sufficient to compensate the thermally induced phase delay effect up to the second-order term. This work could be used to compensate the thermal distortion effects in laser systems operating under various output conditions. Further research on the development of this compensation system and the photo-elastic effect will be performed.
Funding
European Regional Development Fund (CZ.02.1.010.0/0.0/15_006/0000674); Horizon 2020 Framework Programme (739573); Ministerstvo Školství, Mládeže a Tělovýchovy (LO1602); Korea Institute for Advancement of Technology (P0008763).
Disclosures
The authors declare no conflicts of interest.
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