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In direct drive ICF, optical zooming is an effective way to mitigate cross-beam energy transfer and increase the hydrodynamic efficiency, by reducing the spot size of the laser beams while target compressing. In this paper, a novel optical zooming scheme is proposed, which employs a focusing grating to focus the broadband laser pulse, changing the spot size on the target within single beamlet. Experimentally, a focusing grating with clean aperture of 40-mm × 40-mm placed after the collimated light successfully realized the peak-valley of defocusing wavefront distribution of 0.73 µm as the wavelength ranging from 1052.43 nm to 1053.23 nm. Extended to the full-sized focusing grating with laser beam of 360-mm × 360-mm, it is derived that the focal spot reduction reaches to 21.8% with the 3rd harmonic light ranging from 350.81 nm to 351.08 nm, decreasing from 375 µm to 294 µm with 300 µm shaping continuous phase plate.
© 2016 Optical Society of America
1. Introduction
Optical zooming is an important technique to promote energy utilization efficiency in direct drive inertial confinement fusion (ICF) [1, 2]. During target compression, the critical surface recedes in time. It results in the degradation of hydrodynamic efficiency while a significant part of incoming laser is lost around the imploding target capsule without contributing efficiently to the ablation process [3–7]. Moreover, incoming laser beams traversing a higher density coronal plasma can excite ion-acoustic waves and facilitate the energy transfer away from regions of interest [8, 9]. Studies have shown that dynamical reduction of the focal spot size during the implosion, that is to say also known as optical zooming can reduce the energy loss of incoming laser and mitigate cross-beam energy transfer (CBET) [10].
Optical zooming was first proposed by the Naval Research Laboratory for KrF laser facility [11]. It obtained the desired focal spot size by using a time-delayed beam aperture modification to shape three time-delayed beamlets. A few years ago, they experimentally demonstrated a two-stage focal zooming capability on the Nike laser by cutting two split and time-delayed beams with Pockels cell and then shaping the two to different spot size [12]. Later, a three-stage focus zooming system of XeCl laser was established by the same way and the zooming process was recorded by a streak camera [13]. However, the zooming scheme applied on molecular laser is complex and not feasible for the solid-state lasers such as National Ignition Facility (NIF), laser Megajoule (LMJ), High Power laser Energy Research Facility (HiPER), Omega laser Facility (OMEGA) and Shenguang-Ш Facility (SG-Ш). An arbitrary beam shaping zooming (ABS-zooming) concept was proposed for a quad character architecture like NIF and LMJ. It consists of turning on and off each beamlet in time dependently and each having a specific with its own laser pulse and focal shape [7]. Their corresponding simulation showed 30% improvement of laser-target coupling efficiency with ABS-zooming. Similarly, optical zooming scheme for HiPER was proposed to separate the nine beamlets of each bundle into more groups to reduce the focal spot step by step during the pulse [14, 15]. ABS-zooming for the quad architecture laser facilities is not feasible for the single-beamlet character of other high-power lasers. Moreover, the ABS-zooming is not using each beamlet at its maximum potential in terms of deliverable energy, resulting in overall decrease of the facility performance. Zooming phase plate (ZPP) design proposed by OMEGA was to realize two-state optical zooming of single-beamlet [16]. It produces a larger focal spot during the pickets and a smaller one during the main pulse, reducing the spot by 40% and mitigating kinetic energy loss of CBET [17, 18]. Another optical zooming scheme for single-beamlet character was realized by controlling a special-designed electro-optic crystal with electrode [19, 20]. The electro-optic crystal introduces variable wavefront to the laser beam, thus the location and size of the focal spot could be, in principle, controlled in real time. As for this scheme, it needs an electronic drive pulse of several thousand volts and response time of less than one hundred picoseconds, which is difficult for large optics and can’t be applied at the end of the laser system [21, 22]. While if the wavefront shaping is applied at the front of the laser system, it would probably raise concerns in terms of pinhole closure due to the defocus in the main laser.
In this paper, we develop an optical zooming for high power solid lasers of single-beamlet character architecture. By employing a focusing grating to focus broadband laser pulse like in the LMJ and LIL designs [23, 24], the location and size of the focal spot could be controlled as wavelength varying, reducing the focal spot gradually as pulse duration. Different from ABS zooming and ZPP scheme, this scheme doesn’t need to divide the pulse into different width, which reduces energy extraction, limits the deliverable peak power on target and requires precise control of pulse splicing and synchronization.
2. Optical zooming scheme and simulation
One beamlet in high power solid lasers, such as SG-III [25], generates from front-end at the central wavelength of 1053 nm, and then propagates through pre-amplifiers and main-amplifiers to gain energy. Next, the harmonic convertors convert the high power laser light into ultraviolet light at the central wavelength of 351 nm. Finally, the ultraviolet light is focused at the target by lens. In this paper, a focusing grating is proposed instead of traditional lens to focus broadband pulse, which is generated in front-end by frequency-modulation or using gratings to disperse broadband pulse. Figure 1 shows the entire process of propagation. Placing the target at the location of the shortest focal length, optical zooming is naturally achieved with increasing wavelength as Fig. 2 revealed.
Fig. 1 The beamlet propagation based on focusing grating. The pulse upon front-end varying from purple to red means wavelength of broadband pulse getting longer as pulse duration.
Fig. 2 Geometry of single-beamlet optical zooming based on focusing grating. The beam color varying from purple to red also means wavelength of broadband pulse getting longer as pulse duration
One thing need to be noted is that, when a broadband laser pulse propagates in the Nd:Glass amplifiers, the output energy will decrease due to gain narrowing. Meanwhile, frequency conversion is sensitive to wavelength variation, which further reduces the energy conversion efficiency. As shown in Fig. 3, the performance of amplifying and frequency conversion on SG-Ш is evaluated for narrowband and broadband pulses respectively using the SG99 code [26], which is a laser propagation program for high-peak-power laser setups, and has been used in designing the SG-Ш facility in China. Figure 3(a) shows the results of narrowband pulse with frequency converter consists of a 12-mm-thick Type I potassium-dihydrogen phosphate (KDP) doubler and a 9-mm-thick Type II KDP tripler, the corresponding energy of the injection to main amplifier, fundamental output and ultraviolet output is 0.23 J, 6,600 J and 3,940 J respectively. Figure 3(b) shows the results of 1 nm broadband pulse with the same injection and configuration of frequency converter, the fundamental and ultraviolet output energy is 6,550 J and 3,730 J, representing the reduction of 0.8% and 6% compared with narrowband. Further increasing the bandwidth to 3 nm shown in Fig. 3(c), the fundamental output is decreased to 6,180 J with reduction of 6%, and the frequency conversion that must employ three crystals with configuration of “Type-I + Type-II/Type-II” to expand the conversion bandwidth [27], can output ultraviolet energy of 3,150 J with 20% reduction. However, in high power laser facilities, the output laser fluence and power are typically limited by optics damage particularly these working at 351nm (3ω), and the limitation of SG-III is 4 kJ (~3ns, 3ω). By enhancing the injection, the decreasing output of broadband pulse could be compensated. Figure 3(d) shows the compensated results of 1 nm broadband pulse, the energy of injection, fundamental and ultraviolet is 0.28 J, 7,350 J and 3,920 J respectively. Although the fundamental energy and power is 11% and 6% higher than narrowband case, the SG-III facility still stay away from the safety margin, which is quantified by ∆B of 1.4 rad in the condition less than the typical limit of 1.8 rad. Thus, the propagation of a broadband laser pulse for optical zooming will not significantly degrade the 3ω output performances of SG-III facility.
Fig. 3 Amplification and frequency conversion respectively with narrowband and broadband pulse for the SG-III laser architecture. (a) Narrow band laser pulse with frequency converter consists of a 12-mm-thick Type I KDP doubler and a 9-mm-thick Type II KDP tripler. (b) 1 nm broadband pulse with the same injection and frequency converter as narrow band. (c) 3 nm broadband pulse with the same injection as narrow band and different frequency converter configuration of Type-I + Type-II/Type-II. (d) Compensation results of 1 nm broadband pulse to equal 3rd output of narrowband.
Focusing grating can be recorded by interference from a beam of referable light and a beam of object light [28]. Figure 4 shows the geometry of focusing grating record and image reproduction. Under polar coordinates, the light radius vectors Ri, Rc, Ro, Rr of I, C, O, R have a simple relationship [29, 30].
λ is the wavelength of reproducing light, while λo is the recording light. Here, if referable light and reproducing light are collimated light, thenRi and Ro are respectively the focal length of reproducing light and recording light. Obviously, Eq. (2) can be simplified byFig. 4 Geometry of focusing grating record. Focusing grating is interfered by referable light source (R) and object light source (O). Image (I) reappears when reproducing light source (C) irradiates grating.
According to Eq. (3) and Fresnel diffraction transmission theory, the focal spot variation on the target plane can be calculated. The beam size of SG-III is 360-mm × 360-mm, and the focal length is 4 m. If the wavelength of broadband light ranges from 1052.5 nm to 1053.5 nm, the ultraviolet light should be from 350.83 nm to 351.17 nm. A designed continuous phase plate (CPP) is adopted to shape the beam with a 300 μm focal spot into size. The focal spot size is defined by the diameter of circle area containing 95% of beam energy. Optical propagation simulation is conducted with the above parameters. Figure 5(a) shows the simulated results of 33% focal spot diameter reduction from 436 µm to 292 µm, and Fig. 5(b) presents azimuthally averaged intensity curve of the focal spot at 350.83 nm and 351.17 nm.
Fig. 5 The simulation of focal spot variation. (a) Focal spot size getting smaller with decreasing wavelength. (b) Azimuthally averaged intensity distribution of the focal spot at 350.83 nm and 351.17 nm.
This scheme of Optical zooming is also compatible with other beam smooth technologies, such as smoothing by spectral dispersion (SSD) and polarization smoothing (PS). In laser fusion, SSD is an effective way to homogenize focal spot in time, by employing phase modulation coupled with a dispersion system. There are two kinds of SSD, transverse (resp. longitudinal) SSD is characterized by a variation of the focal spot in the transverse (resp. longitudinal) plane with wavelength, and both configurations use gratings (plane or focusing). The focusing grating used in this paper for optical zooming, is applicable for longitudinal SSD, which has similar configuration as LMJ [31, 32]. Moreover, if the laser pulse is modulated not only linear chirped but also sinusoidal as Fig. 6(a) shown, the wavelength varies linear coupled with sinusoidal, optical zooming and longitudinal SSD are both achieved as Fig. 6(b) revealed.
Fig. 6 The simulation of focal spot variation with chirped (1.0 nm at 1ω) and sinusoidal phase modulations (modulation frequency of 2.488 GHz, bandwidth of 0.3 nm at 1ω). (a) Phase and phase derivative of 3ω light varies as pulse duration. (b) Focal spot section varies as pulse duration.
3. Test configuration
Here a small sized focusing grating is fabricated and a simple experimental scheme is conducted to verify single-beamlet optical zooming. Focusing grating produces reflected light in the −1R order, transmission light in the −1T and 0T order like in [28]. The focusing grating used in test configuration is designed as an off-axis transmission grating, which could use −1R order to diagnose −1T order and also separate 0T order from −1T order. It is recorded by collimated light which is incident perpendicular to the grating plate and point light source which is tilted 10o to the collimated light. The distance between point light and grating center is 400 mm when the wavelength of the recording light is 1053 nm. The clean aperture of the grating is 40-mm × 40-mm. Figure 7 shows part structure of focusing grating at 50 times of amplification ratio. The whole grating structure is a part of concentric circles whose radius of each circle is
Where m is the concentric circles’ level and the center’s level is 0, ρm is the radius, f is the distance between spot light source and grating center, λ is the wavelength of recording light, θ is the tilted angle.Test configuration is shown in Fig. 8. A distributed feedback (DFB) fiber laser generates continuous light with controllable wavelength ranging from 1052.43 nm to 1053.23 nm and the output power reaches to 100 mW. Our goal is to measure focal spot at different wavelength. An Φ = 100 mm, f = 500 mm lens turns the spot light source into a beam of collimated light. The focusing grating is located after the lens to focus the collimated light. A focal spot detector should be located at the focus plane at the wavelength of 1053.23 nm to detect the reducing focal spot with the light wavelength varying from 1052.43 nm to 1053.23 nm. According to diffraction theory, the focal spot varies ~30 µm in the experiment which is a minor change relative to the original spot with wavefront distortions, so the direct detection by CCD is not adopted. An indirect method of detecting the wavefront distribution within 40-mm × 40-mm sized area by a Hartman sensor is employed, which could reflect defocusing amount as the following relationship,
∆w is the peak-valley (PV) of wavefront in 40-mm × 40-mm sized area without tilt, Deff is the effective beam aperture, ∆f is the defocusing amount, ftarget is the distance from grating to target which equals to the focal length at the maximum wavelength. The focusing grating is recorded by the light at the wavelength of 1053 nm, so the focal length at the wavelength of 1052.43 nm and 1053.23 nm respectively are about 400.20 mm and 399.91 mm calculated by Eq. (3). The maximum defocusing amount ∆f from 400.20 mm to 399.91 mm is 292 µm. Taking ∆f into the Eq. (5), the PV of wavefront ∆w ≈0.73 µm.Due to chromatic effects of off-axis grating, the focal spot not only moves longitudinally, but also transversely. In this test, the tilted angle of 10o is chosen to ensure a clean detection space, and the calculated transverse motion amount is ~54 µm according to diffraction equation through grating. However, we ignore transverse motion as the main purpose of this test is to verify longitudinal motion. In normal application of full-sized grating with laser beam of 360-mm × 360-mm and focal length of 4 m on SG-III facility, the key limit factor of the grating designing is to separate the fundamental, the 2nd and 3rd harmonic lights. In this condition, the tilted angle is designed as 0.3 o, which leads to 20 µm transverse motion of the 3rd harmonic light with the wavelength ranging from 350.83 nm to 351.17 nm, 41.8 mm of the fundamental light and 10.5 mm of the 2nd harmonic light. It is a relative small transverse motion of 3ω that is tolerable for typical fusion experiments. When a larger tilted angle or bandwidth of laser pulse is required in other applications, and the transverse motion is unacceptable for experiments, a grating without focusing function could be added to compensate the transverse motion.
4. Test results
In the experiment, three tests are carried out to measure the wavefront distribution while the wavelength is increased. The wavefront distribution at the wavelength of 1052.43 nm is the reference data. Figure 9(a) and 9(b) respectively show the wavefront distribution in the first test within 40-mm × 40-mm sized area at the wavelength of 1052.43 nm and 1053.23 nm. Figure 9(c) is the defocusing distribution separated from Fig. 9(b), and Fig. 9(d) is the residual. The PV of wavefront in Figs. 9(b)–9(d) is 0.85 µm, 0.73 µm and 0.12 µm respectively. The defocusing amount ∆w in the next two tests are respectively 0.73 µm and 0.74 µm, which are all corresponding to calculation of 0.73 ± 0.1 µm. Figure 10 compares the results by theoretical calculation and three experimental tests at each 0.1 nm of wavelength variation, which have the same variation trend as theory.
Fig. 9 Measured wavefront distribution. (a) The wavefront distribution at minimum wavelength (taken as reference); (b) The wavefront distribution at maximum wavelength; (c)The defocusing distribution separated from (b); (d) The residual wavefront distribution wiping off defocusing from (b).
For normal applied grating with beam size of 360-mm × 360-mm and focal length of 4 m at 351 nm focusing a beamlet with the wavelength ranging from 350.81 nm to 351.08 nm, it has the relationship with 40-mm × 40-mm sized one with 0.4 m focal length at the wavelength of 1053 nm according to Eq. (3),
∆flg is the defocusing amount under 360-mm × 360-mm beam size grating condition. Obviously, taking each experimental ∆w into Eq. (5) and Eq. (6), ∆flg can be obtained. Then, just calculating light transmission with ∆flg on target plane by Fresnel diffraction, the spot size reduces from 375 µm to 294 µm with shaping CPP of 300 µm, equaling to 21.8% of reduction. Figure 11(a) shows the spot size variation derived by one of experimental tests and the comparison with theoretical simulation, which shows good agreement with each other. Although CPP is widely used in high power laser facility, still we do not always use CPP. The focal spot size variation without CPP is given in Fig. 11(b). Without the CPP, the size of focal spot reduces from 322 µm to 75 µm, equaling to 76.6% of reduction, which is much larger than the case of using CPP.Fig. 11 Results of the spot size variation derived by one of experimental tests and comparison with theoretical simulation in large grating condition. (a) With 300 µm shaping CPP; (b) Without CPP.
5. Summary
In summary, a method of single-beamlet zooming by using an ultraviolet light focusing grating to focus broadband light beam in the high power laser system is proposed. Experiments are successfully conducted with a 40-mm × 40-mm clean aperture focusing grating placed in a collimated light with the beam while its wavelength ranging is varied from 1052.43 nm to 1053.23 nm. The PV of wavefront ∆w detected in experiment shows good agreement with calculation of 0.73 ± 0.1 µm. As for the normal full-size applied grating with laser beam of 360-mm × 360-mm, focal length of 4 m and shaping CPP of 300 µm, the spot size reduces from 375 µm to 294 µm with wavelength ranging from 350.81 nm to 351.08 nm, representing a reduction of 21.8%, which is consistent with the theoretical expectation and proves this scheme is applicable for optical zooming.
Acknowledgment
This work has been supported by the National Natural Science Foundation of China (NSFC) under Cooperative Agreement No. 61205110. The authors would also like to gratefully acknowledge valuable technical discussions and auspices with professor Gao from Sichuan University.
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