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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 16799–16813
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Fabrication of spherical mitigation pit on KH2PO4 crystal by micro-milling and modeling of its induced light intensification

Jian Cheng, Mingjun Chen, Wei Liao, Haijun Wang, Yong Xiao, and Mingquan Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 16799-16813 (2013)
http://dx.doi.org/10.1364/OE.21.016799


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Abstract

Micro-machining is the most promising method for KH2PO4 crystal to mitigate the surface damage growth in high power laser system. In this work, spherical mitigation pit is fabricated by micro-milling with an efficient machining procedure. The light intensification caused by rear surface features before and after mitigation is numerically modeled based on the finite-difference time-domain method. The results indicate that the occurrence of total internal reflections should be responsible for the largest light intensification inside the crystal. For spherical pits after mitigation, the light intensification can be greatly alleviated by preventing the occurrence of total internal reflections. The light intensification caused by spherical mitigation pit is strongly dependent on the width-depth ratio and it is suggested that the width-depth ratio of spherical mitigation pit must be devised to be larger than 5.0 to achieve the minimal light intensification for the mitigation of surface damage growth. Laser damage tests for KH2PO4 crystal validate that the laser damage resistance of initially damaged surface can be retrieved to near the level of ideal surface by replacing initial damage site with predesigned mitigation pit.

© 2013 OSA

1. Introduction

KH2PO4 (Potassium dihydrogen phosphate, also known as KDP for short) crystals are widely used as terminal frequency converter and optoelectronic switch–Pockels cell in high power laser systems, such as NIF (National Ignition Facility, in USA), LMJ (Laser MegaJoule, in France) and ShenGuang-III Laser Facility (in China) [1

1. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47, 113–152 (2002). [CrossRef]

3

3. R. A. Negres, S. O. Kucheyev, P. DeMange, C. Bostedt, T. van Buuren, A. J. Nelson, and S. G. Demos, “Decomposition of KH2PO4 crystals during laser-induced breakdown,” Appl. Phys. Lett. 86(17), 171107 (2005). [CrossRef]

]. Under such powerful laser irradiation with high fluences, optical components are susceptible to suffer laser induced damage on the surface or in the bulk that largely restricts the enhancement of laser energy output required for ICF (Inertial Confinement Fusion) [4

4. C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004). [CrossRef] [PubMed]

]. So far, the bulk damage threshold of KDP crystal component can be comparable with the surface damage threshold by using the latest techniques like growth temperature control, solution purification and super-saturation, continuous solution filtration, laser conditioning and thermal annealing [5

5. G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express 17(13), 10434–10456 (2009). [CrossRef] [PubMed]

8

8. F. Guillet, B. Bertussi, L. Lamaignère, and C. Maunier, “Effects of thermal annealing on KDP and DKDP on laser damage resistance at 3ω,” Proc. SPIE 7842, 78421T, 78421T-5 (2010). [CrossRef]

]. However, the surface damage on KDP crystal suffers a catastrophic threat that it can grow dramatically during subsequent laser shots, which is opposed to bulk damage and similar to surface damage on fused silica [3

3. R. A. Negres, S. O. Kucheyev, P. DeMange, C. Bostedt, T. van Buuren, A. J. Nelson, and S. G. Demos, “Decomposition of KH2PO4 crystals during laser-induced breakdown,” Appl. Phys. Lett. 86(17), 171107 (2005). [CrossRef]

, 9

9. F. Guillet, B. Bertussi, L. Lamaignere, X. Leborgne, and B. Minot, “Preliminary results on mitigation of KDP surface damage using the ball dimpling method,” Proc. SPIE 6720, 672008, 672008-9 (2007). [CrossRef]

]. Therefore, it is particular important to deal with the laser induced surface damage on KDP crystal to extend its useful life and optical performance in ICF.

The modified material and surface cracks during laser damage on surface are believed to be associated with nonlinear heat absorption, enhanced scattering and light intensification, which is responsible for the “re-ignition” and growth of damage sites under subsequent laser shots [10

10. S. G. Demos, M. R. Kozlowski, M. Staggs, L. L. Chase, A. Bumham, and H. B. Radousky, “Mechanisms to explain damage growth in optical materials,” Proc. SPIE 4347, 277–284 (2001). [CrossRef]

]. For KDP/DKDP crystal, micro-machining with single crystal diamond tool has been proved to be a particularly promising method to hinder the growth of surface damage by replacing the absorbing damaged material and surface cracks with a predesigned benign mitigation pit [11

11. C. J. Stolz, “The National Ignition Facility: The Path to a Carbon-Free Energy Future,” Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 370(1973), 4115–4129 (2012). [CrossRef]

13

13. P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE 6403, 64030Q, 64030Q-7 (2006). [CrossRef]

]. A simple and efficient strategy is proposed in this work to produce spherical mitigation pits on KDP surface by micro-milling with a ball end milling cutter.

In this paper, we firstly utilize an efficient machining procedure to fabricate a series of spherical mitigation pits on diamond-turned KDP surface by micro-milling with a ball end milling cutter. Then, three-dimensional finite difference time domain (3D FDTD) method based on electromagnetic field theory is employed to numerically model and quantitatively compare the light intensification inside the crystal caused by initial damage sites (taking cracks as representative) and spherical mitigation pits. The light intensification caused by spherical pits after mitigation is largely alleviated by preventing the occurrence of total internal reflections on the mitigation pits and rear surface of the crystal. The geometries of the spherical mitigation pits have significant impact on the light intensity enhancement inside the crystal. According to our simulation results, it is proposed that the width-depth ratio of the micro-machined mitigation pits must be larger than 5.0 to achieve the minimal light intensification. Finally, the laser damage test validates that laser damage resistance of initially damaged surface can be largely improved by replacing the damage site with spherical mitigation pit. With these theoretical and experimental results, the optimal repairing strategy can be developed to better mitigate the growth of surface damage for KDP/DKDP crystals.

2. Fabrication of spherical mitigation pits by micro-milling

The mitigation pits are fabricated using a miniature vertical five-axis NC milling machine with ball end cutter shown in Fig. 1
Fig. 1 Miniature five-axis milling set-up for fabrication of spherical mitigation pits on KDP/DKDP crystal surface. (a) Configuration of the machining set-up. (b) Double-edged micro-milling cutters with ball end. (c) Schematic of the machining process and the motion of various axes.
. The set-up consists of one high-speed spindle, two rotating axes (C- and B-Axis) and three moving axes (X-, Y- and Z-Axis) as shown in Fig. 1(a). KDP crystal sample is mounted on the precision positioning stage driven by linear motor with maximum resolution of 0.1 μm per step. The gas spindle is fixed on the rotary table of B-Axis, while the milling tool is embedded in the spindle. As shown in Fig. 1(b), the cemented carbide milling tool (Type MSB 230), made by NSK company is double-edged with ball end. In this work, the larger milling tool with 500 μm ball nose diameter is adopted in order to fabricate the spherical mitigation pits to the desired size with higher cutting speed. A CCD camera with optical magnification of 100 to 1000 times is mounted opposite to the cutting tool to precisely preset the tip of the machining tool on the working surface of the crystal shown in Fig. 1(a). In the process of micro-machining after tool presetting, the camera keeps focused on the machining region to monitor the fabricated mitigation pit and the milling tool.

The machining procedure is as follows. Firstly, the KDP sample is mounted on the worktable and the tool is preset at the damage size on KDP crystal surface using CCD camera. Then, the commands are imported to the control computer to vertically feed the milling tool to a specified cutting depth. The moving speed of the tool is 0.5 mm/s and the spindle rotated at a speed of 70, 000 RPM (the highest speed is 80, 000 RPM). The cutting depth is determined according to the lateral and vertical size of the damage site. At last, the tool is lifted to the original position once the damaged material is completely removed. The schematic diagram of the machining process and the motion of all axes are shown in Fig. 1(c). The tilted angle of the rotary cutter axis to the crystal surface is adjusted to 20 degree by rotating the B-Axis enabling the damaged material to be cut by the side of the tool with higher linear velocity and avoiding the zero cutting velocity point (interaction of the cutter and its rotating axis) [13

13. P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE 6403, 64030Q, 64030Q-7 (2006). [CrossRef]

]. This proposed machining procedure is a kind of single-plunge milling that can largely improves the cutting efficiency of damaged material when compared with other reported micro-machining methods (hold ball polishing in [9

9. F. Guillet, B. Bertussi, L. Lamaignere, X. Leborgne, and B. Minot, “Preliminary results on mitigation of KDP surface damage using the ball dimpling method,” Proc. SPIE 6720, 672008, 672008-9 (2007). [CrossRef]

] and multiple-plunge cutting in [13

13. P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE 6403, 64030Q, 64030Q-7 (2006). [CrossRef]

]). The single-plunge method in this work just requires less than one minute to fabricate a spherical mitigation pit. Furthermore, this method can greatly solve the issue of surface roughness of mitigation pit fabricated by polishing and multiple-plunge cutting [19

19. C. J. Stolz, J. Adams, M. D. Shirk, M. A. Norton, and T. L. Weiland, “Engineering meter-scale laser resistant coatings for the near IR,” Proc. SPIE 5963, 59630Y, 59630Y-9 (2005). [CrossRef]

].

3. Simulation model and theory

The morphology of fabricated mitigation pit on KDP crystal is tested using 3D stereoscopic microscope with super depth of field. Figure 2
Fig. 2 Microscopic image of a fabricated 240 μm wide and 30 μm deep mitigation pit. (a) 3D stereoscopic view and (b) sectional profile trace of the pit.
shows the stereoscopic image and sectional profile trace of a representative mitigation pit. The pit is part-of-sphere with 240 μm wide and 30 μm deep, and the scaling law of width and depth depends on the geometry of the milling tool. In order to simulate the light propagation through surface features before and after mitigation, 3D FDTD method is employed to solve the Maxwell curl equations based on rigorous electromagnetic field theory [20

20. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Academic, 2000).

]. The scattering issues by isolated surface features must be modeled using 3D FDTD algorithm, which requires much more computing time and computer memory than 2D algorithm. The light intensification is characterized by light intensity enhancement factor (LIEF), which has similar physical meaning to modulation degree in [21

21. M. J. Chen, M. Q. Li, J. Cheng, W. Jiang, J. Wang, and Q. Xu, “Study on characteristic parameters influencing laser-induced damage threshold of KH2PO4 crystal surface machined by single point diamond turning,” J. Appl. Phys. 110(11), 113103 (2011). [CrossRef] [PubMed]

]. The LIEF is referenced to the uniform distribution of light intensity inside the ideal KDP crystal (without any surface feature), and its amplitude is responsible for non-uniform energy distribution, nonlinear increase of intense laser and consequent decline of laser damage resistance. For plane wave input, the light intensity is proportional to the square of electrical field (|E|2), which is associated with the electromagnetic energy density, 1/2ε0η2|E|2. Here ε0 is the vacuum permittivity and η is the refractive index of material [16

16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

, 22

22. C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45(7), 1594–1601 (2006). [CrossRef] [PubMed]

]. When the amplitude of electric field in the simulation domain is obtained by FDTD method, the LIEF can be directly achieved to indicate the non-uniform distribution of light intensity inside the crystal.

Based on the tested profile and geometry of the mitigation pit, the FDTD model for spherical mitigation pit is designed and built, which is shown in Fig. 3
Fig. 3 Schematic of the 3D FDTD model for spherical mitigation pit and its centric x-z cross section in the simulation domain.
. The simulation domain is 3D rectangular and gridded with a uniform grid size. The grid size is δ = 50 nm, which is less than λ/10 to weaken the effect of numerical dispersion caused by differencing in 3D FDTD and consequently guarantee the accuracy of the simulation [20

20. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Academic, 2000).

]. The initial field excitation is a plane wave with amplitude normalized to 1 V/m in TE or TM mode that irradiates along + z direction normal to the crystal surface in the simulation. The reference wavelength is 1064 nm and the refractive index of the KDP crystal is η = 1.49. In order to investigate the light intensity enhancement caused by the output surface features only, the LIEF is referenced to the light intensity inside the crystal during the simulation to avoid the influence of reflections that occur at the input air-glass surface [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

]. Furthermore, in the simulations, the perfectly matched layers are set at the x-y transverse planes (in the ± z directions) and the periodic boundary conditions are adopted at x-z and y-z transverse planes (in the ± x and y directions) [16

16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

, 18

18. S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, M. D. Feit, T. V. Pistor, and C. J. Stolz, “Searching for optimal mitigation geometries for laser-resistant multilayer high-reflector coatings,” Appl. Opt. 50(9), C373–C381 (2011). [CrossRef] [PubMed]

].

For KDP crystal at 1064 nm (η = 1.49), the total internal reflection of the incident light occurs at some locations of the mitigation pit where the incident angles (βi) are larger than 42.2°. For angle larger than 45° and smaller than 68.9°, the incident light is totally reflected at both mitigation pit and output surface. The total internal reflections will generate a series of standing waves near the surface causing the largest light intensification [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

, 23

23. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986). [CrossRef]

]. As shown in Fig. 3, the incident angles at different spots of the mitigation pit are different and all incident angles (βi) share a tangent relationship with the slope (ki) of the mitigation contour. Therefore, the total internal reflections will not occur unless the slope (ki) at the spherical contour is larger than 1 and smaller than 2.59. The spot slope at the spherical contour increases monotonically from zero at the bottom to kmax at the interface of back surface and mitigation pit. The maximum slope kmax at the spherical contour can be given by:
kmax=4wmdmwm24dm2=4ζζ24
(1)
Where wm and dm are the width and depth of the mitigation pit, and ζ = wm/dm, is the width-depth ratio. It can be inferred from Eq. (1) that the width-depth ratio of the mitigation pit determines the range of incident angle and the occurrence of double total internal reflections. Therefore, the dependence of light intensification on width-depth ratio should be deeply investigated for devising the optimal mitigation geometries for KDP/DKDP crystals.

The light intensification due to cracks is the major factor leading to laser damage growth for fused silica and nonlinear crystals [10

10. S. G. Demos, M. R. Kozlowski, M. Staggs, L. L. Chase, A. Bumham, and H. B. Radousky, “Mechanisms to explain damage growth in optical materials,” Proc. SPIE 4347, 277–284 (2001). [CrossRef]

, 14

14. N. Bloembergen, “Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surfaces of transparent dielectrics,” Appl. Opt. 12(4), 661–664 (1973). [CrossRef] [PubMed]

, 15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

]. Therefore, surface cracks (single crack and adjacent cracks) as shown in Fig. 4
Fig. 4 Schematics of the 3D FDTD models for superficial cracks and their centric x-z cross sections in the simulation domain: (a) single crack and (b) adjacent cracks.
are designed for the purpose of quantitative analysis and comparison of light intensification caused by surface features before and after mitigation. The surface features are located on the rear surface, since the output surface of diamond fly-cut KDP crystal is more susceptible to laser damage and the damage is more serious than that on the front surface. Similar to the case of mitigation pits, light intensification caused by crack is also associated with total internal reflections that determined by the slope at the crack. The difference is that the slope (k = 2d/w = 2/ζ) at the crack keeps constant. It is worth noting that the surface cracks and mitigation pit in the simulations should be accurately designed to assure that the cracks can be completely removed by the mitigation pit. Only in this way would the comparative analysis of light intensification caused by cracks and mitigation pit be reasonable and convincing.

4. Results and discussion

The following sections are three-fold. The first part is focused on quantitatively comparing the light intensification caused by superficial features before (surface cracks) and after (spherical pits) mitigation. The work of this part aims to get insight into mitigation mechanism of surface damage growth for optical components, and also to evaluate the corresponding laser damage resistance after mitigation. The second part is to investigate the influence of width-depth ratio of the mitigation pit on the light intensification inside KDP crystal. The work of this part has significant implication in developing the optimal mitigation procedure to arrest surface damage growth for KDP crystal. The light intensity distribution strongly depends on the polarization of incident wave [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

, 16

16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

, 18

18. S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, M. D. Feit, T. V. Pistor, and C. J. Stolz, “Searching for optimal mitigation geometries for laser-resistant multilayer high-reflector coatings,” Appl. Opt. 50(9), C373–C381 (2011). [CrossRef] [PubMed]

]. Therefore, the light intensification caused by surface features are modeled for light incidence with both TE and TM modes. The last part of this work is laser damage testing that aims to experimentally validate the enhancement of laser damage resistance of repaired KDP crystal with spherical mitigation pit.

4.1 Comparison of light intensification before and after mitigation

The centric x-z cross sections of light intensification distribution within the simulation domain are shown in Figs. 5
Fig. 5 Distribution of light intensity caused by single cracks with various widths for TE-mode light irradiation. The lengths and depths of the cracks are all 1.0 μm, while the widths are deliberately specified to enable the incident angles at the cracks to be (a) β = 75°; (b) β = 50°; (c) β = 45° and (d) β = 15°.
and 6
Fig. 6 Distribution of light intensity caused by single cracks with various widths for TM-mode light irradiation. The lengths and depths of the cracks are all 1.0 μm, while the widths are deliberately specified to enable the incident angles at the cracks to be (a) β = 75°; (b) β = 50°; (c) β = 45° and (d) β = 15°.
with the presence of single cracks on the output surface under the normal-incidence of both TE and TM-mode waves. The lengths l and depths d of the cracks are all 1.0 μm and the widths w are deliberately set to enable the crack angles to be 15°, 40°, 45°, and 75°. Accordingly, the incident angles βi at the cracks (complements of crack angles) will be 75°, 50°, 45° and 15°, which covers both the cases that double total internal reflections occur or not. The total simulation domain is 20 μm × 20 μm × 10 μm and the incident wave is located in the glass at z = 0.5 μm. In the x-z cross-sectional profiles of light intensification, the areas with higher color scales indicate the location of larger light intensity enhancement.

For the incidence of TE-mode wave, it is shown in Fig. 5 that the initial plane wave is obviously modulated by the surface cracks on the output surface, resulting in a series of light intensification fringes inside the crystal. This is because that the incident wave constructively interferes with the reflected waves, especially with totally reflected waves from the crack and rear surface. In Figs. 5(b) and 5(c), the incident angles at the cracks are 50° and 45°, which meets the condition for occurrence of double total internal reflections at the crack and rear surface. And, it is shown that an array of the largest light intensification spots are generated in the vicinity of the crack. The regions with largest light intensification are depicted with red spots. The LIEFs in Figs. 5(b) and 5(c) are 3.99 and 3.75, respectively. However, for the cases in Figs. 5(a) and 5(d), the incident light is partially or hardly reflected at the rear surface. As a result, the induced light intensifications are smaller than that caused by total internal reflections. The LIEFs are 3.08 and 1.81, respectively in Figs. 5(a) and 5(d), while in Figs. 5(b) and 5(c) they are 3.99 and 1.81, respectively. The simulated distribution profiles of light intensity by single cracks are similar to those presented in [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

]. Furthermore, the peak light intensifications are mostly located at the back surface of the crystal. For example, the peak light intensifications in Figs. 5(b) and 5(c) reside at x = ± 1.00 μm, z = 8.5 μm, and x = ± 1.15 μm, z = 8.5 μm, respectively. This result can interpret the experimentally observed phenomenon that the rear surface is more prone to laser damage and the rear surface damage is more destructive than that of front surface under subsequent laser irradiation [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

, 16

16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

].

For TM-mode light incidence, the x-z cross sections of light intensification profile caused by single cracks with identical geometries as in Fig. 5 are demonstrated in Fig. 6. Unlike TE mode, it is found that the peaks of enhanced light intensity under TM-wave incidence are all located inside the cracks. While, we just investigate the light intensification inside the crystal, since the peak intensities inside the crack or in the air beyond the surface are not regarded to cause the optical breakdown. The locations of peak light intensity (located inside the crystal for TE mode, while inside the crack for TM mode) coincide with the results in [16

16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

]. For TM mode wave irradiation, all of the identical cracks in Fig. 6 cause smaller LIEFs than that under TE-mode wave irradiation in Fig. 5. In Figs. 6(a)-6(d), the LIEFs are 2.11, 2.60, 2.87 and 2.81, respectively. Like TE mode, the cracks with incident angles of 50° and 45° in Figs. 6(b) and 6(c) also produce the largest light intensification due to the occurrence of double total internal reflections.

The simulation results of light intensification distribution caused by adjacent cracks under the irradiation of TE and TM waves are shown in Fig. 7
Fig. 7 Distribution of light intensity caused by adjacent surface cracks with crack length l = 1.0 μm, width w = 2.0 μm, depth d = 1.0 μm and crack interval a = 1.0 μm (incident angle β = 45°): (a) TE mode; (b) TM mode.
in order to take the combined action of multiple cracks into consideration. It can be seen in Fig. 7 that when the incident angle at the cracks is 45°, the incident waves are firstly totally reflected at the surfaces of neighboring cracks and then directly constructively interfere with each other in the interval region, resulting more significant light intensification. An array of hot spots with seriously enhanced light intensity is shown in red color between the adjacent cracks. For TE and TM modes, the LIEFs are 6.03 and 3.23, respectively, which are both larger than those caused by single surface cracks. Since the morphology of actual damage site is considerably complex, the light intensification caused by surface features before mitigation is much larger than the numerically calculated values based on simple models like single and adjacent cracks.

The calculated LIEFs caused by surface cracks under the irradiation of TE and TM-mode waves are summarized in Table 1

Table 1. Summary of the LIEFs for various irradiation conditions and surface cracks before mitigation with the occurrence of double total internal reflections (βi is larger than 45° and smaller than 68.9°)

table-icon
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to quantitatively compare the light intensification before and after mitigation. It shows that for TE mode wave, the largest LIEFs caused by single and adjacent cracks are 3.99 and 6.90, respectively. When compared with the LIEF after mitigation, the value can be reduced to 76.9% and 44.5%. In the case of TM mode wave, though, the LIEFs caused by the cracks are generally smaller than that of TE mode, the LIEF for single crack with 45° incident angle can reach 2.87 with 25.4% reduction after mitigation. Especially, for the adjacent cracks with 45° incident angle and no interval, the LIEF can be greatly reduced to 51.2%. Since the morphology of actual damage site is more complex and the actual LIEF is much larger than the simply modeled cracks, the light intensification can be more largely mitigated by micro-machining to arrest the surface damage growth in the practical application of KDP crystal.

The results above can be concluded that the total internal reflections can be responsible for the largest light intensification caused by surface features. The LIEFs caused by cracks are very large, especially for the surface features with more complex morphology, while for the spherical mitigation pits, the double total internal reflections can be prevented and accordingly the LIEFs can be minimized. As a result, the possibility of laser induced damage can be largely reduced to achieve the purpose of damage growth mitigation by micro-machining.

4.2 Width-depth ratio effect

Under the illumination of TE polarized light, it is shown in Fig. 9 that the variation of LIEF with respect to the width-depth ratio shares a generally similar tendency for spherical mitigation pits with different pit widths. For mitigation pits with relatively small width-depth ratios, the LIEF is very large. For example, when the width-depth ratio is 3.0, the LIEFs are 4.9 for 4 μm wide pit, 5.4 for 8 μm wide pit and 6.5 for 10 μm wide pit, respectively. Large LIEFs caused by surface pits are not expected to achieve benign mitigation effect for the growth of surface damage. However, once the width-depth ratio is larger than 5.0, the LIEFs sharply decline and finally keep stable at 2.4 with the increase of width-depth ratios. This phenomenon can be attributed to the occurrence of total internal reflections at the contour of mitigation pit and rear surface of the crystal. As we discussed in Section 3, when the slope (ki) anywhere at the spherical pit belongs to the range of 1< ki <2.59, the double total internal reflections will be generated at both mitigation pit and output surface resulting largest light intensity enhancement. The maximum slope (kmax) at the pit is determined by the width-depth ratio according to Eq. (1) that kmax decreases with the increasing ζ. Therefore, to obtain relatively smaller light intensification, the maximum slope kmax must be smaller than 1.0 to prevent the occurrence of total internal reflections. However, it can be derived from Eq. (1) that the width-depth ratio equals to 4.8 when the maximum slope is 1.0. Based on this, we can explain the results that the LIEF is large when the width-depth ratio is near 5.0, while the light intensification is relatively smaller when the width-depth ratio is larger.

The simulation result for TM polarized light incidence is shown in Fig. 10. Similar to that of TE polarized light incidence, it is shown that the LIEFs are very large for mitigation pits with smaller width-depth ratios. However, when the width-depth ratio is larger than 5.0, the LIEFs dramatically decrease and ultimately remain stable at 2.2. The occurrence of total internal reflections at mitigation pit and back surface discussed above should be still responsible for this phenomenon. Compared with the simulation results in Fig. 9, it is also found that for mitigation pits with identical geometries, the LIEFs under TM mode wave incidence are smaller than that of TE mode wave incidence. This is consistent with the results for surface cracks before mitigation that analyzed in Section 4.1. According to the discussions for TE and TM modes, it can be concluded that in the actual micro-machining process for the mitigation of surface damage growth, the width-depth ratio of mitigation pit must be devised to be larger than 5 to achieve the lightest light intensification after surface damage mitigation.

Figure 11
Fig. 11 Plot of LIEFs caused by spherical mitigation pits as a function of width-depth ratio for both TE and TM modes. The pit depth keeps constant at 0.5 μm and 1.0 μm. Since the largest pit width that we can accurately modeled is 10 μm, the maximum width-depth ratio for 1.0 μm depth pit is 10.
shows the LIEFs caused by spherical pits with respect to width-depth ratio for the incidence of both TE and TM polarized light. The depth of the pit is designed to be stable when the width-depth ratio changes. It is demonstrated that for a specified pit depth, the LIEF quickly rises at the beginning and then gradually decreases to a certain degree with the increase of pit width. When the width is large enough, the LIEF remains roughly unchanged. The LIEF reaches the peak when the width-depth ratio is near 4~5. This is consistent with the simulation results that discussed above for the case of stable pit width. It can be found that the peak LIEF is not so large for mitigation pit with depth dm = 0.5 μm. This is because that the depth of the pit is too small, the difference in path length between incident and totally reflected waves is smaller than one wavelength (1.064 μm) and constructive interference cannot take place [15

15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

]. So, for an actual damage site with a particular damage depth, we should micro-machine the width of the spherical mitigation pit to be large enough in order to obtain the lower light intensification.

4.3 Laser damage tests

The laser damage resistance of repaired KDP crystal with spherical mitigation pit fabricated by micro-milling is characterized by testing the laser induced damage threshold (LIDT). The laser damage experiment is performed using a Nd:YAG SAGA laser with single longitudinal mode operating at 355 nm wavelength, 10 Hz repetition rate and 6.4 ns pulse width. The output beam is shaped into approximate Gaussian distribution in near field and the KDP sample is placed behind the focal spot of the focusing lens to enable the laser energy on the surface to be higher than that in the bulk. The specified experimental parameters are listed in Table 2

Table 2. The experimental parameters for laser damage test on KDP crystal

table-icon
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. The LIDTs of KDP surface with various features are measured following the R-on-1 test protocol [13

13. P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE 6403, 64030Q, 64030Q-7 (2006). [CrossRef]

]. In short, an array of identical features are produced on the sample and the testing laser exposes each site with pulse fluence ramped up until damage occurs. The damage fluence is defined as the lowest fluence at which any damage is observed. The LIDT is the average damage fluence of the tested spots (for each type of surface feature, a total of 5 spots are tested).

Surface indentation is mechanically produced on the sample as initial damaged feature and its LIEF is tested for quantitatively comparing the improvement of laser resistance of surface features before and after mitigation. Figure 12
Fig. 12 Comparison of measured LIDTs for KDP crystal with ideal surface, initially damaged surface and repaired surface with spherical mitigation pit.
illuminates the tested LIDTs for ideal surface, mechanically damaged surface and repaired surface with spherical mitigation pit. It is shown that the initially damaged surface feature can largely reduce the LIDT of diamond cut KDP crystal from 7.85 J/cm2 to 2.33 J/cm2. However, after replacing the damaged feature with spherical mitigation pit, the laser damage resistance can be retrieved to 6.23 J/cm2, which is close to the damage initiation threshold of ideal surface, but nearly 2 times larger than that of the damaged surface. The enhancement of laser damage resistance of spherical mitigation pit fabricated by micro-milling can be further verified by the experimental comparison shown in Fig. 13
Fig. 13 The first row of images was obtained by confocal microscopy (C) and the second by stereoscopic microscope with super depth of field (S). The first column (DS) is the evolution of initially damaged surface before and after laser exposure with 2 shots at 2.40 J/cm2, and the second (RS) shows the repaired surface with spherical mitigation pit before and after laser exposure with 50 shots at 3.43 J/cm2.
. As depicted using confocal microscopy, the surface indentation is about 30 μm in length, 6 μm in depth and the spherical mitigation pit is 280 μm in width and 20 μm in depth (C-DS and C-RS). After laser exposure with 2 shots at 2.40 J/cm2, the initially damaged surface feature dramatically grows to hundreds of microns wide and tens of microns deep (S-DS). While, for repaired surface with mitigation feature (S-RS), after laser exposure with 50 shots at 3.43 J/cm2, the mitigation pit keeps stable and no new damage is observed on the surface (noting that the cutting marks in Fig. 13 are caused by tool wear). Therefore, the damage resistance of KDP crystal can be successfully improved by removing the initial growing damage site with predesigned stable mitigation pit using micro-milling method.

5. Conclusion

Using a simple and efficient procedure, spherical mitigation pits have been fabricated on the KDP surface by micro-milling with a ball end milling cutter. The light intensifications caused by isolated surface features before and after mitigation are investigated by employing 3D FDTD method. The occurrence of total internal reflections at both surface features and rear surface can account for the largest light intensification inside the crystal. The LIEFs caused by surface cracks before mitigation are very large, especially for the surface features with more complex morphology (e.g., adjacent cracks). While, for surface features after mitigation, the double total internal reflections can be prevented by controlling the geometries of the mitigation pits to achieve the slightest light intensification. The light intensification caused by the spherical mitigation pits is significantly dependent on the width-depth ratio of the fabricated pit. Based on the simulation results under the incidence of TE and TM polarized light, we suggest an optimal mitigation strategy for KDP crystal by fabricating spherical pits with width-depth ratio restricted to be larger than 5.0. By performing laser damage experiment, it is verified that the growth behavior of initially damaged KDP surface can be largely mitigated by removing the damaged material, and the laser damage resistance of repaired surface with mitigation pit can be restored to near the level of ideal surface.

Acknowledgment

The authors gratefully acknowledge the National Natural Science Foundation of China (Grant No. 51275113 and No. 50935003) for their financial support of this work.

References and links

1.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47, 113–152 (2002). [CrossRef]

2.

S. Reyné, G. Duchateau, J. Y. Natoli, and L. Lamaignère, “Laser-induced damage of KDP crystals by 1ω nanosecond pulses: influence of crystal orientation,” Opt. Express 17(24), 21652–21665 (2009). [CrossRef] [PubMed]

3.

R. A. Negres, S. O. Kucheyev, P. DeMange, C. Bostedt, T. van Buuren, A. J. Nelson, and S. G. Demos, “Decomposition of KH2PO4 crystals during laser-induced breakdown,” Appl. Phys. Lett. 86(17), 171107 (2005). [CrossRef]

4.

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004). [CrossRef] [PubMed]

5.

G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express 17(13), 10434–10456 (2009). [CrossRef] [PubMed]

6.

J. A. Jarboe, J. J. Adams, and R. P. Hackel, “Analysis of output surface damage resulting from single 351nm, 3ns pulses on sub-nanosecond laser conditioned KD2PO4 crystals,” Proc. SPIE 6720, 67200J, 67200J-12 (2007). [CrossRef]

7.

R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett. 30(20), 2766–2768 (2005). [CrossRef] [PubMed]

8.

F. Guillet, B. Bertussi, L. Lamaignère, and C. Maunier, “Effects of thermal annealing on KDP and DKDP on laser damage resistance at 3ω,” Proc. SPIE 7842, 78421T, 78421T-5 (2010). [CrossRef]

9.

F. Guillet, B. Bertussi, L. Lamaignere, X. Leborgne, and B. Minot, “Preliminary results on mitigation of KDP surface damage using the ball dimpling method,” Proc. SPIE 6720, 672008, 672008-9 (2007). [CrossRef]

10.

S. G. Demos, M. R. Kozlowski, M. Staggs, L. L. Chase, A. Bumham, and H. B. Radousky, “Mechanisms to explain damage growth in optical materials,” Proc. SPIE 4347, 277–284 (2001). [CrossRef]

11.

C. J. Stolz, “The National Ignition Facility: The Path to a Carbon-Free Energy Future,” Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 370(1973), 4115–4129 (2012). [CrossRef]

12.

L. W. Hrubesh, R. B. Brusasco, W. Grundler, M. A. Norton, E. E. Donohue, W. A. Molander, S. L. Thompson, S. R. Strodtbeck, P. K. Whitman, M. D. Shirk, P. J. Wegner, M. C. Nostrand, and A. K. Burnham, “Methods for mitigating growth of laser-initiated surface damage on DKDP optics at 351nm,” Proc. SPIE 4932, 180–191 (2003). [CrossRef]

13.

P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE 6403, 64030Q, 64030Q-7 (2006). [CrossRef]

14.

N. Bloembergen, “Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surfaces of transparent dielectrics,” Appl. Opt. 12(4), 661–664 (1973). [CrossRef] [PubMed]

15.

F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18(10), 2607–2616 (2001). [CrossRef] [PubMed]

16.

L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt. 49(35), 6668–6674 (2010). [PubMed]

17.

J. E. Wolfe, S. R. Qiu, and C. J. Stolz, “Fabrication of mitigation pits for improving laser damage resistance in dielectric mirrors by femtosecond laser machining,” Appl. Opt. 50(9), C457–C462 (2011). [CrossRef] [PubMed]

18.

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, M. D. Feit, T. V. Pistor, and C. J. Stolz, “Searching for optimal mitigation geometries for laser-resistant multilayer high-reflector coatings,” Appl. Opt. 50(9), C373–C381 (2011). [CrossRef] [PubMed]

19.

C. J. Stolz, J. Adams, M. D. Shirk, M. A. Norton, and T. L. Weiland, “Engineering meter-scale laser resistant coatings for the near IR,” Proc. SPIE 5963, 59630Y, 59630Y-9 (2005). [CrossRef]

20.

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Academic, 2000).

21.

M. J. Chen, M. Q. Li, J. Cheng, W. Jiang, J. Wang, and Q. Xu, “Study on characteristic parameters influencing laser-induced damage threshold of KH2PO4 crystal surface machined by single point diamond turning,” J. Appl. Phys. 110(11), 113103 (2011). [CrossRef] [PubMed]

22.

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45(7), 1594–1601 (2006). [CrossRef] [PubMed]

23.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986). [CrossRef]

OCIS Codes
(140.3330) Lasers and laser optics : Laser damage
(160.4330) Materials : Nonlinear optical materials
(220.4610) Optical design and fabrication : Optical fabrication

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: April 19, 2013
Revised Manuscript: June 26, 2013
Manuscript Accepted: June 27, 2013
Published: July 5, 2013

Citation
Jian Cheng, Mingjun Chen, Wei Liao, Haijun Wang, Yong Xiao, and Mingquan Li, "Fabrication of spherical mitigation pit on KH2PO4 crystal by micro-milling and modeling of its induced light intensification," Opt. Express 21, 16799-16813 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-16799


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References

  1. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev.47, 113–152 (2002). [CrossRef]
  2. S. Reyné, G. Duchateau, J. Y. Natoli, and L. Lamaignère, “Laser-induced damage of KDP crystals by 1ω nanosecond pulses: influence of crystal orientation,” Opt. Express17(24), 21652–21665 (2009). [CrossRef] [PubMed]
  3. R. A. Negres, S. O. Kucheyev, P. DeMange, C. Bostedt, T. van Buuren, A. J. Nelson, and S. G. Demos, “Decomposition of KH2PO4 crystals during laser-induced breakdown,” Appl. Phys. Lett.86(17), 171107 (2005). [CrossRef]
  4. C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett.92(8), 087401 (2004). [CrossRef] [PubMed]
  5. G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express17(13), 10434–10456 (2009). [CrossRef] [PubMed]
  6. J. A. Jarboe, J. J. Adams, and R. P. Hackel, “Analysis of output surface damage resulting from single 351nm, 3ns pulses on sub-nanosecond laser conditioned KD2PO4 crystals,” Proc. SPIE6720, 67200J, 67200J-12 (2007). [CrossRef]
  7. R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett.30(20), 2766–2768 (2005). [CrossRef] [PubMed]
  8. F. Guillet, B. Bertussi, L. Lamaignère, and C. Maunier, “Effects of thermal annealing on KDP and DKDP on laser damage resistance at 3ω,” Proc. SPIE7842, 78421T, 78421T-5 (2010). [CrossRef]
  9. F. Guillet, B. Bertussi, L. Lamaignere, X. Leborgne, and B. Minot, “Preliminary results on mitigation of KDP surface damage using the ball dimpling method,” Proc. SPIE6720, 672008, 672008-9 (2007). [CrossRef]
  10. S. G. Demos, M. R. Kozlowski, M. Staggs, L. L. Chase, A. Bumham, and H. B. Radousky, “Mechanisms to explain damage growth in optical materials,” Proc. SPIE4347, 277–284 (2001). [CrossRef]
  11. C. J. Stolz, “The National Ignition Facility: The Path to a Carbon-Free Energy Future,” Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci.370(1973), 4115–4129 (2012). [CrossRef]
  12. L. W. Hrubesh, R. B. Brusasco, W. Grundler, M. A. Norton, E. E. Donohue, W. A. Molander, S. L. Thompson, S. R. Strodtbeck, P. K. Whitman, M. D. Shirk, P. J. Wegner, M. C. Nostrand, and A. K. Burnham, “Methods for mitigating growth of laser-initiated surface damage on DKDP optics at 351nm,” Proc. SPIE4932, 180–191 (2003). [CrossRef]
  13. P. Geraghty, W. Carr, V. Draggoo, R. Hackel, C. Mailhiot, and M. Norton, “Surface damage growth mitigation on KDP/DKDP optics using single-crystal diamond micro-machining ball end mill contouring,” Proc. SPIE6403, 64030Q, 64030Q-7 (2006). [CrossRef]
  14. N. Bloembergen, “Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surfaces of transparent dielectrics,” Appl. Opt.12(4), 661–664 (1973). [CrossRef] [PubMed]
  15. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A18(10), 2607–2616 (2001). [CrossRef] [PubMed]
  16. L. Zhang, L. Huang, S. J. Fan, G. X. Bai, K. F. Li, W. Chen, and L. L. Hu, “Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses,” Appl. Opt.49(35), 6668–6674 (2010). [PubMed]
  17. J. E. Wolfe, S. R. Qiu, and C. J. Stolz, “Fabrication of mitigation pits for improving laser damage resistance in dielectric mirrors by femtosecond laser machining,” Appl. Opt.50(9), C457–C462 (2011). [CrossRef] [PubMed]
  18. S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, M. D. Feit, T. V. Pistor, and C. J. Stolz, “Searching for optimal mitigation geometries for laser-resistant multilayer high-reflector coatings,” Appl. Opt.50(9), C373–C381 (2011). [CrossRef] [PubMed]
  19. C. J. Stolz, J. Adams, M. D. Shirk, M. A. Norton, and T. L. Weiland, “Engineering meter-scale laser resistant coatings for the near IR,” Proc. SPIE5963, 59630Y, 59630Y-9 (2005). [CrossRef]
  20. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Academic, 2000).
  21. M. J. Chen, M. Q. Li, J. Cheng, W. Jiang, J. Wang, and Q. Xu, “Study on characteristic parameters influencing laser-induced damage threshold of KH2PO4 crystal surface machined by single point diamond turning,” J. Appl. Phys.110(11), 113103 (2011). [CrossRef] [PubMed]
  22. C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt.45(7), 1594–1601 (2006). [CrossRef] [PubMed]
  23. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys.54(7), 601–607 (1986). [CrossRef]

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