Surface control apparatus and method of optical transmission with large aperture based on self-adaptive force-moment technology

Qin Tinghai; Quan Xusong; Pei Guoqing; Yan Han; Xu Xu; Ye Lang; Du Weifeng; Xiong Zhao; Liu Changchun

doi:10.1364/OE.25.015358

1. Introduction

A large number of transmission optics systems with large apertures are used in high-power solid-state laser facilities, such as the National Ignition Facility (NIF) in the USA [1], the Laser Mega Joule (LMJ) in France [2], and the SG-III system in China [3]. In the on-line working state, the distortion of optics induced by both gravity and clamping stress weaken the efficiency so much that surface control is urgently needed. In the off-line testing state, surface control is also needed to simulate the distortion of on-line working state for the validation of its operational efficiency. Actually, surface control of optics, in both the on-line working state, and the off-line testing state, is perceived as one of the most important requirements in this area, and also its greatest engineering challenge.

A variety of schemes have been proposed in the field of high-power solid-state laser facilities to solve this type of problem. L.H. Zheng et al. [4], studied the influence of wavefront aberration on imaging performance. Jae Sung Shin et al. [5], proposed a method to predict wavefront distortion and beam quality for various optical arrangements and optimised the design therewith. Fuling Zhang et al. [6], investigated the effect of wavefront phase distortions on the beam quality of an OPA. Lei Huang et al. [7], R.A. Zacharias et al. [8], Daiwan Jun et al. [9], S. Bonora et al. [10], and Q Xue et al. [11], proposed the use of a deformable mirror for wavefront control. Hua Chen et al. [12] and B. Canuel et al. [13], realised wavefront aberration compensation with an electric film heater matrix and a thermally deformable mirror, respectively. V.A. Banarh et al. [14, 15], studied the compensation of aberration distortions of laser beam wavefronts based on the atmospheric backscatter signal. A. Haber [16] and Steven C. West [17], also proposed a method with which to predict and control wavefront aberrations in optical systems.

In general, the aforementioned studies concentrate on the reflection optics. Here, a surface control apparatus and method is proposed to clamp the transmission optics and compute the load distribution, based on self-flexible force-moment technology and principle of load linearity respectively. A series of analyses are conducted to validate the proposed apparatus and method both mechanically and numerically. Furthermore, the principle of phase mismatch induced by distortion and SHG efficiency is analysed theoretically. Finally, the trends of the surface RMS value and efficiency under different loading regimes on certain loading states are deduced, and the trends in the best surface RMS value and efficiency of each loading state are analysed.

2. Opto-mechanical configuration

2.1 Optical configuration

Before converging radially on the target, the laser beams travel through every sub-system in the high-power solid-state laser facility, and finally pass through the FOA where SHG is achieved [18]. The FOA is composed of a type-I KDP crystal and a type-II KDP crystal [19]. The input fundamental wave (1053 nm) generates the remnant fundamental and outputs a second harmonic (527 nm) wave when passing through the type-I KDP crystal (Fig. 1). The remnant fundamental (1053 nm) and second harmonic (527 nm) wave generate the third harmonic (351 nm) wave when passing through the type-II KDP crystal.

Fig. 1 Optical configuration.

Download Full Size | PDF

2.2 Mechanical configuration

The KDP crystal, measuring 410 mm × 410 mm × 9 mm, is supported and loaded by three support blocks and eight loading modules in the Z-direction (Fig. 2). The three support blocks are distributing along the lower surface border of the optics in the form of an equilateral triangle and are fixed on the frame. The eight loading modules are equidistant and are distributed around the border of the optics. The X- and Y-directions of the optics are restrained by screws which are ignored together with some other accessories as they are beyond the scope of this research. Each loading module is composed of a force unit and a moment unit that could load the optics independently. The force unit consisted of beam A, a loading screw, spring A, a force sensor, and spring B. Beam A is loaded by the loading screw through spring A, the force sensor, and spring B. As the interface between beam A and the optics faces right (relative to the interface between the support block and the optics), once a load is acting on Beam A, the corresponding reaction will act on the optics. The value of the force can be controlled by adjusting the loading screw. The moment unit consisted of beam B, beam C, a loading screw, spring A, a force sensor, and spring B. Beams B and C are loaded by adjusting the loading screw through spring A, the force sensor, and spring B. As the interface between beam B and the optics is staggered with the interface between beam C and the optics, once a load acts on beams B and C, the corresponding reaction acts on the optics, and the two forces generate the required moment. The value of the moment can be controlled by adjusting the loading screw; however, the force unit and the moment unit can work independently due to the characteristics of the structure.

Fig. 2 Mechanical configuration.

Download Full Size | PDF

2.3 Principle of the double beam

A double-beam structure is used for beams A to C: comparing this with the configuration of a simple cantilever beam, the principle and predominance of the double beam are shown in Fig. 3. In a simple cantilever beam, the small distance (δ₁) between the optics and the beam would contribute to the rotation (θ₁) of the cantilever beam, which reduces the contact area between the red double beam and the green optics so much, and increases the concentration of stress as shown in Fig. 3(a). While in a double-beam configuration, the contact interface could be kept parallel to the surface of the optics, which reduces the contact area between the red double beam and the green optics so little, and decreases the concentration of stress as shown in Fig. 3(b).

Fig. 3 Distortion conditions for different beams (a) cantilever, and (b) double beam.

Download Full Size | PDF

3. Theory

3.1 SHG analysis

As a type-I angle phase matching (o + o→e) uniaxial KDP crystal, the refractive indices thereof for the fundamental and second harmonic waves are calculated as follows [20]:

{\begin{cases} n_{1} (ω, θ) = n_{2} (ω, θ) = n_{o} (ω) \\ n_{3} (2 ω, θ) = n_{e} (2 ω, θ) = [^{\frac{n_{o}^{2} (2 ω) n_{e}^{2} (2 ω)}{n_{o}^{2} (2 ω) \sin^{2} θ + n_{e}^{2} (2 ω) \cos^{2} θ}] 1 / 2} \end{cases}

where n₁(ω, θ), n₂(ω, θ), and n_o(ω) are the refractive indices along the ordinary axes of the fundamental waves, respectively; n₃(2ω, θ), and n_e(2ω, θ) are the refractive indices along the extraordinary axes of the second harmonic waves; n_o(2ω) and n_e(2ω) are the refractive indices along the ordinary and extraordinary axes of the second harmonic waves, respectively; θ is the angle of phase match as given by Eq. (2):

n_{o} (ω) = n_{e} (2 ω, θ)

The optimum angle of phase match is obtained by substituting Eq. (1) into Eq. (2), as shown in Eq. (3):

\sin^{2} θ_{m} = \frac{n_{e}^{2} (2 ω) [n_{o}^{2} (2 ω) - n_{o}^{2} (ω)]}{n_{o}^{2} (2 ω) [n_{o}^{2} (2 ω) - n_{e}^{2} (2 ω)]}

where θ_m is the optimum angle of phase match. Setting θ to θ_m + △θ, the phase mismatch induced by variations in the incident angle is calculated using Eq. (4).

Δ K = K_{3} - (K_{2} + K_{1}) = ω_{3} n_{3} (ω_{3}, θ) / c - ω_{2} n_{2} (ω_{2}, θ) / c - ω_{1} n_{1} (ω_{1}, θ) / c

where ΔK is the phase mismatch, K₁, K₂, and K₃, ω₁, ω₂, and ω₃, and n₁, n₂, and n₃ are the wave vectors, frequencies, and refractive indices of the fundamental and second harmonic waves, respectively; and c is the speed of light in vacuo. The Taylor series expansion of Eq. (4) in θ_m is given by Eq. (5).

Δ K = Δ K |_{θ = θ_{m}} + \frac{\partial Δ K}{\partial θ} |_{θ = θ_{m}} Δ θ + \frac{1}{2} \frac{\partial^{2} Δ K}{\partial θ^{2}} |_{θ = θ_{m}} {(Δ θ)}^{2} + \dots

Where △k|_θ _{= 0} = 0 is the ideal condition where the incident angle is equal to the phase matching angle. As an approximation, Eq. (5) is simplified to the form shown in Eq. (6):

Δ K = \frac{\partial Δ K}{\partial θ} |_{θ = θ_{m}} Δ θ

Substituting Eq. (1) into Eq. (6), and taking the derivative of ΔK with respect to θ, gives:

\frac{d Δ K}{d θ} = - \frac{1}{2} \frac{ω_{3}}{c} n_{3}^{3} {(ω_{3}, θ)}^{3} [n_{e}^{- 2} (2 ω) - n_{o}^{- 2} (2 ω)] \sin (2 θ)

Substituting Eq. (7) into Eq. (6) gives the phase mismatch, as induced by distortion, as shown in Eq. (8).

Δ K = - \frac{1}{2} \frac{ω_{3}}{c} n_{3}^{3} {(ω_{3}, θ)}^{3} [n_{e}^{- 2} (2 ω) - n_{o}^{- 2} (2 ω)] \sin (2 θ) |_{θ = θ_{m}} Δ θ

As for the SHG in a KDP crystal exhibiting type-I phase matching, the coupling wave equation is calculated as follows [21], and the Runge-Kutta method is used to solve the equations numerically.

{\begin{cases} \frac{d E (2 ω, z)}{d z} = \frac{2 i ω^{2}}{k_{2 ω} c^{2}} χ_{e f f}^{(2)} E^{2} (ω, z) e^{i Δ k z} \\ \frac{d E (ω, z)}{d z} = \frac{i ω^{2}}{k_{ω} c^{2}} χ_{e f f}^{(2)} E (2 ω, z) E^{*} (ω, z) e^{- i Δ k z} \end{cases}

The SHG efficiency is calculated by using Eq. (10).

{\begin{cases} η = \frac{P_{2}}{P_{1}} \\ P_{1} = \frac{1}{2} n_{1 o} C ε_{0} {| E_{1} |}^{2} \\ P_{2} = \frac{1}{2} n_{2 e} C ε_{0} {| E_{2} |}^{2} \end{cases}

3.2 Calculation method

To meet the requirements of both the on-line working, and off-line testing, states, the aim of the proposed calculation method was to control the optical surface to the level of a given target surface which was a non-ideal plane. As a problem of micro-distortion, the principle of load linearity is applied to the proposed calculation of surface control parameters [22]. The distribution of the eight loading modules is shown in Fig. 4. The calculation method is described below.

Fig. 4 The distribution of each support block and load module.

Download Full Size | PDF

The optical surface is divided into several points from 1 to n. As an ideal plane, the original surface equation is shown in Eq. (11).

x_{o} = [\begin{matrix} x_{o 1} & x_{o 2} & \dots & x_{o n} \end{matrix}]

where x_o* (1 ≤ * ≤ n) are the normal displacements of the optical surface, which are all zero. With a unit force acting from A to H respectively, the corresponding surfaces are shown in each row of Eq. (12).

[\begin{array}{l} x_{F A} \\ x_{F B} \\ ⋮ \\ x_{F H} \end{array}] = [\begin{array}{l} \begin{matrix} x_{F A 1} & x_{F A 2} & \dots & x_{F A n} \end{matrix} \\ \begin{matrix} x_{F B 1} & x_{F B 2} & \dots & x_{F B n} \end{matrix} \\ ⋮ \\ \begin{matrix} x_{F H 1} & x_{F H 2} & \dots & x_{FHn} \end{matrix} \end{array}]

where x_F* (A ≤ * ≤ H) is the surface of the optical element under forces A to H, respectively. With unit moment acting from A to H respectively, the corresponding surfaces are shown in each row of Eq. (13).

[\begin{array}{l} x_{M A} \\ x_{M B} \\ ⋮ \\ x_{M H} \end{array}] = [\begin{array}{l} \begin{matrix} x_{M A 1} & x_{M A 2} & \dots & x_{M A n} \end{matrix} \\ \begin{matrix} x_{M B 1} & x_{M B 2} & \dots & x_{M B n} \end{matrix} \\ ⋮ \\ \begin{matrix} x_{M H 1} & x_{M H 2} & \dots & x_{MHn} \end{matrix} \end{array}]

where x_M* (A ≤ * ≤ H) is the surface of the optical element under moments A to H, respectively. The target surface is assumed to be given by Eq. (14).

x_{T} = [\begin{matrix} x_{T 1} & x_{T 2} & \dots & x_{Tn} \end{matrix}]

To achieve the desired target surface, it was assumed that a load of *1 (a ≤ * ≤ h) times the unit force and *2 (a ≤ * ≤ h) times the unit moment act on the optical element. Its calculated surface form, under this regime, is given by Eq. (15).

x_{C} = a 1 * x_{F 1} + a 2 * x_{M 1} + b 1 * x_{F 2} + b 2 * x_{M 2} \dots h 1 * x_{F 8} + h 2 * x_{M 8} + x_{0}

The difference between the target surface and calculation surface is given by Eq. (16).

Δ x = x_{C} - x_{T}

The method of least squares is used for computing the parameters a₁, a₂, to h₁, h₂ minimising △x. The final values of force and moment at locations A to H were obtained by substituting a₁, a₂, to h₁, h₂ into Eqs. (12) and (13).

3.3 Finite element modelling

The proposed surface control apparatus and method are modelled and mechanically analysed by “Creo Parametric” and “ANSYS Workbench”, respectively. A mesh comprised of 280,440 nodes was used. The density of the KDP crystal is 2340 kg/m³, and the anisotropic elasticity is as given by Eq. (17). Eight forces and moments were applied to the corresponding location on each loading block, and three fixed supports were applied to the other surface of the optical element (Fig. 5). The value of each force and moment arose as the result of the proposed calculation method, and these differed during this process.

Fig. 5 The finite element model.

Download Full Size | PDF

[\begin{array}{l} E_{X X} \\ E_{Y Y} \\ E_{Z Z} \\ E_{Y Z} \\ E_{X Z} \\ E_{X Y} \end{array}] = [\begin{matrix} 71.2 & - 5.0 & 14.1 & 0 & 0 & 0 \\ - 5.0 & 71.2 & 14.1 & 0 & 0 & 0 \\ 14.1 & 14.1 & 56.8 & 0 & 0 & 0 \\ 0 & 0 & 0 & 12.6 & 0 & 0 \\ 0 & 0 & 0 & 0 & 12.6 & 0 \\ 0 & 0 & 0 & 0 & 0 & 6.22 \end{matrix}]

4. Results and discussion

4.1 Loading status

The loading module is designed to apply force and moment independently (see below). In force-application mode, a normal force is applied by beam A, while beams B and C are unrestrained in the normal direction (Fig. 6(a)). In moment-application mode, moment is applied by beams B and C, while beam A is unrestrained in the normal direction (Fig. 6(b)). In force- and moment-application mode, a normal force is applied by beam A, and moment is applied by beams B and C (Fig. 6(c)).

Fig. 6 The loading modes of (a) force, (b) moment, and (c) force and moment.

Download Full Size | PDF

4.2 Loading modes

Analysis of the four modes applying a uniformly distributed force (F), free distributed force ([F]), uniformly distributed force and moment (M), and free distributed force and moment ([M]) is undertaken (Fig. 7). The deformation seen in Fig. 7 represents the difference between the position of the analysis surface and a given target surface. Based on the proposed calculation method, 1.0F is calculated as the best load distribution under uniform distributed force. So, to validate the accuracy of the proposed calculation method, eleven analyses were conducted around load distribution 1.0F (Fig. 7(a)). As a result, from load distribution 0.0F to load distribution 2.0F, relatively low deformations were obtained with load distribution 1.0F. Similarly, based on the proposed calculation method, 1.0[F], 1.0M, and 1.0[M] were calculated as the best load distributions under the modes of free distributed force, uniformly distributed force and moment, and free distributed force and moment, respectively. Furthermore, eleven analyses were conducted around load distribution 1.0[F], 1.0M, and 1.0[M] (Figs. 7(b)-7(d)), respectively. A similar result was obtained: under uniform load, relatively low deformations were obtained with load distributions 1.0[F], 1.0M, and 1.0[M] under the free distributed force, uniform distributed force and moment, free distributed force and moment, respectively. The accuracy of the proposed calculation method is validated, and the best load distribution calculated by the proposed calculation method is actually the best load distribution.

Fig. 7 Optical deformation in loading modes (a) uniform distributed force, (b) free distributed force, (c) uniform distributed force and moment, and (d) free distributed force and moment.

Download Full Size | PDF

4.3 Distortion on the surface of the optical element

To investigate the relationship between the surface deformation and the distribution of load, the direction of action of gravity is set so as to be parallel to the X-axis. So, the deformation of the optical surface in the normal direction is affected by its self-weight slightly. The given target surface on the optical surface is shown in Fig. 8(a). The best surfaces under load distributions of 1.0F, 1.0 [F], 1.0M, and 1.0 [M] are shown in Figs. 8(b)-8(e), respectively. The maximum deformation of the given target surface was 0.010252 mm, and the maximum deformation of the optical element under load distributions of 1.0F, 1.0 [F], 1.0M, and 1.0[M] were 0.014253 mm, 0.012331 mm, 0.0095082 mm, and 0.01102 mm, respectively. The maximum deformation of the given target surface was located at the centre of the underside of the surface. The sub-maximum deformation of the given target surface was found at the top-left corner and the top-right corner. The minimum deformation of the given target surface was located at the upper centre, bottom-left corner, and at the bottom-right corner. On the one hand, the layout of the surface of the optical element under load distributions of 1.0[F], 1.0M, and 1.0 [M] approached the given target surface by more than that under distribution 1.0F. On the other hand, with a view to the likely deformations, the maximum deformation under load distributions of 1.0M and 1.0[M] was closer to the given target surface. It can be confirmed that, among all load distributions, 1.0M and 1.0[M] offered the best means with which to approach the given target surface.

Fig. 8 Optical deformation of (a) target surface, (b) best surface under 1.0F, (c) best surface under 1.0[F], (d) best surface under 1.0M, and (e) best surface under 1.0[M].

Download Full Size | PDF

4.4 Distortion induced efficiency

The variation in RMS values of distortion and SHG efficiency induced by distortion under different load regimes (uniform distributed force, free distributed force, uniform distributed force and moment, and free distributed force and moment) are shown in Figs. 9(a)-9(d), respectively. The minima in the RMS value are located at 1.0F, 1.0[F], 1.0M, and 1.0[M], respectively. The maxima of the efficiency are located at the minima of the RMS values under uniform distributed force and moment, and free distributed force and moment. While under uniform distributed force, and free distributed force, the minima in the RMS values and maxima in the efficiency diverge, because the RMS value is the main factor affecting the efficiency under relatively low deformations, while this was not the case under relatively high deformation states. Under uniform distributed force and moment, and free distributed force and moment, the deformation was very low when it was in the region of an RMS minimum. The RMS value was, therefore, the main factor affecting the efficiency at this location, thus the maxima in the efficiency are located at the RMS minima. While under uniform distributed force, or a free distributed force, the deformation was relatively high in the vicinity of RMS minima. Therefore the RMS value was not the main factor affecting the efficiency at this location, thus the location of RMS minima and efficiency maxima diverge. Therefore, these findings can be used to realise a higher efficiency through controlling the surface deformation to within a relatively low level.

Fig. 9 Efficiency in modes (a) uniform distributed force, (b) free distributed force, (c) uniform distributed force and moment, and (d) free distributed force and moment.

Download Full Size | PDF

The best state RMS values of distortion and SHG efficiency induced by distortion under different load regimes (uniform distributed force, free distributed force, uniform distributed force and moment, and free distributed force and moment) are shown in Fig. 10. As expected, the RMS value decreased (in turn) under different load regimes (uniform distributed force, free distributed force, uniform distributed force and moment, and free distributed force and moment), as the means of controlling the system became complex and requiring increasing refinement; however, the efficiency was affected not only by the surface RMS value but also the laser phase mismatch value, stress anisotropy, and so on. So, the best efficiency was found under uniform distributed force and moment conditions, but not under free distributed force and moment conditions. To sum up, the result of the analysis based on the proposed surface control apparatus and method can instruct the maximisation of efficiency.

Fig. 10 Distortion-induced efficiency under four load regimes.

Download Full Size | PDF

5. Conclusions

A surface control device and method was proposed to clamp the optics and compute the load distribution thereon: these were based on self-flexible force-moment technology and the principle of load linearity, respectively. The proposed apparatus and method were analysed, verified, and validated, both mechanically and numerically. Furthermore, the principle of phase mismatch induced by distortion and SHG efficiency was analysed theoretically. Finally, the trends in the surface RMS value and efficiency under different load regimes were deduced, and the trends in the best surface RMS value and efficiency under each load regime were analysed with the proposed calculation method. This study provided an approach with which to make the deformation surface of an optical element approach a given target surface, realising the maximisation of efficiency of laser conversion in high-power solid-state laser facility, satisfying key requirements in both on-line working, and off-line testing, states.

Funding

Unified Planning Fund of China Academy of Engineering Physics (TCGH0805).

References and links

1. J. A. Paisner, J. D. Boyes, S. A. Kumpan, W. H. Lowdermilk, and M. S. Sorem, “Conceptual design of the National Ignition Facility,” Proc. SPIE 2633, 2–12 (1995). [CrossRef]

2. N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Megajoule (LMJ) Project dedicated to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74(1), 147–154 (2005). [CrossRef]

3. Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, Z. Dang, and X. W. Deng, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013). [CrossRef]

4. L. H. Zheng, C. H. Rao, N. T. Gu, L. H. Huang, and Q. Qiu, “Influence of wavefront aberration on the imaging performance of the solar grating spectrometer,” Opt. Express 24(1), 153–167 (2016). [CrossRef] [PubMed]

5. J. S. Shin, Y.-H. Cha, B. H. Cha, H. C. Lee, H. T. Kim, and J. H. Lee, “Simulation of the wavefront distorting and beam quality for a high-power zigzag slab laser,” Opt. Commun. 380, 446–451 (2016). [CrossRef]

6. F. L. Zhang, Y. H. Wang, M. Z. Sun, Q. Y. Bi, X. L. Xie, and Z. Q. Lin, “Numerical simulations of the impact wavefront phase distortions of pump on the beam quality of OPA,” Chin. Opt. Lett. 8(2), 217–220 (2010). [CrossRef]

7. L. Huang, X. Ma, Q. Bian, T. Li, C. Zhou, and M. Gong, “High-precision system identification method for a deformable mirror in wavefront control,” Appl. Opt. 54(14), 4313–4317 (2015). [CrossRef] [PubMed]

8. R. A. Zacharias, N. R. Beer, E. S. Bliss, S. C. Burkhart, S. J. Cohen, S. B. Sutton, R. L. Vanttta, S. E. Winters, J. T. Salmon, M. R. Latea, C. J. Stolz, D. C. Pigg, and T. J. Arnold, “Alignment and wavefront control systems of the National Ignition Facility,” Opt. Eng. 43(12), 2873–2884 (2004). [CrossRef]

9. D. Wanjun, H. Dongxia, Z. Wei, Z. Junpu, J. Feng, Y. Zeping, Z. Kun, J. Xuejun, D. Wu, Z. Runchang, P. Zhitao, and F. Bin, “Beam wavefront control of a thermal inertia laser for inertial confinement fusion application,” Appl. Opt. 48(19), 3691–3694 (2009). [CrossRef] [PubMed]

10. S. Bonora, D. Coburn, U. Bortolozzo, C. Dainty, and S. Residori, “High resolution wavefront correction with photocontrolled deformable mirror,” Opt. Express 20(5), 5178–5188 (2012). [CrossRef] [PubMed]

11. Q. Xue, L. Huang, D. Yan, M. L. Gong, Y. T. Qiu, T. H. Li, Z. X. Feng, and G. F. Jin, “Structure and closed-loop control of a novel compact deformable mirror for wavefront correction in a high power laser system,” Laser Phys. Lett. 10(4), 045301 (2013). [CrossRef]

12. H. Chen, L. Hou, and X. Zhou, “Active compensation of wavefront aberrations by controllable heating of lens with electric film heater matrix,” Appl. Opt. 55(24), 6634–6638 (2016). [CrossRef] [PubMed]

13. B. Canuel, R. Day, E. Genin, P. L. Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Class. Quantum Gravity 29(8), 085012 (2012). [CrossRef]

14. V. A. Banakh, V. V. Zhmylevskii, A. B. Ignatiev, V. V. Morozov, I. A. Razenkov, A. P. Rostov, and R. S. Tsvyk, “Optical beam wavefront control based on the atmospheric backscatter signal,” Quantum Electron. 45(2), 153–160 (2015). [CrossRef]

15. V. A. Banakh and I. N. Smalikho, “Compensation of aberration distortions of a laser beam wavefront in the bistatic location scheme,” Opt. Spectrosc. 117(6), 976–982 (2014). [CrossRef]

16. A. Haber, A. Polo, I. Maj, S. F. Pereira, H. P. Urbach, and M. Verhaegen, “Predictive control of thermally induced wavefront aberrations,” Opt. Express 21(18), 21530–21541 (2013). [CrossRef] [PubMed]

17. S. C. West, S. H. Bailey, J. H. Burge, B. Cuerden, J. Hagen, H. M. Martin, and M. T. Tuell, “Wavefront control of the large optics test and integration site (LOTIS) 6.5m collimator,” Appl. Opt. 49(18), 3522–3537 (2010). [CrossRef] [PubMed]

18. Z. Xiong, H. Wang, T. F. Cao, X. D. Yuan, C. Yao, Z. Zhang, M. X. Zhou, and G. H. Ma, “Error analysis on assembly and alignment of laser optical unit,” Adv. Mech. Eng. 7(7), 1–10 (2015). [CrossRef]

19. Y. C. Liang, R. F. Su, H. T. Liu, and L. H. Lu, “Analysis of torque mounting configuration for nonlinear optics with large aperture,” Opt. Laser Technol. 58, 185–193 (2014). [CrossRef]

20. P. X. Ye, Nonlinear Optics (Sci. Technol. China, 1998).

21. R. W. Boyd, Nonlinear Optics (Academic, 2008).

22. Z. H. Shan, Mechanics of Material (National Defense Industry, 1986).

Surface control apparatus and method of optical transmission with large aperture based on self-adaptive force-moment technology

Abstract

1. Introduction

2. Opto-mechanical configuration

2.1 Optical configuration

2.2 Mechanical configuration

2.3 Principle of the double beam

3. Theory

3.1 SHG analysis

3.2 Calculation method

3.3 Finite element modelling

4. Results and discussion

4.1 Loading status

4.2 Loading modes

4.3 Distortion on the surface of the optical element

4.4 Distortion induced efficiency

5. Conclusions

Funding

References and links

Cited By

Figures (10)

Equations (17)

Optics Express