An algorithm based on singular value decomposition (SVD) is presented to fit the wavefront with Zernike polynomials. In the current algorithm, SVD is applied to decompose the matrix of the linear equations directly. In the process of computing the inverse matrix, a threshold value is employed to modify the reciprocals of singular values which are zero or too small. Then the Zernike coefficients can be worked out immediately. Compared with the typical Gram-Schmidt orthogonalization, SVD has good stabilization when solving the least square problem of the ill-conditioned equations or singular matrix. And also because of avoiding construction of normal equation group, the computational error is eliminated. Moreover, it is quite easy to be programmed.

Using methyl triethoxysilicane as precursor, a moisture-resistant coating for neodymium-doped laser glass was developed by the sol-gel process. Colloidal silica was added in coating solution as modifier. The refractive index of this coating varied from 1.31 to 1.42. A porous antireflective (AR) silica coating with the index of 1.27 was coated on the moisture-resistant coating surface. The two-layer coating possessed transmission up to 99.1% at wavelength of 966 nm, surface root-mean-square (RMS) roughness of 1.245 nm, and roughness of average (RA) of 0.961 nm. In the case of laser of 1053-nm laser wavelength and 1-ns pulse duration, the damage threshold of the two-layer coatings was more than 15 J/cm2.

Using di-ethoxy-silicane as precursor，a colloidal prepolymer was developed from sol-gel process. With silica colloid as modifier，the modified moisture-resistant films were prepared on neodymium-doped phosphate glass by spin coating. When the mole ratio of di-ethoxy-silicane to silica was 1: 1，the films after cure had improved abrasion-resistance. RMS was 1. 245 nm，while laser-damage threshold value more than 15 J / cm2 at the condition of 1 053 nm，1 ns. After staying in a closed circumstance at 80 ℃ and 95%RH，the films had approximately constant transmission and contact angle. It indicates that the films have a stable hydrophobic structure，good moisture-resistance，improved abrasion-resistant feature and longer service life.

Grating tiling technology using small aperture multilayer dielectric coating diffraction gratings to form large-aperture high-damage threshold gratings is the key technology to solve the output energy of the PW laser system. There are errors of five degrees of freedom between each adjacent pair of gratings within a tiled-grating system, affecting the spatial and temporal property of the laser beam. The authors express the relationship of far-field intensity distribution as the function of individual error by analyzing the effect of tiling gratings errors on the laser beam spatial distribution with Fraunhofer diffraction method and simulate it with numerical method. The results indicate the distortion in the pulse shape caused by angle error is negligible, the piston errors including in-plane shift and out-of-plane shift errors are the critical effects on the far-field intensity distribution.

The transmission of porous silica antireflective (AR) coating after heat treatment is correlative with environmental relative humidity because there are many Si-OH hydrophilic groups on the coating surface. The aim of the experiment is to add hydrophobic groups to the coating to enhance its hydrophobic performance and improve its stability. In this paper, Si-CH3 non-polar hydrophobic groups appear on the coating surface through dash with organic silica, raising its hydrophobic performance, and thus the stability and life of AR coating are improved greatly. When the molar content of organic silica (Si-CH3) is 17.5% (mass concentration 0.35%), the antireflectivity of coatings is high, while the performance of high laser damage threshold is not affected.

In SHENGUANGII (SGII) facility, the optomechanical system is the optics and optomechanical support hardware which necessary to transport the laser beams through the system from the laser drivers to the target. In order to satisfy the laser beam accurately positioned, the system must provide a stable platform for the optical elements before and during a shot. While the ambient vibration such as thermal impact, ground borne, acoustic and noise usually disturbs the stability of the system when the facility on working. This paper put forward the concept of system stability, and the method of test and vibration isolation control presented. The finite element analysis has been used to analysis the stability of the typical system. Base on the result, the working performance of system can be confirm, even the stability of SGII facility in future long-time work can be estimated, also the key points of stability design for the important parts and system can be suggested. It offers design guidance on the next upgrade of SG facility design and guarantee for the procedure of facility’s precision. This information also can be used to the structure and system of the similar facilities.

As the resolution of the interferometer is rapidly. increasing, the higher requirement is proposed fo the interferometry. For avoiding losing of the useful information of the actual interferogram, an algorithm is presented based on singular value decomposition (SVD). which is more stable than other algorithms to some extent. The weight . coefficients of the orthogonal polynomials can be worked out directly, which can eliminate.the}computational error. Then an evaluation criterion is developed to choose the optimum Zernike polynomial number. The computer simulations of this algorithm are also made. The simulation experiments have proved that it is an efficient algorithm and can reconstruct the wavefront accurately ami stably.

The mode-area scaling properties of helical-core optical fibres are numerically studied and the limit of core size for achievable single-mode operation is explored. By appropriate design, helical-core fibres can operate in a single mode with possible scaling up to 300μm in core diameter with numerical aperture 0.1.

In this paper, a refractive index profile design enabling us to obtain a flat modal field around the fibre centre is investigated. The theoretical approach for designing such multilayer large flattened mode (LFM) optical fibres is presented. A comparison is made between the properties of a three-layer LFM structure and a standard step-index profile with the same core size. The obtained results indicate that the effective area of the LFM fibre is about twice as large as that of the standard step-index fibre, but the LFM fibre has less effective ability to filter out the higher order modes than the standard step-index fibre with the same bending radius.

Theoretical method to analyze three-layer large flattened mode (LFM) fibers is presented. The modal fields, including the fundamental and higher order modes, and bending loss of the fiber are analyzed. The reason forming the different modal fields is explained and the feasibility to filter out the higher order modes via bending to realize high power, high beam quality fiber laser is given. Comparisons are made with the standard step-index fiber.

Microstructure optical fibers with flat-top fundamental mode are first proposed by introducing a low-index inner core into the core of index-guiding microstructure optical fibers. The design guidelines and characteristics of beam-shaping microstructure optical fibers are demonstrated. The interrelationships of inner-core index with laser wavelength, air hole diameter and size of inner core are investigated. The influence of the relative size of inner core on the spatial profile of the fundamental mode is demonstrated. Moreover, sensitivity of the flat-top fundamental mode profile from the slight change of the optimum inner-core index value is studied. Starting from these results we deduce that it is possible to fabricate beam-shaping microstructure fibers with nowadays technique.

We present a nondestructive technique to predict the refractive index profiles of isotropic planar waveguides, on which a thin gold film is deposited to as the cladding. The negative dielectric constant of the metal results in significant differences of effective indices between TE and TM modes. The two polarized modes and a surface plasmon resonance (SPR) with abundant information of the surface index can be used to construct the refractive index profiles of single-mode and two-mode waveguides at a fixed wavelength.

The pumping configurations for realizing high average power solid state laser are summarized, including Nd:GGG crystal slab laser in heat capacity operating mode, Yb-doped slab lasers and thin-disk lasers etc., which provide a reference for designing high average power solid state lasers pumping modes.

A theoretical calculation is presented for third-harmonic generation in KDP crystal for type Ⅱ- type Ⅱ polarization-mismatch scheme by using the four-stepped Runge-Kutta method. For the “Shenguang Ⅱ” frequency tripling system, the doubling angle θd and the tripling angle θt are located at optimized situation, by changing detuned values of the polarization angle θp, the corresponding changes of pulse shape properties was gotten. The results show that when the polarization angle θp is located at optimized situation, the full width at half maximum (FWHM) τ is minimum and the pulse shape rises fastest. Increasing the θp from optimized situation causes the τ widens faster and the pulse shape rises slower than decreasing the θp from optimized situation. In the experiment, by changing the polarization angle θp, the pulse shapes consistency of the “Shenguang Ⅱ” eight frequency tripling beams has been accomplished. This work offers a method for adjusting crystals and actualizing power balance.

Considering some necessary factors in the design of SSHCL, material properties of Nd doped glass, YAG and GGG were compared. Transient temperature fields and thermal stress in these slab mediums during one working cycle were simulated. Numerical analysis results showed that the internal external temperature difference in a neodymium doped glass slab was 75 K and the peak temperature value was 400 K when pumping time arrived 5 s. The maximum stress came to 50% of glass fracture limit. During subsequent water cooling period, the initial state was recovered after 120 s. On the same boundary conditions, Nd:YAG and Nd:GGG slabs could maintain relatively smooth temperature profile while the temperature rising and equivalent thermal stress were lower compared to glass. In later cooling phase, both of them could reach their operating commencement within 30 s. As cooling, the maximum stress of Nd:YAG overran 50% of the stress limit, thus increasing its tendency to fracture. Taken cooling time, fracture limit and obtainable size of the crystal into account, Nd:GGG should be the suitable active medium for high average power, repetitive frequency heat capacity laser.

Approximate formulas of transient temperature and stress distributions in the slab of a two-side pumped heat capacity laser are attained by solving the heat diffusion equation. Based on the formulas, the distributions of temperature and stress during the pump period of a two-sided symmetrically laser diode array (LDA) pumped Nd:GGG slab laser with 5-kW average output power are numerically simulated. The results show that the temperature in the slab will averagely increase by more than 70 Celsius degrees after operating for 10 seconds; the stress and maximum of the temperature difference in the slab are about 30 MPa and 24 Celsius degrees, respectively. The thermal induced effects are discussed also.

Based on the fundamental theory of heat transfer, the mathematical formulas that describing the transient temperature distributions of two-sided laser diode (LD) pumped Nd∶GGG (gadolinium gallium garnet) heat capacity slab laser were derived in this paper. By means of finite element analysis by ANSYS, transient temperature fields and stress distribution in the slab medium were simulated with various boundary conditions, while the beam distortions induced by thermal gradients were analyzed briefly. The obtained results could benefit to the primary designing of solid state heat capacity laser (SSHCL). Numerical analysis proved that under incomplete adiabatic boundary conditions, it would result in temperature gradients perpendicular to the optical axis. About 0.2 μm optical path differences would occur between the edge and optical axis of the slab. In addition, the thermal distributions in the slab during the subsequent cooling stage were mainly studied. The influences of different cooling methods such as air cooling, water cooling and mist cooling were discussed and cooling methods suitable for a SSHCL were briefly studied.

As the best candidate for the high power lasers in next generation, the solid state heat capacity laser (SSHCL) has attracted extensive attention. The principles, power scaling of SSHCL, distributions of fluorescence, temperature in a pumped slab cooling, and slab are presented. The effects of temperature in medium slab on the output power of laser are discussed in detail. Several key points about design are also described.

Tris-thenoyltrifluroacetonate of Nd³⁺has been prepared and dissolved in DMF solation with very high concentration, and the contained hydrogen has not been substituted by deuterium. The absorption spectrum, emission spectrum, and fluorescence lifetime of the solution were measured. Very obvious characteristic fluorescence peaks were observed at 898 and 1058 nm. Based on Judd-Ofelt theory, three intensity parameters were obtained: Ω2=4.9×10-20 cm2, Ω4=5.1×10-20 cm2 and Ω6=2.5×10-20 cm2. Line strengths Scal, oscillator strengths fcal, radiative transition probabilities Aed, radiative lifetimes τr and branch ratios β were calculated too. The measured lifetime τ of 1058 nm peak is 460 μs, and that of 898 nm 505 μs. Comparison between theoretically computed radiative lifetime τr (682 μs) and the measured lifetime indicates that the non-radiative transition probability of the solution is very low and the fluorescence quantum efficiency very high. High values of three intensity parameters prove the high asymmetric surroundings of Nd3+, which is important for Nd3+ to absorb the excitation energy. Spectropic quality factor Ω4/Ω6>1 makes radiation at 898 nm stronger than at 1058 nm.

Three sets of lens array (LA) uniform illumination system were designed, which were used in double-frequency laser direct drive experiments on "Shenguang-II" laser facility. Experimental investigations on shock planarity were carried out. The results show that the shock planarity has strong relationship with the LA's parameters, plane target's thickness and target's position. the shock planarity driven by the LA with 121 elements is the best, and which indirectly indicates that the illumination of the 121-element LA is the most uniform, too. Moreover, with the target thickness increasing, the shock planarity becomes worse, and the planar area becomes smaller. Also, the shock planarity showes some periodical change with the target's position, and the shock planarity at focal plane is the best for 121-element LA.

By using the superposition of N suitably weighted Laguerre-Gaussian beams, the analytical expressions of all six electromagnetic field components of focused Flattened Gaussian Beams (FGBs) are obtained in the Lorentz gauge. The phase velocity distributions of the field near the focus of FGBs propagating in vacuum are investigated. There exists a subluminous wave phase velocity region surrounding the laser beam axis. We further apply this focused FGB to vacuum laser acceleration. As with the focused Standard Gaussian Beam (SGB), electrons injected into the focused FGB can be captured in the acceleration phase and then violently accelerated.

The 30° Au conical targe tand Au foil target were irradiated by 20 TW ps P-polarized laser plasma, the characteristics of the forward produced hot electrons were studied. The hot electron number of the cone target was larget than that of the foil target, especially within the range of 2.0～2.5 MeV. The divergence of the forward hot electrons of the cone target was larger than that of the plane one, which was caused by different elecgron density of the pre-plasma with dissimilar target geometry produced by the driving laser.

A on-line program which can process laser equation of state experimental data more effectively has been developed. The processing program can decrease random error due to manual process, and it can process data much more effectively and process experimental data on-line.

This paper int roduces fabrication of polystyrene and aluminum surface perturbation targets used for flank illumination Rayleigh2Taylor instability experiment . By figure transfer, incising targets, cont rolling constructional technique and measuring targets’ parameters, we obtained surface perturbation target s with sinusoidal surface perturbation figures with thickness of several tens micrometer, the wavelength about 50 micrometer and amplitude f rom several to several tens micrometer. The width of two kinds of eargets is about 200 micrometer and the profile is clear.

This paper presented the reults of experimental studies on transient soft X-ray laser using a picosecond pulsed laser facility. A rather intensity Ni-like Ag X-ray laser at 13.9 nm with output energy of about 5～10 nJ was obtained by irradiating the solid last targets with a several hundred picosecond long laser pulse in combination with an 1 ps ultra-short laser pulse.

It is important in fast ignition (FI) to drill a channel in the coronal plasma by a long intense pulse firstly, since we expect the following ultra-intense pulse will reach more easily the dense core to obtain the fuel burning. An experimental design to study the plasma channeling was presented at two beams laser sub-picosecond (SPS) Facility of National Laboratory of High Power Laser and Physics. One beam with 1.053 μm and 350 ps full width at half maximum (FWHM) was used to form the pre-plasma. And then, a most part of another one with the same wavelength and 1 ps FWHM was focused on the plasma for channeling. The rest part of the 1 ps laser beam, frequency quadrupled to λ=0.263 μm, was as a probe used in Normaski polarization interferometry to diagnosis the electron density distribution of the channel.

The dual-tripler scheme for third harmonic generation (THG) is studied by the coupled equations under the small signal and high power condition (1.5 GW/cm2). The design has been proved in the experiment. It found that this design can increase the third harmonic conversion efficiency of broad bandwidth, but the distance between two triplers has an important impact on the third harmonic conversion efficiency in the experiment. 19.75% THG efficiency with chirp pulse of 3.5 nm bandwidth at average power of 1.5 GW/cm2 was achieved at 25 mm optimum distance between two triples in the experiment. It will be useful to solving the problem of the large bandwidth of the THG in the high power laser system.

A new shaping method for producing nanosecond pulses with specific shape is introduced. When a Gaussian laser pulse passes through an electro-optic deflector, it has been scanned as a line on the focal plane according to time precedence. Through controlling the intensity of transmitted light on each pixel of the liquid crystal spatial light modulator (LCSLM), various complicated pulses can be easily produced. Using this method, various specific shaped pulses with pulse duration varying from 750 ps to 5 ns are achieved.

In order to investigate the characters of the periodic phase-modulating beam amplifying, the model of pulse laser amplifying is improved based on the analysis of the parameters influenced by the transition lineshape of the media, such as the loss, stimulated radiation cross-section and saturated energy-density during the progress of amplifying, and the case of phase-modulated pulse laser in Nd:YLF is studied also. The pulse period of simulation based on the model is 330 ps, which is consistent with the experiment with period of 300 ps. The main factors affecting output time-waveform are studied by simulation, and the effect of phase modulation to amplitude modulation (PM-AM) conversion may be weaken if the center frequency of incident beam matches the center frequency of transition lineshape, which is useful for suppressing the effect of PM-AM conversion.

To improve the ability of beam smoothing in the device of inertial confinement fusion (ICF) in China, the theory of smoothing by spectral dispersion (SSD) is studied, and some experiments are carried out to analyze the mechanism of SSD in contrast with another technology of smoothing—distributed phase plane (DPP). It is found that the uniformity of focal spot in direction of dispersion is improved markedly using sinusoidal phase modulation (PM) and dispersion in SSD. And the intensity modulation of focal spot in this direction is smoothed by SSD. According to the experiments results, the changes of spectral intensity of spatial frequency at low-mode are very limited, and at high-mode are obviously; the nonuniformity varies from 40% to 12.5%. The ability of smoothing depends on the parameter of SSD. It also shows that the color cycle is very important in the process of smoothing, although the smoothing by broaden of laser spectral width for PM is poor.

To improve the energy efficiency of the inertial confined fusion (ICF) high\|power laser system and sufficiently use the optical energy, it is important to convert Gaussian laser beam into uniform beam. From the Jones matrix of spheric lenses, the intensity transmittance distribution of birefringent lenses spatial beam shaping system has been analyzed in detail by optical transmission matrix. The shaping effect has been numerically simulated. The choice of the parameters of birefringent lenses is discussed. The factors, which will influence the shaping effect, such as the fabrication error of center thickness, have also been analyzed. In the experiment, the uniform laser beam is obtained. In the ninth beamline of “Shenguang-Ⅱ” device, the static beam filling factor of near field is improved from 66% to 80%.

The small-scale self-focusing of divergent beams is studied. Based on the nonlinear paraxial wave equation, the propagation equation of small-scale perturbation of divergent beams has been deduced with a coordinate transformation. The evolvement law of the growth critical frequency of small-scale perturbation, maximum growth frequency and relative B integral is obtained. The influence of the initial radius of divergent beams on small-scale self-focusing is discussed. It is found that for a given propagation distance, the fastest growing frequency, the maximum perturbation growth, and thus the B integral decrease with the decrease of the initial radius of divergent beams. For a given initial radius, as the propagation distance increases, the growth of the B-integral becomes slow and stops at last. Also, the expression for the distance at which the filaments are formed is obtained by local energy conservation, and it is shown that a small initial radius extends the filamentation distance.

Using the Huygens-Fresnel diffraction integral and the Fourier transform, the propagation representations of pulses with Hermite-Gaussian transverse modes passing through a hard-edged aperture are derived. Influences of the bandwidth on the transverse intensity distributions are analyzed in detail from numerical calculations. It is found that lots of intensity spikes emerge and the near field intensities are non-uniformity when the pulses pass through the aperture. However, when the bandwidth increases, the number and the amplitude of the spikes are reduced and thus the beam uniformity is improved, the intensity spike does not appear in the far field, and also the beam width decreases in the far field. Therefore, the smoothing and narrowing effects can be brought forth by increasing the bandwidth. In addition, it is found from the numerical results that the effects are similar in the pulses with Hermite-Gaussian transverse modes of mode indices 1 and 2.

A scheme employing a lens array and the technique of smoothing by spectral dispersion is presented for uniform irradiation on targets in inertial confinement fusion. Quasi-near field spots with a profile of sharp edge and flat top can be obtained with a diffraction-weakened lens array, while the speckles imposed on the spot by beamlets interference can be smoothed by spectral dispersion. Simulation results indicate that this scheme is a good candidate for improving the irradiation uniformity. The dependence of the smoothing performance on the characteristics of phase modulation and dispersion is further discussed, and it is found that parameters of the system of spectral dispersion and lens array must be chosen carefully to make optimal compromise between uniformity and usable energy of the laser beam.

To improve the stability of pumping source of optical parametric amplifier, the concept of stable area in the frequency-doubling is proposed, with the numerical simulation of the frequency doubling process. Under certain intensity of the fundamental light, less than the breakdown threshold of the frequency-doubling crystal, the valid length of the frequency-doubling crystal is prolonged with the nonlinear two-pass frequency-doubling or the tandem frequency-doubling, with which the frequency-doubling course is located in the stable area and the highly stable second harmonic output with high conversion efficiency is realized. The experiments prove the above conclusion, and in the experiment the nonlinear two-pass frequency-doubling method is used to ensure the work area of the frequency-doubling in the stable area. The fluctuation of the second harmonic is less than ±2% for the 1064 nm fundamental Gaussian pulse with flutuation ±5.7%, and the conversion efficiency exceeds 70% for high-order Gaussian pulses. The experimental results show that the stability of the second harmonic is near 3 times higher than that of the fundamental light.

It is simulated numerically the transmission of beams phase modulated and spectrally dispersed by the unit for smoothing by spectral dispersion put in the laser driver for inertial confinement fusion. The results show that the diffraction spot of a spectrally dispersed beam becomes larger and its near-field uniformity is improved, while there exists area where the intensity is nearly even within the far-field spot. The effects of the main parameters of the electro-optic phase modulator and the grating in the unit on the diffraction characteristics of the beams are further discussed, and it is found that intensity modulation emerges in the far-field spot under some conditions.

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens–Fresneldiffraction integral. Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigatedin detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns ofdifferent frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patternsin the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved.

Based on the Huygens–Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulsepassing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-fieldand far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by themodulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity.A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect isachieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite–Gaussian transverse profile whenthe frequency chirp increases.

Starting from the Huygens-Fresnel diffraction integral and the Fourier transform, the propagation expression of a chirped pulse passing through a hard-edged aperture is derived. Using the obtained expression, the intensity distributions of the pulse with different chirp in the near and far fields are analyzed in detail. Due to the modulation of the aperture, many intensity peaks emerge in the intensity distributions of the chirped pulse in the near field. However, the amplitudes of the intensity peaks decrease on increasing the chirp, which results in the smoothing effect in the intensity distributions. The beam smoothing brought by increasing the chirp is explained physically. Also, it is found that the radius of the intensity distribution of the chirped pulse decreases when the chirp increases in the far field.

We systematically investigate the square-lattice dielectric photonic crystals that have been used to demonstrate flat slab imaging experimentally. A right-handed Bloch mode is found in the left-handed frequency region by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Using the multiple scattering theory, numerical simulations demonstrate that the left-handed mode and the right-handed mode are excited simultaneously by a point source and result in two kinds of transmitted waves. Impacted by the evanescent waves, superposition of these transmitted waves brings on complicated near field distributions such as the so-called imaging and its disappearance.

In contrast to previous two-dimensional coated photonic crystals, in this paper we propose a left-handed one that is made of dielectric tubes arranged in a close-packed hexagonal lattice. Without metallic cores, this structure is low-loss and convenient to fabricate. Negative refraction and its resulting focusing are investigated by dispersion characteristic analysis and numerical simulation of the field pattern. With proper modification at the interface, the image is improved. With better isotropy than that with noncircular rods, planoconcave lenses made by dielectric tubes focus a Gaussian beam exactly at R/|n?1|.

Different form previous two-dimensional coated photonic crystals, in this paper we investigate an optically thinner one that is made of dielectric tubes arranged in a close-packet square lattice. Without the metallic cores, this structure is low-loss and convenient to fabricate. A low-pass spatial filter made from this novel photonic crystal is demonstrated by dispersion analysis and numerical simulations. The high-spatial-frequency components, whose incident angles exceed the critical value, are reflected totally. However, the low-spatial-frequency components are coupled to the left-handed Bloch modes of the photonic crystal and transmit.

Image relaying is presented as a technique for aligning beams onto mm-sized target of high power laser. On the basis of summarizing the preceeding work on the near-field image relaying of multiple spatial filters, the far-filed image relaying is suggested firstly. The near-field and far-field image relaying properties of multiple spatial filters in laser beams automatic alignment system are analyzed. A geometrical optics approach and an ABCD ray matrix theory are used throughout. The reasonable and optimum scheme for automatically aligning multi-pass beam paths is presented and demonstrated on the multi-pass amplifier system of the SG-III prototype.