^{1,a)}

### Abstract

The development of high-energy lasers requires optical windows capable of handling megajoule beam energies without compromising the system’s performance. Calcium fluoride has been identified as a prime candidate for windows operating at chemical laser wavelengths due to very low bulk absorption and exceptionally small thermal lensing coefficients; it is, however, vulnerable to structural failure owing to poor mechanical strength characteristics and a large thermal stress factor. It is, therefore, essential to properly assess the ultimate potential of this material, which we attempt to do here in the following manner: (a) We assemble reliable numbers for all pertinent properties of (111)-oriented single crystals and polycrystalline isotropic aggregates (PIAs), such as fusion-cast , which requires addressing issues relating to the elastic properties, the stress-optic coefficients, and the flexural strength. (b) We provide correct analytical expressions for evaluating the impact of pressure- and beam-induced effects on wave-front phase distortions and mechanical failure modes, taking advantage of a previous investigation [J. Appl. Phys.98, 043103 (2005)]. (c) We perform detailed calculations on “model” windows made of either or that transmit optimally truncated Gaussian beams at wavelengths of 1.15 and , for run times such that lateral heat conduction and surface cooling can be ignored. Our main conlusions are as follows: (a) With windows thermal lensing, as measured in terms of the Strehl ratio and on assuming coating absorptances of no more than , is of no consequence in the sense that catastrophic failure may occur at fluence levels way below the threshold for optical distortion. (b) Evidence of a poor Weibull shape factor degrades the design safety margins, which requires operating at peak intensities of no more than to achieve optimum on-target fluences. (c) Regarding the issue of vs , we note that fusion-cast material outperforms single crystals based on the figure of merit for distortion, as well as fracture and yield strengths, but contrary to (111)-oriented material, it exhibits birefringence that may rule out its use if depolarization is of concern.

The absorptance data displayed in Fig. 2 reflect the results of laser-calorimetry work performed by Richard P. Miller at the former Raytheon Research Division, Waltham, Massachusetts.

I. INTRODUCTION

II. KEY PROPERTIES

A. Elastic properties

B. Flexural strength

C. Optical properties

III. MODEL WINDOWS

A. Window diameter

B. Window thickness

C. Prediffusion regime

IV. OPTICAL DISTORTION

A. Pressure-induced distortion

B. Beam-induced distortion

C. Strehl ratio

V. STRESS ANALYSIS

A. Pressure-induced stress

B. Beam-induced stresses

C. Peak combined stresses

VI. WINDOW PERFORMANCE

A. Allowable peak fluences

B. Focal point irradiance

C. Focal point fluence

VII. CONCLUSION

### Key Topics

- Materials properties
- 15.0
- Single crystals
- 15.0
- Thermal blooming
- 14.0
- Stress strain relations
- 10.0
- Optical aberrations
- 9.0

## Figures

Fracture-strength Weibull plots. The single-crystal plot is based on test data recorded in Ref. 12; the broken line refers to fusion-cast as in Ref. 15. Note that the fusion-cast “fit” holds for test bars measuring .

Fracture-strength Weibull plots. The single-crystal plot is based on test data recorded in Ref. 12; the broken line refers to fusion-cast as in Ref. 15. Note that the fusion-cast “fit” holds for test bars measuring .

Total absorptance of fusion-cast test rods as a function of path length, at laser wavelengths of 2.7 (filled squares) and (open squares). The straight lines are least-squares fits. The bulk absorption is seen to be wavelength independent; surface absorptance reflects the impact of adsorbed water.

Total absorptance of fusion-cast test rods as a function of path length, at laser wavelengths of 2.7 (filled squares) and (open squares). The straight lines are least-squares fits. The bulk absorption is seen to be wavelength independent; surface absorptance reflects the impact of adsorbed water.

Cumulative failure probability of (111)-oriented and fusion-cast model windows as a function of the applied biaxial stress. The stress is assumed uniform over the entire aperture. Relevant Weibull statistical parameters are listed in Table II.

Cumulative failure probability of (111)-oriented and fusion-cast model windows as a function of the applied biaxial stress. The stress is assumed uniform over the entire aperture. Relevant Weibull statistical parameters are listed in Table II.

Pressure-induced optical path differences (OPDs), measured in “waves,” as a function of radial position. The calculation assumes a diameter of , a thickness of , and a differential pressure of . Relevant wavelengths are 1.15 and .

Pressure-induced optical path differences (OPDs), measured in “waves,” as a function of radial position. The calculation assumes a diameter of , a thickness of , and a differential pressure of . Relevant wavelengths are 1.15 and .

Radial and azimuthal phase-shift dependences on radial position, for model windows as specified in Sec. III. The transmitted peak fluence is set equal to . (a) Laser wavelength ; (b) Laser wavelength .

Radial and azimuthal phase-shift dependences on radial position, for model windows as specified in Sec. III. The transmitted peak fluence is set equal to . (a) Laser wavelength ; (b) Laser wavelength .

Focal intensity degradation as a function of the transmitted peak fluence, for the two model windows described in Sec. III. The figure illustrates the cases of a laser wavelength of and a laser wavelength of . Note that this evaluation ignores the impact of stress-related limitations on allowable fluences.

Focal intensity degradation as a function of the transmitted peak fluence, for the two model windows described in Sec. III. The figure illustrates the cases of a laser wavelength of and a laser wavelength of . Note that this evaluation ignores the impact of stress-related limitations on allowable fluences.

Peak tensile stress as a function of beam-exposure time for (a) the (111)-oriented model window and (b) the fusion-cast model window. The symbol refers to the peak irradiance level. The allowable stresses are as discussed in Sec. VI A.

Peak tensile stress as a function of beam-exposure time for (a) the (111)-oriented model window and (b) the fusion-cast model window. The symbol refers to the peak irradiance level. The allowable stresses are as discussed in Sec. VI A.

Peak compressive stress as a function of the beam-exposure time for (a) the (111)-oriented model window and (b) the fusion-cast model window. The symbol refers to the peak irradiance level. The yield strengths are as listed in Table II.

Peak compressive stress as a function of the beam-exposure time for (a) the (111)-oriented model window and (b) the fusion-cast model window. The symbol refers to the peak irradiance level. The yield strengths are as listed in Table II.

Allowable peak fluences as a function of the peak intensity for model windows as specified in Sec. III. The plot is based on allowable beam-exposure times obtained from Figs. 7 and 8. Note that the allowable fluences fall off rapidly at peak intensities that exceed , owing to surface-compression induced yieding.

Allowable peak fluences as a function of the peak intensity for model windows as specified in Sec. III. The plot is based on allowable beam-exposure times obtained from Figs. 7 and 8. Note that the allowable fluences fall off rapidly at peak intensities that exceed , owing to surface-compression induced yieding.

Illustrates the performance of (111)-oriented and fusion-cast windows in terms of (a) focal-point irradiances and (b) focal-point fluences, at a distance of . The optical train—but for the output window—is assumed to be aberration-free; the output windows are as specified in Sec. III. Taking the truncation into account, the transmitted beam power amounts to 9.2 and for and windows, respectively.

Illustrates the performance of (111)-oriented and fusion-cast windows in terms of (a) focal-point irradiances and (b) focal-point fluences, at a distance of . The optical train—but for the output window—is assumed to be aberration-free; the output windows are as specified in Sec. III. Taking the truncation into account, the transmitted beam power amounts to 9.2 and for and windows, respectively.

## Tables

List of symbols (see also Table II).

List of symbols (see also Table II).

Key properties of (111)-oriented and fusion-cast at room temperature.

Key properties of (111)-oriented and fusion-cast at room temperature.

Key optical-distortion related results for model windows as specified in Sec. III; all relevant numbers are based on property values listed in Table II.

Key optical-distortion related results for model windows as specified in Sec. III; all relevant numbers are based on property values listed in Table II.

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