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Figure 1:
Intensity distribution in an ![]() |
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Figure 2:
Intensity distribution in an axisymmetric ![]() |
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Figure 3:
Solid line: Intensity profile of a normalized mesa mode of parameters ![]() ![]() |
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Figure 4:
Surface of a mirror matching the mesa beam of parameters ![]() ![]() |
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Figure 5:
Power distribution of a Gauss–Bessel mode of parameters ![]() ![]() ![]() ![]() |
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Figure 6:
Surface of a mirror matching a Gauss–Bessel mode of parameters ![]() ![]() ![]() ![]() |
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Figure 7:
Notations for a cylindrical mirror |
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Figure 8:
Error in intensity reconstruction (50 Fourier–Bessel terms) for ![]() ![]() ![]() |
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Figure 9:
Reconstructed intensity (FB series) for ![]() ![]() |
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Figure 10:
Temperature field in the substrate, 1 W dissipated in the coating, mode ![]() ![]() |
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Figure 11:
Temperature field in the substrate, 1 W dissipated in the bulk substrate, mode ![]() ![]() |
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Figure 12:
Temperature field in the substrate, 1 W dissipated in the coating, flat mode, b = 9.1 cm ( ![]() |
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Figure 13:
Temperature field in the substrate, 1 W dissipated in the bulk substrate, flat mode, b = 9.1 cm ( ![]() |
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Figure 14:
Temperature field in the substrate, 1 W dissipated in the coating, mode ![]() ![]() |
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Figure 15:
Temperature field in the substrate, 1 W dissipated in the bulk substrate, mode ![]() ![]() |
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Figure 16:
Nonaxisymmetric mode ![]() ![]() |
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Figure 17:
Nonaxisymmetric mode ![]() ![]() |
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Figure 18:
Temperature at various depths in the substrate (coating absorption) case of ![]() ![]() |
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Figure 19:
Temperature at various depths in the substrate (flat mode, bulk absorption) ( ![]() |
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Figure 20:
Coupling losses as functions of the dissipated power on the coating. Solid line: total losses, numerical integration of Equation (3.76 ![]() ![]() |
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Figure 21:
Thermal lens, heating by 1 W bulk absorption. The dashed line is the nearest paraboloid ![]() |
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Figure 22:
Thermal lens for 1 W absorbed from the mesa mode (solid line) and the flat mode (dashed line) |
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Figure 23:
Thermal deformation of the mirror under three types of readout beams (1 W absorbed power in the coating and exaggerated by a factor of 2 × 105) |
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Figure 24:
Deformation of the reflecting coating for three types of readout beams (coating absorption). Dashed line: best parabolic fit ![]() |
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Figure 25:
Thermal expansion of the mirror under three types of readout beams (heating by 1 W internal absorption of light, exaggerated by a factor of 2 × 105) |
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Figure 26:
Thermal aberration caused by internal heating for 1 W absorbed power. Dashed lines: nearest paraboloid (weighted by the intensity distribution) |
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Figure 27:
Normalized intensity ![]() |
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Figure 28:
Thermal lensing from a ring radiator. Red dashed curve: nearest paraboloid (weighted by the readout beam intensity). The readout beam is ![]() |
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Figure 29:
Thermal compensation with a ring radiator: minimization of coupling losses |
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Figure 30:
Ring radiator: correction of the thermal lensing caused by a ![]() |
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Figure 31:
Thermal lens profile created by an axicon system |
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Figure 32:
Thermal compensation with an axicon: minimization of coupling losses. Solid line, short dashed, long dashed: resp. 10 mW, 20 mW, 30 mW, dissipated by the readout beam. |
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Figure 33:
Source of heat on the mirror rear face for a power mask according to Equation (4.14 ![]() ![]() |
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Figure 34:
Source of heat on the mirror rear face for a power mask according to Equation (4.15 ![]() ![]() |
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Figure 35:
Corrected thermal lens by a power mask according to Equation (4.15 ![]() ![]() ![]() |
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Figure 36:
Time evolution of the thermal lens from room temperature to the steady state limit. Heating from coating absorption, ![]() |
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Figure 37:
Time evolution of the thermal lens from room temperature to steady state limit. Heating from coating absorption, ![]() |
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Figure 38:
Time evolution of the thermal lens from room temperature to the steady state limit. Heating from coating absorption, Flat mode, b = 9.1 cm |
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Figure 39:
Coating absorption: time evolution of the curvature radius of the thermal lens ![]() |
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Figure 40:
Coating absorption: time evolution of the curvature radius of the thermal lens, ![]() |
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Figure 41:
Coating absorption: time evolution of the curvature radius of the thermal lens, flat mode, b = 9.1 cm |
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Figure 42:
Coating absorption: time evolution of the curvature radii of thermal lenses for three examples |
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Figure 43:
Bulk absorption: Time evolution of the thermal lens curvature radii for three examples |
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Figure 44:
Coating absorption: time evolution of the reflecting surface caused by thermal expansion. Mode ![]() |
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Figure 45:
Coating absorption: time evolution of the reflecting surface caused by thermal expansion. Flat mode, b = 9.1 cm |
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Figure 46:
Coating absorption: time evolution of the reflecting surface caused by thermal expansion. Mode ![]() |
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Figure 47:
Coating absorption: time evolution of the curvature radius of the thermal lens caused by thermal expansion. Mode ![]() |
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Figure 48:
Coating absorption: time evolution of the curvature radius of the thermal lens caused by thermal expansion. Flat mode, b = 9.1 cm |
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Figure 49:
Coating absorption: time evolution of the curvature radius of the thermal lens caused by thermal expansion. Mode ![]() |
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Figure 50:
Bulk absorption: time evolution of the reflecting surface caused by thermal expansion. Mode ![]() ![]() |
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Figure 51:
Bulk absorption: time evolution of the reflecting surface caused by thermal expansion. Flat mode, b = 9.1 cm |
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Figure 52:
Bulk absorption: time evolution of the reflecting surface caused by thermal expansion. Mode ![]() |
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Figure 53:
Bulk absorption: time evolution of the curvature radius caused by thermal expansion. Mode ![]() |
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Figure 54:
Bulk absorption: time evolution of the curvature radius caused by thermal expansion. Flat mode, b = 9.1 cm |
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Figure 55:
Bulk absorption: time evolution of the curvature radius caused by thermal expansion. Mode ![]() |
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Figure 56:
Coating absorption: transfer function from power to displacement. Dashed line: asymptotic regime |
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Figure 57:
Bulk absorption: transfer function from power to displacement. Dashed line: asymptotic regime. |
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Figure 58:
Gain in thermal noise PSD1/2 for LG modes having each a w parameter tuned for 1 ppm clipping losses, with respect to the Virgo input mirrors and beams |
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Figure 59:
Virtually deformed mirror under beam pressure. (1 N integrated pressure) by modes having 1 ppm clipping losses. For more clarity, the displacements have been amplified by a factor of 7 × 107. |
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Figure 60:
Distribution of strain energy in the mirror substrate ( ![]() |
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Figure 61:
Distribution of strain energy in the mirror substrate (Flat mode b = 9.1 cm, logarithmic scale) |
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Figure 62:
Distribution of strain energy in the mirror substrate ( ![]() |
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Figure 63:
Distribution of ![]() ![]() |
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Figure 64:
Distribution of ![]() |
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Figure 65:
Distribution of ![]() ![]() |
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Figure 66:
Distribution of the square gradient of the trace of the strain tensor in the case of an ![]() |
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Figure 67:
Mode ![]() ![]() |
http://www.livingreviews.org/lrr-2009-5 | ![]() This work is licensed under a Creative Commons License. Problems/comments to |