\contentsline {chapter}{\numberline {1}Introduction}{3}{chapter.1}
\contentsline {section}{\numberline {1.1}Requirements}{3}{section.1.1}
\contentsline {chapter}{\numberline {2}Optical Configuration}{5}{chapter.2}
\contentsline {section}{\numberline {2.1}Overview}{5}{section.2.1}
\contentsline {section}{\numberline {2.2}Arm Cavity Parameters}{6}{section.2.2}
\contentsline {subsubsection}{g-factor}{6}{section*.2}
\contentsline {subsection}{\numberline {2.2.1}Arm Cavity Higher Order Mode Resonances}{6}{subsection.2.2.1}
\contentsline {subsubsection}{g-factor}{7}{section*.3}
\contentsline {subsection}{\numberline {2.2.2}RF Sidebands Resonances in the Arm Cavities}{10}{subsection.2.2.2}
\contentsline {subsubsection}{Fine Adjustment of the RF Sideband Frequencies}{10}{section*.4}
\contentsline {subsubsection}{HOM Resonances of the RF Sidebands}{11}{section*.5}
\contentsline {subsubsection}{g-factor and the RF SB resonances}{13}{section*.6}
\contentsline {subsection}{\numberline {2.2.3}Parametric Instability}{13}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}Angular Instability by the Radiation Pressure}{15}{subsection.2.2.4}
\contentsline {subsection}{\numberline {2.2.5}Conclusion on g-factors}{16}{subsection.2.2.5}
\contentsline {section}{\numberline {2.3}Recycling Cavities}{16}{section.2.3}
\contentsline {subsubsection}{Overview}{16}{section*.7}
\contentsline {subsection}{\numberline {2.3.1}Reflectivities}{16}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Length and RF SB frequencies}{18}{subsection.2.3.2}
\contentsline {subsubsection}{Constraints}{18}{section*.8}
\contentsline {subsubsection}{SRCL linear range}{18}{section*.9}
\contentsline {subsubsection}{Selected Length and Frequencies}{19}{section*.10}
\contentsline {subsection}{\numberline {2.3.3}Radius of Curvature of the RC mirrors}{20}{subsection.2.3.3}
\contentsline {section}{\numberline {2.4}Output mode-cleaner system}{20}{section.2.4}
\contentsline {chapter}{\numberline {3}Length Sensing and Control Scheme}{24}{chapter.3}
\contentsline {section}{\numberline {3.1}Overview}{25}{section.3.1}
\contentsline {section}{\numberline {3.2}Simulation Conditions}{25}{section.3.2}
\contentsline {subsubsection}{Arm Cavity Asymmetry}{25}{section*.11}
\contentsline {subsubsection}{PD}{26}{section*.12}
\contentsline {section}{\numberline {3.3}Signal Name Convention}{26}{section.3.3}
\contentsline {section}{\numberline {3.4}Signal Extraction Ports}{26}{section.3.4}
\contentsline {section}{\numberline {3.5}Loop Noise}{28}{section.3.5}
\contentsline {subsection}{\numberline {3.5.1}Servo loop model}{28}{subsection.3.5.1}
\contentsline {subsection}{\numberline {3.5.2}Feed forward}{31}{subsection.3.5.2}
\contentsline {section}{\numberline {3.6}PD Dynamic Range}{31}{section.3.6}
\contentsline {chapter}{\numberline {4}Noise Requirements}{35}{chapter.4}
\contentsline {section}{\numberline {4.1}Mirror Displacement Noise}{35}{section.4.1}
\contentsline {section}{\numberline {4.2}Laser Noises}{35}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Frequency stabilization servo}{37}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Frequency noise requirement}{37}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}Intensity noise}{38}{subsection.4.2.3}
\contentsline {section}{\numberline {4.3}RF Oscillator Noises}{38}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}Phase Noise}{38}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}Amplitude Noise}{42}{subsection.4.3.2}
\contentsline {section}{\numberline {4.4}Scattered Light Noise}{42}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}Light power in the interferometer}{47}{subsection.4.4.1}
\contentsline {chapter}{\numberline {5}Alignment Sensing and Control Scheme}{52}{chapter.5}
\contentsline {section}{\numberline {5.1}Overview}{52}{section.5.1}
\contentsline {section}{\numberline {5.2}Soft and Hard Modes}{52}{section.5.2}
\contentsline {section}{\numberline {5.3}Simulation Conditions}{54}{section.5.3}
\contentsline {section}{\numberline {5.4}Signal Extraction Ports}{54}{section.5.4}
\contentsline {section}{\numberline {5.5}Angular noise coupling to DARM}{54}{section.5.5}
\contentsline {subsection}{\numberline {5.5.1}Structure of the ASC model}{54}{subsection.5.5.1}
\contentsline {subsection}{\numberline {5.5.2}Simulation results}{56}{subsection.5.5.2}
\contentsline {chapter}{\numberline {6}Lock Acquisition Scheme}{58}{chapter.6}
\contentsline {section}{\numberline {6.1}Overview}{58}{section.6.1}
\contentsline {section}{\numberline {6.2}Green Laser Pre-Lock}{58}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}Overview}{58}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}Noise Analysis}{59}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}Third Harmonics Demodulation}{60}{subsection.6.2.3}
\contentsline {section}{\numberline {6.3}Non-Resonant Sideband for Lock Acquisition}{62}{section.6.3}
\contentsline {chapter}{\numberline {7}Optical Layout}{64}{chapter.7}
\contentsline {section}{\numberline {7.1}Basic design}{64}{section.7.1}
\contentsline {section}{\numberline {7.2}Wedge angle error tolerance}{64}{section.7.2}
\contentsline {section}{\numberline {7.3}Tunnel Slope}{64}{section.7.3}
\contentsline {chapter}{\numberline {8}Installation/Adjustment Procedure}{66}{chapter.8}
\contentsline {chapter}{\numberline {9}iKAGRA}{67}{chapter.9}
\contentsline {section}{\numberline {9.1}Overview}{67}{section.9.1}
\contentsline {section}{\numberline {9.2}Changes from bKAGRA}{67}{section.9.2}
\contentsline {subsection}{\numberline {9.2.1}Mirrors}{67}{subsection.9.2.1}
\contentsline {subsection}{\numberline {9.2.2}Optical Layout}{67}{subsection.9.2.2}
\contentsline {subsection}{\numberline {9.2.3}Mode Matching}{68}{subsection.9.2.3}
\contentsline {subsection}{\numberline {9.2.4}Interferometer Control}{69}{subsection.9.2.4}
\contentsline {chapter}{\numberline {A}Recycling Cavity Length Determination Algorithm}{70}{appendix.A}
\contentsline {chapter}{\numberline {B}SRCL non-linearity}{71}{appendix.B}
\contentsline {chapter}{\numberline {C}Mixed PM and AM for f1}{72}{appendix.C}
\contentsline {chapter}{\numberline {D}Terminology}{73}{appendix.D}
\contentsline {chapter}{\numberline {E}Contributors}{74}{appendix.E}