1 Plane Wave Propagation in Dispersive Media |
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1 | (24) |
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1.1 Maxwell's Equations in SI Units |
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1 | (1) |
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2 | (2) |
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1.3 Wave Equation with Refractive Index |
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4 | (12) |
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1.3.1 Derivation of the Wave Equation |
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4 | (3) |
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1.3.2 Solution of the Wave Equation: Plane Wave |
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7 | (3) |
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1.3.3 Summary of the Notation in Vacuum and in a Dispersive Medium |
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10 | (1) |
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1.3.4 TEM Wave and Impedance |
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10 | (3) |
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13 | (2) |
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1.3.6 Energy Density, Poynting Vector, and Intensity |
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15 | (1) |
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16 | (9) |
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1.4.1 Dispersion for Electromagnetic Waves |
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16 | (1) |
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1.4.2 Sellmeier Equation in the Visible and Near-Infrared |
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17 | (4) |
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1.4.3 Refractive Index from the VUV to the X-Ray Region |
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21 | (4) |
2 Linear Pulse Propagation |
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25 | (48) |
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25 | (3) |
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2.2 Wave Equation in the Spectral Domain: Helmholtz Equation |
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28 | (4) |
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28 | (2) |
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2.2.2 Derivation of the Helmholtz Equation |
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30 | (2) |
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2.3 Linear Versus Nonlinear Wave Propagation |
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32 | (3) |
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2.3.1 Superposition Principle |
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32 | (1) |
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2.3.2 Linear System Theory |
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32 | (3) |
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35 | (1) |
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35 | (7) |
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2.4.1 Pulse Wave Packet and Pulse Envelope |
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35 | (2) |
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2.4.2 Time-Bandwidth Product. Analogy with Heisenberg's Uncertainty Relation |
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37 | (3) |
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2.4.3 Spectral Phase Yielding Shortest Pulse |
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40 | (2) |
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2.5 Linear Pulse Propagation in a Dispersive Material |
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42 | (31) |
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2.5.1 Linear Pulse Propagation Versus Linear Dispersion |
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42 | (1) |
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2.5.2 Slowly-Varying-Envelope Approximation |
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42 | (2) |
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2.5.3 First and Second Order Dispersion |
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44 | (1) |
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2.5.4 Phase Velocity and Group Velocity |
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45 | (2) |
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2.5.5 Dispersive Pulse Broadening |
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47 | (5) |
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2.5.6 Dispersion as a Function of Frequency and Wavelength |
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52 | (4) |
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2.5.7 Optical Communication |
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56 | (3) |
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2.5.8 Can a Pulse Propagate Faster Than the Speed of Light in Vacuum? |
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59 | (4) |
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2.5.9 Definition of the Group Index |
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63 | (1) |
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2.5.10 Higher Order Dispersion |
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63 | (2) |
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2.5.11 Slowly-Evolving-Wave Approximation |
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65 | (8) |
3 Dispersion Compensation |
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73 | (58) |
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3.1 Introduction and Motivation |
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73 | (4) |
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77 | (15) |
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3.2.1 Second Order Dispersion of the Four-Prism Compressor |
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77 | (8) |
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3.2.2 Third Order Dispersion of the Four-Prism Compressor |
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85 | (3) |
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3.2.3 Continuous Adjustment of Dispersion |
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88 | (4) |
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3.3 Grating Compressor, Stretcher, and Pulse Shaper |
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92 | (17) |
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3.3.1 Diffraction Grating Compressor |
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92 | (11) |
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3.3.2 Turning a Grating Compressor into a Stretcher |
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103 | (3) |
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3.3.3 Grating-Based Pulse Shaper |
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106 | (3) |
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3.4 Gires-Tournois Interferometer (GTI) |
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109 | (4) |
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3.5 Summary of Dispersion Compensation with Angular Dispersion and GTI |
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113 | (1) |
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3.6 Mirrors with Controlled Phase Properties |
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113 | (11) |
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113 | (2) |
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3.6.2 Dielectric GTI-Type Mirrors |
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115 | (1) |
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116 | (5) |
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3.6.4 Design of Chirped Mirrors |
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121 | (3) |
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124 | (2) |
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3.8 Dispersion Measurements |
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126 | (5) |
4 Nonlinear Pulse Propagation |
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131 | (54) |
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4.1 Self-Phase Modulation (SPM) |
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131 | (18) |
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4.1.1 Kerr Effect and SPM |
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131 | (2) |
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4.1.2 Pulse Compressors Such as Fiber-Grating, Fiber-Prism, and Fiber-Chirped-Mirror Compressors |
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133 | (10) |
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4.1.3 Nonlinear Optical Pulse Cleaner |
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143 | (1) |
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4.1.4 Average Power Scaling of Pulse Compressors |
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144 | (5) |
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4.2 Self-Focusing and Filamentation Compressor |
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149 | (5) |
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4.2.1 Self-Focusing via a Kerr Lens |
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149 | (2) |
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151 | (2) |
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4.2.3 Filament Pulse Compression |
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153 | (1) |
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154 | (18) |
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4.3.1 Discovery of the Soliton |
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154 | (4) |
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4.3.2 Solution of the NSE: The Fundamental Soliton |
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158 | (4) |
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4.3.3 Solution of the NSE: Higher-Order Solitons |
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162 | (2) |
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4.3.4 Optical Communication with Solitons |
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164 | (4) |
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4.3.5 Periodic Perturbations of Solitons |
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168 | (4) |
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172 | (6) |
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4.4.1 Higher-Order Nonlinear Effects |
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172 | (2) |
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4.4.2 Optical Shock Front |
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174 | (2) |
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4.4.3 Effect of GDD on Optical Shock |
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176 | (2) |
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4.5 Nonlinear Propagation in a Saturable Absorber or Saturable Amplifier |
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178 | (7) |
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4.5.1 Saturable Amplifier |
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178 | (1) |
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179 | (3) |
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4.5.3 Nonlinear Pulse Propagation in a Saturable Absorber or Amplifier |
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182 | (3) |
5 Laser Rate Equations, Steady-State Solutions, Relaxation Oscillations, and Transfer Functions |
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185 | (40) |
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5.1 What Do We Need to Know About Lasers? |
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185 | (12) |
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5.1.1 Diode-Pumped Solid-State Laser |
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185 | (5) |
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5.1.2 Rate Equations for an Ideal Four-Level Laser |
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190 | (1) |
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5.1.3 Steady-State Solutions (Four-Level Laser) |
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190 | (2) |
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5.1.4 Gain Saturation (Four-Level Laser) |
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192 | (2) |
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194 | (3) |
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5.2 Relaxation Oscillations in a Four-Level Laser |
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197 | (12) |
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5.2.1 Linearized Rate Equations |
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197 | (1) |
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5.2.2 Ansatz for Solution After Perturbation |
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198 | (1) |
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5.2.3 Over-Critically Damped Lasers |
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199 | (1) |
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5.2.4 Under-Critically Damped Lasers |
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200 | (2) |
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5.2.5 Examples of Relaxation Oscillations Using Different Laser Materials |
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202 | (4) |
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5.2.6 Measurement of the Small-Signal Gain |
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206 | (3) |
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5.3 Transfer Function Analysis |
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209 | (16) |
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5.3.1 Rate Equations for Power and Gain |
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210 | (3) |
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5.3.2 Relaxation Oscillations |
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213 | (2) |
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215 | (5) |
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5.3.4 Transfer Function Measurement |
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220 | (5) |
6 Active Modelocking |
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225 | (54) |
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225 | (6) |
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6.1.1 Basic Principle of Modelocking |
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225 | (3) |
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6.1.2 Modelocked Frequency Comb and Axial Cavity Modes |
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228 | (2) |
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6.1.3 Difference Between Q-Switching and Modelocking |
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230 | (1) |
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6.2 Basic Principles of Active Modelocking |
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231 | (3) |
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6.3 Optical Loss Modulators |
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234 | (3) |
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6.3.1 Acousto-Optic Modulator (AOM) |
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234 | (3) |
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6.4 Active Modelocking Without SPM and GDD |
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237 | (11) |
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6.4.1 Gaussian Pulse Analysis |
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237 | (5) |
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6.4.2 Derivation and Solution of the Haus Master Equation |
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242 | (5) |
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6.4.3 Explanation of Active Modelocking in the Spectral Domain |
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247 | (1) |
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6.5 Active Modelocking with SPM, but Without GDD |
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248 | (10) |
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248 | (2) |
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6.5.2 Solution of the Master Equation: A Chirped Gaussian Pulse |
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250 | (6) |
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6.5.3 Example: Nd:YLF Laser |
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256 | (2) |
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6.6 Soliton Modelocking with Active Modelocking |
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258 | (9) |
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6.6.1 Derivation and Solution of the Master Equation with SPM and GDD |
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259 | (5) |
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6.6.2 Soliton Modelocked Nd:glass Laser Stabilized with an Intracavity AOM |
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264 | (3) |
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6.7 Modelocking with Homogeneously Versus Inhomogeneously Broadened Gain |
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267 | (6) |
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6.7.1 Homogeneously Versus Inhomogeneously Broadened Gain: CW Lasing |
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268 | (1) |
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6.7.2 Modelocking Results Better for Inhomogeneous Gain Broadening |
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269 | (1) |
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6.7.3 Modelocking with Spatial Hole Burning |
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270 | (3) |
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6.8 Synchronous Modelocking |
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273 | (2) |
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6.9 Selected Results of Active Modelocked Solid-State Lasers |
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275 | (4) |
7 Saturable Absorbers for Solid-State Lasers |
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279 | (94) |
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279 | (2) |
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7.2 Slow and Fast Saturable Absorbers |
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281 | (14) |
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7.2.1 Saturable Absorber Parameters and Rate Equation |
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281 | (4) |
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7.2.2 Justification for the Simplified Saturable Absorber Rate Equation |
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285 | (2) |
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7.2.3 Slow Saturable Absorber |
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287 | (3) |
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7.2.4 Fast Saturable Absorber |
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290 | (3) |
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7.2.5 Summary of Relevant Equations |
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293 | (2) |
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7.3 Nonlinear Reflectivity Model Functions |
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295 | (11) |
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295 | (1) |
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7.3.2 Time-Dependent Reflectivity |
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296 | (2) |
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7.3.3 Pulse-Averaged Reflectivity |
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298 | (3) |
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7.3.4 Correction for Gaussian Beam Profile |
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301 | (1) |
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7.3.5 Inverse Saturable Absorption (ISA) |
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302 | (3) |
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7.3.6 Summary of Relevant Model Functions for Nonlinear Reflectivity |
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305 | (1) |
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7.4 Semiconductor Saturable Absorbers |
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306 | (22) |
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7.4.1 Semiconductor Saturable Absorber Materials |
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306 | (4) |
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7.4.2 Introduction to Semiconductor Relaxation Dynamics |
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310 | (3) |
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7.4.3 Fast Saturable Absorbers with Carrier Trapping Engineering |
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313 | (5) |
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7.4.4 Fast Saturable Absorbers with Quantum-Confined Stark Effect |
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318 | (1) |
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7.4.5 Saturable Absorber Optimization with Quantum Confinement |
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319 | (6) |
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7.4.6 Derivation of the Density of States |
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325 | (3) |
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7.5 Semiconductor Saturable Absorber Mirror (SESAM) |
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328 | (27) |
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7.5.1 SESAM Design: A Historical Perspective |
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329 | (2) |
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7.5.2 Resonant Versus Antiresonant SESAM |
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331 | (3) |
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7.5.3 Antiresonant High-Finesse SESAM |
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334 | (2) |
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7.5.4 Reflectivity, Phase, Dispersion, and Penetration Depth of a DBR |
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336 | (10) |
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7.5.5 Antiresonant Low-Finesse SESAM |
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346 | (2) |
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348 | (1) |
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7.5.7 Ultrabroadband SESAMs |
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349 | (2) |
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7.5.8 SESAM Optimization with Standing Wave Field Enhancement |
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351 | (4) |
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355 | (8) |
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7.6.1 SESAM Damage Measurements |
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355 | (4) |
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7.6.2 SESAM Damage Theory |
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359 | (2) |
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7.6.3 SESAM Design for High Average Power Thin-Disk Lasers |
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361 | (2) |
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7.7 SESAM Characterization |
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363 | (7) |
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7.7.1 One-Beam Measurement of Nonlinear Reflectivity |
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363 | (5) |
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7.7.2 Pump-Probe Measurement of Recovery Time |
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368 | (1) |
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7.7.3 Pump-Probe Measurement of Nonlinear Reflectivity |
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369 | (1) |
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7.8 Novel Saturable Absorber Materials |
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370 | (3) |
8 Q-Switching |
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373 | (46) |
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374 | (4) |
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8.1.1 Fundamental Principle of Active Q-Switching |
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374 | (2) |
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8.1.2 Acousto-Optic Q-Switched Diode-Pumped Solid-State Laser |
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376 | (1) |
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8.1.3 Pulsed Single-Frequency Laser |
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377 | (1) |
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8.1.4 Actively Q-Switched Microchip Laser |
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377 | (1) |
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8.2 Theory for Active Q-Switching |
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378 | (6) |
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378 | (1) |
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8.2.2 Inversion Build-Up Phase |
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378 | (2) |
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8.2.3 Pulse Build-Up Phase: Leading Edge of the Pulse |
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380 | (1) |
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8.2.4 Dynamics During the Pulse Duration |
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381 | (3) |
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8.2.5 Pulse Depletion Phase: Trailing Edge of the Pulse |
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384 | (1) |
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384 | (6) |
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8.3.1 Fundamental Principle of Passive Q-Switching |
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384 | (2) |
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8.3.2 Passively Q-Switched Microchip Laser |
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386 | (1) |
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8.3.3 Passively Q-Switched Monolithic Ring Laser |
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386 | (4) |
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8.4 Theory for Passive Q-Switching |
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390 | (12) |
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390 | (5) |
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8.4.2 Model for SESAM Q-Switched Microchip Laser |
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395 | (1) |
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396 | (4) |
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8.4.4 Pulse Duration and Pulse Shape |
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400 | (1) |
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8.4.5 Pulse Repetition Rate |
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400 | (1) |
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8.4.6 Remarks on Three-Level Lasers |
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401 | (1) |
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8.5 Passively Q-Switched Microchip Lasers Using SESAMs |
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402 | (17) |
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402 | (3) |
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405 | (1) |
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8.5.3 SESAM Q-Switching Results |
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406 | (7) |
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413 | (4) |
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8.5.5 Summary of the Q-Switched Microchip Laser |
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417 | (2) |
9 Passive Modelocking |
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419 | (128) |
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9.1 Introduction and Basic Principle |
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419 | (10) |
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419 | (2) |
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9.1.2 Starting Passive Modelocking |
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421 | (2) |
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9.1.3 Historical Development |
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423 | (6) |
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9.2 Coupled Cavity Modelocking |
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429 | (3) |
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9.3 Passive Modelocking with a Slow Saturable Absorber and Dynamic Gain Saturation |
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432 | (11) |
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9.3.1 Modelocking Conditions |
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433 | (1) |
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9.3.2 Example: Colliding Pulse Modelocking (CPM) |
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434 | (2) |
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9.3.3 Pulse Formation through Saturable Absorption and Gain |
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436 | (4) |
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9.3.4 Master Equation and Solution |
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440 | (3) |
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9.4 Passive Modelocking with a Fast Saturable Absorber |
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443 | (18) |
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9.4.1 Definition of an Ideally Fast Saturable Absorber |
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444 | (1) |
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9.4.2 Example: Kerr Lens Modelocking (KLM) |
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445 | (1) |
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445 | (2) |
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9.4.4 Solution without SPM and GDD |
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447 | (2) |
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9.4.5 Comparison with Active Modelocking without SPM and GDD |
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449 | (1) |
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9.4.6 Solution with SPM and GDD for Soliton Formation |
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450 | (10) |
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9.4.7 Problem for Self-Starting Modelocking |
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460 | (1) |
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9.5 Passive Modelocking with Slow Saturable Absorber and Without Dynamic Gain Saturation |
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461 | (22) |
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9.5.1 Soliton Modelocking |
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462 | (5) |
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9.5.2 Example: Soliton Modelocked Ti:sapphire Laser |
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467 | (3) |
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9.5.3 Soliton Modelocking with GDD > 0 and n2 < 0 |
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470 | (9) |
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9.5.4 What Happens Without Soliton Formation |
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479 | (4) |
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9.6 Summary of Analytical Solutions for all Modelocking Techniques |
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483 | (8) |
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9.7 Q-Switching Instabilities of Passively Modelocked Solid-State Lasers |
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491 | (17) |
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9.7.1 Q-Switching Instabilities: A More Serious Issue for Solid-State Lasers |
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491 | (5) |
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9.7.2 Q-Switching Instabilities Without ISA: Derivation and Discussion of (9.126) |
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496 | (4) |
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9.7.3 Q-Switching Instabilities with Soliton Modelocking but Without ISA: Derivation and Discussion of (9.127) |
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500 | (4) |
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9.7.4 Q-Switching Instabilities with ISA: Discussion of (9.129) |
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504 | (2) |
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9.7.5 Special Cavity Designs to Prevent Q-Switching Instabilities |
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506 | (1) |
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9.7.6 Negative n2 to Prevent Q-Switching Instabilities |
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507 | (1) |
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9.8 Passively Modelocked Diode-Pumped Semiconductor Lasers |
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508 | (5) |
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9.8.1 Optically Pumped VECSELs |
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508 | (2) |
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9.8.2 Optically-Pumped MIXSELs and SESAM-Modelocked VECSELs |
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510 | (3) |
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9.9 Dual-Comb Modelocking |
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513 | (3) |
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9.10 Performance Frontiers in Ultrafast Lasers |
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516 | (31) |
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9.10.1 Pulse Generation in the Few-Cycle Regime |
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516 | (6) |
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9.10.2 High Average Power |
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522 | (11) |
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9.10.3 Gigahertz Pulse Repetition Rates |
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533 | (14) |
10 Pulse Duration Measurements |
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547 | (42) |
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10.1 Electronic Measurements of the Pulse Duration |
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547 | (11) |
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10.1.1 Cables and Connectors |
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547 | (1) |
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547 | (5) |
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10.1.3 Estimating the Time Resolution and Measurement Bandwidth |
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552 | (2) |
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10.1.4 Sampling Oscilloscope |
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554 | (1) |
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10.1.5 Microwave Spectrum and Signal Analyzers |
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555 | (1) |
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10.1.6 Equivalent-Time Sampling |
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556 | (2) |
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10.2 Optical Autocorrelation |
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558 | (14) |
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558 | (1) |
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10.2.2 Intensity Autocorrelation |
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558 | (5) |
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10.2.3 Interferometric Autocorrelation (IAC) |
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563 | (7) |
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10.2.4 High-Dynamic-Range Autocorrelation |
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570 | (1) |
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10.2.5 Temporal Smearing in Noncollinear Autocorrelation |
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571 | (1) |
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10.3 Frequency-Resolved Optical Gating (FROG) |
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572 | (10) |
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573 | (6) |
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10.3.2 Second Harmonic Generation FROG (SHG-FROG) |
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579 | (3) |
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10.4 Spectral Phase Interferometry for Direct Electric Field Reconstruction (SPIDER) |
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582 | (7) |
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582 | (2) |
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10.4.2 Experimental Realization |
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584 | (5) |
11 Intensity Noise and Timing Jitter of Modelocked Lasers |
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589 | (50) |
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589 | (6) |
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11.1.1 Definition of Intensity Noise and Timing Jitter |
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590 | (2) |
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11.1.2 Basic Mathematical Principles for Noise |
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592 | (3) |
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11.2 Measurement Techniques for Intensity Noise and Timing Jitter |
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595 | (7) |
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11.2.1 General Remarks on Intensity Noise |
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595 | (2) |
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11.2.2 General Remarks on Timing Jitter |
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597 | (1) |
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11.2.3 Measurement Based on Microwave Spectrum Analyzers |
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597 | (2) |
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11.2.4 Measurement Based on Electronic Reference Signals |
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599 | (1) |
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11.2.5 Measurement Based on Optical Cross-Correlations |
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600 | (1) |
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11.2.6 Measurement with an Indirect Phase Comparison Method |
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|
601 | (1) |
|
11.3 Noise Measurements with Power Spectral Densities |
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|
602 | (11) |
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11.3.1 Ideal Laser Without Amplitude Fluctuations and Timing Jitter |
|
|
602 | (2) |
|
11.3.2 Pulse Train with Intensity Noise |
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|
604 | (5) |
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11.3.3 Pulse Train with Timing Jitter |
|
|
609 | (4) |
|
11.3.4 Summary of Intensity Noise and Timing Jitter |
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|
613 | (1) |
|
11.4 Noise Characteristics of Modelocked Lasers |
|
|
613 | (11) |
|
11.4.1 Some Basic Remarks on Noise, Stabilization, and Coupling Mechanisms |
|
|
613 | (4) |
|
11.4.2 Ultrafast Dye Lasers |
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|
617 | (2) |
|
11.4.3 Flashlamp-Pumped Solid-State Lasers |
|
|
619 | (1) |
|
11.4.4 Diode-Pumped SESAM-Modelocked Solid-State Lasers |
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|
620 | (3) |
|
11.4.5 Argon-Ion Versus Diode-Pumped Ti:Sapphire Lasers |
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|
623 | (1) |
|
11.5 Some Words of Caution About Noise Characterization |
|
|
624 | (4) |
|
11.5.1 General Remarks About Nonstationary Processes and Finite Measurement Durations |
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|
624 | (3) |
|
11.5.2 Noise Measurements in the Frequency Domain |
|
|
627 | (1) |
|
11.5.3 Noise Measurements in the Time Domain |
|
|
627 | (1) |
|
11.6 Signal-to-Noise Ratio (SNR) Optimization Techniques |
|
|
628 | (11) |
|
11.6.1 Basic Principle of Pump-Probe Measurements |
|
|
628 | (2) |
|
11.6.2 High Frequency Chopping with Lock-in Detection |
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|
630 | (1) |
|
11.6.3 Minimal Detectable Signal for Shot-Noise-Limited Detection |
|
|
631 | (2) |
|
11.6.4 Short Measurement Durations for Lower SNR |
|
|
633 | (6) |
12 Optical Frequency Comb from Modelocked Lasers |
|
639 | (64) |
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|
639 | (3) |
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12.2 Carrier Envelope Offset (CEO) Phase and Frequency |
|
|
642 | (6) |
|
12.3 Measurement of the CEO Frequency |
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|
648 | (13) |
|
12.3.1 Basic Principle with Heterodyne (Interference) Signals |
|
|
648 | (2) |
|
12.3.2 Method 1: f-to-2f Interferometer |
|
|
650 | (6) |
|
12.3.3 Method 2: Frequency-Doubled Transfer Oscillator with Lower Bandwidth Requirement |
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|
656 | (3) |
|
12.3.4 Method 3: Frequency-Tripled Transfer Oscillator |
|
|
659 | (1) |
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12.3.5 Method 4: SHG and THG of Two Auxiliary Oscillators and Self-Referenced 2f-to-3f Interferometer |
|
|
659 | (1) |
|
12.3.6 Method 5: Frequency Interval Bisection |
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|
660 | (1) |
|
12.4 Phase and Frequency Noise |
|
|
661 | (19) |
|
12.4.1 Spectrally Resolved CEO Frequency Noise |
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|
661 | (3) |
|
12.4.2 Basic Mathematical Principle of Phase and Frequency Noise |
|
|
664 | (3) |
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12.4.3 Integrated Phase and Frequency Noise |
|
|
667 | (3) |
|
12.4.4 Phase Noise from Cavity Mirror Vibrations |
|
|
670 | (1) |
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12.4.5 Intensity Noise, Timing Jitter, and CEO Frequency Noise |
|
|
671 | (2) |
|
12.4.6 Phase-Time and Fractional (or Relative) Frequency Noise |
|
|
673 | (2) |
|
12.4.7 Polynomial Model: White, 1/f (Flicker), and 1/f 2 Noise |
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|
675 | (1) |
|
|
676 | (4) |
|
12.5 Connection Between the Optical Laser Spectrum and the Phase Noise |
|
|
680 | (14) |
|
12.5.1 Optical Laser Spectrum |
|
|
680 | (1) |
|
12.5.2 Variance of the Phase Noise Change and Optical Autocorrelation |
|
|
680 | (2) |
|
12.5.3 Optical Spectral Linewidth from Frequency and Phase Noise |
|
|
682 | (2) |
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12.5.4 Optical Linewidth for (Low-Pass Filtered) White Frequency Noise |
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|
684 | (3) |
|
|
687 | (1) |
|
12.5.6 Optical Linewidth from Flicker Noise |
|
|
688 | (2) |
|
12.5.7 Quantum Noise Limit |
|
|
690 | (1) |
|
12.5.8 Optical Interferometers, Coherence, and Phase Noise |
|
|
691 | (3) |
|
12.6 Stabilized Optical Frequency Combs |
|
|
694 | (6) |
|
12.6.1 Basic Principle of Active Stabilization |
|
|
694 | (1) |
|
12.6.2 CEO Frequency Stabilization with Laser Feedback Control |
|
|
695 | (3) |
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12.6.3 Full Optical Frequency Comb Stabilization |
|
|
698 | (1) |
|
12.6.4 External CEO Frequency Stabilization |
|
|
699 | (1) |
|
12.7 Laser Technology for Optical Frequency Combs |
|
|
700 | (3) |
Appendix A: Fourier Transform |
|
703 | (4) |
Appendix B: Dispersion for Quantum Mechanical Particles |
|
707 | (2) |
Appendix C: Delta-Function |
|
709 | (4) |
Appendix D: Delta-Comb |
|
713 | (4) |
Appendix E: Soliton Algebra |
|
717 | (4) |
Appendix F: Linearized Operators for the Master Equation |
|
721 | (6) |
References |
|
727 | (64) |
Index |
|
791 | |