From the Series Editor Brian J.Thompson ..................................... v Preface ................................................................... vii Chapter 1: A Brief History of Spectral Analysis ............................. 1 1.1 Work Before the Year 1800 ........................................... 1 1.2 The Early Work in Gratings .......................................... 2 1.3 The Beginnings of Spectral Analysis ................................. 3 1.4 Nobert .............................................................. 5 1.5 Kirchhoff and Bunsen ................................................ 6 1.6 Georg Quincke ....................................................... 7 1.7 Progress in Solar Spectroscopy ...................................... 8 1.8 The Era of Rowland .................................................. 9 1.9 Origin of Spectral Lines ........................................... 10 1.10 The Vacuum UV ...................................................... 10 1.11 Some Special Effects ............................................... 11 1.12 Some Historical Aspects of Ruled Gratings .......................... 12 1.12.1 Blazing and Efficiency ...................................... 12 1.12.2 Defects of Grating Ruling ................................... 13 1.13 Spectrographs and Spectrophotometers ............................... 13 1.13.1 Infrared Spectrometry ....................................... 14 1.13.2 Raman Spectrometry .......................................... 15 1.13.3 Atomic Absorption Spectrometry .............................. 16 1.13.4 Fluorescence Spectrometry ................................... 17 1.13.5 Colorimetry ................................................. 18 1.14 Transformation of the Field to the Present Day ..................... 19 References .............................................................. 19 Chapter 2: Fundamental Properties of Gratings .............................. 25 2.1 The Grating Equation ............................................... 25 2.2 Propagating and Evanescent Orders .................................. 28 2.3 Dispersion ......................................................... 30 2.4 Free Spectral Range ................................................ 33 2.5 Passing-Off of Orders .............................................. 33 2.6 Guided Waves ....................................................... 34 2.7 Diffraction Efficiency ............................................. 35 2.7.1 Definition ................................................... 35 2.7.2 Classical Model of Grating Efficiency ........................ 36 2.7.3 Reciprocity Theorem and Symmetry with Respect to Littrow Mount ............................................. 38 2.7.4 Perfect Blazing - Does It Really Exist? ...................... 39 2.8 Resolution ......................................................... 42 2.9 Mountings .......................................................... 44 2.10 Some Electromagnetic Characteristics ............................... 47 2.10.1 Energy Flow (Poynting) Vector ............................... 47 2.10.2 Electromagnetic Energy Density .............................. 48 2.11 Two Simple Methods of Determining the Grating Frequency ............ 48 2.12 Pulse Compression by Diffraction Gratings .......................... 49 References .............................................................. 53 Additional Reading ...................................................... 53 Chapter 3: The Types of Diffraction Gratings ............................... 57 3.1 Introduction ....................................................... 57 3.2 Amplitude and Phase Gratings ....................................... 58 3.3 Phase and Relief Gratings .......................................... 59 3.4 Reflection and Transmission Gratings ............................... 59 3.5 Symmetrical and Blazed Gratings .................................... 60 3.6 Ruled, Holographic and Lithographic Gratings ....................... 61 3.7 Plane and Concave Gratings ......................................... 62 3.8 Bragg Type and Raman-Nath Type Gratings ............................ 62 3.9 Waveguide Gratings ................................................. 63 3.10 Fiber Gratings ..................................................... 64 3.11 Binary Gratings .................................................... 66 3.12 Photonic Crystals .................................................. 66 3.13 Gratings for Special Purposes ...................................... 67 3.13.1 Filter Gratings ............................................. 67 3.13.2 Gratings for Electron Microscope and Scanning Microscope Calibration ................................................. 67 3.13.3 Electron Interaction Gratings ............................... 67 3.13.4 Rocket and Satellite Spectroscopy ........................... 68 3.13.5 Metrology ................................................... 68 3.13.6 Synchrotron Monochromators .................................. 68 3.13.7 X-Ray Gratings .............................................. 68 3.13.8 Chemical/Biological Monitoring .............................. 68 3.14 "Good" and "Bad" Gratings .......................................... 69 References .............................................................. 69 Chapter 4: Efficiency Behavior of Plane Reflection Gratings ................ 71 4.1 Introduction ....................................................... 71 4.2 General Rules ...................................................... 74 4.2.1 Reflection Coatings .......................................... 74 4.2.2 Scalar Behavior of Reflection Gratings ....................... 75 4.2.3 Gratings Supporting Only Two Diffraction Orders: The Equivalence Rule ......................................... 80 4.3 Absolute Efficiencies of 1200 gr/mm Aluminum Echelettes ............ 81 4.3.1 Discussion of Efficiency Behavior of 1200 gr/mm Echelettes ... 81 4.3.2 Reflection Efficiencies of 1200 gr/mm Echelettes in Orders 2, 3 and 4 ............................................ 88 4.3.3 Effect of A.D. on Peak Efficiency Values and Location in Orders Two to Four of 1200 gr/mm Echelettes ............... 88 4.4 Reflection Efficiencies of Echelettes at High Groove Frequencies and the Roles of Aluminum vs. Gold and Silver Coatings ............. 94 4.5 Effect of Groove Apex Angle on Echelette Efficiency ............... 106 4.6 Plane Sinusoidal Reflection Grating Behavior ...................... 106 4.6.1 Absolute Efficiency of Plane 1200 gr/mm Aluminum Sinusoidal Gratings ......................................... 108 4.6.2 Absolute Efficiency of 1200 gr/mm Sinusoidal Reflection Gratings in Orders 2 to 4 ................................... 118 4.6.3 Absolute Efficiency of Aluminum Sinusoidal Gratings at Higher Groove Frequencies (1800, 2400, 3600 gr/mm) .......... 118 4.6.4 Absolute Efficiency of Higher Groove Frequency Sinusoidal Gratings with Silver Overcoating ................. 125 4.6.5 Absolute Efficiency of Higher Groove Frequency Sinusoidal Gratings with Gold Overcoating ................... 125 4.7 The Efficiency Surface ............................................ 125 4.8 Efficiency Behavior of Very Deep Gratings ......................... 132 4.9 Efficiency Behavior in Grazing Incidence .......................... 136 4.10 X-Ray Gratings .................................................... 139 4.11 Single Wavelength Efficiency Peak in Unpolarized Light ............ 141 4.12 Conclusions ....................................................... 142 References ............................................................. 143 Additional Reading ..................................................... 145 X-Ray Gratings .................................................... 146 Chapter 5: Transmission Gratings .......................................... 149 5.1 Introduction ...................................................... 149 5.2 Transmission Grating Physics ...................................... 150 5.3 Scalar Transmission Efficiency Behavior ........................... 153 5.4 Efficiency Behavior of Blazed Transmission Gratings ............... 154 5.5 Transmission Grating Prisms ....................................... 156 5.6 Fresnel Lenses and Zone Plates .................................... 158 5.6.1 Geometrical Properties of Plane Lenses ...................... 159 5.6.2 Imaging Properties .......................................... 161 5.6.3 Diffraction Efficiency ...................................... 162 5.7 Blazed Transmission Gratings as Beam Dividers ..................... 167 5.8 Trapezoidal Gratings as Beam Splitters ............................ 168 5.9 Multiple Order Transmission Gratings (Fan-Out Gratings) ........... 172 5.10 Bragg Transmission Gratings ....................................... 179 5.11 Transmission Gratings Under Total Internal Reflection ............. 182 5.12 Zero Order Diffraction (ZOD) Microimages .......................... 184 5.13 Ronchi Rulings .................................................... 186 References ............................................................. 188 Additional Reading ..................................................... 189 Chapter 6: Echelle Gratings ............................................... 191 6.1 Introduction ....................................................... 191 6.1.1 History ...................................................... 192 6.2 Production of Echelles ............................................. 193 6.3 Physics of Echelles ................................................ 194 6.3.1 The Grating Equation ......................................... 194 6.3.2 Angular Dispersion ........................................... 195 6.3.3 Free Spectral Range .......................................... 196 6.3.4 Resolution ................................................... 198 6.3.5 Immersion of Echelles ........................................ 198 Anamorphic Immersion System .................................. 199 6.4 Efficiency Behavior of Echelles .................................... 200 6.4.1 Scalar Model for Efficiency .................................. 202 6.4.2 Rigorous Electromagetic Efficiency Theory .................... 204 6.4.3 Efficiency Behavior in High Orders ........................... 205 6.4.4 Efficiency Behavior in Medium Orders ......................... 211 6.4.5 Efficiency Behavior in Low Orders ............................ 217 6.4.6 Confirmation of Theory ....................................... 222 6.4.7 Efficiency Behavior in Spectrometer Modes .................... 226 6.4.8 Effects of Severe Groove Shape Disturbance ................... 231 6.4.9 A Useful Role for Anomalies .................................. 231 6.5 The Role of Overcoatings ........................................... 232 6.6 Instrument Design Concepts ......................................... 233 6.6.1 Choice of Echelle ............................................ 233 6.6.2 Cross Dispersion: Prisms vs. Gratings ........................ 234 6.6.3 Examples of Echelle Instruments .............................. 235 UV Rocket Spectrograph ....................................... 237 HIRES: High Resolution Echelle Spectrometer .................. 238 Compact High Resolution Spectrograph ......................... 238 Ultra-Short Wavelength Satellite Spectrograph ................ 241 6.7 Maximum Resolution Systems ......................................... 242 6.7.1 The MEGA Spectrometer ........................................ 243 6.8 Transmission Echelles .............................................. 245 6.9 Comparing Echelles with Holographic Gratings ....................... 246 References ............................................................. 247 Additional Reading ..................................................... 249 Chapter 7: Concave Gratings ............................................... 253 7.1 Introduction ....................................................... 253 7.2 Aberrations in Concave Gratings .................................... 255 7.2.1 Aberration Function of Concave Gratings ...................... 255 7.2.2 Aberrations of Concave Diffraction Gratings .................. 259 Astigmatism .................................................. 261 Coma ......................................................... 262 Spherical Aberration ......................................... 263 7.3 Focal Curves ....................................................... 264 7.3.1 Definition and Properties .................................... 264 7.3.2 Types of Focal Curves ........................................ 266 7.4 Grating Image Deformation Estimation and Optimization: Flat-Field Spectrograph and Monochromator .......................... 269 7.5 Types of Concave Gratings .......................................... 272 7.5.1 Schemes for Holographic Recording of Concave Gratings ........ 272 7.5.2 Commercial Types of Concave Gratings and Their Design ........ 276 7.6 Efficiency Behavior of Concave Gratings ............................ 277 7.6.1 Efficiency of Holographic Concave Gratings ................... 279 7.6.2 Blazed Concave Gratings ...................................... 280 References ............................................................. 280 Additional Reading ..................................................... 282 Chapter 8: Surface Waves and Grating Anomalies ............................ 285 8.1 Grating Anomalies .................................................. 285 8.2 Phenomenological Approach .......................................... 288 8.2.1 Guided Wave and a Pole of the Scattering Matrix .............. 291 8.2.2 Pole of the Scattering Matrix and Diffraction Efficiencies ... 292 8.3 Types of Surface Waves ............................................. 296 8.4 Influence of Surface Waves on Metallic Grating Properties .......... 297 8.4.1 Total Absorption of Light by Metallic Gratings ............... 298 8.4.2 Gratings Supporting Several Orders ........................... 305 8.5 Resonance Anomalies in Dielectric Overcoated Metallic Grating ...... 306 8.6 Resonance Anomalies in Corrugated Dielectric Waveguides ............ 310 8.7 Multilayered Dielectric Gratings ................................... 310 References ............................................................. 317 Additional Reading ..................................................... 319 Chapter 9: Waveguide, Fiber, and Acousto-Optic Gratings ................... 323 9.1 Introduction ...................................................... 323 9.2 Mode Coupling by Gratings ......................................... 325 9.2.1 Couple-Mode Approach ........................................ 326 9.2.2 Types of Mode Coupling ...................................... 328 9.2.3 Contra-Directional Coupling ................................. 331 9.3 Distributed Planar Waveguide Grating Laser Mirrors ................ 334 9.4 Wavelength Demultiplexing in Planar Waveguides .................... 336 9.5 Input/ Output Waveguide Grating Couplers .......................... 340 9.6 Photonic Band-Gap in Waveguide Gratings ........................... 345 9.7 Fiber Grating Physics ............................................. 346 9.8 Fiber Grating Lasers .............................................. 350 9.9 Fiber Grating Filters ............................................. 351 9.10 Fiber Grating Sensors ............................................. 355 9.11 Mode Conversion by Fiber Gratings ................................. 356 9.12 Acousto-Optic and Electro-Optic Gratings .......................... 356 References ............................................................. 360 Additional Reading ..................................................... 365 Chapter 10: Review of Electromagnetic Theories of Grating Efficiencies .... 367 10.1 Introduction ..................................................... 367 10.2 The Physical Problem ............................................. 367 10.3 The Rayleigh Hypothesis .......................................... 373 10.4 Scalar Theory .................................................... 375 10.5 Classical Differential Method .................................... 376 10.6 Modal Methods .................................................... 379 10.6.1 The Method of Moharam and Gaylord ......................... 379 10.6.2 The Classical Modal Method ................................ 380 10.7 The Integral Method .............................................. 381 10.8 The Finite-Element Method ........................................ 383 10.9 The Method of Fictitious Sources ................................. 384 10.10 The Method of Coordinate Transformation .......................... 387 10.11 Theory of Waveguide Gratings ..................................... 388 10.12 Conclusions ...................................................... 391 References ............................................................. 394 Additional Reading ..................................................... 395 Reviews on Theoretical Methods ................................... 395 General Theoretical Problems ..................................... 396 Differential Methods ............................................. 396 Modal Methods .................................................... 396 Conformal Mapping Methods ........................................ 397 Transformation of Coordinate System .............................. 327 Integral Methods ................................................. 397 Fictitious Sources Methods ....................................... 398 Rayleigh Methods ................................................. 398 Yasuura Method ................................................... 399 Approximate Methods .............................................. 399 Chapter 11: Testing of Gratings ........................................... 401 11.1 Introduction ...................................................... 401 11.2 Spectral Purity ................................................... 402 11.2.1 Effects of Grating Deficiencies on Spectral Purity ......... 402 11.2.2 Non-Periodic Groove Position Errors ........................ 406 Random Errors .............................................. 406 Satellites ................................................. 407 Roughness Induced Scattering ............................... 409 Effect of Variations in Groove Depth ....................... 409 11.2.3 The Measurement of Grating Stray Light ..................... 410 11.2.4 Locating Stray Light Sources on a Grating Surface .......... 413 11.3 The Measurement of Efficiency ..................................... 413 11.3.1 Efficiency Measurement Systems - Plane Gratings ............ 414 11.3.2 Efficiency Measurement Systems - Concave Gratings .......... 417 11.3.3 Efficiency Measurement Systems - Echelle Gratings .......... 418 11.3.4 Checking Blaze Specifications .............................. 420 11.4 The Measurement of Resolution ..................................... 423 11.4.1 Testing with the Mercury Spectrum .......................... 425 11.4.2 The Foucault Knife Edge Test ............................... 426 11.4.3 Resolution Testing by Wavefront Interferometry ............. 428 11.5 Testing of Concave Interference Gratings .......................... 432 11.5.1 Measurement of Imaging Properties .......................... 432 11.6 Role of Replication ............................................... 434 11.7 Cosmetics ......................................................... 434 References ............................................................. 434 Additional Reading ..................................................... 435 Chapter 12: Instrumental Systems .......................................... 437 12.1 Introduction ..................................................... 437 12.2 Terminology ...................................................... 439 12.3 Classification of Instruments .................................... 439 12.4 How to Choose a Design ........................................... 441 12.5 Plane Grating Mounts ............................................. 443 12.5.1 The Czerny - Turner Mount ................................. 445 12.5.2 The Ebert - Fastie Mount .................................. 449 12.5.3 The Monk - Gillison Mount ................................. 451 12.5.4 Grating Drives ............................................ 452 12.6 Concave Grating Mounts ........................................... 453 12.6.1 The Rowland Mounting ...................................... 455 12.6.2 The Abney Mount ........................................... 455 12.6.3 The Paschen - Runge Mount ................................. 456 12.6.4 The Eagle Mount ........................................... 457 12.6.5 The Wadsworth Mount ....................................... 458 12.6.6 The Seya - Namioka Mount .................................. 461 12.6.7 Flat Field Concave Grating Spectrographs .................. 462 12.6.8 Grazing Incidence Mounts .................................. 463 12.7 Tandem Monochromators ............................................ 464 12.8 Imaging Spectrometers ............................................ 466 12.9 Multiplexing Spectrographs ....................................... 468 12.10 The Role of Fiber Optics in Spectrographs ........................ 471 12.11 Laser Tuning ..................................................... 472 12.12 On Absolute Groove Spacing ....................................... 475 12.13 Multiple Entrance Apertures ...................................... 476 References ............................................................. 476 Additional Reading ..................................................... 480 Chapter 13: Grating Damage and Control .................................... 481 13.1 Introduction ...................................................... 481 13.2 Reflection Gratings ............................................... 482 13.2.1 The Fingerprint Problem .................................... 482 13.2.2 Vacuum System Residues ..................................... 483 13.2.3 Laser Beam Damage - CW ..................................... 484 13.2.4 Laser Damage with Pulsed Lasers ............................ 485 13.2.5 Dielectric Reflection Gratings ............................. 487 13.2.6 Synchrotron Grating Applications ........................... 489 13.3 Transmission Gratings ............................................. 490 13.3.1 Photoresist Gratings ....................................... 490 13.3.2 Monolithic Dielectric Gratings ............................. 491 13.4 Overcoatings ...................................................... 491 References ............................................................. 492 Additional Reading ..................................................... 493 Chapter 14: Mechanical Ruling of Gratings ................................. 495 14.1 Introduction ...................................................... 495 14.2 History ........................................................... 496 14.3 Generating Grooves ................................................ 500 14.3.1 Metallic Ruling Coatings ................................... 505 14.3.2 Master Blanks for Gratings Ruling .......................... 506 14.4 Accuracy Requirements ............................................. 507 14.4.1 Constancy of Spacing ....................................... 507 14.4.2 Groove Straightness ........................................ 509 14.4.3 Random Spacing Errors ...................................... 509 14.4.4 Periodic Errors ............................................ 509 14.5 Ruling Engine Design Concepts ..................................... 510 14.5.1 The Mechanical Motions ..................................... 510 14.5.2 Grating Carriage Drives .................................... 513 14.5.3 Concepts for Error Reduction ............................... 514 14.5.4 Interferometer Feedback Control ............................ 515 Optical Systems ............................................ 516 14.5.5 Examples of Ruling Engines ................................. 518 The Michelson Engine ....................................... 518 The B-Engine ............................................... 521 The Bartlett - Wildy Engine ................................ 525 The Hitachi Ruling Engine .................................. 525 14.5.6 Environmental Factors ...................................... 527 Temperature Control ........................................ 527 Vibration Isolation ........................................ 528 References ............................................................. 528 Additional Reading ..................................................... 530 Chapter 15: Holographic Gratings Recording ................................ 531 15.1 Introduction ...................................................... 531 15.2 Photoresist Layer and Groove Formation ............................ 534 15.3 Two-Beam Symmetrical Recording .................................... 538 15.4 Blazing of Holographic Gratings ................................... 542 15.4.1 Asymmetrical 2-Beam Recording .............................. 542 15.4.2 Fourier Synthesis (Multiple-Beam Recording) ................ 544 15.4.3 Blazing Through Ion Etching ................................ 548 15.4.4 The Practical Result of Blazing ............................ 548 References ............................................................. 552 Additional Readings .................................................... 553 Chapter 16: Alternative Methods of Gratings Manufacture ................... 555 16.1 Introduction ...................................................... 555 16.2 Tools of Alternative Methods for Generating Gratings .............. 556 16.3 The Problem of Blazing ............................................ 556 16.3.1 Blazing With Multiple Mask Lithography ..................... 557 16.3.2 Blazing by Direct Methods .................................. 559 The Use of Charged Beams ................................... 559 The Use of Light Beams ..................................... 562 16.4 Pattern-Generating Equipment ...................................... 563 16.5 Single Beam Writing with Surface Waves ............................ 566 16.6 Photomask Interference Method ..................................... 567 16.7 Single Beam Writing of Fiber Gratings ............................. 571 16.8 Grating Etched Inside Planar Waveguide ............................ 572 16.9 Conclusions ....................................................... 573 References ............................................................. 573 Additional Reading ..................................................... 574 Chapter 17: Replication of Gratings ....................................... 577 17.1 Introduction ...................................................... 577 17.2 The Basic Grating Replication Process ............................. 577 17.2.1 The Substrate .............................................. 579 Choice of Materials ........................................ 579 Surface Properties ......................................... 580 Aspheric Replication ....................................... 580 17.2.2 Replication Resins ......................................... 581 Thickness of Replica Films ................................. 582 17.2.3 High Temperature Resistance ................................ 582 17.2.4 Environmental Resistance ................................... 582 17.2.5 Transmission Grating Replication ........................... 583 17.2.6 Overcoatings ............................................... 583 17.3 Separation of Master and Replica .................................. 584 17.4 Replication Testing ............................................... 585 17.5 Multiple Replication .............................................. 585 17.6 Alternative Replication Methods ................................... 586 17.6.1 Injection Molding .......................................... 586 17.6.2 Embossing .................................................. 586 17.6.3 Soft Replication ........................................... 586 References ............................................................. 587 Additional Reading ..................................................... 587 Index ..................................................................... 589