Geometrical optics of inhomogeneous media:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1990
|
| Series: | Springer series on wave phenomena
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 291 - 310. - Forts. bildet: Kravcov, Jurij A.: Caustics, catastrophes and wave fields |
| Physical Description: | XIII, 312 S. graph. Darst. |
| ISBN: | 3540519440 0387519440 |
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| 245 | 1 | 0 | |a Geometrical optics of inhomogeneous media |c Yu. A. Kravtsov ; Yu. I. Orlov |
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| 500 | |a Literaturverz. S. 291 - 310. - Forts. bildet: Kravcov, Jurij A.: Caustics, catastrophes and wave fields | ||
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
YU. A. KRAVTSOV YU. I. ORLOV
GEOMETRICAL OPTICS
OF INHOMOGENEOUS MEDIA
WITH 108 FIGURES
SPRINGER-VERLAG BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO HONG KONG
BARCELONA
IMAGE 2
CONTENTS
1. INTRODUCTION 1
2. THE SCALAR WAVE FIELD 3
2. 1 EQUATIONS OF GEOMETRICAL OPTICS 3
2.1.1 MATHEMATICAL BACKGROUND 3
2.1.2 FIELD EXPANSION IN A DIMENSIONLESS PARAMETER 5
2.1.3 FIELD EXPANSION IN INVERSE WAVE NUMBERS 7
2.1.4 INITIAL CONDITIONS FOR THE EIKONAL AND AMPLITUDE EQUATIONS 8
2.1.5 ASYMPTOTIC NATURE OF THE RAY SERIES 8
2.2 RAYS AND THE EIKONAL 9
2.2.1 THE METHOD OF CHARACTERISTICS 9
2.2.2 RAY EQUATIONS AND THE EIKONAL 11
2.2.3 CURVATURE AND TORSION OF RAYS 13
2.2.4 INITIAL CONDITIONS FOR RAYS. RAY COORDINATES 14
2.2.5 RAY FAMILIES AND PHASE FRONTS 15
2.2.6 THE FERMAT PRINCIPLE 17
2.2.7 RAY EQUATIONS IN CURVILINEAR COORDINATES 18
2.2.8 OTHER TYPES OF RAY 20
2.3 WAVE AMPLITUDE 22
2.3.1 FORMAL SOLUTION OF THE TRANSPORT EQUATION 22
2.3.2 RAYS AND THE DIRECTION OF ENERGY FLOW 23
2.3.3 CONSERVATION OF ENERGY FLUX IN A RAY TUBE 24
2.3.4 THE FIELD DUE TO A POINT SOURCE IN AN INHOMOGENEOUS MEDIUM 26
2.3.5 THE RESULTANT FIELD IN THE RAY-OPTICS APPROXIMATION . 26 2.3.6 THE
FIELD AMPLITUDES OF HIGHER-ORDER APPROXIMATIONS . 28 2.3.7 ACCOUNTING
FOR WEAK ABSORPTION 28
2.4 CAUSTICS 29
2.4.1 FUNDAMENTAL PROPERTIES 29
2.4.2 WAVE-FIELD FOCUSING ON CAUSTICS 31
2.4.3 TYPES OF CAUSTICS 32
2.4.4 STRUCTURALLY STABLE AND UNSTABLE CAUSTICS IN PHYSICAL PROBLEMS 38
2.4.5 OTHER TYPES OF CAUSTICS 39
2.4.6 SINGULARITIES OF PHASE FRONTS 39
2.4.7 PHASE SHIFTS AT CAUSTICS 40
2.5 REFLECTION AND REFRACTION OF WAVES AT INTERFACES 41
2.5.1 THE LOCALITY PRINCIPLE IN WAVE REFLECTION 41
VII
IMAGE 3
2.5.2 RELATIONS FOR RAYS AND EIKONALS 42
2.5.3 REFLECTION FORMULAS FOR AMPLITUDE 43
2.5.4 REFLECTION FROM WEAK INTERFACES 45
2.5.5 THE GEOMETRICAL OPTICS OF SURFACE WAVES 46
2.6 RECIPROCITY OF RAYS AND CAUSTICS 47
2.6.1 THE RECIPROCITY THEOREM 47
2.6.2 RECIPROCITY RELATIONS FOR RAYS AND CAUSTICS 47
2.7 SPACE-TIME GEOMETRICAL OPTICS 49
2.7.1 THE WAVE EQUATION FOR MEDIA WITH TEMPORAL (FREQUENCY) DISPERSION
49
2.7.2 NECESSARY CONDITIONS FOR THE GEOMETRICAL-OPTICS APPLIED TO
QUASI-MONOCHROMATIC WAVE PACKETS 50
2.7.3 DIFFERENTIAL FORM OF THE CONSTITUTIVE EQUATION (2.7.2) .. 51 2.7.4
EIKONAL AND TRANSPORT EQUATIONS 52
2.7.5 SPACE-TIME RAYS 53
2.7.6 INITIAL CONDITIONS 55
2.7.7 EIKONAL AND WAVE AMPLITUDE 57
2.7.8 SPACE-TIME CAUSTICS 60
2.7.9 PROPAGATION OF FIELD DISCONTINUITIES IN NONDISPERSIVE MEDIA 61
2.8 SEPARATION OF VARIABLES IN THE EIKONAL EQUATION 64
2.8.1 THE COMPLETE INTEGRAL OF THE EIKONAL EQUATION 64
2.8.2 SEPARATION OF VARIABLES IN TWO DIMENSIONS (CARTESIAN COORDINATES)
65
2.8.3 SEPARATION OF VARIABLES IN TWO DIMENSIONS (CURVILINEAR ORTHOGONAL
COORDINATES) 66
2.8.4 SEPARATION OF VARIABLES IN THREE-DIMENSIONAL SPACE . .. 68 2.8.5
INCOMPLETE SEPARATION OF VARIABLES 70
2.8.6 THE COMPLETE INTEGRAL OF EIKONAL AND RAY EQUATIONS . . 71 2.9
PERTURBATION TECHNIQUES FOR GEOMETRICAL-OPTICS EQUATIONS 73
2.9.1 THE PERTURBATION METHOD FOR THE EIKONAL 73
2.9.2 THE PERTURBATION METHOD FOR RAYS 74
2.9.3 PERTURBATIONS IN HOMOGENEOUS MEDIA 75
2.9.4 PERTURBATIONS IN NONHOMOGENEOUS MEDIA 77
2.10 APPLICABILITY OF GEOMETRICAL OPTICS 79
2.10.1 EXISTENT ESTIMATORS OF METHOD S ERRORS 79
2.10.2 FRESNEL ZONES AND FRESNEL VOLUME OF RAYS IN INHOMOGENEOUS MEDIA
80
2.10.3 THE PHYSICAL MEANING OF THE RAY 87
2.10.4 HEURISTIC CRITERIA ON GEOMETRICAL-OPTICS APPLICABILITY 88 2.10.5
APPLICABILITY CONDITIONS FOR SPACE-TIME GEOMETRICAL OPTICS 89
2.10.6 HEURISTIC ACCURACY ESTIMATES OF GEOMETRICAL OPTICS . . 93 2.10.7
ESTIMATING THE WIDTH OF A CAUSTIC ZONE 93
2.10.8 INDISTINGUISHABILITY OF RAYS IN THE CAUSTIC ZONE 96
2.10.9 OBSERVABILITY OF CAUSTICS 96
2.10.10 FIELD ESTIMATIONS BEYOND THE VALIDITY REGION OF GEOMETRICAL
OPTICS 97
VIII
IMAGE 4
2.10.11 FIELD-FOCUSING INDICES AT CAUSTICS 98
2.10.12 STABILITY WITH RESPECT TO SMALL PERTURBATIONS 99
2.10.13 WAVE-PATTERN ANALYSIS IN GENERAL 99
3. APPLICATIONS OF THE RAY METHODS 101
3.1 WAVES IN HOMOGENEOUS MEDIA 101
3.1.1 RAYS AND THE EIKONAL 101
3.1.2 THE WAVE AMPLITUDE 102
3.1.3 CAUSTICS 104
3.1.4 THE PLANE PHASE-AMPLITUDE SCREEN 105
3.1.5 THE SINUSOIDAL PHASE SCREEN. AN ILLUSTRATIVE EXAMPLE . 107 3.1.6
APPLICABILITY CONDITIONS FOR GEOMETRICAL OPTICS 109
3.1.7 GEOMETRICAL OPTICS IN FAR AND NEAR ANTENNA FIELDS. WAVE BEAM
PROPAGATION 110
3.1.8 ON THE PHASE CENTER OF AN ANTENNA OR A SCATTERER . . .. 113
3.1.9 FIELD NEAR A LENS FOCUS 114
3.1.10 FIELD AT THE FOCUS OF A LENS WITH CYLINDRICAL (SPHERICAL)
ABERRATION 116
3.2 REFLECTION AND REFRACTION AT AN INTERFACE BETWEEN HOMOGENEOUS MEDIA
121
3.2.1 REFLECTION FORMULAS 121
3.2.2 DIVERGENCE OF REFLECTED AND REFRACTED RAYS 121
3.2.3 EFFECTIVE SCATTERING SURFACE OF A BODY IN THE GEOMETRICAL-OPTICS
APPROXIMATION 125
3.2.4 REFLECTION FAR FIELD OF A DIRECTIONAL POINT SOURCE . .. 125 3.2.5
CAUSTICS OF REFRACTED AND REFLECTED RAYS 126
3.2.6 EXAMPLES OF CATACAUSTICS AND DIACAUSTICS 127
3.2.7 APPLICABILITY OF REFLECTION FORMULAS 128
3.2.8 THE INVALIDITY DOMAIN IN THE VICINITY OF A TANGENT RAY 131 3.2.9
WAVE DIFFRACTION AT A SURFACE OF VARIABLE IMPEDANCE . 131 3.3 RAYS AND
CAUSTICS IN PLANE-STRATIFIED MEDIA 132
3.3.1 RAY EQUATIONS 132
3.3.2 RAY TRACING IN A PLANE-STRATIFIED MEDIUM 135
3.3.3 EQUATIONS OF CAUSTICS, AND THE GEOMETRY OF THE RAY FAMILY 136
3.3.4 RAYS AND CAUSTICS DUE TO A POINT SOURCE IN AN INHOMOGENEOUS MEDIUM
137
3.3.5 RAYS AND CAUSTICS IN A LINEAR LAYER 139
3.3.6 LAYERS OF OTHER PROFILES 142
3.3.7 PLANE WAVES IN A PARABOLIC LAYER 143
3.3.8 A POINT SOURCE IN A PARABOLIC LAYER 145
3.4 WAVE FIELDS IN PLANE-STRATIFIED MEDIA 146
3.4.1 THE FIELD OF AN ARBITRARY WAVE 146
3.4.2 THE FIELD OF A PLANE WAVE 148
3.4.3 FIELDS OF POINT AND LINEAR SOURCES 150
3.4.4 A POINT SOURCE IN A LINEAR LAYER 152
3.4.5 A POINT SOURCE IN A PARABOLIC LAYER 155
3.4.6 THE FRESNEL VOLUMES IN PLANE-STRATIFIED MEDIA 156
IX
IMAGE 5
3.4.7 VALIDITY CONDITIONS
OF THE GEOMETRICAL-OPTICS APPROXIMATION 159
3.5 WAVES IN RADIALLY INHOMOGENEOUS MEDIA 160
3.5.1 RAY EQUATIONS FOR SPHERICALLY STRATIFIED MEDIA 160
3.5.2 THE EIKONAL FUNCTION FOR SPHERICALLY STRATIFIED MEDIA . 163 3.5.3
CYLINDRICALLY STRATIFIED MEDIA 164
3.5.4 RAY GEOMETRY 165
3.5.5 THE FIELD DUE TO A POINT SOURCE 167
3.5.6 THE FIELD OF A PLANE WAVE 169
3.5.7 CAUSTICS 170
3.6 TAPERED AND OTHER INHOMOGENEOUS MEDIA 172
3.6.1 THE EIKONAL AND RAYS IN A TAPERED MEDIUM 172
3.6.2 THE FIELD OF A PLANE WAVE 174
3.6.3 THE FIELD DUE TO A LINEAR SOURCE 175
3.6.4 RAY EQUATIONS IN A TWO-DIMENSIONAL MEDIUM WITH A SPECIAL PROFILE
176
3.6.5 THE FIELD OF A POINT SOURCE (AXIALLY SYMMETRIC PROBLEM) 178
3.6.6 A PLANE WAVE INCIDENT ON THE TWO-DIMENSIONALLY INHOMOGENEOUS
MEDIUM . . 180 3.6.7 WEAKLY INHOMOGENEOUS, QUASI-STRATIFIED, AND RANDOM
MEDIA 181
3.7 GEOMETRICAL OPTICS OF WAVEGUIDES AND RESONATORS 182
3.7.1 GEOMETRICAL OPTICS OF WAVEGUIDES 182
3.7.2 RAY DESCRIPTION OF MODES IN UNIFORM WAVEGUIDES . .. 184 3.7.3
ADIABATIC MODES OF SMOOTHLY NONUNIFORM WAVEGUIDES 187 3.7.4 IONOSPHERIC
WAVE CHANNELS. THE ADIABATIC INVARIANT METHOD 188
3.7.5 UNDERWATER-SOUND DUCTS. SUMMING-UP INCOHERENT WAVE FIELDS 190
3.7.6 OPTICAL FIBERS 190
3.7.7 MODE CONVERSION IN SMOOTHLY NONUNIFORM WAVEGUIDES 192 3.7.8 NORMAL
MODES IN CAVITY RESONATORS 192
3.8 WAVE SCATTERING AT LOCALIZED INHOMOGENEITIES 192
3.8.1 EFFECTIVE SCATTERING SURFACE 192
3.8.2 SCATTERING BY A BODY IN AN INHOMOGENEOUS MEDIUM . . 196 3.8.3
EFFECTIVE SCATTERING SURFACE OF A SPHERICALLY STRATIFIED INHOMOGENEITY
197
3.8.4 EFFECTIVE SCATTERING SURFACE OF A PERFECTLY CONDUCTING SPHERE IN A
SPHERICALLY STRATIFIED MEDIUM 199
3.8.5 EFFECTIVE SCATTERING SURFACE OF A SPECIFIC TWO-DIMENSIONALLY
INHOMOGENEOUS FORMATION 201
3.8.6 SCATTERING OF A SPHERICAL WAVE BY A LOCALIZED INHOMOGENEITY 202
3.8.7 SCATTERING BY WEAK LOCALIZED INHOMOGENEITIES 204
3.9 PULSE PROPAGATION 205
3.9.1 GENERAL RELATIONS FOR THE PLASMA (GUIDED) DISPERSION LAW 205
X
IMAGE 6
3.9.2 A HOMOGENEOUS MEDIUM WITH AN ARBITRARY
DISPERSION LAW 206
3.9.3 A PLANE, FREQUENCY-MODULATED PULSE IN A HOMOGENEOUS MEDIUM 207
3.9.4 DISPERSIVE COMPRESSION OF FM PULSES IN HOMOGENEOUS MEDIA 211
3.9.5 PLANE-STRATIFIED DISPERSIVE MEDIA 213
3.9.6 NEAR AND FAR FIELDS OF A PULSE 214
3.10 NUMERICAL METHODS IN THE GEOMETRICAL OPTICS OF INHOMOGENEOUS MEDIA
216
3.10.1 THE RAY-TRACING ANALYSIS 216
3.10.2 COMPUTING THE EIKONAL AND WAVE AMPLITUDE 218
3.10.3 PROBLEMS OF NUMERICAL ANALYSIS 221
3.11 INVERSE PROBLEMS OF GEOMETRICAL OPTICS 222
3.11.1 REFLECTION AND REFRACTION AT INTERFACES 222
3.11.2 INVERSE PROBLEMS FOR GIVEN MODELS OF THE INHOMOGENEOUS MEDIUM 223
3.11.3 MULTIDIMENSIONAL INVERSE PROBLEMS 224
3.11.4NONSTATIONARY INVERSE PROBLEMS 225
4. VECTOR WAVE FIELDS 226
4.1 TRANSVERSE ELECTROMAGNETIC WAVES IN ISOTROPIC MEDIA 226
4.1.1 MAXWELL EQUATIONS FOR MONOCHROMATIC WAVES 226
4.1.2 THE DEBYE EXPANSION AND THE ITERATIVE EQUATIONS . . . 227 4.1.3
THE EIKONAL EQUATION 227
4.1.4 TRANSVERSE NATURE OF ZERO APPROXIMATION WAVES. POLARIZATION
DEGENERACY 228
4.1.5 CONSISTENCY OF THE FIRST-APPROXIMATION EQUATIONS . . . 229 4.1.6
CONSERVING ENERGY FLOW IN A RAY TUBE 230
4.1.7 PRESERVING THE POLARIZATION ELLIPSE 230
4.1.8 ROTATION OF FIELD VECTORS (RYTOV S LAW) 231
4.1.9 POLARIZATION OF TRANSVERSE WAVES 233
4.1.10 LONGITUDINAL COMPONENTS OF THE FIELD 233
4.1.11 REFLECTION OF TRANSVERSE ELECTROMAGNETIC WAVES FROM INTERFACES
234
4.1.12 POLARIZATION DEGENERACY IN PROBLEMS OF QUANTUM MECHANICS AND
THEORY OF ELASTICITY 234
4.2 INDEPENDENT NORMAL WAVES IN AN ANISOTROPIC MEDIUM . . .. 235 4.2.1
EQUATION OF THE EIKONAL 235
4.2.2 INDEPENDENT NORMAL MODE 236
4.2.3 RAY EQUATIONS 237
4.2.4 SOLVING THE EIKONAL EQUATION 239
4.2.5 DEFINITION OF MODE POLARIZATION VECTORS 240
4.2.6 CONSISTENCY OF EQUATIONS OF THE FIRST APPROXIMATION . 240 4.2.7
THE TRANSFER EQUATION 241
4.2.8 EQUATION FOR THE ARGUMENT OF A COMPLEX AMPLITUDE 242 4.2.9 RAYS
AND ENERGY PATHS. THE FRESNEL VOLUMES IN ANISOTROPIC MEDIA 243
XI
IMAGE 7
4.2.10 AN ACCOUNT OF WEAK ABSORPTION 244
4.2.11 REFLECTION AND REFRACTION AT THE BOUNDARIES OF ANISOTROPIC MEDIA
245
4.2.12 SOME SPECIFIC RESULTS 246
A) THE FIELD OF A POINT SOURCE IN AN ANISOTROPIC MEDIUM 247
B) WAVES IN PLANE-STRATIFIED ANISOTROPIC MEDIA 247
C) SEPARATION OF VARIABLES IN THE EQUATION OF EIKONAL IN THE GENERAL
CASE 249
D) PERTURBATION THEORY 249
4.2.13 DIVERGENCE OF FIRST-APPROXIMATION FIELDS AT POLARIZATION
DEGENERACY 249
4.2.14 OTHER VECTOR PROBLEMS 251
INTERACTION OF NORMAL MODES IN INHOMOGENEOUS ANISOTROPIC MEDIA 251
4.3.1 WAVES IN WEAKLY ANISOTROPIC MEDIA. THE QUASI-ISOTROPIC
APPROXIMATION 251
4.3.2 DIFFERENT FORMS OF THE EQUATIONS OF THE QUASI-ISOTROPIC
APPROXIMATION 253
4.3.3 SOLUTION TECHNIQUES FOR THE QUASI-ISOTROPIC APPROXIMATION 255
4.3.4 ON THE ERROR OF THE QUASI-ISOTROPIC APPROXIMATION . . 255 4.3.5
APPLICATIONS OF THE QUASI-ISOTROPIC APPROXIMATION . . . 256 4.3.6 THE
QUASI-DEGENERATE APPROXIMATION OF GEOMETRICAL OPTICS 257
EQUATIONS OF GEOMETRICAL OPTICS FOR NONHARMONIC ELECTRO MAGNETIC WAVES
IN THE GENERAL CASE OF INHOMOGENEOUS AND NONSTATIONARY DISPERSIVE MEDIA
258
4.4.1 THE MAXWELL EQUATIONS IN INHOMOGENEOUS AND NONSTATIONARY MEDIA OF
TEMPORAL AND SPATIAL DISPERSION . . 258 4.4.2 THE CONSTITUTIVE EQUATION
IN DIFFERENTIAL FORM 260
4.4.3 EQUATIONS FOR THE FIELDS IN ZEROTH AND FIRST APPROXIMATIONS 261
4.4.4 THE EIKONAL EQUATION. SPACE-TIME RAYS 262
4.4.5 THE TRANSFER EQUATION FOR INDEPENDENT NORMAL MODES IN AN
ANISOTROPIC MEDIUM 263
4.4.6 THE GROUP VELOCITY THEOREM 264
4.4.7 INTEGRATING THE TRANSFER EQUATION ALONG SPACE-TIME RAYS 266
4.4.8 TRANSVERSE MODES IN AN ISOTROPIC MEDIUM 267
4.4.9 LONGITUDINAL WAVES IN AN ISOTROPIC MEDIUM 269
4.4.10 WAVES IN WEAKLY ANISOTROPIC MEDIA 270
CONSTITUTIVE EQUATIONS FOR NONSTATIONARY AND INHOMOGENEOUS DISPERSIVE
MEDIA. EXISTENCE OF ADIABATIC INVARIANCE 270
4.5.1 CORRECTIONS TO THE QUASI-STATIONARY PERMITTIVITY TENSOR 270 4.5.2
PHYSICAL PHENOMENA DUE TO THE DEVIATION OF E A SS FROM ITS
QUASI-STATIONARY VALUE 271
4.5.3 EXISTENCE OF THE ADIABATIC INVARIANT 272
IMAGE 8
4.5.4 PHENOMENOLOGICAL EVALUATION OF THE ANTI-HERMITIAN
PART OF THE CORRECTION FOR THE QUASI-STATIONARY PERMITTIVITY TENSOR IN
TRANSPARENT MEDIA 273
4.6 WAVE PROCESSES IN NONSTATIONARY MEDIA 274
4.6.1 ONE-DIMENSIONAL PROBLEM. GENERAL RELATIONSHIPS . . . 274 4.6.2
NONSTATIONARY NONDISPERSIVE MEDIA 276
4.6.3 NONSTATIONARY DISPERSIVE MEDIA 279
4.6.4 EVOLUTION OF SHORT PULSES 281
4.6.5 REFLECTION FROM MOVING INTERFACES 282
4.6.6 PERTURBATION THEORY IN NONSTATIONARY PROBLEMS 286
5. CONCLUSION 287
REFERENCES 291
SUBJECT INDEX 311
XIII
|
| any_adam_object | 1 |
| author | Kravcov, Jurij A. 1937- Orlov, Jurij I. |
| author_GND | (DE-588)120181665 |
| author_facet | Kravcov, Jurij A. 1937- Orlov, Jurij I. |
| author_role | aut aut |
| author_sort | Kravcov, Jurij A. 1937- |
| author_variant | j a k ja jak j i o ji jio |
| building | Verbundindex |
| bvnumber | BV004096209 |
| classification_rvk | UH 5080 |
| classification_tum | PHY 351f |
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| dewey-full | 535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535 |
| dewey-search | 535 |
| dewey-sort | 3535 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV004096209 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:08:21Z |
| institution | BVB |
| isbn | 3540519440 0387519440 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002556000 |
| oclc_num | 246671193 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-384 DE-703 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-384 DE-703 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| physical | XIII, 312 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series | Springer series on wave phenomena |
| series2 | Springer series on wave phenomena |
| spelling | Kravcov, Jurij A. 1937- Verfasser (DE-588)120181665 aut Geometričeskaja optica neodnorodnich sred Geometrical optics of inhomogeneous media Yu. A. Kravtsov ; Yu. I. Orlov Berlin u.a. Springer 1990 XIII, 312 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series on wave phenomena 6 Literaturverz. S. 291 - 310. - Forts. bildet: Kravcov, Jurij A.: Caustics, catastrophes and wave fields Inhomogenes Medium (DE-588)4228459-4 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 s DE-604 Inhomogenes Medium (DE-588)4228459-4 s Orlov, Jurij I. Verfasser aut Springer series on wave phenomena 6 (DE-604)BV000022763 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002556000&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kravcov, Jurij A. 1937- Orlov, Jurij I. Geometrical optics of inhomogeneous media Springer series on wave phenomena Inhomogenes Medium (DE-588)4228459-4 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| subject_GND | (DE-588)4228459-4 (DE-588)4020241-0 |
| title | Geometrical optics of inhomogeneous media |
| title_alt | Geometričeskaja optica neodnorodnich sred |
| title_auth | Geometrical optics of inhomogeneous media |
| title_exact_search | Geometrical optics of inhomogeneous media |
| title_full | Geometrical optics of inhomogeneous media Yu. A. Kravtsov ; Yu. I. Orlov |
| title_fullStr | Geometrical optics of inhomogeneous media Yu. A. Kravtsov ; Yu. I. Orlov |
| title_full_unstemmed | Geometrical optics of inhomogeneous media Yu. A. Kravtsov ; Yu. I. Orlov |
| title_short | Geometrical optics of inhomogeneous media |
| title_sort | geometrical optics of inhomogeneous media |
| topic | Inhomogenes Medium (DE-588)4228459-4 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| topic_facet | Inhomogenes Medium Geometrische Optik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002556000&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022763 |
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