Вынужденное явление Рамана
Рассеяние Рамана[1] в стоксову сторону.
Пусть пучок света падает на прозрачную среду, не содержащую никаких включений посторонних тел и тщательно очищенную. Даже при максимально возможной частоте свет пучка рассеивается во все стороны, хотя и очень слабо. Рассеяние имеет место как в газообразных, так и в жидких и твердых телах. В газах рассеяние происходит, главным образом, на атомах и молекулах, в жидкостях и кристаллах—на флуктуациях и неоднородностях среды. В рассеянном свете имеются волны тех же длин, что и в падающем, но разной интенсивности в зависимости от длины волны. Это рассеяние называется релеевским по имени Релея. Помимо рассеяния света с той же длиной волны наблюдается еще слабое свечение с длиной волны, большей, чем падающая,—рамановское рассеяние. Механизм этого явления можно объяснить на основе как квантовой теории, так, и классической волновой. Особенно просто выглядит квантовое описание этого явления.
Пусть квант излучения
или, иначе, ![](data:image/png;base64,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)
(поскольку
![](data:image/png;base64,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)
, a
![](data:image/png;base64,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)
) рассеивается на молекуле, находящейся в основном состоянии с энергией
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAXCAYAAAC8oJeEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIOSURBVFjD7Vc7bsJAEJ0DcACQ2HQcAK+5wmaFUiMZiyqICq2EqNGazk0OkHR0oUidAk7ADVJwA+6QMHYGlrUNRsEUsYuRtf7szJt5b3YM8/kcymqlBV6Br8CXHbxWss0AdgDwHVlTrqULH4f13pgYTwOfP5nvjMKwdqtgwnBUk01Yk6+7Vl7rQYMDbLkfPNG9GCzfDrRu0L2xYNOigsMYHGAbqXT7vuCj6rMvckzJMCuM73ChhkWAjnwZTANguyKTcBa8EqLnOLAi8EhLwcXsllS3DVkFvL/IK49Ldo6hJwuT4lThPocFBaMEHxZZCQKFsjsy4VRypiz6nL2kxRPhuJDABPgo63tnnlYtrLAKVB2DwexdQ/coYecqkhFYzDxn4yvZxaunvbat/0CpOjIPfVBvSsgV10wuLzE0CX5PceXLLm5ElUDwvpTPRdL9UDHHWfGHxzf0lQWC4qT7cbKPDIn2yXESJSuGzrmvzSbkuu6reQIUZTaItFPFLIj5nRmfKdXrwBvOD2d/jo3+SntKNIGKQDK2tDVtU9xuwvbzXODNZmNr0Gw4RZnti9aoeyFUzx7GKE5seoy5n/hdGivyTXiY+V+tmRq8x6SVRtXjJHna7W1mYRLMqdOWZ/yM7YTgM5txpZjhfdmZdKQ/Kd2PDTLaZe67p3SrdOCR9lkn1f+nPOc6q2FX//MV+BLaD7w9SkV2dOenAAAAAElFTkSuQmCC)
возбуждая ее до одного из возможных для нее типов колебаний с резонансной частотой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAXCAYAAADk3wSdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVEjHY2hsbGSgNmYYNXTUUDoYWl8fK2nMwHCXgcH4bmx9vWRDtLEPAwPDfwbjqIVkGQozwDi6wYcYcYKG1ud5GMoyyN70yKs3hBsEdV1HRxqPhwzDHlm3nGKiDUXXhM6HBQlJLkV3JcgQIwaj3aAwRcgbnYLxiTIU7FUZjz1pHR08MEM8IuvtYPJRxgwLSY4oSERAYhvkShNZ2e3Gbnkp2CwkOUzBSQdoeGR9niqcj8WFEEfIvnFzM65Fl6cokUd7mBaaekQXUi1HQYLIZEVkXr0q1QwFeR9X8iLf68bG9biS1wgv+gCan8g5cOKrvQAAAABJRU5ErkJggg==)
. В результате рассеянный квант будет иметь меньшую энергию
![](data:image/png;base64,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)
. Баланс энергии
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI0AAAAdCAYAAACXOO/mAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALaSURBVHja7Vk9UsJAFH4H8ALMZKm8gG5arZiQwtoZYWwtGCYNtRPpaLgAnZ0W1hbaeggLbsAd1AQWlmU3u0l4S5BXfAWB7L6fb99+7wHj8RgIhDKgIBCINAQiDYFIQyDSEP41nvr8BgB+eP/pxkqaNIkvGMAie4FFw5Ft8fz3LH59mEzOTjG4k8nDWbfNZ/dp2vK5b9k8lUWPwzMAW8RJeuFUaZYs231BxTBiIwA+9x2wpkEkUD2VfqqBPU9VDkIcwKeOjAYSwM8OeO9Za3AQf55qhdkhTnrf4gBzH8Qpk6eqvlzC5YeuGOz8eDAYnAuWFRngM0DHpwPwK69rnuqQJoqSW2chrBJClF65VOVMd6gyYi1ZUMl3MYbDVarDvuwrKuvYlU2XJwx/rfekUNA5ViRxZbgooSYn1iX2QMTBsi8XkB6ubVuesPw1B/Nv4yTpXImuKH+2WsxF9C0N2Ag0HdHWzw4gpDHtU9fWdyUaPVJSm9jyhOWvsbxCGL9FPHqUK4sgial/VzsJmdHrQCkOmdo6H50Oln22+OyzuynKE5a/5oCy8F28uHzGvsVnW1CWG2/YumHw9jt1Kk2d04ptnw/SuOQJy1+jwzIr1da6KCgmvaMrmy7CDe2EItrndqjqXU8uecLy13oKxTN5oaLFhTpXv8uMVIMo77VR8LhXVVX76uglDLjkCctfa7sot3Vio6LuSfdd7kwYvjDem+oCKw+SioZKWJXGZl+lhCJ2T655wvLXOpI2/b9RNKfZ6vulMr1VliUn8n0Vp3zoAVf7mjanKZMnDH8bMTLPCKgSsmmTZnESO0lypetQfE+ED4lGjMyPgTTi2gxD9mIq4afy1wpKqay0xtb1xKY+5zauV1oQBF/xXXp9yoTZC2nWAWt3Z1WFnyqE66yFeT1lwlFnV65jGHttGtEbTZr9ibtMlPmdDpfpiOgf/YaRhkCkIRBpCAQiDYFIQ/CJXyA3gJ5hyMlcAAAAAElFTkSuQmCC)
(1)
позволяет рассчитать колебательные уровни
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAXCAYAAAD3CERpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFVSURBVEjH7VY9bsIwFH4H4AJIvG4cIHmwdnStihkpRGwVE7KEmKtHtpyhG1s5AQOcgBt04AbcodVLamJMaMKQDBWDlfjl2d/Pe7YCSZJA2wMeoP8bNE1nHd2DPQB8o5ovW1PKPO2GgAdtOGgcVMAI4Cgqi4GnJsCvAnOFS6DJumphQZKOU+buKqZRRrTG2tKaUrwa+Zu6eRZA8urE/wRlowOE8BAb/SrPiKPAr2+eg182lgH9qrOkq5oQrpiG4Y6eXj5madrJAFBv5L1sU39u3blL6YRg7dop9XVZ+yrzTg93Nt865ZejsnsvVCBuXGszJ3p6b5ULiI74+YL0PY3ks7RzqatSZlw0Su6EkBwgbkmZtzJCtUB9lucj4Njt3lgSj9j0z3NPYb4eT0rRu/+t0Ts21sPFUMeL1i783P7BZ2S43xqo2Hvr6DRnLRHfOjqPP4dGxw+5KM7zL3W+1wAAAABJRU5ErkJggg==)
молекулы. Рассеянный свет имеет частоту
![](data:image/png;base64,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)
, меньшую частоты падающего света
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAYCAYAAAAVibZIAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADzSURBVEjHY2hsbGSgNmYYNXTUUDoYWl8fK2nMwHCXgcH4bmx9vWRDtLEPAwPDfwbjqIVkGQozwDi6wYcYcYKG1ud5GMoyyN70yKs3hBsEdV1HRxqPhwzDHlm3nGKiDUXXhM6HBQlJLkV3JcgQIwaj3aAwRcgbnYLxiTIU7FUZjz1pHR08MEM8IuvtYPJRxgwLkSMqx022GBTG2IIDLSIgsQ1ypYms7HZjt7wUXBbKGkf1QiyT7YX5DmeYgpMO0PDI+jxVOB8tKYFcCQtbkIXoriUrcee5GafAwx7oapiPKDKUJi4lOkxJxeDUQCj2R4s+qmEATwXktif5eKAAAAAASUVORK5CYII=)
. Следовательно, рамановские линии являются стоксовыми. Рассеяние на уже возбужденной молекуле маловероятно, потому что линии с большей частотой
![](data:image/png;base64,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)
, т. е. антистоксовые, имеют столь малую интенсивность, что обычно незаметны. Интенсивность рамановских линий рассчитывают на основе вероятности соответствующих переходов в единицу времени или же по энергии, лучше по гамильтониану взаимодействия излучения с молекулами, или по волновым функциям трех состояний молекулы: исходного, промежуточного (после поглощения кванта
![](data:image/png;base64,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)
) и конечного (после испускания кванта
![](data:image/png;base64,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)
).
Волновой механизм рамановского рассеяния заключается во взаимодействии молекулы, способной к определенному резонансному колебанию с частотой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAXCAYAAADk3wSdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVEjHY2hsbGSgNmYYNXTUUDoYWl8fK2nMwHCXgcH4bmx9vWRDtLEPAwPDfwbjqIVkGQozwDi6wYcYcYKG1ud5GMoyyN70yKs3hBsEdV1HRxqPhwzDHlm3nGKiDUXXhM6HBQlJLkV3JcgQIwaj3aAwRcgbnYLxiTIU7FUZjz1pHR08MEM8IuvtYPJRxgwLSY4oSERAYhvkShNZ2e3Gbnkp2CwkOUzBSQdoeGR9niqcj8WFEEfIvnFzM65Fl6cokUd7mBaaekQXUi1HQYLIZEVkXr0q1QwFeR9X8iLf68bG9biS1wgv+gCan8g5cOKrvQAAAABJRU5ErkJggg==)
(или к нескольким таким колебаниям), с падающей и рассеянной волнами. Колебание молекулы в простейшем виде можно представить как колебание точки с координатой
х (точка является одним из атомов молекулы, имеющим массу
т), с коэффициентом затухания
R и упругим усилием
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAYCAYAAAAYl8YPAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADYSURBVEjH7ZSxDYNADEX/ACyAhIcA74CuYAFAdBEVomGAg+6aDEGZHZiADVIwS6ILoiHAwZF0FG6fvv2fjKZp8KvBBfsfTMrMZWAA8KKwqKxhGhSAelFKv045gie6XCnHCpYw2rU0h2CfJOAhk9K1himVO8JDp280jhm4a0Vw0p5uc2qQ0zo6DyuFTwj6PfcywoqQqjUNrArYo4QRNq5ITy3qUiFLymyvuNJiKkgSJ/fNZBPAdPgy5Ns88RdsjL4tqNZFED2WdDn0YqbEsYx97d+8nOvTHp833ZCg6NeAZHkAAAAASUVORK5CYII=)
, возвращающим точку в положение равновесия. Под влиянием внешней периодической силы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAVCAYAAAAkeuLCAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJ3SURBVFjD7Vg7csIwENUBuAAziC4HAKWmNC6oMwMMXYaKccMBBJ2bXICOMidIEU7ADVJwA+5AIhvZ67VWlknG4IkKFf5pd9++t7sy2263zK9mlwfBg/6PQV8FfM0Yu5CrFx6WcdxpwkEpF90hG34upOy2AVAXf8mPN3MxYYyfw0gOcEJ4sFo3EUDqgzi1BfAM+CgccMa/MHaVoCdsNzBaASHmm0lbGK4AEEH0Sj2P42Vn3Be7v05sCvzwaNqX/Ggm2B4yOgqClyYZh+2bkiIYO2klpKr4KX1itndlnCvo6T7sDEmISZH5A+wnxAXXVtDTDflRO5sY5eE7VceV42GPHbKaDwyVniH1FPtHCiC2by477IIVB++rpME+RKnTlempn3mpS2yBOBN7KDaK7cwWVGEZMgZB1UHBXqCfacZmCbg6h5Op1WSr5Zi9MHhsr0otdUDHoKprHbNWAk6sZj++TxtAMqGcT4ImphkTeNDBTLYooZhVOME4ifoaBmlTC1ZBFcEyslzv49JiYjn0B2NH1kqYHTkNR5TUqYZLgYcdyYAHwVKgY5aX6iqQs82vW2t6Qc0gASY21wKdGhVvGetMtZdyEr5L7YlVpcAIp3KEFYoV8Deg58mGpYViea3ygkuLy2iHu7Ye0/ImmgMIGWgCTQFFlQaYDPXOM+cfehyECdGMn8roqQpQJ9ABY6G6bIA7NdKCzGueOvPxrfytbXop2UTTAGZqcS9xUqBm1+DbfBCoVqxrIy3FaJmIbhoZH+c4TY+N91ozwd9cfLId7lp9nL4HEUR/vKuqALbm2oq/jI/0w0uVrarm/KsfXn75/+kedL886K1b31thHAa+ooP6AAAAAElFTkSuQmCC)
, возникающей в результате взаимодействия со случайным полем волны
Е, создается колебательное движение, которое описывается уравнением
(2) Легко показать, что для резонансной частоты
![](data:image/png;base64,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)
решением этого уравнения является функция
![](data:image/png;base64,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)
(3)
Силу F можно рассчитать по энергии взаимодействия наведенного момента молекулы аЕ с полем волны
, а именно:
![](data:image/png;base64,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)
(4)
Случайное поле волны может быть выражено уравнением
![](data:image/png;base64,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)
(5)
где
![](data:image/png;base64,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)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAXCAYAAAAGAx/kAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADqSURBVDjLY2hsbGSgBmYYwQbluMkWy7rlFJNkUEdHGo+HDMMeBgaG/xhYxmNPWkcHz+AMI5B3GRiM78bW10tiNai+PlbSmIHhLsgruMIF7n3jqIV4XQQyzIhB9pRHXr0hPoOMoxt88BuU52EoK+uxElfAgl0t5z4LXR67/9GcjW6Qm1teGFHRD3I22GUMDG9g0U8oLWF6i8HoFCg2wF4wjq4nK/ph3kI2kCyDoowZFiJSM2o6Idog5GiHuEj2Jq4kgNeghmhjH1h+ggU6KIDBbI/oZKINAnkLOWYg2QDkRdk3xLhsJJeQxGIAX0BdjF9iuOYAAAAASUVORK5CYII=)
—волновые векторы падающей и рассеянной волн,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACESURBVCjPY2hsbGQgBTPQT0N9noehLAPDGwYG47ux9fWSDdHGPgwMDP+Noxt8cNoA1iTrsTIv2jSCwchotxGD7CmPvHpDnBpy3GSLZU1MVsgaR/US5YcoY4aFDDIee9I6OngI+6E+VtKIwWg3yP1EeRrsSeOohUSHEsg56CEywBFHLAYANTzlP49zLvAAAAAASUVORK5CYII=)
—пространственная координата, а
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAQCAYAAADESFVDAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACLSURBVCjPY2hsbGQghBloq6g+z8PQ2C0vBacikAJZBtmbHnn1hlgVRRkzLGRgYPgPw8bRDT5YTQIplHXLKcbppvr6WEkjBtlTyFZhKMpxky1mkPHYk9bRwYNVUUdHGo+HDMMedKtQFEF8ZXQqsj5P1V3OeFZsfb0khqKGaGMfiK9k3+B10wDFHToGANia0e/7/OItAAAAAElFTkSuQmCC)
—временная координата. Сильное взаимодействие этой волны с молекулой может произойти только вблизи резонанса, а следовательно, при частоте в инфракрасном диапазоне
![](data:image/png;base64,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)
, которая является частотой биений. Поэтому для вычисления силы
F мы будем использовать только ту часть общего выражения, которая содержит разностную частоту. Общее выражение имеет вид
![](data:image/png;base64,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)
Его решением аналогично выражению (3) будет
![](data:image/png;base64,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)
(6)
Колебания молекулы совершаются с частотой биений
![](data:image/png;base64,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)
. Изменение
х влечет за собой изменение поляризованности молекулы
![](data:image/png;base64,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)
, что в электрическом поле падающей волны приведет к изменению дипольного момента
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcsAAAAzCAYAAAD4tCOHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA1NSURBVHja7V27ktzEGhYJCRAScNFmpkg9GoeHcuAaZDAnW8ry1J4ALw5cexQYV03gAtmZA/sBIKCwo3V6AlxgXsC8AFBn/QLYr3DWZ1rS32r1dLda95b2C76qnYt2enp+9df/7Wvv3r17HgAAAAAAemASAAAAAABkCQAAAAAgSwAAAAAAWQIA0A+S5OC9wPNOPM977a+OvsGcAADIEgAACfFq9eVBkrzHSHPhLZ6xvzEvAACyBABAg2uB/zCMk/OYCwAAWQKAc7i7Dq54XvCiS6+OwqvB+u4V22vWYXj9xv37b+M3AQCQJQA45s15j7zg2qO+/v868H6yyUUywq5DrFPD0cr/ZrshOTnYbN6H3QEgSwCY2AI+BEGxzzERZurZbgnb87w3hp6DOPRvbT/3lBUYqRBEyRdtr79//8bboe89G+s7AiDL0ZGFr7Y3xYfhbwgfAWMjXZQ/9H6zscckDs/7wbWHQ9m7Lh+ZeVwF2YzhXWbfy3956eadhTiXl33/2CaHarqePUdkOWfPGQBZtt41A8AQEFswqsiMLd6f7gU/NMlRNrX3lJz98ImLm8qUsNmcbTbvlLzGvFK37fXst1nuhd/LrwPAmSHLbMfoP0EFH+Dcwm8gJUZcwSo+HNreXa12ZXlb2gCk3zFcX69zvZiXVV3PyHK1ir+EfQJnlizT3fzepz8gBAtMiSzjVXDYhLTa2jsLV7oWheFVu1HyBcsn1h1j2+sBYLZkmVYP5qGueH3hqlxJmOdgXnue/2q1Cr5FPhNwiSzrhmAt7f3Uxt5d3FzmedjTOkU9XV4PALMjy3wH+YIWizQH43mvKGnPiyvo9fz92GUCLpFlapfBOunJ3k9M9t4mV9rr5jevUk2/097y+zrjYyHYNtcDwKzIUl4YVDe+3K9G16ACzl1SmeNGppIsLfKVfdq7S3lLlXBCHWEEMQTb5Hqge7BWHnZfz7FFZxKDVCmcUG+Y7vVsJ774HbtMhzY7ql64mYXJq8jy7sV3b70V/PvhWPb+r4/f+tG/klx3574ut3zwRVfI61KoebsI325yPdDjfc36V1V9rorqZJDlgKGa8sJQhKR0u+w+lVEAoClZvnvx7q2x7P3g4zcfVX3+oPe1YlEVW0GoH5V5KuvAfyASYBqCrbgeNgmcWbLM+sWWT5f+8ngdh5+FUfJJ6XXK9bBE/8HBYRRhdwmMTwBNyJIRhMne09eF/k4be3eBLHPyf6lT3RGPCxNVjqjStc71Zx2ZwtG4Mn8ujEE1nv3N5oNOyNKl3iTaWfOqwCQ6lxJivoPnyiYpghdREp3PCLO9OHVRXauR0xo5JzqFo5XEDUybRYzynC5+55IoQV6NrQoD2pBliQwKez+R7P1UsvcTG3t3ybO0WtiEcGrT/lRXbKNOlW52TfBrG4LpW+Yv/17/ze/r26rPMI1hjPwmH8/y4n/YGlKHMBuHk84S8txIafFzQRChj9Mq+iV1/3fb+arKc8bxpX/4nv/X1PJSNmTZJyZHltsFVfYs506W+X3d2hPjMn89ttJk381/rsobi2O4EB1FLuQ3xTlhm689b++P7diDxmQpLlSoJtVvHGzluKboUXa9i+9Dbm2KRVwgywa/sSZnOUd04VGK/0uW+aP7uitvLruvLx/ryK6t1CBvB+oohCuPJ1tDguc2HqZ2Z3NhHV+tKhrIPqi8u5+jR9pWjqvvMWl2sjwMzcPUlgVPqt+1kw1HDwVXff3fPqMBY25AhzrppEukhTxZNezs85Ak3VdFZkXYf3uPb4mEh+YX1x7TtZRK448zT+pPnRfY1PM3hXnZGMIw3m9KznXJMk9h/M3Cwvmc/I+tfeejb/9JOX55PFXfQUuWYj9Xlq9T515UxEge6RSMushzFt9PdaoDEU+bUNBOSFFVyahppSjnTDPyM4U06TvIC6LueRUJd52TFXsAS/lnQw6zeF+Z8OXxTM27BFnOG+UjwzIiE8Ow9HcpLJkTXFVIU7qXT0nijz9/EHxOz+s2HF2qHMkhTbHoSs5hEonJ5C5/hzZkKRbuiB5vVUGPrXdpDL+ZVHBUxFjlkcgL8Q5G8BDIM9F5KOXiofoEIjeLi/lPeQ7lI57k0CWFfXW5Snn+xd68OhsZk9faOFSTE5qtgk0R4gmfpDJvi8Uz1QZB3sy4bnMgyxmHUKWQZByG+0XxFVs31l8XRWD+K0aKYq+oTa5S9g6ze3z9E1cw2pKXzjO19Vrr3dfBc74hCNbfmf43zc9RdCHyguBXdj9XbQxsyZLmjgiPct1UUW7yqKlQqYq4FWGAIBEX4WyxqV6Y7000BEsejI4cxLaUJnJh6Y+omRN9c3nWU8e9K6UeaPk6HfHS4ypSEQ3HVIjThHxoI1LXC0yrX5fLY9O5j33IGvZJsCDLmZMl866kkB49L3pg5NmJC3l+X2vJUiZD+bGpkKjKa5U9T5XNq6pZ2fN3bl5aEGlWeX50P5tIqXIsi6uPxeuFebhdkj3Mx5N53AbPMidLXUWvkixVRR1yQ/TQIVjjolUDtp5flddSV07LtIFQkZ68+JfClvkirbxO2rzIBUC2RNXHhqdMPvbVu7xn0XTc1cgawMabWmF/VWRp+/8s8EZXZNnhmOaKHWLMFvU8vFpBlvS4iixlD0kuBhI9PWWI0g+fdVl1Wia1LLxa+f6ala82nuXOvKRFYesH9LtEFR51I7JU6UaqTn9vEoJ1NQzL+riWS/9YH4JV52yp/4tyirrF2tTeocrD6TxA8b1aOTQx17r9PVgDu8pDLpN1MfY+Njyip6qzEdUc2lb7IgwLz9JFiDk5W7KsCsOmrwuEJ9/joqi8ySPt6r4mT9WmcKhplW8TshRDsHJ4tpMwrCmXJJOGHLoUC2PSBmrLnJQLBs0VQfLcoNgErfNsyPtKe/3yEKFOoFo+PUL04IvinoL4RM9ORXhFU345VCoSaFoe7ftPKUqgCgVTSb44dvI+oyQ+19XpFOJni2RMVcWqcfDrLIgMBT4gS5fCsOx+pQWXcoRZmHKXLHe8zopQKYUTKUe4vcd/DlZHX3NS0HiOvIDlzs2PumrDED9PDINuNjfe2d7XX8mkI+ZWOydLEkdYXH2cfn7+flulHpNHriTLKqUacRfOCMX3vb/E54vr3W+S52OVil/Iu5ErNnVyWiopLpP3o6p4NVXD7oxDIA+5CKf8f5iqS3yOP9bkEeWxqyqEuwjBiuMUzxslz1w1h+w6m0V9cq0j6LOcf85SuF83m4P3y8pOhcLTKlodFu/PCn5MRThl4fLgRUp+9NjQ+kBVsvQZXYVgxXEWVcDqz2Dvr/LcmpKlMPd/S2v0bZvPy3KvGZGLVbsyyTZzvx07QHYsjCnFVVcRx6WxdzWOKUj9gSyBpuFNzEczEq9DyrrwcBKFn8hrazOvzKGdvKo3coyQ1hhSXG3EA8Yee9tx2Fb3jmaTugrolmTZ1t7bkmVe1FFZKVm1GE0FVHSzf2d/MdT36EM84OxsNOx/I1Wukod0g2jHpmsNxtUDlcc6SFiXbxvaQJp4Vy6Mvek4XPYoecjd0C7U9v5pY+9d5Cx5O5nUXK4mdndOm6gLWQR8SBKb+iZjlE0qCzdb5kXz+f2lzvxOfoLGFjSnasspSnG5MvYpz+Gu5xUkly/7D/oiy7b23hlZlo/EO5F/uzks9lyhRqxWtywGAeaHebjeyKECLuxscyI09aq2DXm3tXcxR9zCcz4hAqGiFvk7WWgX7+qa9nSUVK0xSNqqKhFwWy1RAGTpjEeUtm8wKbSt4dpqvQJAb4tv3jJlIssmxVQGey9VH/LnDPbeNuTOW5S2BMPDlFKjuYV28U7Y1hTO7WNTYzMG3Zm+8C5BltNYkISeRZW6UJXWKwD0AVEm0kiWdbRxO7b3JnKNMvLWn1OTqINIqDLJ7OqaZh6a2Djf6xpiOQajxmmDw5wBkOVg4H2E0okd8s1fpfUKAH0swKJ4BCdLRYO4LWHVtPeXNvbeNoQrikroCLEg1PJrMhnKj+Xwrv0mxV7TtI22qoosbfv4AJDloNBKvEk7W1crdoH5wiSpp7JDm7xhH/beOl+ae2Wp2pOBWFRk2UbXtC+vsukYxKImkCXI0s0FSZKMUwm8m7ReAWAIVInR2+Qt+7D3tvlK2WPWaZGqvE7ee1pT17TzDXcHY0AYFmQ5GbLMtFyXT5f+8ngdh5+RwVdpvQKAC2RpE4ole+cSXDb2zg661dh7nVxplTdVJsVdeTOVCo3Yc1nomsaHJl1Tyo+ycGdnZFlzDLrNDgp8QJbOoqSTSoLtefP3OvQTk9YrfmjAJbLkC7fBGyzpjBb2fiLY+2nJ3jON0Nf6c1mbe5W6op6i/WK30Ie0Q8UNAo1R0jVVKgCRWAV7fh34D7rY8DbVVlXOB1pHQJYAAAxHqkPk1keRYmypceqKHKP6e0FZB2QJAMCgsD1dpQ1RjpW/byMP54rQ/y5RIlcJsgQAYDTC7PpoOx4iHbnQrakn5ppnCY8SwCQAAOAc+shZAgDIEgCA2YEEB1CkB4AsAQAAAABkCQAAAAAgSwAAAACYPf4PUVAFxJBrOrcAAAAASUVORK5CYII=)
(7)
если отбросить член, связанный с генерацией второй гармоники. Энергия взаимодействия этого момента с рассеянной волной равна
![](data:image/png;base64,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)
поле рассеянной волны, мощность же
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAARCAYAAADdRIy+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADHSURBVDjLY2hsbGSgJmYYmgY2RBv7MDAw/MfExndj6+slQWpy3GSLkfkEXVif52Eoy8Dwxji6wQfE7+hI4/GQYdjDIOOxJ68hTwLMNo5aSLSXIa5EdQHMVZH1eaogA2GWEWVglDHDQnQXgMVALqyPVDWWc5+V1tHBQ5SB9fWxksYMDHeRXQBxHcN/kBhI3s0tL4zCSMGMAKINhHkNm5dINhDmXVm3nGKqpENIcpG96ZFXb0gVA7HFLlkGwhIyPBKoFYbDv7QBAPl57oSUtNI3AAAAAElFTkSuQmCC)
рассеянной волны составит
![](data:image/png;base64,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)
(8)
где черта сверху означает усреднение во времени. Выполнив это простое действие, получим выражение
![](data:image/png;base64,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)
(9)
из которого видно, что для стоксовой линии, т. е. для
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
и рассеянная волна усиливается взаимодействием с молекулами, тогда как для антистоксовой линии, т. е. для
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
и рассеянная волна угасает.
Рассеяние Рамана в антистоксову сторону.
При возбуждении спектров Рамана лазерным светом в полости резонатора возникают не только стоксовы линии, но и антистоксовы. Какие условия должны быть выполнены, чтобы произошло такое рассеяние?
Рассмотрим поле Е волны, состоящей из падающей волны с частотой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAYCAYAAAAVibZIAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADzSURBVEjHY2hsbGSgNmYYNXTUUDoYWl8fK2nMwHCXgcH4bmx9vWRDtLEPAwPDfwbjqIVkGQozwDi6wYcYcYKG1ud5GMoyyN70yKs3hBsEdV1HRxqPhwzDHlm3nGKiDUXXhM6HBQlJLkV3JcgQIwaj3aAwRcgbnYLxiTIU7FUZjz1pHR08MEM8IuvtYPJRxgwLkSMqx022GBTG2IIDLSIgsQ1ypYms7HZjt7wUXBbKGkf1QiyT7YX5DmeYgpMO0PDI+jxVOB8tKYFcCQtbkIXoriUrcee5GafAwx7oapiPKDKUJi4lOkxJxeDUQCj2R4s+qmEATwXktif5eKAAAAAASUVORK5CYII=)
и из двух рассеянных волн с частотами
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Амплитуды этих волн обозначим соответственно через
, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAXCAYAAAD+4+QTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVEjH7ZWxDYMwFERvABZAwtkB/R2IC+oUICoiKkTDAIaOGdJRZgdWYQN2SASJg4UMKMEpkCiucfN07x8CZVni38EB2Qck9VgO4DEXCgvfSJMiJB9gHc+EK9+qKrE4Y3f1bRNkaOPwJqkqS33PPO8SCWEbgQSEmnlp/mnAw9joTYSIbAJa6b5XJ4HGIK97bDv2KqRXBQpqqep8otu3d1iETFX1CTmPpwPYBNFNd1wWXefmO4zDQQNQO22tV6WZ7tykpyCd2lFTxl0GdEtf+trCViEmYgwyuldavjXuq8lShtEozY4/4095At0AS9ZAPVmTAAAAAElFTkSuQmCC)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAXCAYAAADpwXTaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADdSURBVDjLY2hsbGSgFmYYNYw6huW4yRYzMDD8x4WNoxt8SHJZQ7SxDwOD7BuPvHpDmFhHRxqPh6zsSmQxogwDu07GY09aRwcPsniem1tYbH29JEmGRRkzLJR1yymGu8gjOpmsMKuvj5U0ZmC4CwsbkJdhBpNsGCS8iAt0goaBvMhgHLUQ5kV3OeNZuMIJr2HoXgThaA+PZPSIIMowbEkCEZPGKSBxcITIMOxhYDC+i+xi7F7EkiTQkwo27yO8l+dhKMvA8AZfykeOUbyGkYpHiGHgiAKFJVKkjJCSFgClh319MtmaXgAAAABJRU5ErkJggg==)
, используя одинаковые индексы для волновых векторов и фаз. Случайное поле может быть описано выражением
![](data:image/png;base64,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)
(10)
Решая уравнение (2) с учетом выражений (4) для силы и (10) для поля волны, получаем
![](data:image/png;base64,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)
(11)
Мощности
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAXCAYAAADgKtSgAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADKSURBVEjHY2hsbGSgFWYYNXxwGN4QbezDwMDwHxMb342tr5ek2OX1eR6GsgwMb4yjG3xA/I6ONB4PGYY9DDIee9I6OngoMhzielSX5rjJFpPiepwSUcYMCxmMoxZiiFHq8vr6WEljBoa7sCBBuJrhP7IYFSOUtMjEaTip3ifacFiQyLrlFFM9nUOSoOxNj7x6Q2IMgCdRLMFGVCohxgJ3OeNZOA2HZRp4BJIQ5gQNpwRTbDgibJGSJ9R3g9vl+DA4EWCJp9GaCCsGAIfCCMbBoPCoAAAAAElFTkSuQmCC)
и
, отдаваемые молекулой двум рассеянным волнам—стоксовой и антистоксовой—вычислим так же, как и раньше:
![](data:image/png;base64,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)
(12)
![](data:image/png;base64,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)
(13)
Из выражения (12) видно, что в нормальных условиях опыта
![](data:image/png;base64,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)
всегда
![](data:image/png;base64,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)
, без дополнительных условий, связывающих волновые векторы. Это означает, что стоксово рассеяние не имеет ограничений по направ-