{"title":"声光行波调制器固态激光器中QML激光的产生机理","authors":"O. Nanii, A. Fedoseev, A. Odintsov, A. Smirnov","doi":"10.1109/PIERS.2017.8261772","DOIUrl":null,"url":null,"abstract":"Lasing which simultaneously combines Q-switch and mode locking (QML lasing) is of interest as it demonstrated high peak intensity of the pulse sequence. Recently a new method was offered and demonstrated experimentally for achieving QML lasing using only a single acousto-optic modulator (AOM) with travelling wave in combination with a spherical mirror of a cavity [1,2]. In this report we present for the first time theoretical description of QML lasing in solid-state lasers with travelling wave AOM. Traditionally travelling wave AOM is used to modulate the Q-factor and forced the laser to operate in Q-switch regime. The same AOM can be used for simultaneous mode-locking by returning twice diffracted beam into the cavity. In this case the frequency of the light beam, injected into the cavity is shifted in a frequency by a value equal to double frequency of the acoustic wave. If an intermode interval δv<inf>c</inf> = vj<inf>+1</inf> — vj is equal to double frequency of the acoustic wave a part of the field of j mode will be injected into following (j + 1) mode. In our model the dynamics of lasing is described by a set of balance equations for complex amplitudes Ej and phases φj. The simulations were performed for a set of numerical parameters, which specifies Nd:YAG lasing at the significant excess of the gain over the threshold. The value of I<inf>d</inf> were varied in the range from 10<sup>∼2</sup> to 10<sup>∼3</sup>. We assumes that the gain line is broadened uniformly in frequency and in a space. Field damping increment is consisted of two parts: γ = γ<inf>ph</inf> + γ<inf>d</inf>. First one γ<inf>ph</inf> is associated with permanent losses of resonator and the second Y<inf>d</inf> varies with the AOM characteristics variations: γ<inf>d</inf> = −2 ln(1 − κ<inf>d</inf>)δv<inf>C</inf>. Here κ<inf>d</inf> is diffractive coupling coefficient, which shows the rate of the injection defined as £ = I<inf>d</inf> δ5v<inf>c</inf>. The injection of the field into the following mode predetermines the regime of each mode. Only fundamental mode (j = 0) operates at saturated inversion, the rest operate in the regenerative amplification regime. The injection process forms the distribution of Ej in frequency. The distribution has a characteristic maximum. The position of the maximum is determined by I<inf>d</inf> value and does not depend on time. The main contribution into the average intensity Ī = Σ<inf>j</inf> E<sup>2</sup><inf>j</inf> gives a relatively small number of modes, located near the maximum of E<sup>2</sup><inf>j</inf>(j) distribution. Under these conditions, the interference of coherent optical fields results in a complex structure of each pulse of mode locking. Changing γ<inf>d</inf> leads to noticeable changes in Ī and the inversion. In this way a variation of the κ<inf>d</inf> value forms the mechanism of Q factor changing. Periodic alteration of the K<inf>d</inf> value provides periodic Q-switch regime of the laser.","PeriodicalId":387984,"journal":{"name":"2017 Progress In Electromagnetics Research Symposium - Spring (PIERS)","volume":"187 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A mechanism of QML lasing in solid-state laser with an acousto-optic travelling wave modulator\",\"authors\":\"O. Nanii, A. Fedoseev, A. Odintsov, A. Smirnov\",\"doi\":\"10.1109/PIERS.2017.8261772\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Lasing which simultaneously combines Q-switch and mode locking (QML lasing) is of interest as it demonstrated high peak intensity of the pulse sequence. Recently a new method was offered and demonstrated experimentally for achieving QML lasing using only a single acousto-optic modulator (AOM) with travelling wave in combination with a spherical mirror of a cavity [1,2]. In this report we present for the first time theoretical description of QML lasing in solid-state lasers with travelling wave AOM. Traditionally travelling wave AOM is used to modulate the Q-factor and forced the laser to operate in Q-switch regime. The same AOM can be used for simultaneous mode-locking by returning twice diffracted beam into the cavity. In this case the frequency of the light beam, injected into the cavity is shifted in a frequency by a value equal to double frequency of the acoustic wave. If an intermode interval δv<inf>c</inf> = vj<inf>+1</inf> — vj is equal to double frequency of the acoustic wave a part of the field of j mode will be injected into following (j + 1) mode. In our model the dynamics of lasing is described by a set of balance equations for complex amplitudes Ej and phases φj. The simulations were performed for a set of numerical parameters, which specifies Nd:YAG lasing at the significant excess of the gain over the threshold. The value of I<inf>d</inf> were varied in the range from 10<sup>∼2</sup> to 10<sup>∼3</sup>. We assumes that the gain line is broadened uniformly in frequency and in a space. Field damping increment is consisted of two parts: γ = γ<inf>ph</inf> + γ<inf>d</inf>. First one γ<inf>ph</inf> is associated with permanent losses of resonator and the second Y<inf>d</inf> varies with the AOM characteristics variations: γ<inf>d</inf> = −2 ln(1 − κ<inf>d</inf>)δv<inf>C</inf>. Here κ<inf>d</inf> is diffractive coupling coefficient, which shows the rate of the injection defined as £ = I<inf>d</inf> δ5v<inf>c</inf>. The injection of the field into the following mode predetermines the regime of each mode. Only fundamental mode (j = 0) operates at saturated inversion, the rest operate in the regenerative amplification regime. The injection process forms the distribution of Ej in frequency. The distribution has a characteristic maximum. The position of the maximum is determined by I<inf>d</inf> value and does not depend on time. The main contribution into the average intensity Ī = Σ<inf>j</inf> E<sup>2</sup><inf>j</inf> gives a relatively small number of modes, located near the maximum of E<sup>2</sup><inf>j</inf>(j) distribution. Under these conditions, the interference of coherent optical fields results in a complex structure of each pulse of mode locking. Changing γ<inf>d</inf> leads to noticeable changes in Ī and the inversion. In this way a variation of the κ<inf>d</inf> value forms the mechanism of Q factor changing. Periodic alteration of the K<inf>d</inf> value provides periodic Q-switch regime of the laser.\",\"PeriodicalId\":387984,\"journal\":{\"name\":\"2017 Progress In Electromagnetics Research Symposium - Spring (PIERS)\",\"volume\":\"187 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 Progress In Electromagnetics Research Symposium - Spring (PIERS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/PIERS.2017.8261772\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 Progress In Electromagnetics Research Symposium - Spring (PIERS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PIERS.2017.8261772","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A mechanism of QML lasing in solid-state laser with an acousto-optic travelling wave modulator
Lasing which simultaneously combines Q-switch and mode locking (QML lasing) is of interest as it demonstrated high peak intensity of the pulse sequence. Recently a new method was offered and demonstrated experimentally for achieving QML lasing using only a single acousto-optic modulator (AOM) with travelling wave in combination with a spherical mirror of a cavity [1,2]. In this report we present for the first time theoretical description of QML lasing in solid-state lasers with travelling wave AOM. Traditionally travelling wave AOM is used to modulate the Q-factor and forced the laser to operate in Q-switch regime. The same AOM can be used for simultaneous mode-locking by returning twice diffracted beam into the cavity. In this case the frequency of the light beam, injected into the cavity is shifted in a frequency by a value equal to double frequency of the acoustic wave. If an intermode interval δvc = vj+1 — vj is equal to double frequency of the acoustic wave a part of the field of j mode will be injected into following (j + 1) mode. In our model the dynamics of lasing is described by a set of balance equations for complex amplitudes Ej and phases φj. The simulations were performed for a set of numerical parameters, which specifies Nd:YAG lasing at the significant excess of the gain over the threshold. The value of Id were varied in the range from 10∼2 to 10∼3. We assumes that the gain line is broadened uniformly in frequency and in a space. Field damping increment is consisted of two parts: γ = γph + γd. First one γph is associated with permanent losses of resonator and the second Yd varies with the AOM characteristics variations: γd = −2 ln(1 − κd)δvC. Here κd is diffractive coupling coefficient, which shows the rate of the injection defined as £ = Id δ5vc. The injection of the field into the following mode predetermines the regime of each mode. Only fundamental mode (j = 0) operates at saturated inversion, the rest operate in the regenerative amplification regime. The injection process forms the distribution of Ej in frequency. The distribution has a characteristic maximum. The position of the maximum is determined by Id value and does not depend on time. The main contribution into the average intensity Ī = Σj E2j gives a relatively small number of modes, located near the maximum of E2j(j) distribution. Under these conditions, the interference of coherent optical fields results in a complex structure of each pulse of mode locking. Changing γd leads to noticeable changes in Ī and the inversion. In this way a variation of the κd value forms the mechanism of Q factor changing. Periodic alteration of the Kd value provides periodic Q-switch regime of the laser.