{"title":"利用时间分数塔尔博特效应产生脉冲并倍增其重复率","authors":"Rustem Shakhmuratov","doi":"10.1088/1555-6611/ad6d4f","DOIUrl":null,"url":null,"abstract":"The generation of pulses from a periodic phase-modulated continuous wave (CW) laser field, which is transmitted through a group-delay-dispersion (GDD) circuit, is considered. A time lens (TL), consisting of a quadratic phase modulator and a GDD circuit is proposed in combination with temporal array illuminators (TAI) using another GDD circuit. The time lens producing field compression into pulses is realized for a particular value of the normalized fractional Talbot length (NFTL) <inline-formula>\n<tex-math><?CDATA $L/L_{T} = P_{1}/Q_{1}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>L</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn1.gif\"></inline-graphic></inline-formula>, where <italic toggle=\"yes\">L</italic> is the physical length of the GDD circuit, <italic toggle=\"yes\">L</italic><sub><italic toggle=\"yes\">T</italic></sub> is the Talbot length, <inline-formula>\n<tex-math><?CDATA $P_{1} = 1$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn2.gif\"></inline-graphic></inline-formula>, and <italic toggle=\"yes\">Q</italic><sub>1</sub> is an integer. The length of the GDD circuit is selected to convert a given parabolic phase-modulated CW laser field into short pulses repeated with a phase modulation period <italic toggle=\"yes\">T</italic> in accordance with the chirp radar concept. If NFTL is increased by <inline-formula>\n<tex-math><?CDATA $1/Q_{2}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn3.gif\"></inline-graphic></inline-formula>, where <inline-formula>\n<tex-math><?CDATA $Q_{2} = 4$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn4.gif\"></inline-graphic></inline-formula>, 6, or 8, the pulse sequence period is shortened as <inline-formula>\n<tex-math><?CDATA $T/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn5.gif\"></inline-graphic></inline-formula>, <inline-formula>\n<tex-math><?CDATA $T/3$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn6.gif\"></inline-graphic></inline-formula>, and <inline-formula>\n<tex-math><?CDATA $T/4$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn7.gif\"></inline-graphic></inline-formula>, respectively. This is because the additional GDD circuit with NFTL <inline-formula>\n<tex-math><?CDATA $1/Q_{2}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn8.gif\"></inline-graphic></inline-formula>, performs repetition rate multiplication of the initially prepared pulse sequence as TAI does. The maximum multiplication number considered in this paper is 12, which makes it possible to reduce the time interval between pulses by a factor of 12 and obtain a repetition rate 120 GHZ of picosecond pulses generated by phase modulation with frequency <inline-formula>\n<tex-math><?CDATA $f = 1/T = 10$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"lpad6d4fieqn9.gif\"></inline-graphic></inline-formula> GHz. The proposed method of pulse sequence generation with a discretely tunable period provides a new tool for optical signal processing in optical communication.","PeriodicalId":17976,"journal":{"name":"Laser Physics","volume":"69 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generation of pulses and multiplying their repetition rate using the temporal fractional Talbot effect\",\"authors\":\"Rustem Shakhmuratov\",\"doi\":\"10.1088/1555-6611/ad6d4f\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The generation of pulses from a periodic phase-modulated continuous wave (CW) laser field, which is transmitted through a group-delay-dispersion (GDD) circuit, is considered. A time lens (TL), consisting of a quadratic phase modulator and a GDD circuit is proposed in combination with temporal array illuminators (TAI) using another GDD circuit. The time lens producing field compression into pulses is realized for a particular value of the normalized fractional Talbot length (NFTL) <inline-formula>\\n<tex-math><?CDATA $L/L_{T} = P_{1}/Q_{1}$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>L</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn1.gif\\\"></inline-graphic></inline-formula>, where <italic toggle=\\\"yes\\\">L</italic> is the physical length of the GDD circuit, <italic toggle=\\\"yes\\\">L</italic><sub><italic toggle=\\\"yes\\\">T</italic></sub> is the Talbot length, <inline-formula>\\n<tex-math><?CDATA $P_{1} = 1$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn2.gif\\\"></inline-graphic></inline-formula>, and <italic toggle=\\\"yes\\\">Q</italic><sub>1</sub> is an integer. The length of the GDD circuit is selected to convert a given parabolic phase-modulated CW laser field into short pulses repeated with a phase modulation period <italic toggle=\\\"yes\\\">T</italic> in accordance with the chirp radar concept. If NFTL is increased by <inline-formula>\\n<tex-math><?CDATA $1/Q_{2}$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn3.gif\\\"></inline-graphic></inline-formula>, where <inline-formula>\\n<tex-math><?CDATA $Q_{2} = 4$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn4.gif\\\"></inline-graphic></inline-formula>, 6, or 8, the pulse sequence period is shortened as <inline-formula>\\n<tex-math><?CDATA $T/2$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn5.gif\\\"></inline-graphic></inline-formula>, <inline-formula>\\n<tex-math><?CDATA $T/3$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn6.gif\\\"></inline-graphic></inline-formula>, and <inline-formula>\\n<tex-math><?CDATA $T/4$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn7.gif\\\"></inline-graphic></inline-formula>, respectively. This is because the additional GDD circuit with NFTL <inline-formula>\\n<tex-math><?CDATA $1/Q_{2}$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn8.gif\\\"></inline-graphic></inline-formula>, performs repetition rate multiplication of the initially prepared pulse sequence as TAI does. The maximum multiplication number considered in this paper is 12, which makes it possible to reduce the time interval between pulses by a factor of 12 and obtain a repetition rate 120 GHZ of picosecond pulses generated by phase modulation with frequency <inline-formula>\\n<tex-math><?CDATA $f = 1/T = 10$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"lpad6d4fieqn9.gif\\\"></inline-graphic></inline-formula> GHz. The proposed method of pulse sequence generation with a discretely tunable period provides a new tool for optical signal processing in optical communication.\",\"PeriodicalId\":17976,\"journal\":{\"name\":\"Laser Physics\",\"volume\":\"69 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Laser Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1555-6611/ad6d4f\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Laser Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1555-6611/ad6d4f","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPTICS","Score":null,"Total":0}
Generation of pulses and multiplying their repetition rate using the temporal fractional Talbot effect
The generation of pulses from a periodic phase-modulated continuous wave (CW) laser field, which is transmitted through a group-delay-dispersion (GDD) circuit, is considered. A time lens (TL), consisting of a quadratic phase modulator and a GDD circuit is proposed in combination with temporal array illuminators (TAI) using another GDD circuit. The time lens producing field compression into pulses is realized for a particular value of the normalized fractional Talbot length (NFTL) L/LT=P1/Q1, where L is the physical length of the GDD circuit, LT is the Talbot length, P1=1, and Q1 is an integer. The length of the GDD circuit is selected to convert a given parabolic phase-modulated CW laser field into short pulses repeated with a phase modulation period T in accordance with the chirp radar concept. If NFTL is increased by 1/Q2, where Q2=4, 6, or 8, the pulse sequence period is shortened as T/2, T/3, and T/4, respectively. This is because the additional GDD circuit with NFTL 1/Q2, performs repetition rate multiplication of the initially prepared pulse sequence as TAI does. The maximum multiplication number considered in this paper is 12, which makes it possible to reduce the time interval between pulses by a factor of 12 and obtain a repetition rate 120 GHZ of picosecond pulses generated by phase modulation with frequency f=1/T=10 GHz. The proposed method of pulse sequence generation with a discretely tunable period provides a new tool for optical signal processing in optical communication.
期刊介绍:
Laser Physics offers a comprehensive view of theoretical and experimental laser research and applications. Articles cover every aspect of modern laser physics and quantum electronics, emphasizing physical effects in various media (solid, gaseous, liquid) leading to the generation of laser radiation; peculiarities of propagation of laser radiation; problems involving impact of laser radiation on various substances and the emerging physical effects, including coherent ones; the applied use of lasers and laser spectroscopy; the processing and storage of information; and more.
The full list of subject areas covered is as follows:
-physics of lasers-
fibre optics and fibre lasers-
quantum optics and quantum information science-
ultrafast optics and strong-field physics-
nonlinear optics-
physics of cold trapped atoms-
laser methods in chemistry, biology, medicine and ecology-
laser spectroscopy-
novel laser materials and lasers-
optics of nanomaterials-
interaction of laser radiation with matter-
laser interaction with solids-
photonics