{"title":"调频锁模激光器产生高阶厄米高斯脉冲的实验","authors":"Masataka Nakazawa;Masato Yoshida;Toshihiko Hirooka","doi":"10.1109/JQE.2023.3305121","DOIUrl":null,"url":null,"abstract":"We experimentally generated higher-order Hermite-Gaussian (HG) pulses from an FM mode-locked laser that had a specific optical filter \n<inline-formula> <tex-math>$F_{HG{\\mathrm {m}}}(\\omega)$ </tex-math></inline-formula>\n characterized by a Bessel function \n<inline-formula> <tex-math>$J_{n}\\mathit {(M_{PM}})$ </tex-math></inline-formula>\n and \n<inline-formula> <tex-math>$A_{HG{\\mathrm {m}}}(\\omega)$ </tex-math></inline-formula>\n and \n<inline-formula> <tex-math>$A_{HG\\mathrm {m}}(\\omega +n\\Omega _{m})$ </tex-math></inline-formula>\n with n = \n<inline-formula> <tex-math>$- \\infty \\sim $ </tex-math></inline-formula>\n+ \n<inline-formula> <tex-math>$\\infty $ </tex-math></inline-formula>\n. Here, \n<inline-formula> <tex-math>$M_{PM}$ </tex-math></inline-formula>\n is the phase-modulation index and \n<inline-formula> <tex-math>$A_{HG\\mathrm {m}}(\\omega)$ </tex-math></inline-formula>\n was the Fourier transformed spectrum of the \n<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\nth HG pulse \n<inline-formula> <tex-math>$a_{HG\\mathrm {m}}(t)$ </tex-math></inline-formula>\n in the time domain and \n<inline-formula> <tex-math>$\\Omega _{m}$ </tex-math></inline-formula>\n was the fixed angular phase-modulation frequency. The laser we constructed was a 10 GHz polarization-maintained FM mode-locked erbium fiber laser emitting at a wavelength of \n<inline-formula> <tex-math>$1.56 \\mu \\text{m}$ </tex-math></inline-formula>\n, which included a liquid crystal on silicon (LCoS) optical device to implement the specific filter function needed to generate HG pulses. We successfully generated \n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\n= 0 \n<inline-formula> <tex-math>$\\sim $ </tex-math></inline-formula>\n 7th HG pulses with pulse widths of 10\n<inline-formula> <tex-math>$\\sim $ </tex-math></inline-formula>\n50 ps. For the generation of \n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\n = 1, 3, 5,...odd-numbered HG waveforms, the corresponding \n<inline-formula> <tex-math>$F_{HG\\mathrm {m}}(\\omega)$ </tex-math></inline-formula>\n has no center frequency mode. Since these waveforms are odd functions in the time domain, their spectral profiles are given entirely by imaginary components with the same shape as those in the time domain. For the generation of \n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\n = 0, 2, 4,...even-numbered HG waveforms, the corresponding \n<inline-formula> <tex-math>$F_{HG\\mathrm {m}}(\\omega)$ </tex-math></inline-formula>\n has a center frequency component. Since these waveforms are even functions in the time domain, their spectral profiles are given entirely by real-value components with the same shape as those in the time domain. Finally, we generated \n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\n= 1 \n<inline-formula> <tex-math>$\\sim $ </tex-math></inline-formula>\n 3 dark and bright higher-order HG pulses by introducing a CW amplitude offset. To generate these pulses, a new bandwidth-limiting filter was installed since these pulses have a rectangular pulse component, which creates many high-frequency sidebands.","PeriodicalId":13200,"journal":{"name":"IEEE Journal of Quantum Electronics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Experiments on the Generation of Higher-Order Hermite-Gaussian Pulses From an FM Mode-Locked Laser\",\"authors\":\"Masataka Nakazawa;Masato Yoshida;Toshihiko Hirooka\",\"doi\":\"10.1109/JQE.2023.3305121\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We experimentally generated higher-order Hermite-Gaussian (HG) pulses from an FM mode-locked laser that had a specific optical filter \\n<inline-formula> <tex-math>$F_{HG{\\\\mathrm {m}}}(\\\\omega)$ </tex-math></inline-formula>\\n characterized by a Bessel function \\n<inline-formula> <tex-math>$J_{n}\\\\mathit {(M_{PM}})$ </tex-math></inline-formula>\\n and \\n<inline-formula> <tex-math>$A_{HG{\\\\mathrm {m}}}(\\\\omega)$ </tex-math></inline-formula>\\n and \\n<inline-formula> <tex-math>$A_{HG\\\\mathrm {m}}(\\\\omega +n\\\\Omega _{m})$ </tex-math></inline-formula>\\n with n = \\n<inline-formula> <tex-math>$- \\\\infty \\\\sim $ </tex-math></inline-formula>\\n+ \\n<inline-formula> <tex-math>$\\\\infty $ </tex-math></inline-formula>\\n. Here, \\n<inline-formula> <tex-math>$M_{PM}$ </tex-math></inline-formula>\\n is the phase-modulation index and \\n<inline-formula> <tex-math>$A_{HG\\\\mathrm {m}}(\\\\omega)$ </tex-math></inline-formula>\\n was the Fourier transformed spectrum of the \\n<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\\nth HG pulse \\n<inline-formula> <tex-math>$a_{HG\\\\mathrm {m}}(t)$ </tex-math></inline-formula>\\n in the time domain and \\n<inline-formula> <tex-math>$\\\\Omega _{m}$ </tex-math></inline-formula>\\n was the fixed angular phase-modulation frequency. The laser we constructed was a 10 GHz polarization-maintained FM mode-locked erbium fiber laser emitting at a wavelength of \\n<inline-formula> <tex-math>$1.56 \\\\mu \\\\text{m}$ </tex-math></inline-formula>\\n, which included a liquid crystal on silicon (LCoS) optical device to implement the specific filter function needed to generate HG pulses. We successfully generated \\n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\\n= 0 \\n<inline-formula> <tex-math>$\\\\sim $ </tex-math></inline-formula>\\n 7th HG pulses with pulse widths of 10\\n<inline-formula> <tex-math>$\\\\sim $ </tex-math></inline-formula>\\n50 ps. For the generation of \\n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\\n = 1, 3, 5,...odd-numbered HG waveforms, the corresponding \\n<inline-formula> <tex-math>$F_{HG\\\\mathrm {m}}(\\\\omega)$ </tex-math></inline-formula>\\n has no center frequency mode. Since these waveforms are odd functions in the time domain, their spectral profiles are given entirely by imaginary components with the same shape as those in the time domain. For the generation of \\n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\\n = 0, 2, 4,...even-numbered HG waveforms, the corresponding \\n<inline-formula> <tex-math>$F_{HG\\\\mathrm {m}}(\\\\omega)$ </tex-math></inline-formula>\\n has a center frequency component. Since these waveforms are even functions in the time domain, their spectral profiles are given entirely by real-value components with the same shape as those in the time domain. Finally, we generated \\n<inline-formula> <tex-math>${m}$ </tex-math></inline-formula>\\n= 1 \\n<inline-formula> <tex-math>$\\\\sim $ </tex-math></inline-formula>\\n 3 dark and bright higher-order HG pulses by introducing a CW amplitude offset. To generate these pulses, a new bandwidth-limiting filter was installed since these pulses have a rectangular pulse component, which creates many high-frequency sidebands.\",\"PeriodicalId\":13200,\"journal\":{\"name\":\"IEEE Journal of Quantum Electronics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Journal of Quantum Electronics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10216956/\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Journal of Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10216956/","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Experiments on the Generation of Higher-Order Hermite-Gaussian Pulses From an FM Mode-Locked Laser
We experimentally generated higher-order Hermite-Gaussian (HG) pulses from an FM mode-locked laser that had a specific optical filter
$F_{HG{\mathrm {m}}}(\omega)$
characterized by a Bessel function
$J_{n}\mathit {(M_{PM}})$
and
$A_{HG{\mathrm {m}}}(\omega)$
and
$A_{HG\mathrm {m}}(\omega +n\Omega _{m})$
with n =
$- \infty \sim $
+
$\infty $
. Here,
$M_{PM}$
is the phase-modulation index and
$A_{HG\mathrm {m}}(\omega)$
was the Fourier transformed spectrum of the
$m$
th HG pulse
$a_{HG\mathrm {m}}(t)$
in the time domain and
$\Omega _{m}$
was the fixed angular phase-modulation frequency. The laser we constructed was a 10 GHz polarization-maintained FM mode-locked erbium fiber laser emitting at a wavelength of
$1.56 \mu \text{m}$
, which included a liquid crystal on silicon (LCoS) optical device to implement the specific filter function needed to generate HG pulses. We successfully generated
${m}$
= 0
$\sim $
7th HG pulses with pulse widths of 10
$\sim $
50 ps. For the generation of
${m}$
= 1, 3, 5,...odd-numbered HG waveforms, the corresponding
$F_{HG\mathrm {m}}(\omega)$
has no center frequency mode. Since these waveforms are odd functions in the time domain, their spectral profiles are given entirely by imaginary components with the same shape as those in the time domain. For the generation of
${m}$
= 0, 2, 4,...even-numbered HG waveforms, the corresponding
$F_{HG\mathrm {m}}(\omega)$
has a center frequency component. Since these waveforms are even functions in the time domain, their spectral profiles are given entirely by real-value components with the same shape as those in the time domain. Finally, we generated
${m}$
= 1
$\sim $
3 dark and bright higher-order HG pulses by introducing a CW amplitude offset. To generate these pulses, a new bandwidth-limiting filter was installed since these pulses have a rectangular pulse component, which creates many high-frequency sidebands.
期刊介绍:
The IEEE Journal of Quantum Electronics is dedicated to the publication of manuscripts reporting novel experimental or theoretical results in the broad field of the science and technology of quantum electronics. The Journal comprises original contributions, both regular papers and letters, describing significant advances in the understanding of quantum electronics phenomena or the demonstration of new devices, systems, or applications. Manuscripts reporting new developments in systems and applications must emphasize quantum electronics principles or devices. The scope of JQE encompasses the generation, propagation, detection, and application of coherent electromagnetic radiation having wavelengths below one millimeter (i.e., in the submillimeter, infrared, visible, ultraviolet, etc., regions). Whether the focus of a manuscript is a quantum-electronic device or phenomenon, the critical factor in the editorial review of a manuscript is the potential impact of the results presented on continuing research in the field or on advancing the technological base of quantum electronics.