TY - JOUR

T1 - A generalized mode-locking theory for a Nyquist laser with an arbitrary roll-off factor Part I

T2 - Master equations and optical filters in a Nyquist laser

AU - Nakazawa, Masataka

AU - Hirooka, Toshihiko

N1 - Funding Information:
Manuscript received August 3, 2020; revised February 3, 2021; accepted March 9, 2021. Date of publication March 15, 2021; date of current version April 2, 2021. This work was supported by a JSPS Grant-in-Aid for Specially Promoted Research under Grant 26000009. (Corresponding author: Masataka Nakazawa.) The authors are with the Research Organization of Electrical Communication, Tohoku University, Sendai 980-8577, Japan (e-mail: nakazawa@riec.tohoku.ac.jp).
Publisher Copyright:
0018-9197 © 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

PY - 2021/6

Y1 - 2021/6

N2 - In this paper (PART I), we describe master equations and specific optical filters designed to generate a periodic Nyquist pulse train with an arbitrary roll-off factor α that can be emitted from a mode-locked Nyquist laser. In the first part, we derive a perturbative master equation for a Nyquist pulse laser with a “single” α ≠ 0 Nyquist pulse, where we obtain a new filter function F(ω) that determines filter shapes at both low and high frequency edges. A second-order differential equation that satisfies a periodic Nyquist pulse train with α ≠ 0 is derived and utilized for the direct derivation of a single Nyquist pulse solution in the time domain for a mode-locked Nyquist laser. Then, by employing the concept of Nyquist potential, we describe the differences between the spectral profiles and filter shapes of a Nyquist pulse when α ≠ 0 and α ≠ 0. In the latter part, we describe a non-perturbative master equation that provides the solution to a “periodic” Nyquist pulse train with an arbitrary roll-off factor. We show first that the spectral profile of an α ≠ 0 periodic Nyquist pulse train, which consists of periodic δ functions, has a different envelope shape from that of a single α ≠ 0 Nyquist pulse. This is because a periodic α ≠ 0 pulse train consists of two independent periodic functions, which give rise to a different spectral envelope. Then, by Fourier transforming the master equation, we derive new filters consisting of F1(ω) at a low frequency edge and F2(ω) at a high frequency edge to allow us to generate arbitrary Nyquist pulses.

AB - In this paper (PART I), we describe master equations and specific optical filters designed to generate a periodic Nyquist pulse train with an arbitrary roll-off factor α that can be emitted from a mode-locked Nyquist laser. In the first part, we derive a perturbative master equation for a Nyquist pulse laser with a “single” α ≠ 0 Nyquist pulse, where we obtain a new filter function F(ω) that determines filter shapes at both low and high frequency edges. A second-order differential equation that satisfies a periodic Nyquist pulse train with α ≠ 0 is derived and utilized for the direct derivation of a single Nyquist pulse solution in the time domain for a mode-locked Nyquist laser. Then, by employing the concept of Nyquist potential, we describe the differences between the spectral profiles and filter shapes of a Nyquist pulse when α ≠ 0 and α ≠ 0. In the latter part, we describe a non-perturbative master equation that provides the solution to a “periodic” Nyquist pulse train with an arbitrary roll-off factor. We show first that the spectral profile of an α ≠ 0 periodic Nyquist pulse train, which consists of periodic δ functions, has a different envelope shape from that of a single α ≠ 0 Nyquist pulse. This is because a periodic α ≠ 0 pulse train consists of two independent periodic functions, which give rise to a different spectral envelope. Then, by Fourier transforming the master equation, we derive new filters consisting of F1(ω) at a low frequency edge and F2(ω) at a high frequency edge to allow us to generate arbitrary Nyquist pulses.

KW - Fourier analysis

KW - Mode-locked laser

KW - Nyquist pulse train

KW - Roll-off factor

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U2 - 10.1109/JQE.2021.3065960

DO - 10.1109/JQE.2021.3065960

M3 - Article

AN - SCOPUS:85103018348

SN - 0018-9197

VL - 57

JO - IEEE Journal of Quantum Electronics

JF - IEEE Journal of Quantum Electronics

IS - 3

M1 - 09378560

ER -