TY - JOUR

T1 - Mode locking theory of the Nyquist laser

AU - Nakazawa, Masataka

AU - Hirooka, Toshihiko

N1 - Funding Information:
This work was supported by the JSPS Grant-in-Aid for Specially Promoted Research (26000009). We especially thank to Prof. Erich Ippen of MIT for fruitful discussions and valuable comments regarding our research of the Nyquist laser and Nyquist pulse transmission

PY - 2016/3/7

Y1 - 2016/3/7

N2 - We derive a master equation for a mode-locked Nyquist laser that can emit a sinc function pulse. To derive the master equation, we used a method involving exponential perturbative expressions for gain, loss, and amplitude modulation, and a flat-top optical filter with edge enhancement. The master equation is expressed as an integral equation, where a rectangular-like optical filter with edge enhancement plays an important role in generating a sinc function pulse with a flat-top spectral profile. It is important to note that the sinc function solution satisfies the spherical wave propagation of the Maxwell equation in the polar axis and is also the lowest order solution of the spherical Bessel equation. A differential equation was introduced as an operator into the master equation, which is different from the substitution of an assumed sinc function solution into the master equation, and we directly derived a sinc function solution. The time-independent Schrödinger equation approach in the spectral domain also proved that there is a sinc-like solution under a dual flat potential well.

AB - We derive a master equation for a mode-locked Nyquist laser that can emit a sinc function pulse. To derive the master equation, we used a method involving exponential perturbative expressions for gain, loss, and amplitude modulation, and a flat-top optical filter with edge enhancement. The master equation is expressed as an integral equation, where a rectangular-like optical filter with edge enhancement plays an important role in generating a sinc function pulse with a flat-top spectral profile. It is important to note that the sinc function solution satisfies the spherical wave propagation of the Maxwell equation in the polar axis and is also the lowest order solution of the spherical Bessel equation. A differential equation was introduced as an operator into the master equation, which is different from the substitution of an assumed sinc function solution into the master equation, and we directly derived a sinc function solution. The time-independent Schrödinger equation approach in the spectral domain also proved that there is a sinc-like solution under a dual flat potential well.

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U2 - 10.1364/OE.24.004981

DO - 10.1364/OE.24.004981

M3 - Article

AN - SCOPUS:84962166697

VL - 24

SP - 4981

EP - 4995

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 5

ER -