PT对称光纤激光器的双稳态与动态特性

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本文探讨了"双稳态激光在帕里-蒂（Parity-Time, PT）对称耦合光纤环中的行为"。帕里-蒂对称性是一种非线性光学现象，它在光子晶体和量子系统中引起了广泛兴趣，尤其是在平衡和失衡状态下实现非线性光学现象的新途径。在这个研究中，作者提出了一种特殊的光纤激光器设计，它由两个相互连接的环形腔组成，这两个腔体分别包含增益和损耗，从而形成PT对称结构。激光器的工作模式取决于静态相移，能够在PT对称（即平衡）和对称破缺（即失衡）两种状态之间切换。在PT对称状态下，通过采用转移矩阵方法进行理论分析，并考虑了增益饱和的影响，研究人员预测了一个显著的特性：激光表现出双稳态行为。这意味着激光器可以在两个稳定的输出功率水平间切换，这种现象与传统的单模稳定运行形成了鲜明对比。相反，在PT对称被打破的阶段，一个反直觉的现象发生了：随着腔体损失的增加，激光器的生成功率反而会增强。这种非传统的增长关系揭示了PT对称光纤激光器中复杂且有趣的动态行为，挑战了传统激光动力学的理解。此外，该研究还涉及到实验技术，如数值模拟，这些工具对于理解这种新型激光器的物理机制至关重要。论文的作者来自诺夫哥罗德国立大学和澳大利亚国立大学的非线性物理中心，Sergey V. Smirnov作为通讯作者，他的电子邮件地址为smirnov@lab.nsu.ru。这项工作不仅推动了对PT对称系统在光子学领域的理解，而且可能为设计新型高性能、多功能的激光器提供了新的可能性，比如用于数据存储、信息处理或光开关等应用。同时，它也展示了如何通过调整对称性参数来调控激光器的行为，这对于未来的量子信息处理和光通信技术具有重要意义。

Bistable lasing in parity-time symmetric coupled

fiber rings

SERGEY V. S MIRNOV,

*MAXIM O. MAKARENKO,

SERGEY V. S UCHKOV,

DMITRY CHURKIN,

AND

ANDREY A. SUKHORUKOV

Novosibirsk State University, 2 Pirogova Street, Novosibirsk 630090, Russia

Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia

*Corresponding author: smirnov@lab.nsu.ru

Received 20 September 2017; accepted 12 January 2018; posted 12 January 2018 (Doc. ID 307530); published 20 March 2018

We propose a parity-time (PT) symmetric fiber laser composed of two coupled ring cavities with gains and losses,

which operates both in PT-symmetric and symmetry-broken regimes depending on the static phase shifts. We

perform analytical and numerical analysis by the transfer matrix method taking into account gain saturation

and predict laser bistability in the PT-symmetric regime in contrast to a symmetry-broken single-mode operation.

In the PT-broken regime, the generation power counterintuitively increases with an increase of the cavity

losses.

OCIS codes: (060.3510) Lasers, fiber; (190.1450) Bistability; (140.3560) Lasers, ring.

https://doi.org/10.1364/PRJ.6.000A18

1. INTRODUCTION

The concept of parity-time (PT) symmetry in optics has at-

tracted a great deal of attention following the first experimental

demonstrations only a few years ago [1,2]. It suggests new pros-

pects for the design of optical structures with symmetrically

distributed regions of gain and losses; see review papers [3–5]

and references therein.

Recently, PT-symmetric lasers were demonstrated experi-

mentally in microrings [6–9]. Importantly, a single-mode laser

operation was achieved in an initially multi-mode system

through stronger mode discrimination, when the system oper-

ates in the PT-broken regime close to a PT-symmetry-breaking

transition. Also, a single transverse-mode operation in a system

of coupled microring lasers was demonstrated near the excep-

tional point [10], and enhanced sensitivity [11,12] was realized.

In a pair of coupled microdisk quantum cascade lasers, the

reversal of generated power dependence [13] was identified in

the vicinity of exceptional points (EPs), where spontaneous

emission is enhanced [14], and EPs were observed direc tly

in photonic-crystal lasers [15]. Furthermore, a realization of

PT-symmetry-based mode locking [16] and a PT-symmetric

laser absorber [17] were theoret ically proposed, and lasing and

anti-lasing in a single cavity were demonstrated [18]. Recently,

a statistical PT-symmetric lasing has been achieved in an optical

fiber network incorporating semiconductor amplifiers [19].

In this work, we develop the theoretical concept of a

PT-symmetric fiber laser based on coupled cavities. We use a

conventional ring cavity laser design and predict PT-symmetric

and PT-broken lasing by means of tunable coupling of a ring

cavity laser with a passive cavity.

2. METHODS AND RESULTS

We present a diagram of the proposed PT-symmetric fiber ring

laser in Fig. 1. The scheme comprises two similar fiber cavities:

one of them is active (with gain), and the other cavity is passive

(with losses). Tunable coupling between cavities is controlled

by means of adjustable phase shifts inside a Mach–Zehnder

interferometer. In the case of zero phase shifts, passive and ac-

tive cavities are uncoupled, so the system acts as a conventional

ring cavity laser if properly pumped. As we demonstrate below,

tunable coupling enables one to switch between PT-symmetric

and PT-broken lasing regimes.

To describe the laser operation and associated PT transi-

tions, we use a discrete transfer matrix model governing the

evolution of the field amplitudes in both fiber cavities. Field

evolution over a cavity round-trip in the first approximation

is described by a transfer operator L,

L 



∕2

0 e

∕2



1∕

ﬃﬃﬃ

i∕

ﬃﬃﬃ

i∕

ﬃﬃﬃ

1∕

ﬃﬃﬃ





iφ

0 e

iφ



1∕

ﬃﬃﬃ

i∕

ﬃﬃﬃ

i∕

ﬃﬃﬃ

1∕

ﬃﬃﬃ



∕2

0 e

∕2



; (1)

where g

< 0 denotes constant losses and g

> 0 characterizes

total gain. Importantly, crossover coupling as described by the

second matrix in Eq. (1) facilitates PT symmetry with static

A18

Vol. 6, No. 4 / April 2018 / Photonics Research

Research Article

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