Single-modeoutputbycontrollingthespatiotemporalnonlinearitiesinmode-lockedfemtosecondmultimodefiberlasers资源-CSDN文库

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Single-mode output by controlling the

spatiotemporal nonlinearities in mode-locked

femtosecond multimode fiber lasers

U ˘gur Te ˘gin ,

a,b,

* Babak Rahmani,

Eirini Kakkava ,

Demetri Psaltis,

and Christophe Moser

École Polytechnique Fédérale de Lausanne, Optics Laboratory, Lausanne, Switzerland

École Polytechnique Fédérale de Lausanne, Laboratory of Applied Photonics Devices, Lausanne, Switzerland

Abstract. The performance of fiber mode-locked lasers is limited due to the high nonlinearity induced by the

spatial confinement of the single-mode fiber core. To massively increase the pulse energy of the femtosecond

pulses, amplification is performed outside the oscillator. Recently, spatiotemporal mode-locking has been

proposed as a new path to fiber lasers. However, the beam quality was highly multim ode, and the calculated

threshold pulse energy (>100 nJ) for nonlinear beam self-cleaning was challenging to realize. We present an

approach to reach high energy per pulse directly in the mode-locked multimode fiber oscillator with a near

single-mode output beam. Our approach relies on spatial beam self-cleaning via the nonlinear Kerr effect, and

we demonstrate a multimode fiber oscillator with M

< 1.13 beam profile, up to 24 nJ energy, and sub-100 fs

compressed duration. Nonlinear beam self-cleaning is verified both numerically and experimentally for the first

time in a mode-locked multimode laser cavity. The reported approach is further power scalable with larger core

sized fibers up to a certain level of modal dispersion and could benefit applications that require high-power

ultrashort lasers with commercially available optical fibers.

Keywords: fiber lasers; spatiotemporally mode-locked lasers; multimode nonlinear fiber optics.

Received Jul. 17, 2020; revised manuscript received Sep. 1, 2020; accepted for publication Sep. 17, 2020; published online

Oct. 16, 2020.

reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

[DOI: 10.1117/1.AP.2.5.056005]

1 Introduction

Fiber laser dynamics have been studied extensively in the past

decades to generate femtosecond pulses with high energies and

peak powers.

Numerous laser designs are developed to under-

stand nonlinear wave propagation under partial feedback condi-

tions. By tuning complex cavity dynamics in single-mode fiber

cavities, self-organization of longitudinal cavity modes with vari-

ous temporal profiles and central wavelengths has been realized,

such as soliton,

similariton,

3,4

and dissipative soliton.

5,6

Due to

the high spatial confinement in the small single-mode fiber core,

nonlinear effects appear at moderate peak power in solid cores,

and the accumulation of excessive nonlinear phase leads to pulse

breakup, which then limits the achievable pulse energies.

To overcome this limitation, custom-made sophisticated fi-

bers, having large single-mode areas in a photonic crystal fiber,

were proposed to reach the microjoule pulse energy level.

7,8

The

fiber used in these demonstrations with its mode field diameter

of 70 μm needed to be kept straight to avoid bending losses and

ensure stability. They share the same limitations as solid-state

lasers in the sense that they are rigid and cannot be spliced with

conventional techni ques. As a result, such lasers do not share

the features of fiber lasers that render them advantageous in

practice.

Recently, spatiotemporal mode-locking has been demon-

strat ed in commercially available multimode fi ber (MMF)

cavities w ith graded-index multim ode fibers (GRIN MMFs)

by harnessing their low modal dispersio n and inherent periodic

self-focusing to produce a coherent superp osition of transverse

and longitudinal modes in an all-normal dispersion regime.

9–11

These studies presented cavities with dissipative soliton pulse

operation with low-output beam quality despite utilizing gain

fibers with three modes. In a recent study, improvement in the

output beam profile of a spatiotemporal mode-locked fiber laser

*Address all correspondence to U˘gur Te˘gin, E-mail: ugur.tegin@epfl.ch

Research Article

Advanced Photonics 056005-1 Sep∕Oct 2020

•

Vol. 2(5)

was reported by changing the gene rated pulse type from a dis-

sipative soliton to an amplifier similariton. The reported pulses

lead to pulse energies of 2.4 nJ with output beam M

value

<1.4.

Although a better beam profile was reported compared

to previous results, the single-mode beam profile (M

∼ 1)

could not be achieved due to the limitations of amplifier sim-

ilariton pulse type such as the degradation of pulse quality and

peak power with increasing pulse energy.

In this paper, we demonstrate an approach to generate

>20 nJ, sub-100 fs pulses with near Gaussian output beam

shape by controlling the spatiotemporal cavity dynamics of

multimode fiber lasers. This pulse energy represents a tenfold

improvement over previously reported MMF oscillators with

a Gaussian beam shape. Moreover, our method is limited only

by the damage of the threshold fiber splices and can be increased

to the microjoule energy level. The key element in the novel

design that enables the increased pulse energy is the Kerr-

induced beam self-cleaning in a GRIN MMF

that occurs when

a high-intensity pulse propagates in the fiber.

The optical wave propagation inside the cavity is designed

to synergistically achieve nonlinear beam cleaning and spatio-

temporal mode-locking. With our approach, spatiotemporally

mode-locked fiber lasers overcome the power limitations of

mode-locked single-mode fiber lasers without sacrificing the

output beam quality. Moreover, the presented approach is not

limited to the demonstrated power levels and theoretically scal-

able with standard large core mul timode fibers up to a certain

level of modal dispersion.

We experimentally demonstrate that the highly multimode

beam profile observed at the output of a continuous wave multi-

mode fiber cavity is transformed to a stable Gaussian beam pro-

file when the oscillator is spatiotemporally mode-locked. Our

numerical studies verified that there is an energy exchange from

higher-order modes to lower order modes in the propagating

GRIN MMF section of the laser cavity for the experimentally

achieved power level. Inside the spatiotemporal mode-locked

cavity, Kerr-induced beam self-cleaning creates a minimum loss

condition to the emerging mode-locked pulses. The reported

multimode fiber laser generates sub-100 fs pulses with high

pulse energy (>20 nJ) and good beam quality if the M

value

is <1.13.

2 Methods

2.1 Multimo de Oscillator Simulations

Numerical simulations for mode-locked pulse formation are

conducted for the model used by Tegin et al.

For GRIN MMF

sections of the cavity, a multimode nonli near Schrödinger

equation

is solved by considering the five linearly polarized

modes (more details of simulations can be found i n

Supplementary Discussion I in the Supplementary Material).

Simplifications such as simulating few-mode fiber sections as

single mode to decrease the computation time and defining cou-

pling ratios before and after the GRIN MMF sections to mimic

the effect of splice points are performed. Simulations are initi-

ated with quantum noise fields. The integration step for GRIN

MMF sections is defined as the ratio of the self-imaging period

of the fiber with four. For the simulation result shown in Fig. 1 ,

the gain fiber is modeled with a Lorentzian gain shape with

50 nm bandwidth, 30 dB small-signal gain, and 3.2 nJ saturation

energy. The coupli ng condition between the few-mode gain fi-

ber and GRIN MMF is simulated as [20%, 30%, 20%, 20%,

and 10%]. The intracavity spatial filtering is applied to the

Fig. 1 Conceptual outline of the multimode fiber cavity and schematic of spatiotemporal mode-

locking with beam self-cleaning. (a) Conceptual outline of dispersion-managed cavity design with

indicated temporal dynamics. Laser pumping scheme is not presented. (b) Schematic of mode-

locking mechanism and experimentally measured output beam profile evolution. CW, continuous

wave; ML, mode-locked.

Te˘gin et al.: Single-mode output by controlling the spatiotemporal nonlinearities…

Advanced Photonics 056005-2 Sep∕Oct 2020

•

Vol. 2(5)

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