Discrete particle swarm optimization for constructing uniform design on irregular regions

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CThN7

2005 Conference on Lasers &Electro-Optics (CLEO)

Multiplying

the

Repetition

Rate of Passive

Mode-locked

Femtosecond Lasers

by

an

Intracavity

Flat

Surface with

Low

Reflectivity

Tzu-Ming Liu andChi-KuangSun

Graduate InstituteofElectro-Optical EngineeringandDepartmentofElectricalEngineering,National TaiwanUniversity, Taipei 10617, TAIWAN

PhoneLl886-2-23659703,FAX,Y886-2-23677467,E-mailE1J8941002@,ee.ntu.edu.tv FranzX.KartnerandJames G.Fujimoto

DepartmentofElectricalEngineeringandComputerScienceand ResearchLaboratory ofElectronics, Massachusetts InstituteofTechnology, Cambridge,Massachusetts 02139

Abstract: We demonstrate aflexible andphaseinsensitive methodto multiplytherepetition-rate ofpassive mode-locked solid-state lasers in femtosecond regime. It wasachieved by inserting a

low-reflectivityflatsurface inside the oscillatorcavity.

OCIS codes:(140.3070) Infrared and far-infraredlasers, (320.7160) Ultrafast technology.

High repetition-rate (HRRR) femtosecond lasers enable a wide range ofnewapplications in optical communication [1], and frequency metrology [2].Forspectroscopy andsensing applications,HRRlasers reduce thepeakintensities whilemaintaining a high average power, which is important for achieving high signal-to-noise ratios. In order to increase therepetitionrate, thesimplestwayistoshortenthecavity length. Considering highpowerandshort

pulse-width,

passivemode-locked all solid-state lasers withacompactcavityisapopular choice

[3,4].

Butonce aHRR mode-locked laser isbuilt, the repetitionrate cannotbe easily

multiplied

withoutchangingthe cavity design. For passive mode-locked lasers, repetition-rate multiplication with a coupledextemal cavity is amore convenient and

costeffective solution [5]. However,previouslydemonstrated methodsrequirephase-sensitivemodematchingtoan

external coupled cavity and allprevious studiesonly operated in the nanosecond orpicosecond regimes [5-8]. In thisletter, wedemonstraterepetition-ratemultiplication by usinganintracavityflatsurface with lowreflectivity in a passively modelocked Cr:forsterite laser. Incontrast to all previous studies [5-8], ourintracavity low-reflectivity flat surface acts as apulse seeder rather than a couplerto amatched external resonant cavity. By controlling the ratio of the subcavity length, repetition-rate can thus be successfully multiplied in the femtosecond regime in a flexible andphaseinsensitive way.

OC 2% DCM1 Flatsurface SESAM DCM4 Yb:fiber Laser \ @1064 nm L2 Li

Fig. 1. Schematic diagram of the highrepetition-rate femtosecond Cr:fosterite laser. M: folding mirror; L1, L2: mode-matching lenses; PL: pump lens; DC: dichroic curve mirror (R=10 cm);

DCM1,

DCM3: flatdouble chirped mirrors; DCM2, DCM4: curved double chirped mirrors (R=10 cm); SESAM: semiconductor saturableabsorbermirror; OC: output coupler; Cr:F: Cr:forsterite crystal.

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CThN7 2005Conference on Lasers & Electro-Optics (CLEO)

Consider a linear cavity withan optical-path length 1,the pulserepetitionrate

Ro

is equalto c/21, where c is the speed oflight. By inserting a flat surface with low reflectivity, the optical cavity can be partitioned into two subcavities with lengths 1 and12

(II<

12). When

11/12=N/M

isarational number

(N

and Mare

positive

integers

with nocommondenominators), for eachsplitofapulse,thereflectedone lagseither

N/[(M+N)R0]

or

M/[(M+N)RO]

in

timeto thetransmittedone. With this property, the time interval between anysplit

intracavity

pulseandthe initial

single pulse can be expressed as

K/[(M+N)RO],

where K is an integer from 0 to M+N-1. The final number of

intracavity pulses isM+Nand therepetition-rateR canbemultipliedto

(M+N)Ro.

Thismeansthat foragivenmain

laser cavity,we canmultiplytherepetitionratebysettinganappropriateratioof thesubcavitylengths.

The laser we employed to demonstrate this approach is a femtosecond Cr:forsterite laser (Fig. 1). Its cavity is

composed of one dichroic curved mirror (DC), two curved

double-chirped

mirrors (DCM2, DCM4), two plane double-chirped mirrors (DCM1 and DCM3), a semiconductor saturable absorber mirror (SESAM), a 2% output coupler, and a Cr:forsterite crystal. Except for the SESAM and the output

coupler,

all mirrors have high transmission at the pump wavelength (1064 nm) with broadband high reflection

coating

around the lasing wavelength. We usea standard z-fold cavity

design

for

astigmatism compensation.

The radius-of-curvature of the focusing mirrors are all 10-cm. The Cr:forsterite crystal is a Smmx5mm x11.4mm Brewster-cut crystal with an

absorption coefficient of 1.5

cm-'.

The crystal was cooled by liquid and a TE cooler. To prevent water

condensationonthe surface ofthecrystal, itwaspurgedwithdrynitrogen. The SESAM withapicosecondtransient response is for self-starting and enhancement of the

mode-locking

force [9]. The double-pass group-delay-dispersion (GDD) arose from the lasercrystal is 568 fS2 around 1230 nm [10]. Weemploy double-chirped mirrors (DCMs) instead of prism pairs to compensate the crystal GDD [11]. Each DCM provides -150

fs2

GDD around 1230 nm. To make soliton-like pulses operate in the stable regime, the net cavity dispersion should be slightly negative[12]. Howeverforamode-lockedcavity withaSESAM, toomuchintracavity energy will result in double

ormultiple-pulse operation, whichset anupper limit forthe output power[13]. Toincrease the upperlimit, the net GDDshouldbemorenegative. Therefore,weemploy4DCMs(DCM1-4)forhigher availablepower,which results in -632 fS2netGDDwithinoneroundtrip. The pump sourceisanYb:fiberlaseroperating at 1064 nm.After a lens pair

(Li

andL2) andapumplenswitha 10-cm focaldistance,pumpbeamwasfocusedinto the crystal with -30jrm beamradius atthe focus. Usinga self-consistent q-parameter analysis, the radius of beam waist inside the crystal

wasapproximately 28

ltm,

closetothat of the pump beamatthesameposition. With 1°Ccrystaltemperature and

7-Wpump power,we canobtain 40-mW average output powerata 124-MHzrepetition-ratewithoutmultiple pulsing [13]. Without insertingthe flat surface, the output spectrumshowed

11-nm

bandwidth at 1225 nm (Fig. 2(a)). The background free

second-harmonic-generation

autocorrelationtracemeasured253-fs FWHM (Fig. 2(b)), indicating

-164-fspulse width assumingasech2pulseshape.

10 (a)

10(b)

0.8 0.8

(D0C

C:~~~~~~~~~~~ -~0.4 .S 0.4 N ( 0.2- N 0.2-_E__ _0 z 1190 1200 1210 1220 1230 1240 1250 1260 -600 -400 -200 0 200 400 600 Wavelength (nm) Delay (fs)

Fig. 2. The spectrum (a) and the autocorrelation trace (b) of the 124-MHz Cr:forsterite laser without inserting a low-reflectivity flat surfaceinside thecavity.

Wefirst placeda flat surface into thepoint where

11=115,

trying to multiply the repetition rate up five-fold. The employed intracavity flat surface is a BK7 glass with

150-pm

thickness. In order to reduce bandwidth limitation from etaloneffects, one side of the glass is anti-reflection coated for high transmission (transmission T>99.8%). The other uncoated surface provides -4% reflection, serving as the intracavity flat surface. The glass was fixed on a mirrormountandatranslation stage with a

1-gm

resolution. After inserting the glass, without any carefulalignment, the repetitionratedidnotmultiply. Inaddition, under 8.4-Wpump power, the output spectrum showed a narrowed

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CThN7 2005 ConferenceonLasers&

Electro-Optics

(CLEO)

bandwidth

(-0.3

nm)

and theoutputpowerwas80 mW. Aftermaking theglass normal tothe

intracavity

laser

beam,

the average power was increased to 180mW. The detected pulse train showed a 620-MHz repetition rate in the

oscilloscope.

At thesametime, wecanobserve the outputspectrumbroadenedto -9nm FWHM(see

Fig.

3(a)) and the measured autocorrelation trace showed 260-fs FWHM, indicating 168-fs pulse width by assuming

sech2

pulse

shape (Fig. 3(b)).

We also

investigated

thecase of

11=1/10

inorder toreach a 1.24-GHzrepetition-rate and 170-mW output power was obtained. The measured pulse width was around 2 ps. This is the highest repetition rate ever

reported

for a mode-locked Cr:forsterite laser. The detuning range and stability criterion of the repetition rate

multiplication

willbediscussedin the conference.

o .o0 Z 1.0 S

-(1. )

(a) 0 (1.0(b)

>~~~~~ 0.8 >, ~~~~~~~~~~~~~~0.8

C 0.6 C

0.6-a)~ ~ aelnt

(n)Dea

(s

Fi.3Th

pctu

a)adte

uooreaio

rc (b)o h

2-H rfrtrt

ae

ihalw

laser,"Op.4Lett 06, -3-320) N ~~~~~~~~~~N 0.2- = 0.2-0 0.0 0 0.0 _z_

2267~~~~~~~~~~15

126000).

1200 1210 12~20

12i30

124 1201660 -400 -200 0 200 400

6600

Wavelength (nm) Delay (fs)

Fig.

3 The spectrum

(a)

and the autocorrelation trace

(b)

of the

620-tiHiz

Cr:forsterite

laser with a

low-reflectivity

flatsurface inside the

cavity.

4. References

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Liu,

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multiwavelength

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