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odel of a multiple-line distributed-feedback dye laser

asrullah Khan

The theoretical basis for simultaneous oscillation of 2N � 3 laser lines is due to interference of N �for alleven N � 2� pump beams in a distributed-feedback dye laser is described. Multiple gratings areproduced in a dye solution by interference patterns of N�2 pairs of a frequency-doubled Nd:YAG laser.N�2 pairs of mutually time-delayed pulses induce multiple gratings of different periodicities, of which2N � 3 gratings support oscillation of 2N � 3 lines and the remaining gratings, because of their largerperiods, cannot support Bragg scattering. The maximum number of laser lines depends on the mutualdelay between adjacent pairs of beams, coherence, states of polarization, pulse lengths, and of course thenumber of pulses. For three pairs of excitation beams derived from the same source through wave-frontor amplitude phase division techniques, the output lasing lines varied from a minimum of three to amaximum of nine. This research was carried out by pumping of a dye solution with two, four, and sixpulses, but the principle may be extended to multiple output lines, depending on the number of pumppulses and on the gain of the dye solution. © 2004 Optical Society of America

OCIS codes: 140.0140, 140.3490, 140.2050, 230.1480, 050.2770, 050.5080.

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. Introduction

y definition, a distributed-feedback dye laserDFDL� is supposed to support only one narrow spec-ral line that corresponds to the period of spatialodulation of the dye solution. Nevertheless, it is

ossible to operate a single-frequency DFDL at dif-erent repetition rates ranging from single shot toeveral kilohertz. Several pump configurationsave been reported to produce DFDL operation.1–3

ne may produce dynamic gratings that cause DFDLaser action in dye cells by interfering light beamssually derived from same laser source by either am-litude phase division or wave-front division. Theaser source must be temporally coherent for ampli-ude phase division and spatially coherent for wave-ront division if it is to form an interference pattern athe dye cell. The possibility of simultaneous oscilla-ion of multiple laser lines in the same dye solutionas proposed by Efendiev and Rubinov,4 and twoears later Rubinov et al.5 demonstrated successfulperation of three-line DFDLs in a prism-type pump-ng configuration. The idea was based on the strong

The author �khan@eng.upm.edu.my� is with the Department oflectrical and Electronic Engineering, Faculty of Engineering,niversity Putra Malaysia, 43400 UPM Serdand, Selangor, Ma-

aysia.Received 5 April 2003; revised manuscript received 15 October

003; accepted 15 October 2003.0003-6935�04�030678-04$15.00�0© 2004 Optical Society of America

78 APPLIED OPTICS � Vol. 43, No. 3 � 20 January 2004

ependence of the induction of gratings on the inci-ent angles of the pump beams. Multiple pumpeams form a complex pattern of standing waves andence of gratings to cause more than one line to laseimultaneously. Later Muller6 demonstrated multi-le wavelength operation at two different wave-engths with different criteria. The researcheported here is based on the same principle as wassed by Efendiev4 and Rubinov and Rubinov and byubinov et al.,5 but a different configuration was used

o demonstrate simultaneous lasing of nine laserines caused by pumping by three pairs of pulses of ad:YAG laser, as shown in Fig. 1. In this multiple-

ine DFDL operation experiment, the pulse length ofhe pump laser was 30 ps �9 mm�, which is very closeo the pulse’s coherence length �9.5 mm�. It wasointed out by Eichler et al.7 that the behavior of anverall grating pattern becomes highly complex when

ig. 1. Schematic representation of a three-pair-pumped DFDL.

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he pulse length is comparable to the coherenceength of the pump laser. Simultaneous pumping ofdye cell with three time-delayed pump pulse pairs,

t half-angles �1, �5, and �9, induces nine lasing linesn the dye solution. The mathematical expressionshat govern the induction of multiple gratings withhree time-delayed pairs of pulses can be expressedy

�1 ��P

2 sin��1�, (1)

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�5 ��P

2 sin��5�, (5)

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�5 � �9

2 � , (6)

�7 ��P

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2 sin��5 � �9

2 � , (7)

�8 ��P

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2 sin12 ��9 � ��5 � �9

2 �� , (8)

�9 ��P

2 sin��9�. (9)

he wavelengths of the nine laser lines for a DFDLaser pumped by three pairs of pulses can be calcu-ated from above half-angles by

�o ��P

2ns sin��H�, (10)

here ns is the refractive index of the dye solution.or ns � 1.3 and incident beam half-angles �1 �9.5°, �5 � 20.50°, and �9 � 20.75° the calculatedavelengths of multiple spectral lines are listed inable 1. The number of DFDL output laser lines Man be given as a function of the number of pumpulses N �even numbers only� by

M � 2N � 3. (11)

esides, some other gratings are induced that cannotatisfy Bragg scattering conditions to produce laserines. An experimental configuration for N�2 pumpulse pairs at half-angles �1 . . . �n can produce1 . . . �n period gratings, as illustrated �drawn afteref. 5� in Fig. 2. If a 300–400-nm pump laser alongith multiple energy transfer dye solutions3 is used,ven more lines, from the UV to the IR, can be ob-ained.

. Experimental Demonstration

or the study of the effect of the optical path differ-nce �OPD� between multiple pairs of pump beamsnducing anharmonic gratings, the second harmonicf a passively Q-switched and mode-locked Nd:YAGaser was divided into two beams. The three maineams had a total energy of 600 mJ. To investigatehe effect of delay among three pairs of pump pulsesnducing multiple gratings, I divided the second har-

onic of a passively Q-switched and mode-locked Nd:AG laser into three main beams. Three DFDLsere made to operate simultaneously. A solution ofhodamine 6G dye in ethanol at 3 � 10�3 M wasumped by three pairs of second harmonics of a Nd:AG laser. The pump energies of individual DFDLsFDL1, DFDL2, and DFDL3 were 300 10, 200 10,nd 100 10 J, respectively. The experimentalrrangement for writing three overwritten dynamicratings is shown in Fig. 3. The pump energies ofhe DFDLs were high enough to cause laser oscilla-ions above threshold. The main beam-dividingirrors were mounted upon movable stages to vary

he OPDs among the three main beams that pro-

ig. 2. Schematic representation of an N�2-pair-pumped DFDL.

Table 1. Expected Lines in a Six-Pulse-Pumped DFDL:Calculated Wavelength

Half-Angle �°� Lasing Line �nm�

19.50 �1 � 61319.75 �2 � 60520.00 �3 � 59820.25 �4 � 59120.50 �5 � 58420.75 �6 � 57721.00 �7 � 57121.25 �8 � 56421.50 �9 � 558

20 January 2004 � Vol. 43, No. 3 � APPLIED OPTICS 679

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uced three individual DFDLs. Simultaneous oper-tion of three DFDLs produced multiple lasing lines,epending on the OPDs among the pump beams.he observed lasing lines varied from three to nine

or simultaneous operation of three time-delayedFDLs in the same dye solution.The minimum number of lines was obtained when

he OPDs between the DFDLs were more than theoherence length �4 mm� of the pump laser. Simul-aneous operation of two DFDLs was conducted sep-rately by blocking the pumping beams of individualFDLs at a time. The maximum number of output

ines was five in each case. In simultaneous opera-ion of three DFDLs the fundamental lines do not

ig. 3. Experimental setup for the simultaneous operation ofhree DFDLs.

ig. 4. The three upper lines belong to simultaneous operation ofhree DFDLs for 5 mm � OPD1,2,3 � 10 mm, but the bottom nineines belong to three pairs of pump pulses at 0 � OPD1,2,3 � 2 mm.he middle three results, of five lines each, were obtained byimultaneous operation of any two DFDLs for 0 �PD1,2 or 2,3 or 1,3 � 2 mm. The pump energies of the three maineams were 300, 200 and 100 J at 10–30-ps pulse durations andrepetition rate of 0.1 Hz.

80 APPLIED OPTICS � Vol. 43, No. 3 � 20 January 2004

hange their location in spectrum. The maximumumber of lines was observed when the OPDs were

ess than 2 mm. Spectra for three, five, and nineines are shown in Fig. 4. Multiple line emissionccurs if the angle differences are small and the delayetween the main interfering beams is comparable tor less than the pulse lengths. For pump angles1 � 21°, �5 � 21.18°, and �9 � 21.30° and OPD � 2m, multiple line emission takes place. The inter-

ine spectral differences that correspond to half-angleifferences ��1�2 � 0.075° and ��1�9 � 0.30° are.70 0.01 and 5.3 0.1 nm, respectively.

. Description of Results

he OPDs among three pairs of beams varied from 0o 10 mm to operate DFDL1, DFDL2, and DFDL3.or OPD 0 � OPD1,2 � 2 mm and 0 � OPD2,3 � 2m, a total of nine lasing lines were observed. Usu-

lly nine lines were observed, but sometimes a tenthine was recorded. The number of laser lines in theimultaneous operation of DFDL1 and DFDL2,FDL2 and DFDL3, and DFDL1 and DFDL3 was five

n each case. For three DFDL operations, all theine lasing lines were spaced symmetrically in thepectrum. For 0 � OPD2,3 � 2 mm and 2 mm �PD1,2 � 5 mm the total number of lasing lines was

educed to eight; one line was missing from a regularocation. The location of the missing line depends onhe relative OPD between the pump pulses. Theumber of lasing lines for the simultaneous operationf DFDL1 and DFDL2, DFDL2 and DFDL3, andFDL1 and DFDL3 was always five for the least delaynd two for the longest delay �4–5 mm�. The num-er of theoretically predicted and experimentally ob-erved simultaneous lasing lines varied from five toine for two and three pairs of pump pulses. Theariation of observed numbers of DFDL output laserines as a function of the number of pump pulses ishown in Fig. 5. I reduced the three DFDL opera-ions to two DFDL operations by blocking one beam,roducing a third pair of pump pulses.

. Conclusions

he experiments described here prove that the su-erposition of multiple gratings of different periodsnd phases produce several degenerate gratings thatre responsible for the oscillation of multiple laser

ig. 5. Variation of observed DFDL output laser lines as a func-ion of pump pulse.

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ines to satisfy Bragg scattering. The number ofines depends on the coherence length of the pumpaser, the number of pump beams, the pulse length,nd the length of the interaction region in a dye so-ution. Observation of a sixth line in two-DFDL op-ration and of a tenth line in three-DFDL operationeveals the possibility of more lines at reduced inter-ine spacing �0.5 nm�. The exact physics of this re-ult is not understood, but the overwriting of threeratings of different periods is the most likely reasonor it. Obviously, there is no upper limit as long ashe numbers of excitation pairs of pulses are in-reased and the gain medium supports lasing action.3f the idea of an energy transfer DFDL is integratedy use of multiple dyes, then it may be generalized tohe observation of M-line DFDLs by use of N pumpulses.

This research was carried out as part of Ph.D. re-earch under the supervision of T. A. Hall of theepartment of Physics, School of Science and Engi-eering, University of Essex, Colchester, UK. Thisesearch was sponsored by the Ministry of Sciencend Technology, Islamabad, Pakistan, and later some

nalytical work was sponsored by the Ministry ofcience, Technology, and Environment, Malaysia.

eferences. C. V. Shank, J. E. Bjorkholm, and H. Kogelnik, “Tunable dis-

tributed feedback dye laser,” Appl. Phys. Lett. 18, 395–396�1971�.

. A. N. Rubonov, T. Sh. Efendiev, A. V. Adamushko, and J. Bor,“Multifrequency operation of distributed feedback dye laserwith high repetition rate,” Opt. Commun. 18, 18–23 �1976�.

. M. B. Ahmad and P. K. Palanisamy, “Nd:YAG laser pumpedenergy transfer distributed feedback dye laser in a Rhodamine6G and Acid Blue 7 dye mixture,” Opt. Commun. 213, 67–80�2002�.

. T. Sh. Efendiev and A. N. Rubinov, “Dye laser with a distributedfeedback induced by second harmonic of neodymium laser,” Sov.J. Quantum Electron. 5, 479–482 �1975�.

. A. N. Rubinov, T. Sh. Efendiev, and A. V. Adamushko, “Simul-taneous oscillation of several independently tunable spectrallines in a distributed feedback dye laser,” Opt. Commun. 20,159–162 �1977�.

. A. Muller, “Two independently tunable distributed feedback dyelaser pumped by single picosecond Nd:YAG laser,” Appl. Phys.B 63, 443–444 �1996�.

. H. J. Eichler, P. Gunter, and D. W. Pohl, eds., Laser InducedDynamic Gratings, Vol. 50 of Springer-Verlag Series on OpticalSciences �Springer-Verlag, Berlin, 1986�, pp. 17–18.

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