Energy transfer distributed feedback dye laser using Rhodamine B–Acid blue 7 dye mixture

Journal of Photochemistry and Photobiology B: Biology 69 (2003) 153–160 www.elsevier.com / locate / jphotobiol

Energy transfer distributed feedback dye laser using Rhodamine B–Acid blue 7 dye mixture M. Basheer Ahamed, P.K. Palanisamy* Department of Physics, Crescent Engineering College, Chennai 600 048, India Received 5 August 2002; received in revised form 23 December 2002; accepted 28 December 2002

Abstract The characteristics of energy transfer distributed feedback dye laser (ETDFDL) are studied both theoretically and experimentally in a mixture of Rhodamine B and Acid blue 7 dyes pumped by 532 nm Nd:YAG laser. The behaviour of donor and acceptor DFDL, the dependence of their pulse width and output power on pump power and donor–acceptor concentrations are studied. Experimentally, the tunability is achieved over the spectral range 565–680 nm using a prism dye cell arrangement. The output energy of DFDL is measured at the emission peaks of donor and acceptor for different pump powers and donor–acceptor concentrations. The output pulse of DFDL is found to be as narrow as 40-ps duration, which is nearly 100-fold shorter than the pump pulse. The pulse linewidth is of the order of ˚ 0.1 A.  2003 Elsevier Science B.V. All rights reserved. Keywords: Distributed feedback dye laser; Spectral width; Energy transfer; Q-switching; Rate equations; Tunability PACS: 42.55 Mv; 42.55

1. Introduction Distributed feedback dye lasers are inexpensive reliable sources for generation of ultrashort pulses. Conventional laser oscillators consist of an active medium that provides gain and a resonator structure, which provides the necessary feedback for oscillation. The fundamental characteristic of a DFDL is that the necessary feedback is provided by Bragg scattering from a periodic spatial variation of the refractive index of the gain medium or of the gain itself. Among the different mechanisms for the generation of ultra short pulses, distributed feedback dye lasers have the added advantage of wavelength tunability over a wide spectral range. Kogelnik and Shank demonstrated this for the first time in 1971 by generating periodic spatial gain modulation in dye solution [1]. The advantage of DFDLs is that single pulses tunable in frequency can be produced without pulse selectors by choosing proper operating conditions. In DFDL, pumped by a laser with nanosecond *Corresponding author. Centre for Laser Technology, Department of Physics, Anna University, Chennai 600 025, India. Fax: 191-44-22200660. E-mail address: [email protected] (P.K. Palanisamy).

pulse duration, spiking caused by the relaxation oscillation is observed with pulse duration of several tens of picoseconds for each spike [2,3]. DFDLs have higher efficiency, broader tuning range and lower amplified spontaneous emission (ASE) background level than other dye lasers. Using nanosecond and / or sub-nanosecond pulses as pump source, DFDLs generate 20–100 times shorter pulses [4]. Spatial gain modulation dependence of the feedback results in self Q-switching causing significant pulse shortening. By changing either the spatial frequency of gain modulation and / or the refractive index of the gain medium, frequency tuning is achieved. In dye lasers, the saturable absorber caused Q-switching is also a very useful pulse shortening method even on the nanosecond and picosecond time scale. If a saturable absorber is added to distributed feedback dye medium, double self Q-switching occurs and the DFDL pulses become much shorter and more stable [5]. The study of transfer of energy between donor and acceptor dye molecules in solution has both theoretical and practical importance. For purpose of tunability at any desired wavelength with one pumping source, energy transfer dye laser is advantageous. Energy transfer from an absorber (donor) molecule to acceptor molecule in a dye

1011-1344 / 03 / $ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S1011-1344(03)00003-4

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laser mixture influences the operation and spectral output of the dye laser. The mixture of two dissimilar dye molecules, for example, Rhodamine B (RhB) and Acid blue 7 (Ab7) can increase the efficiency of Ab7. The energy transfer dye lasers (ETDLs) are more efficient because of high gain and low pump power requirements. Though extensive studies have been already carried out on donor and acceptor concentration dependence of the gain spectrum for pulsed laser pumped ETDLs [6–8] not many reports are available on ETDFDL. For a particular donor– acceptor (D–A) pair, it is possible to make both donor and acceptor to lase at their respective gain regions due to energy transfer mechanism. If such a dye mixture is taken as active medium in DFDLs, ultra-short pulses tunable over the entire gain spectrum of donor and acceptor dyes are generated. In this paper, a theoretical model is proposed to study the characteristics of ETDFDLs as a function of pump power, donor and acceptor concentrations and the energy transfer parameters taking into account the contributions resulting from both radiative and non-radiative transfer. Also experimental results obtained from ETDFDL with RhB and Ab7 dye mixture as active medium are presented.

Ref. [10] is modified with two more additional equations. The rate equation model consists of four coupled differential equations. The first two, Eqs. (1) and (2), describe the donor DFDL and the second pair, Eqs. (3) and (4), describes the acceptor DFDL. The calculated parameters used in the rate equation model are given in Table 1. The meanings of the other symbols used in the rate equations are as follows: n d (t), n a (t), spatially averaged density of donor and acceptor dye molecules in the upper (S 1 ) level (cm 23 ); qd (t), qa (t), density of donor and acceptor DFDL 23 photons (cm ); Nd , Na , density of donor and acceptor dye molecules, respectively (cm 23 ); and Ip (t), spatially averaged pump photon intensity (cm 22 21 s ) of Nd:YAG second harmonic laser at 532 nm, Gaussian shaped in time, having pulse width 6.0 ns. The following rate equations describe the behavior of the DFDL containing mixed dyes [5,10,11]. The rate of change of donor dye molecules in the upper (S 1 ) level dn sedl cn dstd qdstd n dstd ]d 5 Ipstdspd f Nd 2 n dstd g 2 ]]]] 2 ]] 2 k F dt n td (1)

2. Theoretical studies

2.1. Rate equations The main mechanisms of energy transfer in donor– acceptor pairs are: (a) radiative transfer, i.e., acceptor molecules absorbing the emission by donor molecules; (b) diffusion-controlled collisional transfer; (c) resonance transfer due to long-range dipole–dipole interaction (nonradiative Forster type of transfer); and (d) molecular complexing which changes the absorption spectrum of the donor on adding acceptor by forming fluorescent exciplex [9]. The rate equation model has been proposed incorporating all the mechanisms involved. The observed emission spectra of RhB (donor) overlaps with the absorption spectra of the Ab7 (acceptor). This suggests that both radiative and Forster type of energy transfer processes are possible between these two dyes. The emission spectra of mixture of these two dyes do not show any new fluorescent peak and hence there is no complex formation. Since the concentrations of donor and the acceptor are always less than 5.0 mM, collisional encounters are very rare and hence collisional type of energy transfer is negligible. Considering the above facts, for the dye mixture laser the collisional and complexing types of transfer processes are neglected under our experimental conditions. Hence, we employ the radiative and the Forster type of transfer (k F ) only in our model. To describe the energy transfer process that takes place in a mixture of dyes the rate equation model described in

The three terms in the right-hand side of the equation denote the stimulated absorption, stimulated emission and spontaneous emission rates of donor dye molecules and the fourth term denotes Forster type transfer (cm 3 / s). The rate of change of donor photon density within the laser cavity

sedl cn dstd qdstd qdstd Vd n dstd dq ]d 5 ]]]] 2 ]] 1 ]] dt n tcstd td saal c f Na 2 n astd g qdstd seal cn astd qdstd 2 ]]]]]] 2 ]]]] n n

(2)

The first term of right-hand side of equation expresses the increase of the photon density by stimulated emission and the second term denotes loss of photons in the cavity due to decay of photons. The third term expresses the rate at which spontaneous emission is added to the laser emission. The fourth term denotes the loss of donor DFDL photons caused by the absorption. The fifth term denotes the loss of donor photons contributed towards stimulated emission of acceptor dye molecules. The second and fourth terms describe the self and passive Q-switching of the ETDFDL, respectively. The rate of change of acceptor dye molecules in the upper (S 1 ) level dn seaa cn astd qastd n astd ]a 5 Ipstdspa f Na 2 n astd g 2 ]]]] 2 ]] dt n ta

saal c f Na 2 n astd g qdstd seal cn astd qdstd 1 ]]]]]] 1 ]]]] 1 k F n n

(3)

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Table 1 Spectral parameters of Rhodamine B and Acid blue 7 used in the rate equation model Symbols

Meaning of the symbol

Numerical value

td ta R0 C0 C1 / 2 kF spd

Donor life time Acceptor life time Critical transfer radius Critical concentration Half quenching concentration Forster type transfer rate Absorption cross-section of donor dye at the pumping wavelength (532 nm) Absorption cross-section of acceptor dye at the pumping wavelength (532 nm) Emission cross-section of donor dye molecules at their lasing wavelength ( ll 5580 nm) of donor Ground-state absorption cross-section of the acceptor dye molecules at the lasing wavelength ( ll 5580 nm) of donor Emission cross-section of acceptor dye molecules at the lasing wavelength ( ll 5580 nm) of donor Emission cross-section of acceptor dye molecules at their lasing wavelength ( la 5655 nm) Length of the transversely excited region Height of the transversely excited region Speed of light Refractive index of the solvent Refractive index of the prism Visibility of the interference pattern Spectral factor contributing to spontaneous emission Factors determining the fraction of the spontaneously emitted photons by excited donor and acceptor dye molecules respectively

4.0 ns 3.3 ns ˚ 57.35 A 1.265310 18 cm 23 0.63310 18 cm 23 0.39310 29 cm 3 / s 2.09310 216 cm 2

spa sedl

saal

seal

seaa

L b c n np V S

Vd and Va

The first three terms in the right-hand side of the equation denotes the stimulated absorption, stimulated emission and spontaneous emission rates of acceptor dye molecules. The fourth term denotes the increase of excited state acceptor molecules caused by their absorption. The fifth term denotes the rate of decrease of acceptor dye molecules in the excited state due to stimulated emission caused by donor photons and the sixth term denotes Forster type transfer (cm 3 / s). The rate of change of acceptor photon density within the laser cavity dq seaa cn astd qastd qastd Va n astd ]a 5 ]]]] 2 ]] 1 ]] dt n tcstd ta

(4)

The right-hand side of Eq. (4) has similar terms as that of Eq. (2). Since the DFDL has no external cavity, the equivalent cavity decay time (in seconds) is given by [5]

S

3

nL f n dstdsedlV g 2 nL tcstd 5 max ]]]]] ,] 10c 8cp 2

D

(5)

0.051310 216 cm 2 3.02310 216 cm 2

0.323310 216 cm 2

0.0832310 216 cm 2

6.9310 216 cm 2

0.9 cm 0.02 cm 3310 10 cm s 21 1.328 1.52 0.4 10 4 2.089310 29 and 0.255310 26

The above equation is given a lower limit by the conditional statement (max), to select every time the maximum value of tc (t) which makes it possible to use the initial values n d (0)50, n a (0)50, qd (0)50, qa (0)50, Nd 5 0 and Na 50. Initially, the second term (which denotes the cavity decay time of short cavity dye laser) will take maximum value when n d 50 or very small. Later on, as n d becomes larger, the first term (which denotes the cavity decay time of DFDL) becomes larger. This lower limit reflects the fact that because of the finite length of the DFDL, the laser photons stay for a finite time tc (t) in the excited volume. The exact value of this limit changes with time. However, the solution of the differential equation system is independent of this limit, if tc (t) significantly exceeds its threshold value before the build-up of laser pulse. The fraction of spontaneous emission contributing to DFDL output [10] b b Vd 5 ]]]] and Va 5 ]]]] 2 p Nd spd L S p Na spa L 2 S

(6)

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where b is the height of the excited volume and S is the spectral factor contributing spontaneous emission. The output power of the donor DFDL from one end of the cavity is calculated as [11] hcqdstdLab Poutstd 5 ]]] 2lltcstd

(7)

where h is Planck’s constant. The output power of the acceptor DFDL from one end of the cavity is calculated as hcqastdLab Poutstd 5 ]]] 2latcstd

(8)

In order to equalize the number of incident and absorbed pump photons it is necessary to take the penetration depth of the pump beam into the dye solution (cm), which is given by [12] 1 a 5 ]]]]] sNd spd 1 Na spad

Fig. 2. Variation in pulse width and peak output power of donor DFDL at fixed acceptor concentration (Na 50.3310 18 cm 23 ) and pump photon intensity (Ip 50.8310 23 cm 22 s 21 ) for different donor concentrations.

(9)

2.2. Results and discussion Fourth-order Runge–Kutta method has been used to solve Eqs. (1)–(8) numerically. Dyes RhB and Ab7 are chosen as active medium and second harmonic of Nd:YAG laser (532 nm, 6-ns pulse width) is used as pump source. The donor dye molecules are found to emit DFDL in the wavelength range 565–650 nm with its peak emission at 580 nm. Similarly, the acceptor dye molecules in the dye mixture are found to emit DFDL in the wavelength range 620–680 nm with its peak emission at 655 nm. The DFDL output is studied at donor and acceptor lasing peak wavelengths. The threshold of the first pulse and its starting time and the threshold of the other pulses are shown in Figs. 1–6 as a function of pump power and donor–acceptor concentrations. With an increase in pump power / donor concentration, the output power of DFDL

Fig. 3. Variation in pulse width and peak output power of donor DFDL at fixed donor concentration (Nd 51.8310 18 cm 23 ) and pump photon intensity (Ip 50.8310 23 cm 22 s 21 ) for different acceptor concentrations.

Fig. 1. Variation in pulse width and peak output power of donor DFDL at fixed donor (Nd 51.8310 18 cm 23 ) and acceptor concentration (Na 50.33 10 18 cm 23 ) for different pump photon intensities.

Fig. 4. Variation in pulse width and peak output power of acceptor DFDL at fixed donor (Nd 51.8310 18 cm 23 ) and acceptor concentration (Na 5 0.3310 18 cm 23 ) for different pump photon intensities.

single pulse is found to increase with decrease in pulse width. At the same time the DFDL pulse is found to emerge earlier compared to the DFDL pulse emitted with lesser pump power / donor concentration. This is due to faster build-up of population inversion with increase of

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the donor wavelength decreases. Also, the output power of the single pulse is found to decrease with increase in pulse width and the DFDL pulse is found to be delayed (Fig. 3 and Table 2). In the case of DFDL emission at acceptor wavelength, as the concentration of acceptor increases, the number of DFDL pulses as well as the peak power are found to increase with decrease of pulse width (Fig. 6). The single pulse energy is computed by multiplying the peak power with its pulse duration (FWHM). From the data generated the total output energy for the train of pulses is also found by calculating the individual pulse energy. The significant results of the simulation are shown in Table 2. It has been found that in the rate equations (1) and (3), the term k F does not have any significant contribution in the simulated data indicating that Forster type energy transfer is insignificant in the present system under study.

Fig. 5. Variation in pulse width and peak output power of acceptor DFDL at fixed acceptor concentration (Na 50.3310 18 cm 23 ) and pump photon intensity (Ip 50.8310 23 cm 22 s 21 ) for different donor concentrations.

3. Experimental studies

3.1. Materials Both the dyes RhB and Ab7 are of laser grade supplied by Central Drug House, Bombay, India. The solvent methanol used is of spectroscopic grade. The absorption and fluorescence spectra are taken using 0.01 mM concentration RhB and Ab7 dyes using a spectrophotometer (ELCO, India) and a spectrofluorometer (Fluoromax II, USA), respectively. The spectral parameters of RhB and Ab7 dyes have been calculated from the observed absorption and fluorescence spectra of the dyes. The calculated spectral parameters are listed in the Table 1.

Fig. 6. Variation in pulse width and peak output power of acceptor DFDL at fixed donor concentration (Nd 51.8310 18 cm 23 ) and pump photon intensity (Ip 50.8310 23 cm 22 s 21 ) for different acceptor concentrations.

3.2. Experimental set-up to study DFDL

pump rate. Above certain pump power / donor concentration the second DFDL pulse emerges out. Calculations show that for higher pump power / donor concentration the DFDL pulse appears earlier with respect to the pump pulse (Figs. 1, 2, 4 and 5 and Table 2). Nevertheless, the DFDL emission at donor wavelength depends on the concentration of acceptor. With an increase in acceptor concentration, the number of DFDL pulses at

Fig. 7a shows the distributed feedback prism-dye cell configuration used for the creation of the interference pattern on the surface of the dye cell. The DFDL is pumped by frequency doubled Nd:YAG laser of 200-mJ pulse energy at repetition rate 5 Hz. The spectral width of the pumping laser is 1 cm 21 and its beam divergence is 0.6

Table 2 Calculated first pulse duration, output energy and time delay of DFDL with respect to pump pulse as a function of pump power and donor–acceptor concentrations Donor DFDL ( ll 5580 nm)

Parameters

Acceptor DFDL ( la 5655 nm)

Ip 5 (310 22 cm 2 s 21 )

Nd 5 (310 18 cm 23 )

Na 5 (310 18 cm 23 )

Pulse duration (ps)

Output energy (mJ)

Delay time (ns)

Pulse duration (ps)

Output energy (mJ)

Delay time (ns)

7 11 8 8 8 8

1.8 1.8 1.8 2.8 1.8 1.8

0.3 0.3 0.3 0.3 0.1 0.6

62 51 56 49 45 92

0.08 0.25 0.12 0.19 0.39 0.01

8.9 7.4 8.5 7.1 7.7 10.2

78 53 65 51 126 51

0.15 0.56 0.23 0.78 0.03 0.33

10.1 8.2 9.5 7.9 10.5 10.3

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Fig. 7. Schematic diagram of the prism-dye cell (a), and of the experimental set-up (b).

mrad. The distributed feedback for the dye laser is obtained using an isosceles right-angled quartz prism. The pump beam is focussed by a cylindrical quartz lens of focal length 15 cm into a line image, which is incident on the hypotenuse AB of the prism (Fig. 7b). The light transmitted by hypotenuse is totally reflected from the side AC of the prism and interferes to form fringes on a dye cell attached to the prism producing periodic modulation of the refractive index and also of the gain. The feedback is obtained from the Bragg reflection from the periodic structure incorporated throughout the active medium. When pumped by the light of wavelength lp incident at an angle u on the medium, the DFDL wavelength is given by [13]

lDFDL 5 nlp /n p sin u Here n and n p are the refractive indices of the dye solution and the prism material, respectively.

3.3. Results and discussion 3.3.1. Energy characteristics For energy measurements, the experimental conditions are chosen to correspond to the parameters of the computer simulations. Assuming that the total DFDL output power is equal on either side of the dye cell, the output energy of the DFDL is measured at one end using power meter (Ophir, Israel), as a function of input pump power, donor and acceptor concentrations. The measured values are graphically represented with the computed data in Figs. 8–10. The experimental values are found to be in close agreement with the theoretical values. 3.3.2. DFDL spectral widths The spectral width of the DFDL at donor and acceptor emission peak wavelengths are measured for single pulse DFDL using a home-built Fabry–Perot etalon having an air space 5 mm (FSR530 GHz) and finesse 17. Since the single pulse emission could not be ascertained in the

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Fig. 8. Donor and acceptor DFDL output energy as a function of pump laser energy for fixed donor (Nd 51.8310 18 cm 23 ) and acceptor concentration (Na 50.3310 18 cm 23 ).

Fig. 10. Donor and acceptor DFDL output energy as a function of acceptor concentration for fixed pump power (Ip 58.0310 22 cm 22 s 21 ) and donor concentration (Nd 51.8310 18 cm 23 ).

Fig. 9. Donor and acceptor DFDL output energy as a function of donor concentration for fixed pump power (Ip 58310 22 cm 22 s 21 ) and acceptor concentration (Na 50.3310 18 cm 23 ).

absence of direct measuring device such as streak camera, care is taken to maintain the pump power just above the single pulse threshold but much below the threshold required for the second pulse emission. Under this condition the output energy and the spectral width are measured. For a Gaussian pulse profile the transform limited time bandwidth product is DnDt50.441 [14]. Using this relation, the pulse duration is calculated indirectly from the measured linewidth. The values thus calculated are compared with the values obtained by solving rate equations and are presented in Tables 3 and 4. The beam divergence of DFDL is measured to be around 6 mrad.

Table 3 DFDL–single pulse energy and pulse width at the donor peak wavelength for fixed donor (Nd 51.8310 18 cm 23 ) and different acceptor concentrations Na 5 (310 18 23 cm )

Pump energy (mJ)

Output energy (mJ) Theoretical

Experimental

0.1 0.2 0.3 0.4 0.5 0.6

1.53 1.78 2.09 2.45 2.85 3.27

0.031 0.024 0.019 0.014 0.010 0.006

0.042 0.031 0.014 0.010 0.015 0.004

Experimental value of line ˚ width (A)

Pulse width (ps) Theoretical

Experimental

0.069 0.059 0.055 0.051 0.047 0.041

88 91 93 94 94 95

72 83 89 96 105 124

Table 4 DFDL–single pulse energy and pulse width at the acceptor peak wavelength for fixed donor (Nd 51.8310 18 cm 23 ) and different acceptor concentrations Na 5 (310 18 cm 23 )

Pump energy (mJ)

Output energy (mJ) Theoretical

Experimental

0.1 0.2 0.3 0.4 0.5 0.6

3.24 2.35 2.50 2.55 2.89 3.37

0.035 0.029 0.047 0.062 0.087 0.100

0.045 0.042 0.058 0.078 0.062 0.128

Experimental value of line ˚ width (A)

Pulse width (ps) Theoretical

Experimental

0.025 0.043 0.079 0.100 0.130 0.160

236 155 92 71 53 51

251 146 79 62 48 41

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4. Conclusion

Fig. 11. Donor DFDL as a function of angle of interference (u ).

We have observed pump power and concentration dependence of Nd:YAG laser pumped ETDFDL in both the donor and acceptor theoretically. From the theoretical studies of donor and acceptor DFDL, it has been found that the pulse width of both the DFDL pulses decreases with increase of pump power and donor concentration. With increase in the acceptor concentration the pulse width of acceptor DFDL decreases while that of donor DFDL increases. The experimental results on energy characteristics are found to be in good agreement with the theoretical results. Experimentally we have observed the continuous tunability of DFDL over yellow and red region (565–680 ˚ This nm). The observed spectral width is 0.025–0.16 A. finds many applications in high resolution and time domain laser spectroscopy.

References

Fig. 12. Acceptor DFDL as a function of angle of interference (u ).

3.3.3. Wavelength tuning RhB dye solution of 3 mM concentration is taken as donor medium for study. Experiment is carried out to study the tunability of donor DFDL by varying the angle of interference u of pump beam at the surface of the dye medium. It is observed that by varying u between 468 and 558, DFDL is emitted with peak at 538. Then the dye mixture is prepared by adding 2 ml of 1 mM concentration of acceptor Ab7 in 1 ml of 3 mM concentration of donor RhB. Experiment is repeated and the dye mixture is found to lase in acceptor region for the angle of interference varying between 438 and 498 with its peak at 458. DFDL output is tuned by changing the angle of interference of pump beam and the tunability range is measured using constant deviation spectrograph. The tunability range studied for the donor DFDL alone is from 565 to 650 nm and on addition of acceptor it extends up to 680 nm. Figs. 11 and 12 show the experimental values of the tuning with the theoretical one and the angular tuning of both the donor and acceptor is found to be nearly linear.

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