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Nd:YAG laser pumped energy transfer distributed feedback dye laser in Rhodamine 6G and Acid blue 7 dye mixture
Optics Communications 213 (2002) 67–80 www.elsevier.com/locate/optcom
Nd:YAG laser pumped energy transfer distributed feedback dye laser in Rhodamine 6G and Acid blue 7 dye mixture M. Basheer Ahamed a, P.K. Palanisamy b,* a
Department of Physics, Crescent Engineering College, Chennai 600 048, India b Centre for Laser Technology, Anna University, Chennai 600 025, India
Received 4 May 2002; received in revised form 9 July 2002; accepted 14 August 2002
Abstract The characteristics of Nd:YAG laser pumped energy transfer distributed feedback dye laser (ETDFDL) is studied theoretically and experimentally in a mixture of Rhodamine 6G and Acid blue 7 dyes. The characteristics of donor DFDL, the acceptor DFDL, the dependence of their pulse width and output power on donor–acceptor concentrations, pump power and lengths of the excited region are studied. Experimentally the output energy of DFDL is measured at the emission peak of donor and acceptor for different pump powers, donor, acceptor concentrations and length of the active medium. In addition, the tunability of DFDL emission both in donor and acceptor emission ranges is measured. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.55.Mv; 42.55 Keywords: Distributed feedback dye laser; Energy transfer; Tunability; Q-switching; Rate equations
1. Introduction Among the different mechanisms for the generation of ultra-short pulses, distributed feedback dye lasers have the added advantage of wavelength tunability. Generating periodic spatial gain modulation in dye solution Kogelnik and Shank demonstrated this for the first time in 1971 [1]. The advantage of DFDLs is that single pulses tunable
*
Corresponding author. Fax: +91-44-220-0660. E-mail address: [email protected] (P.K. Palanisamy).
in frequency can be produced without pulse selectors by choosing proper operating conditions. In DFDL pumped by a laser with nanosecond pulse duration, spiking caused by the relaxation oscillation is observed, with pulse duration of several tens of picosecond 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
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 9 1 1 - 9
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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 pico-second 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. Dyes, which are having low absorption cross-section at the pumping wavelength, are not suitable for efficient dye lasers. Increasing the concentration of the dye can overcome this difficulty but may cause concentration quench. A simple method is to use energy transfer from a dye, which can absorb the pump radiation efficiently. Energy transfer from an absorber (donor) molecule to acceptor molecule in a dye laser mixture affects the operation and spectral output of the dye laser. The mixture of two dissimilar dye molecules, for example, Rhodamine 6G (R6G) and Acid blue 7 (Ab7) can increase the efficiency of Acid blue 7. The energy transfer dye lasers (ETDLs) are more efficient because of high gain and low pump power requirements. Extensive studies have been already carried out on donor and acceptor concentration dependence of the gain spectrum for pulsed laser pumped ETDLs [6–8]. 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, we present a theoretical model, to study the characteristics of ETDFDLs as a function of acceptor and donor concentrations, the pump power, the lengths of the active region 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 R6G and Ab7 dye mixture as active medium are presented.
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 longrange dipole–dipole interaction (non-radiative Forster type of transfer) and (d) molecular complexing which changes the absorption spectrum of the donor on adding acceptor by forming fluorescent exciplex [9]. By considering, the actual mechanisms involved based on our experimental results, the rate equation model has been proposed. The observed emission spectra of R6G (donor) overlaps with the absorption spectra of the Ab7 (acceptor) shown in Fig. 1. 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 experi-
Fig. 1. Schematic diagram of absorption and fluorescence spectra of Rhodamine 6G and Acid blue 7.
M. Basheer Ahamed, P.K. Palanisamy / Optics Communications 213 (2002) 67–80
mental conditions. Hence, we employ the radiative and the Forster type of transfer (kF ) only in our model. Fig. 2 shows the energy level system model for energy transfer DFDL containing donor and acceptor dyes. The subscripts 0, 1, 2 denote the ground and excited states, respectively. In addition, the subscripts d, a indicate the donor and acceptor dye molecules, respectively. Here 1 ! 0 is the lasing transition. It is generally accepted that only S0 , S1 and S2 singlet states of the dye molecules are involved in the lasing process and in that, the S2 ! S1 non-radiative relaxation time is much shorter than the lifetime of the S1 state. Here Ip is the average pump photon flux per unit area (cm2 s1 ) of Nd:YAG second harmonic laser at 532 nm, Gaussian shaped in time, having pulse width 6.0 ns. The terms radl , redl denote the absorption and emission cross-section of donor dye at its lasing wavelength (560 nm), respectively. The terms raal and reaa denote the absorption and emission cross-section of acceptor dye at donor (560 nm) and acceptor lasing peak wavelength (655 nm), respectively. sd and sa are the decay time of donor and acceptor dye molecules which contribute spontaneous emission rates. The terms qd and qa indicate the density of donor and acceptor DFDL photons (cm3 ), respectively. To describe the energy transfer process that take place in a mixture of dyes the rate equation model described in [10] is modified with two more additional equations. The rate equation model consists of four coupled differential equations. The first two equations [(1) and (2)] describe the donor DFDL and the second pair of equations [(3) and (4)] describes the acceptor DFDL. The first equation in each pair is used to calculate the population
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density of the upper S1 level and the other one is for photon density inside the laser cavity. Here the terms Nd , Na in the equations indicate density of donor and acceptor dye molecules in the upper S1 level, respectively (cm3 ). The terms nd ðtÞ, na ðtÞ denote spatially averaged density of donor and acceptor dye molecules (cm3 ), respectively, in the upper S1 level. In this model we assume a uniform transversely excited region of length L, height b and depth a. The calculated parameters and the other symbols used in the rate equation model are given in Table 1. The following rate equations, describe the behavior of the DFDL containing mixed dyes [5,11]. The rate of change of donor dye molecules in the upper (S1 ) level dnd ¼ Ip ðtÞrpd ½Nd nd ðtÞ dt redl cnd ðtÞqd ðtÞ nd ðtÞ kF : n sd
ð1Þ
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 (cm3 /s). The rate of change of donor photon density within the laser cavity dqd redl cnd ðtÞqd ðtÞ qd ðtÞ Xd nd ðtÞ ¼ þ n sc ðtÞ sd dt raal c½Na na ðtÞqd ðtÞ n real cna ðtÞqd ðtÞ : ð2Þ n The first term of right-hand side of equation expresses the increase of the photon density by
Fig. 2. Schematic diagram of the energy transfer DFDL system model.
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Table 1 Spectral parameters of Rhodamine 6G and Acid blue 7 used in the rate equation model Symbols
Meaning of the symbol
Numerical value
sd sa R0 C0 C1=2 kF rpd
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 (k1 ¼ 560 nm) of donor Ground-state absorption cross-section of the acceptor dye molecules at the lasing wavelength (k1 ¼ 560 nm) Emission cross-section of acceptor dye molecules at the lasing wavelength (k1 ¼ 560 nm) of donor Emission cross-section of acceptor dye molecules at their lasing wavelength (ka ¼ 655 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 spontaneous emission Factor determining the fraction of the spontaneously emitted photons by excited donor and acceptor dye molecules
4.0 ns 3.3 ns 42.12 A 3:19 1018 cm3 (5:3 103 M) 1:59 1018 cm3 (2:65 103 M) 1:56 1010 cm3 /s (0:94 1011 l/mol/s) 3:42 1016 cm2
rpa redl raal real reaa L b c n np V S Xd and Xa
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 stimulated emission rate of acceptor dye molecules stimulated by the donor photons. 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 (S1 ) level dna reaa cna ðtÞqa ðtÞ ¼ Ip ðtÞrpa ½Na na ðtÞ n dt na ðtÞ raal c½Na na ðtÞqd ðtÞ þ sa n real cna ðtÞqd ðtÞ þ þ kF : n
ð3Þ
0:051 1016 cm2 3:78 1016 cm2 0:1558 1016 cm2 0:036 1016 cm2 6:9 1016 cm2 0.9 cm 0.02 cm 3 1010 cm s1 1.328 1.52 0.4 104 1:273 109 and 0:255 106
The 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 ground state acceptor molecules caused by their emission. The fifth term denotes the rate of increase of acceptor dye molecules stimulated by the donor photons. The rate of change of acceptor photon density within the laser cavity dqa reaa cna ðtÞqa ðtÞ qa ðtÞ Xa na ðtÞ ¼ þ : ð4Þ n sc ðtÞ sa dt The right-hand side of Eq. (4) has similar terms as that of Eq. (2). Since the DFDL has no external cavity the cavity decay time (in s) is given by [5] ! 2 nL3 ½nd ðtÞredl V nL sc ðtÞ ¼ max ; : ð5Þ 10c 8cp2
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The above equation is given a lower limit, which makes it possible to use the initial values nd ð0Þ ¼ 0, na ð0Þ ¼ 0, qd ð0Þ ¼ 0, qa ð0Þ ¼ 0, Nd ¼ 0 and Na ¼ 0. This lower limit reflects the fact that because of the finite length of the DFDL, the laser photons stay finite time sc ðtÞ in the excited volume. The exact value of this limit changes in time, however the solution of the differential equation system is independent of this limit, if sc ðtÞ significantly exceeds its value before the build-up of laser pulse. Eq. (5) is given a conditional statement to select every time the maximum value of sc ðtÞ in order to use the initial values. In the beginning the second term will take maximum value when nd ð0Þ ¼ 0, or very small. Later on, as nd ðtÞ becomes larger and larger the first term becomes larger Xd ¼
b Nd rpd L2 S
and
Xa ¼
b ; Na rpa L2 S
ð6Þ
where S is the spectral factor contributing spontaneous emission which falls into the DFDL bandwidth. The output power from one end of the DFDL (donor) is calculated as Pout ðtÞ ¼
hcqd ðtÞLab : 2kl sc ðtÞ
ð7Þ
The output power from one end of the DFDL (acceptor) is calculated as Pout ðtÞ ¼
hcqa ðtÞLab : 2ka sc ðtÞ
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2.2.1. Behaviour of donor DFDL at its emission peak (560 nm) The donor dye molecules are found to emit DFDL in the wavelength range 545–640 nm with its peak at 560 nm. At this wavelength, the behaviour of donor DFDL is studied varying pump power, length of the medium, donor and acceptor concentrations. 2.2.2. Dependence on pump power (Figs. 3 and 4) First DFDL output is studied as a function of pump power in the dye mixture with donor concentration Nd ¼ 1:8 1018 cm3 and acceptor concentration Na ¼ 0:3 1018 cm3 . For the emission of DFDL, minimum pump power called threshold is required. The medium starts emitting DFDL output just above the threshold whose value is found to be around 0.121 kW (Ip ¼ 1:8 1022 cm2 s1 ) and a single DFDL pulse is observed (shown in Fig. 3). This DFDL pulse is found to start after a delay of 11.72 ns with respect to the start of the pump pulse. With increase of pump power, output power of DFDL 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. This is due to faster build-up of population inversion with increase of pump rate. For example, when the pump power is increased to 0.132 kW (Ip ¼
ð8Þ
In order to equalize the number of incident and absorbed pump photons it is necessary to take the penetration depth a¼
1 : ðNd rpd þ Na rpa Þ
ð9Þ
2.2. Results and discussion Fourth order Runge–Kutta method has been used to solve Eqs. (1)–(8) numerically. Dyes R6G 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 DFDL emission is studied at both donor and acceptor wavelengths.
Fig. 3. Variation in pulse width and peak output power of donor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
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Fig. 4. Variation in pulse width and peak output power of donor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
1:96 1022 cm2 s1 ), the DFDL pulse is found to emerge after a time delay of 10.12 ns. Above a certain pump power second DFDL pulse emerges out. With increase of pump power, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For pump power of 0.202 kW (Ip ¼ 3:0 1022 cm2 s1 ), five pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 54 ps, the consecutive pulses are found to have their widths 65, 80, 101 and 142 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in pump power. For example when the pump power increases from 0.202 to 0.471 kW (Ip ¼ 3:0– 7:0 1022 cm2 s1 ), the pulse width of the first pulse of DFDL is found to decrease from 54 to 44 ps as shown in Fig. 4. From the data generated the total output energy for the train of pulses is also found by calculating the individual pulse energy. The single pulse energy is computed by multiplying the peak power with its pulse duration (FWHM). It has been found that the output energy increases with increase in pump power. For example, when the pump power is varied from 0.121 to 0.47 kW, the total output energy increases from 0.004 to 0:35 lJ.
2.2.3. Dependence on donor concentration (Figs. 5 and 6) For pump power 0.219 kW (Ip ¼ 3:25 1022 cm2 s1 ) and Na ¼ 0:3 1018 cm3 , the threshold donor concentration for emission of DFDL is found to be 1:0 1018 cm3 as shown in Fig. 5. The DFDL pulse is found to start after a delay of 11.96 ns with respect to start of the pump pulse. With increase of Nd to 1:10 1018 cm3 , output power of DFDL 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 concentration of donor. For example, when Nd is increased to 1:10 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.44 ns. With increase of donor concentration to 1:11 1018 cm3 second DFDL pulse emerges out. With increase of donor concentration further, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Nd ¼ 1:8 1018 cm3 , six pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 52 ps, the consecutive pulses are found to have their widths 62, 74, 90, 112 and 156 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Nd . For example, when Nd
Fig. 5. Variation in pulse width and peak output power of donor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different donor concentrations.
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Fig. 6. Variation in pulse width and peak output power of donor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different donor concentrations.
increases from 1:8 1018 to 2:8 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 52 to 47 ps as shown in Fig. 6. The total output energy for the train of pulses is calculated for different donor concentrations and it is found to increase with increase in donor concentration. For example, when Nd increases from 1:0 1018 to 2:8 1018 cm3 , the total output energy increases from 0.002 to 0:12 lJ. 2.2.4. Dependence on acceptor concentration (Figs. 7 and 8) The DFDL emission at donor wavelength depends on the concentration of acceptor. With
Fig. 7. Variation in pulse width and peak output power of donor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different acceptor concentrations.
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Fig. 8. Variation in pulse width and peak output power of donor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different acceptor concentrations.
increase of acceptor concentration, the number of DFDL pulses as well as the peak power decreases. For pump power 0.219 kW and Nd ¼ 1:8 1018 cm3 , the maximum acceptor concentration up to which emission of DFDL at donor peak (560 nm) occurs is found to be around 1:1 1018 cm3 as shown in Fig. 7. The DFDL pulse is found to start after a delay of 11.59 ns with respect to start of the pump pulse. With decrease of Na , output power of DFDL 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 higher concentration of acceptor. For example, when Na decreases to 0:964 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.03 ns. Below certain Na (Na ¼ 0:952 1018 cm3 ), the second DFDL pulse emerges out. With further decrease of Na the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Na ¼ 0:1 1018 cm3 , six pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 46 ps, the consecutive pulses are found to have their widths 53, 62, 72, 86 and 102 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with decrease in Na . For example, when Na decreases from 0:6 1018 to 0:1 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 65 to 46 ps as shown in Fig. 8.
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The total output energy for the train of pulses is calculated for different acceptor concentrations and it is found to decrease with increase in acceptor concentration. For example, when Na increases from 0:1 1018 to 1:1 1018 cm3 , the total output energy decreases from 0.16 to 0:001 lJ. 2.2.5. Dependence on the length of the DFDL (Fig. 9) For pump power 0.336 kW (Ip ¼ 5:0 1022 cm2 s1 ), Nd ¼ 1:8 1018 cm3 and Na ¼ 0:3 1018 cm3 , donor DFDL emission is found to occur at L ¼ 0:3 cm. The DFDL pulse is found to start after a delay of 10.09 ns with respect to start of the pump pulse. With increase of L, output power of DFDL single pulse is found to increase with increase in pulse width. At the same time, the DFDL pulse is found to emerge earlier compared to the DFDL pulse emitted with lesser length. For example, when L is increased to 0.5 cm the DFDL pulse is found to emerge after a time delay of 8.38 ns. With further increase in length, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For L ¼ 0:5 cm, seven pulses are observed in the emitted DFDL train. While the pulse width of the
Fig. 9. Variation in pulse width and peak output power of donor DFDL at fixed pump photon intensity (Ip ¼ 0:5 1023 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different lengths of the excited region.
first pulse is 39 ps, the consecutive pulses are found to have their widths 44, 50, 57, 68, 74 and 83 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with decrease in L. For example, when L decreases from 0.9 to 0.5 cm, the pulse width of the first pulse of DFDL is found to decrease from 47 to 39 ps as shown in Fig. 9. The total output energy for the train of pulses is calculated for different lengths of the excited region and it is found to increase with increase in length. For example, when L increases from 0.5 to 0.9 cm, the total output energy increases from 0.079 to 0:35 lJ. 2.2.6. Behaviour of acceptor DFDL at its emission peak (655 nm) The acceptor dye molecules are found to emit DFDL in the wavelength range 610–675 nm with its peak at 655 nm. At this wavelength, the behaviour of acceptor DFDL is studied varying pump power, length of the medium, donor and acceptor concentrations. 2.2.7. Dependence on pump power (Figs. 10 and 11) Above a threshold pump power, the medium starts emitting DFDL output. Just above the threshold, a single DFDL pulse is emitted. For example, when Nd ¼ 1:8 1018 and Na ¼
Fig. 10. Variation in pulse width and peak output power of acceptor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
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It has been found that the output energy increases with increase in pump power. For example, when the pump power is varied from 0.21 to 0.47 kW, the total output energy increases from 0.001 to 0:21 lJ.
Fig. 11. Variation in pulse width and peak output power of acceptor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
0:3 1018 cm3 the threshold pump power is found to be 0.208 kW (Ip ¼ 3:1 1022 cm2 s1 ) as shown in Fig. 10. The DFDL pulse is found to start after a delay of 11.69 ns with respect to the start of the pump pulse. With increase of pump power, output power of DFDL 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. For example, when the pump power increased to 0.242 kW (Ip ¼ 3:60 1022 cm2 s1 ), the DFDL pulse is found to emerge after a time delay of 9.93 ns. Above a certain pump power second DFDL pulse emerges out. With further increase in pump power, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For pump power of 0.403 kW, seven pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 80 ps, the consecutive pulses are found to have their widths 117, 181, 231, 287, 362 and 384 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in pump power. For example when the pump power increases from 0.269 to 0.471 kW, the pulse width of the first pulse of DFDL is found to decrease from 119 to 79 ps as shown in Fig. 11.
2.2.8. Dependence on donor concentration (Figs. 12 and 13) For pump power 0.219 kW and Na ¼ 0:3 1018 cm3 , the threshold donor concentration for emission of DFDL is found to be 1:72 1018 cm3 . The DFDL pulse is found to start after a delay of 11.68 ns with respect to start of the pump pulse. With increase of Nd , output power of DFDL 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 concentration of donor. For example, when Nd increases to 2:0 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.22 ns. Above a certain donor concentration, second DFDL pulse emerges out as shown in Fig. 12. With further increase of Nd the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Nd ¼ 2:8 1018 cm3 , five pulses are observed in the emitted DFDL train. While the pulse width of
Fig. 12. Variation in pulse width and peak output power of acceptor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different donor concentrations.
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Fig. 13. Variation in pulse width and peak output power of acceptor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different donor concentrations.
Fig. 14. Variation in pulse width and peak output power of acceptor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different acceptor concentrations.
the first pulse is 81 ps, the consecutive pulses are found to have their widths 121, 147, 179 and 272 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Nd . For example, when Nd increases from 1:8 1018 to 2:8 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 306 to 81 ps as shown in Fig. 13. The total output energy for the train of pulses is calculated for different donor concentrations and it is found to increase with increase in donor concentration. For example, when Nd increases from 1:8 1018 to 2:8 1018 cm3 , the total output energy increases from 0.01 to 0:08 lJ.
Above certain Na second DFDL pulse emerges out. With further increase of Na the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Na ¼ 0:4 1018 cm3 , two pulses are observed in the emitted DFDL train, with pulse widths 127 and 298 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Na . For example, when Na increases from 0:1 1018 to
2.2.9. Dependence on acceptor concentration (Figs. 14 and 15) For pump power 0.219 kW and Nd ¼ 1:8 1018 cm3 , the threshold acceptor concentration for emission of DFDL is found to be around 0:29 1018 cm3 as shown in Fig. 14. The DFDL pulse is found to start after a delay of 11.65 ns with respect to start of the pump pulse. With increase of Na , output power of DFDL 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 concentration of acceptor. For example, when Na increases to 0:39 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.28 ns.
Fig. 15. Variation in pulse width and peak output power of acceptor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different acceptor concentrations.
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0:6 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 127 to 100 ps as shown in Fig. 15. The total output energy for the train of pulses is calculated for different acceptor concentrations and it is found to increase with increase in acceptor concentration. For example, when Na increases from 0:3 1018 to 0:6 1018 cm3 , the total output energy increases from 0.013 to 0:05 lJ. 2.2.10. Dependence on length of the DFDL (Fig. 16) For, Ip ¼ 5:0 1022 cm2 s1 , Nd ¼ 1:8 1018 cm3 and Na ¼ 0:3 1018 cm3 , the acceptor DFDL emission found to occur at a length 0.7 cm. The DFDL pulse is found to start after a delay of 10.89 ns with respect to start of the pump pulse. With increase of L, output power of DFDL 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 lower value of L. For example, when L increases to 0.9 cm the DFDL pulse is found to emerge after a time delay of 8.48 ns. With increase of L the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For L ¼ 0:9 cm, five pulses are ob-
Fig. 16. Variation in pulse width and peak output power of acceptor DFDL at fixed pump photon intensity (Ip ¼ 0:5 1023 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different lengths of the excited region.
77
served in the emitted DFDL train. While the pulse width of the first pulse is 86 ps, the consecutive pulses have their pulse widths 127, 162, 178 and 196 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in L. For example, when L increases from 0.7 to 0.9 cm, the pulse width of the first pulse of DFDL is found to decrease from 139 to 86 ps as shown in Fig. 16. The total output energy for the train of pulses is calculated for different lengths of the excited region and it is found to increase with increase in length. For example, when L increases from 0.7 to 0.9 cm, the total output energy increases from 0.018 to 0:068 lJ. In the rate Eqs. (1) and (3), the term kF does not have any significant contribution in the simulated data indicating that Forster type energy transfer is insignificant [5].
3. Experimental studies 3.1. Materials Both the dyes R6G and Ab7 are of laser grade supplied by Central Drug House, Bombay, India. The solvent methanol used is of spectroscopic grade. The general formula and structure of Acid blue 7 (C.I.42080, Alphazurine A) dye are illustrated in Fig. 17. The chromophore of the dye is the quinonoid group which appears as C@Ar@NR1 R2 and it is a diamino derivative of the triphenylmethane group. The absorption and fluorescence spectra are taken using 0.01 mM concentration R6G and Ab7 dyes using spectrophotometer (ELCO, India) and spectrofluorome-
Fig. 17. The molecular formula and chemical structure of the Acid blue 7 dye.
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ter (Fluoromax II, USA), respectively. The spectral parameters of R6G and Ab7 dyes have been calculated from the observed absorption and fluorescence spectra of the dyes. The calculated spectral parameters are listed in Table 1. 3.2. Experimental set-up to study DFDL Fig. 18 shows the distributed feedback prismdye 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 distributed feedback for the dye laser is obtained using an isosceles rightangled quartz prism. The pump beam is focussed by a cylindrical quartz lens into a line image, which is incident on the hypotenuse AB of the prism. 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 kp incident at an angle h on the medium, the DFDL wavelength is given by [12]
Here n and np 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 is of the DFDL is measured at one end using power meter (Ophir, Israel), as a function of input pump power, donor, acceptor concentrations and length of the medium. The measured values are graphically represented with the computed data in Figs. 19–22. The experimental values are found to be in close agreement with the theoretical values.
kDFDL ¼ nkp =np sin h: Fig. 19. Donor and acceptor DFDL output energy as a function of donor concentration for fixed pump power (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ).
Fig. 18. Schematic diagram of the prism-dye cell.
Fig. 20. Donor and acceptor DFDL output energy as a function of donor concentration for fixed pump power (Ip ¼ 3:25 1022 cm2 s1 ) and acceptor concentration (Nd ¼ 0:3 1018 cm3 ).
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Fig. 23. Donor DFDL as a function of angle of interference (h). Fig. 21. Donor and acceptor DFDL output energy as a function of acceptor concentration for fixed pump power (Ip ¼ 3:25 1022 cm2 s1 ) and donor concentration (Nd ¼ 1:8 1018 cm3 ).
Fig. 24. Acceptor DFDL as a function of angle of interference (h).
Fig. 22. Donor and acceptor DFDL output energy as a function of length for fixed pump power (Ip ¼ 5 1022 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ).
3.3.2. Wavelength tuning Experiments are performed to study the tunability of both the donor and acceptor DFDL by varying the intersection angle. First, the experimental arrangement is set for emission peak of R6G by varying the angle of interference of the pump beam. R6G dye solution of 3 mM concentration is taken for study. Experiments are carried out to study the tunability of donor DFDL by varying the angle of interference. It is observed that by varying h between 47° and 58°, DFDL is emitted with peak at 56°. 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 R6G. This dye mixture is found to lase in acceptor region for the
angle of interference varying between 43° and 50° with its peak at 45°. DFDL output is tuned by changing the angle and is measured using constant deviation spectrograph. The tunability range studied for the donor DFDL alone is from 545 to 640 nm and an addition of acceptor it extends up to 675 nm. Figs. 23 and 24 show the experimental values of the tuning with the theoretical one and the angular tuning of both the donor and acceptor is linear.
4. Conclusion We have observed pump power, concentration and length 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 pump power and donor concentration. Whereas with increase in the acceptor concentration and length of the DFDL the pulse width of acceptor DFDL decreases while that of donor DFDL
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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 (545–675 nm). This finds many applications in high resolution and time domain laser spectroscopy.
References [1] H. Kogelnik, C.V. Shank, Appl. Phys. Lett. 18 (1971) 152. [2] Z. Bor, A. Muller, IEEE J. Quantum Electron. QE-22 (8) (1986) 1524.
[3] M. Maeda, Y. Oki, K. Imamura, IEEE J. Quantum Electron. 33 (12) (1997) 2146. [4] Z. Bor, B. Racz, A. Muller, Appl. Opt. 22 (1983) 3327. [5] J. Hebling, Appl. Phys. B 47 (1988) 267. [6] Tsuneo, Urisu, K. Kajiyama, J. Appl. Phys. 47 (1976) 3563. [7] N.P. Ernsting, B. Nikolaus, Appl. Phys. B 41 (1986) 25. [8] M. Fukuda, K. Mito, Jpn. J. Appl. Phys. 39 (2000) 3470. [9] Th. Forster, Discuss. Faraday Soc. 27 (1959) 7. [10] Z.S. Bor, A. Muller, B. Racz, F.P. Schafer, Appl. Phys. B 27 (1982) 9. [11] J. Hebling, J. Seres, Z.S. Bor, Opt. Quantum Electron. 22 (1990) 375. [12] S. Chandra, W. Takeuchi, S.R. Hartmann, Appl. Phys. Lett. 21 (1972) 144.
Nd:YAG laser pumped energy transfer distributed feedback dye laser in Rhodamine 6G and Acid blue 7 dye mixture M. Basheer Ahamed a, P.K. Palanisamy b,* a
Department of Physics, Crescent Engineering College, Chennai 600 048, India b Centre for Laser Technology, Anna University, Chennai 600 025, India
Received 4 May 2002; received in revised form 9 July 2002; accepted 14 August 2002
Abstract The characteristics of Nd:YAG laser pumped energy transfer distributed feedback dye laser (ETDFDL) is studied theoretically and experimentally in a mixture of Rhodamine 6G and Acid blue 7 dyes. The characteristics of donor DFDL, the acceptor DFDL, the dependence of their pulse width and output power on donor–acceptor concentrations, pump power and lengths of the excited region are studied. Experimentally the output energy of DFDL is measured at the emission peak of donor and acceptor for different pump powers, donor, acceptor concentrations and length of the active medium. In addition, the tunability of DFDL emission both in donor and acceptor emission ranges is measured. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.55.Mv; 42.55 Keywords: Distributed feedback dye laser; Energy transfer; Tunability; Q-switching; Rate equations
1. Introduction Among the different mechanisms for the generation of ultra-short pulses, distributed feedback dye lasers have the added advantage of wavelength tunability. Generating periodic spatial gain modulation in dye solution Kogelnik and Shank demonstrated this for the first time in 1971 [1]. The advantage of DFDLs is that single pulses tunable
*
Corresponding author. Fax: +91-44-220-0660. E-mail address: [email protected] (P.K. Palanisamy).
in frequency can be produced without pulse selectors by choosing proper operating conditions. In DFDL pumped by a laser with nanosecond pulse duration, spiking caused by the relaxation oscillation is observed, with pulse duration of several tens of picosecond 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
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 9 1 1 - 9
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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 pico-second 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. Dyes, which are having low absorption cross-section at the pumping wavelength, are not suitable for efficient dye lasers. Increasing the concentration of the dye can overcome this difficulty but may cause concentration quench. A simple method is to use energy transfer from a dye, which can absorb the pump radiation efficiently. Energy transfer from an absorber (donor) molecule to acceptor molecule in a dye laser mixture affects the operation and spectral output of the dye laser. The mixture of two dissimilar dye molecules, for example, Rhodamine 6G (R6G) and Acid blue 7 (Ab7) can increase the efficiency of Acid blue 7. The energy transfer dye lasers (ETDLs) are more efficient because of high gain and low pump power requirements. Extensive studies have been already carried out on donor and acceptor concentration dependence of the gain spectrum for pulsed laser pumped ETDLs [6–8]. 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, we present a theoretical model, to study the characteristics of ETDFDLs as a function of acceptor and donor concentrations, the pump power, the lengths of the active region 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 R6G and Ab7 dye mixture as active medium are presented.
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 longrange dipole–dipole interaction (non-radiative Forster type of transfer) and (d) molecular complexing which changes the absorption spectrum of the donor on adding acceptor by forming fluorescent exciplex [9]. By considering, the actual mechanisms involved based on our experimental results, the rate equation model has been proposed. The observed emission spectra of R6G (donor) overlaps with the absorption spectra of the Ab7 (acceptor) shown in Fig. 1. 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 experi-
Fig. 1. Schematic diagram of absorption and fluorescence spectra of Rhodamine 6G and Acid blue 7.
M. Basheer Ahamed, P.K. Palanisamy / Optics Communications 213 (2002) 67–80
mental conditions. Hence, we employ the radiative and the Forster type of transfer (kF ) only in our model. Fig. 2 shows the energy level system model for energy transfer DFDL containing donor and acceptor dyes. The subscripts 0, 1, 2 denote the ground and excited states, respectively. In addition, the subscripts d, a indicate the donor and acceptor dye molecules, respectively. Here 1 ! 0 is the lasing transition. It is generally accepted that only S0 , S1 and S2 singlet states of the dye molecules are involved in the lasing process and in that, the S2 ! S1 non-radiative relaxation time is much shorter than the lifetime of the S1 state. Here Ip is the average pump photon flux per unit area (cm2 s1 ) of Nd:YAG second harmonic laser at 532 nm, Gaussian shaped in time, having pulse width 6.0 ns. The terms radl , redl denote the absorption and emission cross-section of donor dye at its lasing wavelength (560 nm), respectively. The terms raal and reaa denote the absorption and emission cross-section of acceptor dye at donor (560 nm) and acceptor lasing peak wavelength (655 nm), respectively. sd and sa are the decay time of donor and acceptor dye molecules which contribute spontaneous emission rates. The terms qd and qa indicate the density of donor and acceptor DFDL photons (cm3 ), respectively. To describe the energy transfer process that take place in a mixture of dyes the rate equation model described in [10] is modified with two more additional equations. The rate equation model consists of four coupled differential equations. The first two equations [(1) and (2)] describe the donor DFDL and the second pair of equations [(3) and (4)] describes the acceptor DFDL. The first equation in each pair is used to calculate the population
69
density of the upper S1 level and the other one is for photon density inside the laser cavity. Here the terms Nd , Na in the equations indicate density of donor and acceptor dye molecules in the upper S1 level, respectively (cm3 ). The terms nd ðtÞ, na ðtÞ denote spatially averaged density of donor and acceptor dye molecules (cm3 ), respectively, in the upper S1 level. In this model we assume a uniform transversely excited region of length L, height b and depth a. The calculated parameters and the other symbols used in the rate equation model are given in Table 1. The following rate equations, describe the behavior of the DFDL containing mixed dyes [5,11]. The rate of change of donor dye molecules in the upper (S1 ) level dnd ¼ Ip ðtÞrpd ½Nd nd ðtÞ dt redl cnd ðtÞqd ðtÞ nd ðtÞ kF : n sd
ð1Þ
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 (cm3 /s). The rate of change of donor photon density within the laser cavity dqd redl cnd ðtÞqd ðtÞ qd ðtÞ Xd nd ðtÞ ¼ þ n sc ðtÞ sd dt raal c½Na na ðtÞqd ðtÞ n real cna ðtÞqd ðtÞ : ð2Þ n The first term of right-hand side of equation expresses the increase of the photon density by
Fig. 2. Schematic diagram of the energy transfer DFDL system model.
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Table 1 Spectral parameters of Rhodamine 6G and Acid blue 7 used in the rate equation model Symbols
Meaning of the symbol
Numerical value
sd sa R0 C0 C1=2 kF rpd
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 (k1 ¼ 560 nm) of donor Ground-state absorption cross-section of the acceptor dye molecules at the lasing wavelength (k1 ¼ 560 nm) Emission cross-section of acceptor dye molecules at the lasing wavelength (k1 ¼ 560 nm) of donor Emission cross-section of acceptor dye molecules at their lasing wavelength (ka ¼ 655 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 spontaneous emission Factor determining the fraction of the spontaneously emitted photons by excited donor and acceptor dye molecules
4.0 ns 3.3 ns 42.12 A 3:19 1018 cm3 (5:3 103 M) 1:59 1018 cm3 (2:65 103 M) 1:56 1010 cm3 /s (0:94 1011 l/mol/s) 3:42 1016 cm2
rpa redl raal real reaa L b c n np V S Xd and Xa
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 stimulated emission rate of acceptor dye molecules stimulated by the donor photons. 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 (S1 ) level dna reaa cna ðtÞqa ðtÞ ¼ Ip ðtÞrpa ½Na na ðtÞ n dt na ðtÞ raal c½Na na ðtÞqd ðtÞ þ sa n real cna ðtÞqd ðtÞ þ þ kF : n
ð3Þ
0:051 1016 cm2 3:78 1016 cm2 0:1558 1016 cm2 0:036 1016 cm2 6:9 1016 cm2 0.9 cm 0.02 cm 3 1010 cm s1 1.328 1.52 0.4 104 1:273 109 and 0:255 106
The 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 ground state acceptor molecules caused by their emission. The fifth term denotes the rate of increase of acceptor dye molecules stimulated by the donor photons. The rate of change of acceptor photon density within the laser cavity dqa reaa cna ðtÞqa ðtÞ qa ðtÞ Xa na ðtÞ ¼ þ : ð4Þ n sc ðtÞ sa dt The right-hand side of Eq. (4) has similar terms as that of Eq. (2). Since the DFDL has no external cavity the cavity decay time (in s) is given by [5] ! 2 nL3 ½nd ðtÞredl V nL sc ðtÞ ¼ max ; : ð5Þ 10c 8cp2
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The above equation is given a lower limit, which makes it possible to use the initial values nd ð0Þ ¼ 0, na ð0Þ ¼ 0, qd ð0Þ ¼ 0, qa ð0Þ ¼ 0, Nd ¼ 0 and Na ¼ 0. This lower limit reflects the fact that because of the finite length of the DFDL, the laser photons stay finite time sc ðtÞ in the excited volume. The exact value of this limit changes in time, however the solution of the differential equation system is independent of this limit, if sc ðtÞ significantly exceeds its value before the build-up of laser pulse. Eq. (5) is given a conditional statement to select every time the maximum value of sc ðtÞ in order to use the initial values. In the beginning the second term will take maximum value when nd ð0Þ ¼ 0, or very small. Later on, as nd ðtÞ becomes larger and larger the first term becomes larger Xd ¼
b Nd rpd L2 S
and
Xa ¼
b ; Na rpa L2 S
ð6Þ
where S is the spectral factor contributing spontaneous emission which falls into the DFDL bandwidth. The output power from one end of the DFDL (donor) is calculated as Pout ðtÞ ¼
hcqd ðtÞLab : 2kl sc ðtÞ
ð7Þ
The output power from one end of the DFDL (acceptor) is calculated as Pout ðtÞ ¼
hcqa ðtÞLab : 2ka sc ðtÞ
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2.2.1. Behaviour of donor DFDL at its emission peak (560 nm) The donor dye molecules are found to emit DFDL in the wavelength range 545–640 nm with its peak at 560 nm. At this wavelength, the behaviour of donor DFDL is studied varying pump power, length of the medium, donor and acceptor concentrations. 2.2.2. Dependence on pump power (Figs. 3 and 4) First DFDL output is studied as a function of pump power in the dye mixture with donor concentration Nd ¼ 1:8 1018 cm3 and acceptor concentration Na ¼ 0:3 1018 cm3 . For the emission of DFDL, minimum pump power called threshold is required. The medium starts emitting DFDL output just above the threshold whose value is found to be around 0.121 kW (Ip ¼ 1:8 1022 cm2 s1 ) and a single DFDL pulse is observed (shown in Fig. 3). This DFDL pulse is found to start after a delay of 11.72 ns with respect to the start of the pump pulse. With increase of pump power, output power of DFDL 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. This is due to faster build-up of population inversion with increase of pump rate. For example, when the pump power is increased to 0.132 kW (Ip ¼
ð8Þ
In order to equalize the number of incident and absorbed pump photons it is necessary to take the penetration depth a¼
1 : ðNd rpd þ Na rpa Þ
ð9Þ
2.2. Results and discussion Fourth order Runge–Kutta method has been used to solve Eqs. (1)–(8) numerically. Dyes R6G 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 DFDL emission is studied at both donor and acceptor wavelengths.
Fig. 3. Variation in pulse width and peak output power of donor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
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Fig. 4. Variation in pulse width and peak output power of donor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
1:96 1022 cm2 s1 ), the DFDL pulse is found to emerge after a time delay of 10.12 ns. Above a certain pump power second DFDL pulse emerges out. With increase of pump power, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For pump power of 0.202 kW (Ip ¼ 3:0 1022 cm2 s1 ), five pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 54 ps, the consecutive pulses are found to have their widths 65, 80, 101 and 142 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in pump power. For example when the pump power increases from 0.202 to 0.471 kW (Ip ¼ 3:0– 7:0 1022 cm2 s1 ), the pulse width of the first pulse of DFDL is found to decrease from 54 to 44 ps as shown in Fig. 4. From the data generated the total output energy for the train of pulses is also found by calculating the individual pulse energy. The single pulse energy is computed by multiplying the peak power with its pulse duration (FWHM). It has been found that the output energy increases with increase in pump power. For example, when the pump power is varied from 0.121 to 0.47 kW, the total output energy increases from 0.004 to 0:35 lJ.
2.2.3. Dependence on donor concentration (Figs. 5 and 6) For pump power 0.219 kW (Ip ¼ 3:25 1022 cm2 s1 ) and Na ¼ 0:3 1018 cm3 , the threshold donor concentration for emission of DFDL is found to be 1:0 1018 cm3 as shown in Fig. 5. The DFDL pulse is found to start after a delay of 11.96 ns with respect to start of the pump pulse. With increase of Nd to 1:10 1018 cm3 , output power of DFDL 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 concentration of donor. For example, when Nd is increased to 1:10 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.44 ns. With increase of donor concentration to 1:11 1018 cm3 second DFDL pulse emerges out. With increase of donor concentration further, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Nd ¼ 1:8 1018 cm3 , six pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 52 ps, the consecutive pulses are found to have their widths 62, 74, 90, 112 and 156 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Nd . For example, when Nd
Fig. 5. Variation in pulse width and peak output power of donor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different donor concentrations.
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Fig. 6. Variation in pulse width and peak output power of donor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different donor concentrations.
increases from 1:8 1018 to 2:8 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 52 to 47 ps as shown in Fig. 6. The total output energy for the train of pulses is calculated for different donor concentrations and it is found to increase with increase in donor concentration. For example, when Nd increases from 1:0 1018 to 2:8 1018 cm3 , the total output energy increases from 0.002 to 0:12 lJ. 2.2.4. Dependence on acceptor concentration (Figs. 7 and 8) The DFDL emission at donor wavelength depends on the concentration of acceptor. With
Fig. 7. Variation in pulse width and peak output power of donor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different acceptor concentrations.
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Fig. 8. Variation in pulse width and peak output power of donor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different acceptor concentrations.
increase of acceptor concentration, the number of DFDL pulses as well as the peak power decreases. For pump power 0.219 kW and Nd ¼ 1:8 1018 cm3 , the maximum acceptor concentration up to which emission of DFDL at donor peak (560 nm) occurs is found to be around 1:1 1018 cm3 as shown in Fig. 7. The DFDL pulse is found to start after a delay of 11.59 ns with respect to start of the pump pulse. With decrease of Na , output power of DFDL 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 higher concentration of acceptor. For example, when Na decreases to 0:964 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.03 ns. Below certain Na (Na ¼ 0:952 1018 cm3 ), the second DFDL pulse emerges out. With further decrease of Na the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Na ¼ 0:1 1018 cm3 , six pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 46 ps, the consecutive pulses are found to have their widths 53, 62, 72, 86 and 102 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with decrease in Na . For example, when Na decreases from 0:6 1018 to 0:1 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 65 to 46 ps as shown in Fig. 8.
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The total output energy for the train of pulses is calculated for different acceptor concentrations and it is found to decrease with increase in acceptor concentration. For example, when Na increases from 0:1 1018 to 1:1 1018 cm3 , the total output energy decreases from 0.16 to 0:001 lJ. 2.2.5. Dependence on the length of the DFDL (Fig. 9) For pump power 0.336 kW (Ip ¼ 5:0 1022 cm2 s1 ), Nd ¼ 1:8 1018 cm3 and Na ¼ 0:3 1018 cm3 , donor DFDL emission is found to occur at L ¼ 0:3 cm. The DFDL pulse is found to start after a delay of 10.09 ns with respect to start of the pump pulse. With increase of L, output power of DFDL single pulse is found to increase with increase in pulse width. At the same time, the DFDL pulse is found to emerge earlier compared to the DFDL pulse emitted with lesser length. For example, when L is increased to 0.5 cm the DFDL pulse is found to emerge after a time delay of 8.38 ns. With further increase in length, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For L ¼ 0:5 cm, seven pulses are observed in the emitted DFDL train. While the pulse width of the
Fig. 9. Variation in pulse width and peak output power of donor DFDL at fixed pump photon intensity (Ip ¼ 0:5 1023 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different lengths of the excited region.
first pulse is 39 ps, the consecutive pulses are found to have their widths 44, 50, 57, 68, 74 and 83 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with decrease in L. For example, when L decreases from 0.9 to 0.5 cm, the pulse width of the first pulse of DFDL is found to decrease from 47 to 39 ps as shown in Fig. 9. The total output energy for the train of pulses is calculated for different lengths of the excited region and it is found to increase with increase in length. For example, when L increases from 0.5 to 0.9 cm, the total output energy increases from 0.079 to 0:35 lJ. 2.2.6. Behaviour of acceptor DFDL at its emission peak (655 nm) The acceptor dye molecules are found to emit DFDL in the wavelength range 610–675 nm with its peak at 655 nm. At this wavelength, the behaviour of acceptor DFDL is studied varying pump power, length of the medium, donor and acceptor concentrations. 2.2.7. Dependence on pump power (Figs. 10 and 11) Above a threshold pump power, the medium starts emitting DFDL output. Just above the threshold, a single DFDL pulse is emitted. For example, when Nd ¼ 1:8 1018 and Na ¼
Fig. 10. Variation in pulse width and peak output power of acceptor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
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It has been found that the output energy increases with increase in pump power. For example, when the pump power is varied from 0.21 to 0.47 kW, the total output energy increases from 0.001 to 0:21 lJ.
Fig. 11. Variation in pulse width and peak output power of acceptor DFDL at fixed donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different pump photon intensities.
0:3 1018 cm3 the threshold pump power is found to be 0.208 kW (Ip ¼ 3:1 1022 cm2 s1 ) as shown in Fig. 10. The DFDL pulse is found to start after a delay of 11.69 ns with respect to the start of the pump pulse. With increase of pump power, output power of DFDL 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. For example, when the pump power increased to 0.242 kW (Ip ¼ 3:60 1022 cm2 s1 ), the DFDL pulse is found to emerge after a time delay of 9.93 ns. Above a certain pump power second DFDL pulse emerges out. With further increase in pump power, the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For pump power of 0.403 kW, seven pulses are observed in the emitted DFDL train. While the pulse width of the first pulse is 80 ps, the consecutive pulses are found to have their widths 117, 181, 231, 287, 362 and 384 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in pump power. For example when the pump power increases from 0.269 to 0.471 kW, the pulse width of the first pulse of DFDL is found to decrease from 119 to 79 ps as shown in Fig. 11.
2.2.8. Dependence on donor concentration (Figs. 12 and 13) For pump power 0.219 kW and Na ¼ 0:3 1018 cm3 , the threshold donor concentration for emission of DFDL is found to be 1:72 1018 cm3 . The DFDL pulse is found to start after a delay of 11.68 ns with respect to start of the pump pulse. With increase of Nd , output power of DFDL 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 concentration of donor. For example, when Nd increases to 2:0 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.22 ns. Above a certain donor concentration, second DFDL pulse emerges out as shown in Fig. 12. With further increase of Nd the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Nd ¼ 2:8 1018 cm3 , five pulses are observed in the emitted DFDL train. While the pulse width of
Fig. 12. Variation in pulse width and peak output power of acceptor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different donor concentrations.
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Fig. 13. Variation in pulse width and peak output power of acceptor DFDL at fixed acceptor concentration (Na ¼ 0:3 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different donor concentrations.
Fig. 14. Variation in pulse width and peak output power of acceptor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm3 s1 ) for different acceptor concentrations.
the first pulse is 81 ps, the consecutive pulses are found to have their widths 121, 147, 179 and 272 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Nd . For example, when Nd increases from 1:8 1018 to 2:8 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 306 to 81 ps as shown in Fig. 13. The total output energy for the train of pulses is calculated for different donor concentrations and it is found to increase with increase in donor concentration. For example, when Nd increases from 1:8 1018 to 2:8 1018 cm3 , the total output energy increases from 0.01 to 0:08 lJ.
Above certain Na second DFDL pulse emerges out. With further increase of Na the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For Na ¼ 0:4 1018 cm3 , two pulses are observed in the emitted DFDL train, with pulse widths 127 and 298 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in Na . For example, when Na increases from 0:1 1018 to
2.2.9. Dependence on acceptor concentration (Figs. 14 and 15) For pump power 0.219 kW and Nd ¼ 1:8 1018 cm3 , the threshold acceptor concentration for emission of DFDL is found to be around 0:29 1018 cm3 as shown in Fig. 14. The DFDL pulse is found to start after a delay of 11.65 ns with respect to start of the pump pulse. With increase of Na , output power of DFDL 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 concentration of acceptor. For example, when Na increases to 0:39 1018 cm3 the DFDL pulse is found to emerge after a time delay of 10.28 ns.
Fig. 15. Variation in pulse width and peak output power of acceptor DFDL at fixed donor concentration (Nd ¼ 1:8 1018 cm3 ) and pump photon intensity (Ip ¼ 0:325 1023 cm2 s1 ) for different acceptor concentrations.
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0:6 1018 cm3 , the pulse width of the first pulse of DFDL is found to decrease from 127 to 100 ps as shown in Fig. 15. The total output energy for the train of pulses is calculated for different acceptor concentrations and it is found to increase with increase in acceptor concentration. For example, when Na increases from 0:3 1018 to 0:6 1018 cm3 , the total output energy increases from 0.013 to 0:05 lJ. 2.2.10. Dependence on length of the DFDL (Fig. 16) For, Ip ¼ 5:0 1022 cm2 s1 , Nd ¼ 1:8 1018 cm3 and Na ¼ 0:3 1018 cm3 , the acceptor DFDL emission found to occur at a length 0.7 cm. The DFDL pulse is found to start after a delay of 10.89 ns with respect to start of the pump pulse. With increase of L, output power of DFDL 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 lower value of L. For example, when L increases to 0.9 cm the DFDL pulse is found to emerge after a time delay of 8.48 ns. With increase of L the number of DFDL pulses emitted increases. With a train of DFDL pulses emitted for a single pump pulse, the pulse width of the DFDL pulses in the train is found to increase with its pulse number. For L ¼ 0:9 cm, five pulses are ob-
Fig. 16. Variation in pulse width and peak output power of acceptor DFDL at fixed pump photon intensity (Ip ¼ 0:5 1023 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ) for different lengths of the excited region.
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served in the emitted DFDL train. While the pulse width of the first pulse is 86 ps, the consecutive pulses have their pulse widths 127, 162, 178 and 196 ps, respectively. For a particular pulse number, the pulse width of DFDL emission is found to decrease with increase in L. For example, when L increases from 0.7 to 0.9 cm, the pulse width of the first pulse of DFDL is found to decrease from 139 to 86 ps as shown in Fig. 16. The total output energy for the train of pulses is calculated for different lengths of the excited region and it is found to increase with increase in length. For example, when L increases from 0.7 to 0.9 cm, the total output energy increases from 0.018 to 0:068 lJ. In the rate Eqs. (1) and (3), the term kF does not have any significant contribution in the simulated data indicating that Forster type energy transfer is insignificant [5].
3. Experimental studies 3.1. Materials Both the dyes R6G and Ab7 are of laser grade supplied by Central Drug House, Bombay, India. The solvent methanol used is of spectroscopic grade. The general formula and structure of Acid blue 7 (C.I.42080, Alphazurine A) dye are illustrated in Fig. 17. The chromophore of the dye is the quinonoid group which appears as C@Ar@NR1 R2 and it is a diamino derivative of the triphenylmethane group. The absorption and fluorescence spectra are taken using 0.01 mM concentration R6G and Ab7 dyes using spectrophotometer (ELCO, India) and spectrofluorome-
Fig. 17. The molecular formula and chemical structure of the Acid blue 7 dye.
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ter (Fluoromax II, USA), respectively. The spectral parameters of R6G and Ab7 dyes have been calculated from the observed absorption and fluorescence spectra of the dyes. The calculated spectral parameters are listed in Table 1. 3.2. Experimental set-up to study DFDL Fig. 18 shows the distributed feedback prismdye 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 distributed feedback for the dye laser is obtained using an isosceles rightangled quartz prism. The pump beam is focussed by a cylindrical quartz lens into a line image, which is incident on the hypotenuse AB of the prism. 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 kp incident at an angle h on the medium, the DFDL wavelength is given by [12]
Here n and np 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 is of the DFDL is measured at one end using power meter (Ophir, Israel), as a function of input pump power, donor, acceptor concentrations and length of the medium. The measured values are graphically represented with the computed data in Figs. 19–22. The experimental values are found to be in close agreement with the theoretical values.
kDFDL ¼ nkp =np sin h: Fig. 19. Donor and acceptor DFDL output energy as a function of donor concentration for fixed pump power (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ).
Fig. 18. Schematic diagram of the prism-dye cell.
Fig. 20. Donor and acceptor DFDL output energy as a function of donor concentration for fixed pump power (Ip ¼ 3:25 1022 cm2 s1 ) and acceptor concentration (Nd ¼ 0:3 1018 cm3 ).
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Fig. 23. Donor DFDL as a function of angle of interference (h). Fig. 21. Donor and acceptor DFDL output energy as a function of acceptor concentration for fixed pump power (Ip ¼ 3:25 1022 cm2 s1 ) and donor concentration (Nd ¼ 1:8 1018 cm3 ).
Fig. 24. Acceptor DFDL as a function of angle of interference (h).
Fig. 22. Donor and acceptor DFDL output energy as a function of length for fixed pump power (Ip ¼ 5 1022 cm2 s1 ), donor (Nd ¼ 1:8 1018 cm3 ) and acceptor concentration (Na ¼ 0:3 1018 cm3 ).
3.3.2. Wavelength tuning Experiments are performed to study the tunability of both the donor and acceptor DFDL by varying the intersection angle. First, the experimental arrangement is set for emission peak of R6G by varying the angle of interference of the pump beam. R6G dye solution of 3 mM concentration is taken for study. Experiments are carried out to study the tunability of donor DFDL by varying the angle of interference. It is observed that by varying h between 47° and 58°, DFDL is emitted with peak at 56°. 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 R6G. This dye mixture is found to lase in acceptor region for the
angle of interference varying between 43° and 50° with its peak at 45°. DFDL output is tuned by changing the angle and is measured using constant deviation spectrograph. The tunability range studied for the donor DFDL alone is from 545 to 640 nm and an addition of acceptor it extends up to 675 nm. Figs. 23 and 24 show the experimental values of the tuning with the theoretical one and the angular tuning of both the donor and acceptor is linear.
4. Conclusion We have observed pump power, concentration and length 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 pump power and donor concentration. Whereas with increase in the acceptor concentration and length of the DFDL the pulse width of acceptor DFDL decreases while that of donor DFDL
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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 (545–675 nm). This finds many applications in high resolution and time domain laser spectroscopy.
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