1 Introduction

Besides producing tunable photons in visible and UV spectral region, circulation of the active dye laser solutions permits dye lasers operating at tens of kHz repetition rates delivering high-average powers [1] useful for several applications. However, the photo-stability of dye molecules remains one of the most important considerations for applications that require stable and sustainable operation, with minimum maintenance of the laser system. Thus, understanding the various photo-degradation mechanisms of dye molecules and reducing the degradation rate has been a vital issue for improving the performance of liquid dye lasers.

The photo-stability of dyes is generally evaluated by irradiating a known volume of dye solution by the pump laser radiation of a specified power for a fixed duration and estimating the decrease in concentration of dye molecules [2–5]. During pump laser excitation to the excited singlet (S n ) states, depending on the rates of de-excitation in the singlet manifold and intersystem crossing (k ST) to the triplet states, a fraction of the excited dye molecules may leave the lasing cycle and populate long-lived triplet (T n ) states. A fraction of these dye molecules in the excited states undergo photochemical reactions with solvent, dissolved oxygen or other impurities leading to their degradation. For example, photochemical degradation of pyrromethene (PM) dyes through triplet (T1) state, due to its self-sensitized photo-oxidation by reacting with generated singlet oxygen, in air-equilibrated liquid solutions has been extensively reported [3–6]. During these de-excitation processes, excited dye molecules decay primarily by spontaneous emission and residence time of dye molecules in the excited S1 state is governed by fluorescence lifetime.

In earlier works [7, 8], the influence of stimulated emission on the photo-stability of dye laser in a broad-band configuration were reported. However, studies investigating the effect of emission wavelengths of dye laser on photo-stability of dyes in liquid media have not been reported. Since stimulated emission competes with photo-degradation of excited dye molecules, it is expected that the degradation rate would depend on the emission wavelength, and vary across the tuning range of the dye laser. In the present work, we report systematic investigation on photo-stability of ethanol solution of PM567 dye at different emission wavelengths observed with a Q-Switched Nd:YAG-pumped narrow band-pulsed dye laser. Higher photo-stability of dye solution was noticed when dye laser was operated near peak in comparison to edge wavelengths of the dye tuning curve.

Earlier theoretical studies investigating the influence of degradation of dye molecules on the performance of dye lasers have been reported following a steady-state approach [9, 10]. However, in order to simulate the effect of dye degradation on dye laser efficiency at different emission wavelengths in the presence of both spontaneous and stimulated emission processes in a pulsed dye laser, a time-dependent analysis [11] describing laser pulse build up was adopted, which has been found to be in good agreement with the experimental observations.

2 Experimental

Laser grade pyrromethene 567 (PM567) dye was procured from M/s. Radiant dye laser, checked for purity by HPLC and used as such. Spectroscopic grade ethanol was used for preparing dye solutions. A narrow band pulsed dye laser was constructed using a small volume (2 ml) of stirred, air-saturated ethanol solution of PM567 dye in a laser cuvette to accelerate the effect of dye degradation on laser efficiency. The tilted dye cuvette (gain length 7 mm) was located between a grating (2,400 lines/mm) in Littrow configuration with a 4-prisms pre-expander (25×) and an uncoated output coupler (4 % reflectivity) making a cavity length of 280 mm. The dye laser was transversely excited by second harmonic radiation at 532 nm (pulse energy 4.4 mJ, rep. rate 10 Hz, FWHM 6 ns, beam dia. 7 mm) of a Q-switched Nd-YAG laser (Ekspla, NL 303) using a cylindrical lens (f = 10 cm). The gain curve of the dye laser was obtained by the scanning of wavelengths through the gain profile of the dye and measuring the average pump and dye laser powers using power meters (Ophir). The dye laser wavelength was monitored using a monochromator.

To study the effect of dye laser wavelength on the dye photo-stability, the dye laser was tuned to operate at peak (550 nm) and at two symmetrically located wavelengths (543 and 571 nm) on either side of the peak and the gradual decrease in laser efficiency was measured under lasing (L) and non-lasing conditions, with similar pump energy. In this non-lasing case, the feedback in the dye laser resonator was blocked by placing a shutter, allowing only pump excitation but no buildup of dye laser action. The shutter was momentarily removed for a short period during the measurement of decrease in dye laser power. However, in such non-lasing condition two walls (4 % reflectivity) of the dye cuvette served as a resonator to provide weak, broad-band window lasing (WL) action. The quantum yield of photo-stability of dye solutions, in lasing (Q LPS ) and non-lasing with window lasing (Q WLPS ) conditions, was calculated [12] as number of pump photons required to decompose a dye molecule after a fixed irradiation period with similar pump energy by estimating the initial (N i) and final (N f) number of dye molecules. Concentration of dye in the irradiated solution (2 ml) was calculated at start and end of exposure through measurement of peak absorbance (O.D at λ absmax ) using an UV–vis absorption spectrometer. The measurement of photo-stability (Q NLPS ) of dye under entirely non-lasing (NL) condition, i.e., even in absence of cuvette window lasing, was carried out by irradiating the dye solution in the cuvette with the pump of similar pulse energy while the cylindrical lens as well as resonator cavity was removed. The cuvette window-induced lasing was suppressed because of a large reduction in the pump intensity. Here, Q PS = P/(N i − Nf), where P is total number of pump photons absorbed in the dye solutions during the exposure period, and calculated from cumulative dose of absorbed pump energy using the power meter. A stock solution of PM567 dye with a concentration 0.77 mM was used for photo-stability measurement under different conditions such that pump beam was totally absorbed in dye solutions during laser irradiation period. The measurement of Q PS of dye solutions at each condition, i.e., lasing (L), non-lasing with window lasing (WL) and total non-lasing (NL), was repeated thrice and average values were considered. Generally, a measurable decrease in concentration of dye solutions was noticed after pump exposure period of 2–4 h, depending on various conditions. Hence, photo-stability measurements were carried out at peak (550 nm), blue-edge (543 nm) and red-edge (571 nm) wavelengths of the dye tuning curve, as a representative case of different dye laser emission wavelengths.

3 Results and discussion

The tuning curve of PM567 dye laser was obtained in the spectral region 540–575 nm with a peak laser efficiency of 35 % at 550 nm (Fig. 1). While monitoring dye laser power at maxima (550 nm) as a function of cumulative pump energy, the dye laser efficiency was observed to decrease at a faster rate in non-lasing with window lasing (WL) than that in the presence of lasing (L) condition. Similar observations were also noticed at two other periphery wavelengths 543 and 571 nm of the dye tuning curve, which are illustrated in Fig. 2. This may be understood as follows.

Fig. 1
figure 1

Tuning curve of PM567 dye laser. Ethanol solution of dye was excited by 532 nm of a pulsed Nd-YAG laser with pump energy of 4.4 mJ. The dye laser (DL) was operated in Littrow configuration

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Fig. 2
figure 2

Decrease in normalized laser efficiency of PM567 dye at wavelengths 550 nm (peak), 543 nm (blue-edge) and 571 nm (red-edge) during a lasing (L) and b non-lasing with cuvette window lasing conditions (WL). The dye laser efficiency was observed to decrease at a faster rate in non-lasing with window lasing (WL) than that in presence of lasing (L) condition. The observation of faster rate of drop in efficiency, in presence of lasing condition during initial period of exposure at 550 nm, was not a general trend and was not clearly understood (a), could possibly be on account of experimental uncertainty

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The visible excitation of PM567 dye is a single electron promoted transition from S0 to S1 state. In case of non-lasing condition, the residence time of PM567 dye molecules at the excited singlet state (S1) predominantly depends upon the spontaneous emission lifetime (τs) of the dye, which was measured as 6.27 ns [13] in ethanol. However, during lasing process the rate of emission (R) at the emission wavelength from the excited S1 state is the sum of the rates of stimulated (R st) and spontaneous (R s) emissions. Therefore, under steady-state approximation \( R = R_{\text{st}} + R_{\text{s}} \) or,

$$ R = \sigma_{\text{e}} (\nu )I_{\nu } + 1/\tau_{\text{s}} . $$

Thus, the average time that each excited dye molecule resides in the S1 state during lasing condition may be expressed as

$$ T = 1/R = \tau_{\text{s}}/[ {\sigma_{\text{e}} (\nu )I_{\nu } \tau_{\text{s}} + 1} ], $$

where I ν and σ e(ν) are intra-cavity signal intensity and stimulated emission cross-section of dye at laser frequency (ν), respectively. Hence, for given values of σe and τs, an increase of the signal intensity I ν reduces average residence time T of dye molecules in the excited S1 state on account of a higher stimulated emission rate. Thus, residence time of dye molecules at the excited state is much shorter during stimulated emission (lasing process) than that at spontaneous emission (non-lasing) condition.

Photo-degradation studies reported [2–8] so far suggested that degradation of dyes was largely initiated by reactions involving dye molecules in the excited singlet and triplet states. Triplet state population of dye molecules were generally small on account of slow rate of singlet (S1) to triplet (T1) intersystem crossing, when excited by such low-repetition rate (10 Hz), short pulse width (6 ns) laser. Consequently, population and residence time of dye molecules in S1 state largely determined the effective photo-degradation rate of such dye lasers, whether in presence or in absence of laser action. Thus, shorter residence time of dye molecules in the excited S1 state during lasing process facilitated observation of higher photo-stability of dye in comparison to non-lasing condition.

To understand the effect of emission wavelength on the rate of dye photo-stability, the dye laser was tuned to a set wavelength and gradual decrease in dye laser efficiency was monitored as a function of cumulative pump exposure time with similar pump energy. The decrease in dye laser efficiency was found to be slowest at peak wavelength 550 nm followed by 543 and 571 nm, which are illustrated in Fig. 3. These results also pointed to the influence of stimulated emission cross-section (σe) at different emission wavelengths and hence different stimulated emission rate of dye on residence time of dye molecules at the excited S1 state and thus its photo-stability. The dye gain profile at Fig. 1 showed that the stimulated emission rate of PM567 dye increased in the same order 550 > 543 > 571 nm. This was also supported by observations of faster evolution of dye laser pulse at peak wavelength (550 nm), followed by at 543 and 571 nm, which is illustrated in Fig. 4. The faster drop in dye laser efficiency under non-lasing with window lasing (WL) in comparison to lasing (L) condition was also confirmed by measuring photo-stability of dye at these three wavelengths, calculated by measuring concentrations of dye solutions before and after known irradiation period (Table 1) with similar pump energy. Increase in the photo-stability of dye laser, upon lasing (L) to non-lasing with window lasing (WL) condition, was observed to be higher at peak wavelength (550 nm) in comparison to other two extreme wavelengths, in otherwise identical pump condition. Also, it was found to be higher at shorter (543 nm) than that at longer (571 nm) wavelength of the dye gain curve. The photo-stability (Q NLPS ) of dye under total non-lasing condition (NL) was found to be the lowest (Table 1).

Fig. 3
figure 3

Decrease in normalized laser efficiency of PM567 dye under lasing condition when dye laser was operated at a 550 nm, b 543 nm, and c 571 nm

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Fig. 4
figure 4

Temporal evolution of the PM567 dye laser pulses are shown at different wavelengths A 550 nm (peak), B 543 nm (blue-edge), and C 571 nm (red-edge) of the tuning curve. The different laser pulses are indicated as (a) Pump laser, second harmonic of Nd-YAG (b) initial dye laser pulse and c dye laser pulse after a known period of exposure

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Table 1 Photo-stability (Q PS) of PM567 dye solution at various conditions, pumped by 532 nm of a pulsed Nd-YAG laser
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To get an insight of the process these experimental results were theoretically simulated using a time-dependent rate equation model.

3.1 Theoretical modeling

In order to theoretically estimate the extent of improvement in dye photo-stability that can be achieved at different emission wavelengths under typical dye laser operating conditions, a rate equation model approach was followed [11, 14]. In this earlier work, effect of dye photo-degradation leading to reduced dye laser output was simulated on the basis of a rate equation model incorporating both loss of dye molecules on account of degradation and induced absorption and scattering losses of the pump and signal photons resulting from the generated photo-degraded dye products. Theoretical estimate for drop in dye laser energy was derived when it was operated over an extended period of time.

Time-dependent coupled rate equations for population density, n L1 of dye molecules in the first excited singlet state S1 and the dye laser signal photon density q L are described by the following two equations:

$$ {\text{d}}n_{1}^{\text{L}} /{\text{d}}t = \sigma_{01} (\lambda_{\text{P}} )Q_{\text{p}} cN_{1} - n_{1} /\tau_{\text{s}} - q_{\text{L}} (\lambda_{\text{L}} )\sigma_{\text{e}} (\lambda_{L} ) \, n_{1} cl/L $$
(1)
$$ {\text{d}}q_{\text{L}} /{\text{d}}t = q_{\text{L}} (\lambda_{\text{L}} ) \, \sigma_{\text{e}} (\lambda_{\text{L}} ) \, n_{1} cl/L + fn_{1} /\tau_{\text{s}} - q_{\text{L}} (\lambda_{\text{L}} )/\tau_{\text{C}} - \sigma_{01} (\lambda_{\text{L}} ) \, N_{1} q_{\text{L}} (\lambda_{\text{L}} ) \, cl/L - \sigma_{\text{imp}} (\lambda_{\text{L}} )N_{\text{imp}} q_{\text{L}} (\lambda_{\text{L}} )cl/L $$
(2)

where

$$ N = N_{1} + n_{1}^{\text{L}} . $$
(3)

The excited singlet and triplet state absorptions are neglected in above equations. The pump photon density is denoted by Q p while, q L(λL) denotes the signal photon density. Spontaneous decay lifetime for the first excited singlet state is denoted by τ s, c is the velocity of light in the medium, l is the length of the active medium while L denotes the resonator cavity length, σ01(λP) and σ01(λL) are the ground state absorption cross-sections for the dye molecule at the pump (λP), and laser (λL) wavelengths, respectively. N 1 is the population density in the ground state while N is the total population density, of the dye molecules. The spontaneous emission term in Eq. 2 includes a geometrical factor f, which determines the fraction of photons being radiated spontaneously into the angular aperture of the resonator. Emission cross-section at laser wavelength, λL is denoted by σe(λL), and cavity decay time for the laser resonator is τ C. Considering reflectivity of the output coupler, R 1 = 4 % and grating in Littrow configuration, R G = 70 %, a cavity decay time of τC = 0.52 ns was calculated using [15] the relation 1/τC = [−c ln (R 1 R G)]/2L.

Absorption loss of laser emission photons assisted by degraded dye product molecules (N imp) with an absorption cross-section of σimp is denoted by the last term in Eq. 2, However, spectroscopic analysis of the photo-degraded PM567 dye solutions confirmed negligible absorption and scattering losses arising from generated photo-products at both pump and laser emission wavelengths. Hence the last term in Eq. 2 was neglected in our present simulation work. Triplet–triplet absorption loss of laser photons was also neglected in our model since pumping in the present work was carried out by laser with pulse duration of 6 ns (FWHM) which is considerably shorter than the singlet to triplet intersystem crossing time constant for PM567 molecules [16]. Excited singlet–singlet absorption (ESA) cross-section of PM567 dye solution at pump wavelength (532 nm) was reported to be negligible [17], and therefore, not considered. Hence, ESA cross-sections of PM567 dye at laser emission wavelengths (540–575 nm) are expected to be small and thus its effect on photo-stability.

The above set of coupled rate equations were numerically solved for laser parameters pertinent to our experimental set-up. The values for the absorption and emission cross-sections for PM567 at the concerned wavelengths λL and λP have been either calculated from measured absorption/fluorescence spectra of the dye solution or taken from the literature [18]. The temporal shape for the pump laser pulse at 532 nm was closely simulated assuming a Gaussian distribution in time having a FWHM of 6 ns. Thus, the time-dependent pump photon distribution is given by

$$ Q_{\text{p}} (t) = Q_{{{\text{p}}0}} [\exp - (t - t_{0} )^{2} a], $$

where

$$ a = (4\ln 2)/(t_{\text{p}}^{2} ),\quad t_{\text{p}} = {\text{FWHM}} . $$

The peak value Q p0 of the pump photon density used for our calculations was consistent with the total energy contained within the pump laser pulse, which was typically in the region of 4–5 mJ/pulse.

For a transversely pumped dye laser oscillator geometry, although the pump intensity decreased exponentially as the pump beam penetrated into the dye solution starting from the pumped dye cell wall, we have assumed a uniform transverse gain distribution based on a spatially averaged value of the pump intensity determined by the concentration of the dye molecules [19]. In order to estimate the dye laser efficiency (η), laser pulse energy was determined by time and space integrating the instantaneous photon density emerging from the laser cavity. A spatial integration of the laser photon density in the transverse plane translates into a simple multiplication of the photon density by the cross-sectional area of the pumped gain medium. The measurement of decrease in concentrations of dye upon irradiation with the pump laser provided estimates for photo-stability for the dye solutions in different conditions. These photo-stability (Table 1) and initial concentration of dye solutions have been used as input for calculating the values of N that were used for our simulation runs.

Theoretically estimated time evolution of η, shown in Fig. 5 by solid and dashed lines, has been compared with the experimentally observed trend when dye laser was tuned to operate at 550, 543 and 571 nm. The second trend represent non-lasing with window lasing (Q WLPS ). The third variation shown by dashed-dotted lines (Fig. 5) indicate the calculated dependence of laser efficiency when even window lasing in the dye cuvette was not considered. As mentioned earlier, in such total non-lasing (NL) condition the photo-stability (Q NLPS ) of the dye molecules was the lowest. As evident, our calculations showing rapid drop in laser efficiency with time for such a laser system also confirmed this expected trend. Thus, the theoretically calculated variation in laser efficiency with time compared well with our experimentally measured values.

Fig. 5
figure 5

Theoretically estimated time evolution of normalized dye laser efficiencies, at wavelengths 550 nm (peak), 543 nm (blue-edge) and 571 nm (red-edge), have been compared with the experimentally observed trend. The experimentally observed laser efficiencies data are shown by symbol (square) for lasing and (triangle) for non-lasing with window lasing conditions. Theoretically fitted trends are shown by solid (lasing condition), dashed (non-lasing with window lasing condition) and dashed-dotted (total non-lasing condition) lines

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4 Conclusion

Improvement in photo-stability of PM567 dye laser, while it was operated at the peak over edge wavelengths of its tuning curve, was observed and compared with theoretically calculated trends obtained following a rate equation-based theoretical approach. Two factors that critically affected the decrease in laser efficiency with time were the stimulated emission cross-section at the laser wavelength and the decay time of the resonator cavity, essentially intra-cavity losses. The largest effect of enhanced stimulated emission rate on improving dye photo-stability was observed at the maximum of the tuning curve, i.e., for the laser when operated at the peak of its tuning range. Consequently, effect of stimulated emission rate improving the photo-stability of the lasing dye at different emission wavelengths and thus enhancing the operation life time of the system was most prominent in this case. Thus, it can be inferred that the maximum photo-degradation occurred when stimulated emission rate was the weakest during evolution of lasing in the oscillator. Hence, stability of dye is expected to be higher when operated in an amplifier mode with higher stimulated emission rates [7].