1. Introduction

Lasers based on organic pi-conjugated molecules hold the promise of building widely-tunable visible lasers suitable for a large range of resonators and technological platforms. Organic gain media can be found in the solid state, under the form of dye-doped polymers [1,2] or as films of organic semiconductors [3,4], the latter opening the possibility for pumping by electrical injection [5–8]. They can also be used as liquid solutions, either as bulk dye lasers [9] or in a more compact form as optofluidic lasers [10].

In organic lasers in general, true continuous wave (CW) operation is very challenging, and has only been demonstrated to date in liquid dye circulation-based lasers [11]. This strong limitation is not connected to permanent photodegradation or photobleaching, as pulsed pumping (at low enough repetition rates) results in repeatable lasing bursts, each lasting at most a few microseconds whatever the duration of the pump pulse [12]. Photobleaching is indeed usually much slower than lasing extinction, whose decay rate is governed by photophysical and thermal issues. The photophysical part stems from the propensity of all known fluorescent organic molecules to undergo InterSystem Crossing (ISC) from the first singlet excited state $S_1$ towards an excited metastable triplet state $T_1$ [3,13,14]. Subsequent absorption of laser light to a higher-lying triplet state (Triplet Absorption; TA) as well as singlet quenching by triplets cause laser emission to extinguish in usually a few hundreds of ns in the solid state [14]. Many efforts have been done in the last years in order to reduce the effective lifetime of triplet states at the solid state, both by the exploitation of triplets quenchers/scavengers and by synthesizing new organic dyes less affected by triplet states [15–18].

Thermal effects may also cause laser emission to stop well before photodegradation permanently kills lasing [19]. These effects result from a modification of the refractive index of the medium by local heating, creating alteration of the laser beam phase profile referred to as thermal lensing, or blooming for liquids [20–22]. In the presence of axial pumping, because of the negative value of the thermo-optical coefficient $dn/dT$ of most of the solvents, thermal blooming is due to the fact that the non-uniformly-heated liquid medium behaves like a diverging lens. Thermal effects, unlike triplet piling up, can have very different deleterious effects depending on the nature of the resonator and pumping geometry, offering pathways for their mitigation by resonator design.

In liquid dye lasers, triplet piling up is less severe as the triplet lifetime, naturally strongly reduced by dissolved molecular oxygen acting as a quencher, is in the microsecond range or below [23–27]. Only in properly deaerated solutions triplet lifetimes can reach tens of $\mu$s [28].

Since the early ages of dye lasers [29] CW lasing was known to be limited by triplet piling up and thermal effects, but both issues found a natural solution by making the dye flow. This enabled at the same time a replenishment of the medium and an efficient heat transport. True CW lasing was demonstrated by Peterson [11] and later improved by the jet-stream technique [30] that was necessary to provide dye flow speeds in excess of tens of $m/s$ required for stable operation.

The use of (fast) dye circulation, however, is a severe impediment for practical applications and for safe user-friendly operation. Nowadays, optofluidic lasers offer much more compact alternatives to dye lasers [31] but they still operate with dye circulation, at flow rates (limited by capillary forces) which have not yet enabled CW operation to be demonstrated to the best of our knowledge. Suppressing the dye flow system enables miniaturization and would be desirable for building ultracompact foldable or stretchable laser sensors [32,33] that can also be based on liquid organic semiconductors [34].

Gersborg-Hansen et al. [35] have shown that, in optofluidic lasers, natural diffusion can compensate the photobleaching rate if the pumped volume is small enough, without the need for circulation. Coles et al. [36] exploited this concept by using a microcavity with a very small pump volume and obtained lasing, albeit rather unstable, for 200 s, which they attributed to the small diffusion time achieved in this configuration. In our group, we have recently shown that a compact laser structure based on a quiet dye cell was able to produce lasing during 12 days at 1 kHz ($10^9$ pulses, 30 ns) [12]. Lasing was observed until full bleaching of the entire cell, evidencing the role played by self-diffusion even in a macroscopic resonator with a pump volume that is large enough to be compatible with cost-effective diode-pumping [37]. However, natural diffusion was too slow to compensate for triplet/thermal effects within pulses, which lasted no more than $2\,\mu$s. This pulse duration is of the same order of magnitude as the triplet lifetime, which raises a more general question: in liquid dye lasers with no circulation, is the pulse duration limited by thermal or triplet issues?

In this paper we show that pulses lasting up to 80 $\mu$s can be obtained, which is typically two orders of magnitude longer than the triplet lifetime and is furthermore dependent on the pump mode size, demonstrating the purely thermal nature of the limitation. We show that these long pulses can be obtained in a hemispherical external cavity design with a static liquid active medium, at the condition of reducing the mode size ratio between the fundamental cavity mode and the pump mode.

2. Results and discussion

Figure 1 schematizes the experimental setup employed to obtain and observe lasing. Two 445 nm InGaN diodes, driven by a PCO-6131 (Directed Energy Inc.) laser driver (not shown in figure), are used as the optical pump source. The use of this laser driver allows generating pump pulses whose duration can be set in a very wide range (from some tens of ns to the ms range). In this work, excitation pulses lasting tens of $\mu$s have been used. The beams fired by the two laser diodes are polarization-coupled by a polarizing beam splitter (PBS) and injected through an aspherical lens (focal length (FL) = 20 mm) in a multi-mode optical fiber (core diameter 105 $\mu$m, numerical aperature (NA) = 0.22). The fiber output beam is then collimated by a 35-mm FL lens and focused by a second lens whose FL is a variable parameter in the here-presented results. As already shown in Ref. [19], where further details about the experimental setup are reported, this configuration enables getting rid of any undesired asymmetry and astigmatism due to the low beam quality of the diodes, at the expense of a limited injection power loss (around 15%). Moreover, the resulting pump beam has a top-hat profile at the waist. The laser cavity consists in a dielectric plane mirror (high reflectivity (HR) 500-670 nm, high transmission (HT) @445 nm), a 100 $\mu$m-thick cuvette filled with a solution of 4-Dicyanomethylene-2-methyl-6-p-dimethylaminostyryl-4H-pyran (DCM) in dimethyl sulfoxide (DMSO) (absorption $\approx$ 1 optical density (OD) @445 nm), and a dielectric spherical mirror (radius of curvature (ROC) = 25 mm, HR 500 - 670 nm). Laser radiation emitted through the spherical mirror is directly focused by a 80-mm FL lens on a high-speed photodetector (Thorlabs DET025A), connected to a 1 GHz digital oscilloscope (Tektronix). To avoid any detection of the pump signal, a high pass filter (470 nm cutoff wavalength) is set after the cavity.

 

Fig. 1. Schematic representation of the setup employed to observe the laser emission.

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In order to make the cavity as insensitive as possible to any thermal-lens effect due to the liquid dye, a hemispherical cavity is used, with a cavity length very close to the ROC of the output coupler. The cuvette is placed as close as possible to the plane mirror. Simulations based on ray transfer matrix formalism have shown that a hemispherical cavity in which the coupler has a ROC of 25 mm remains stable in the presence of a diverging lens (located 1 mm away from the plane mirror) with FL down to 3 mm in absolute value; furthermore the waist size of the cavity fundamental mode remains almost unchanged for any FL of the thermal lens inside the stability range. Importantly, this condition alone is not enough to obtain the claimed 80 $\mu$s long pulses. In the following, the importance of the size of the pump beam waist on the cuvette plane compared to the cavity fundamental-mode waist will be discussed.

Figure 2(a) shows laser intensity as a function of time for different pump power densities, when a converging lens having a FL of 200 mm is used to focus the pump beam onto the cuvette. In this configuration, the pump beam waist diameter $2w_0$ is 440 $\mu$m (FWHM), while the cavity fundamental mode has a diameter of around 70 $\mu$m ($1/e^2$) at the cuvette position (Fig. S1 in Supplement 1). The top-hat pump profile remains unaltered in size and shape, within the experimental uncertainties, along the cuvette thickness (100 $\mu$m). It is important to note that all the data shown here are single-shot measurements, in order to avoid any cumulative thermal effect, i.e. changes in optical properties of the gain medium caused by previous pulses. The obvious implication is that all the observed effects are relative to processes happening within one single pulse.

 

Fig. 2. Laser pulse intensity as a function of time at several pumping power densities, using a pump spot of (a) 440 $\mu$m, (b) 310 $\mu$m, (c) 140 $\mu$m diameters.

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We highlight that, remarkably, laser radiation is sustained for the entire pump-pulse duration (80 $\mu$s) for all shown pump intensities, except the lowest one, which is really close to lasing threshold.

Fig. S2(a) in Supplement 1 shows an actual photo of a part of the setup: it is possible to clearly observe the red light spot produced by the generated laser beam.

The same experiment was then conducted using shorter FL for the pump focusing lens, namely 125 mm (Fig. 2(b)) and 50 mm (Fig. 2(c)), resulting in tighter focal spots for the pump, 310 and 140 $\mu$m FWHM in diameter, respectively (Fig. S1 in Supplement 1). The laser pulse duration (defined as the time window during which the system is above lasing threshold) is significantly shortened when the pump is more tightly focused, even keeping the power density unchanged, so that pulses last around 60 $\mu$s in the case of 310 $\mu$m pump diameter and around 40 $\mu$s in the case of 140 $\mu$m pump diameter. Fig. S2(b) in Supplement 1 shows pulses obtained at a fixed power density of about 10 kW/cm$^2$, emphasizing that pulse shortening is driven by a reduction of pump spot size and not by an increase of power density.

However, the higher power densities that can be reached when the pump beam is more tightly focused allow to show that pulse duration is affected also by power density. It is possible to better appreciate this shortening effect looking at a selection of normalized curves of Fig. 2(b) and Fig. 2(c) (Fig. S3(b) and S3(c) in Supplement 1). The same effect manifests itself under the form of a saturation effect when looking at the value of the pulse energy (obtained integrating the curves of Fig. 2) as a function of the pump intensity. While in the case of the biggest pump spot an almost linear behavior is recovered (Fig. S4(a) in Supplement 1), a deviation from a linear behavior is observed both for the intermediate and the smallest pump spot (Fig. S4(b) and S4(c) of Supplement 1). Probably, also in the case of the biggest pump spot a linearity loss would have been observed at higher intensities; the power of laser diodes did not however enable exploring a wider range.

In order to exclude any effect that could be due to the specific choice of DCM in DMSO, the same experiments were carried out with coumarin 540 dissolved in ethanol (Fig. S5 in Supplement 1). Also in this case pulses lasting tens of $\mu$s have been obtained, with a qualitatively similar dependence on the size of the pump spot.

More insights into the origin of this limited pulsewidth can be obtained by monitoring the fluorescence emitted by the cuvette during laser action. To do so, a fast intensified CCD camera coupled with a monochromator has been used. The spectral resolution is about 5 nm. Fluorescence signal has been collected using an optical fiber coupled with the monochromator placed near the cuvette inside the cavity. The fiber thus collected at the same time isotropic fluorescence light from the pumped volume as well as scattered laser light, which enables a simultaneous monitoring of laser and fluorescence signals during lasing. Figure 3 shows the collected spectra at different times during the pulse, in an experimental configuration corresponding to Fig. 2(b).

 

Fig. 3. Fluorescence spectra at different times during laser emission (pump spot size 310 $\mu$m). The narrow peak corresponds to laser scattered radiation.

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For each curve, a broad emission band centered around 630 nm is observed, corresponding to the fluorescence signal, on which a much narrower peak centered at around 665 nm, corresponding to laser radiation, is superposed. The spectral shift between the laser and fluorescence peaks is common in organic dye lasers operating in free-running mode (without any wavelength-selective element inside the cavity). In a laser in general, the lasing spectrum is determined by the region where losses are minimal. Ground-state re-absorption causes the laser spectrum to be red-shifted compared to the fluorescence spectrum, and this is here probably the main reason for this shift. The detailed characteristics of the laser spectrum in a similar cavity configuration have been discussed in the supplement of Ref. [12]. In a CW laser, the population inversion is clamped to a value that is directly proportional to cavity losses [38].

The CW approximation holds here as the pulse duration is much longer than the triplet lifetime. Indeed, the typical triplet lifetime in liquids is in the microsecond range or below [23–27], meaning that the triplet population reaches a steady value after at most a few microseconds. The fluorescence signal, directly proportional to the singlet population, can then also be used during lasing to monitor losses. The clear increase of fluorescence can then be attributed to an increase in intracavity losses during lasing.

The slow dynamics of the fluorescence signal variation once again rules out triplet absorption to be involved here; it rather confirms the thermal nature for the observed phenomenon. We ascribe these losses to the onset of thermal blooming in the cuvette during the pumping pulse. For all usual solvents, the refractive index $n$ decreases with the temperature so that, when the liquid dye is locally heated, a temperature profile is produced, and a thermal lens appears [39,40]. Under end-pumping, because of the negative value of the thermo-optical coefficient $dn/dT$, the thermal lens is divergent [41]. When the thermal phase profile is parabolic (case of a perfect thin lens), the thermal lens only modifies cavity stability zones, which is an ideal situation where losses can be minimal. On the contrary, when the thermal lens is aberrant, diffraction losses appear and cause the laser beam to scatter or "bloom" out of the laser mode. In order to investigate more in detail this phenomenon, a pump-probe experiment has been carried out. A HeNe laser was used as a probe, as its wavelength (632.8 nm) is close to the observed lasing wavelength and is not absorbed itself by the gain medium. As shown in Fig. 4, the HeNe probe beam is focused by a 100-mm FL lens, while the cuvette containing the dye is placed about 15 mm beyond the probe waist. At this position, the probe size is about 170 $\mu$m in diameter. This shift is important to detect a thermal-lens signal readily, as placing the dye cuvette at the exact waist results in a minimal alteration of the probe beam (this situation being close, in an approximate ray optics point of view, to a bunch of rays focused to the center of a thin lens). A dielectric mirror (HR 500-670 nm, HT 450 nm), forming an angle of about 30$^\circ$ with respect to laser propagation direction, reflects the laser beam towards an amplified photodiode. At the same time, the 445-nm pump beam is focused onto the cuvette by a 125-mm FL lens, producing a pump spot having a 310 $\mu$m diameter FWHM. Particular care is taken to ensure that the probe beam passes through the center of the pumped volume. In order to measure the HeNe radial beam profile versus time with a microsecond resolution within a single laser pulse (Fig. 5), we used a simple setup consisting in measuring the amount of light passing through a small pinhole (200 $\mu$m in diameter) placed in front of the photodiode. By recording the signal as a function of time at different lateral positions of the photodiode (some examples are reported in Fig. S6(a) in Supplement 1), the radial beam profile can be reconstructed with a 0.1 mm spatial resolution, keeping the temporal resolution determined by the photodiode+oscilloscope bandwidth, here a few ns. We observed a drop of signal intensity at the center of the beam, while the intensity increased on the edges (Fig. 5). A full picture can be seen in Fig. S6(b) in Supplement 1, from which the profiles shown in Fig. 5 are extracted. The spatial profile is progressively enlarged and modified, with the emergence of two side peaks, while a dip appears at the center. Figure S7 in Supplement 1 shows the recovery kinetics, after pump turn off, at the center of the beam. Several milliseconds are necessary for the signal to recover its initial value, as expected in the case of a thermal phenomenon. The same measurement has been carried out without any pinhole in front of the photodiode, in such a way that the probe light is fully collected by the sensor, whatever the pumping power. In this case, no variation of the signal is observed, indicating the absence of any measurable pump-induced absorption (Fig. S8 in Supplement 1). This result, along with the evidence of increasing losses shown in Fig. 3, indicates that the origin of the losses is diffractive (i.e. due to a modification of the phase) rather than absorptive.

 

Fig. 4. Schematic representation of the pump-probe setup employed to evaluate the effect of pumping on the intensity profile of a He-Ne laser beam passing through the cuvette pumped zone.

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Fig. 5. Reconstructed He-Ne laser beam spatial intensity profiles at different times during the pump pulse (pump spot size 310 $\mu$m).

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The dip observed in Fig. 5 clearly shows that the pump-induced phase modification in the cuvette is not only due to a thermal thin (aberration-free) lens, since in this case the probe beam would have been enlarged while keeping its Gaussian shape and spherical wavefront. The slight asymmetry noticed in Fig. 5 is presumably due to an unperfect orthogonality between the beam axis and the photodiode sliding axis, so that the photodiode is also slightly approached or receded during translation, or to a not perfectly axisymmetric heating of the liquid dye.

The ring structure appearing on a gaussian beam is typical of thermal blooming in a liquid with no forced convection [20,42]; it can also be seen as thermal lensing with spherical aberration [43], given that the absence of dye flow preserves the axial symmetry and the absence of astigmatism and other field aberrations. Upon scattering laser light out of the lasing mode, the aberrant thermal lens is responsible for increased cavity losses, without corresponding induced absorption (Fig. 3 and S8 in Supplement 1).

As observed in Fig. 2, the effect of thermal blooming losses, for a fixed cavity structure, is stronger when the pump spot size is smaller. In the three cases discussed in Fig. 2, the pump spot size is always larger than the cavity fundamental-mode size (Fig. S1 in Supplement 1). On the contrary, in the same system when the pump and cavity modes are matched, pulse duration cannot exceed 2 $\mu$s as previously reported [19]. When the pump size is large, the phase gradient imprinted to the laser medium by localized heating is small. Each supported mode experiences a smooth phase modification with moderate diffraction losses. In contrast, when the cavity is close to a mode-matched single mode cavity, the fundamental mode is experiencing strong spherical aberration, feeding more rapidly high-order transverse modes which are not supported by the cavity, causing a rapid lasing extinction.

3. Conclusion

In conclusion, we obtained lasing in a circulation-free liquid dye diode-pumped laser with durations (up to 80 $\mu$s) that are far beyond triplet lifetimes in liquids, and which are highly dependent on the pump-to-cavity mode ratio, ruling out triplet piling up as the main source for pulse shortening and highlighting the predominance of thermal limitations inside a single pulse. In a diode-pumped open resonator, laser pulsewidth is limited by diffraction losses brought by the spherical aberration of the pump-induced thermal lens. Lasing can be made to last longer in the case of a mode-mistached (highly transverse multimode) end-pumping configuration, a situation where diffraction losses are spread out over a large number of modes. This very long pulse duration is two orders of magnitude larger than what was observed in solid-state dye-doped polymers in the same pumping arrangement [37]. Based on this study, true CW operation in low-power liquid oscillators appears feasible, provided appropriate thermal management strategies are employed, such as the active correction of thermal blooming by adaptive optics [44] in open resonators, or the use of single-mode integrated resonators in which thermal blooming is less detrimental. This work suggests that after the advent of organic solid-state lasers, there is room for a new generation of liquid lasers, which can be made as compact and user-friendly as their solid-state counterparts as soon as circulation system is removed, and which present several supplementary advantages such as a much higher photostability, reduced triplet lifetime and a natural mechanical "flexibility".