Thermal effects in thin-film organic solid-state lasers.

With the recent development of organic solid-state lasers (OSSLs) architectures enabling power scaling and progresses towards continuous-wave operation, the question of thermal effects now arises in OSSLs. In this paper, a Rhodamine 640-PMMA based vertical external cavity surface emitting organic laser is investigated. A thermal microscope is used to record temperature maps at the organic thin film surface during laser action; those maps are compared with time-resolved finite element thermal simulations. The measured and simulated peak temperature rises are in good accordance and are shown to remain below 10 K in standard operating conditions, showing a negligible impact on performance. The validated model is used to investigate typical OSSL structures from the literature, in a virtual high average power regime, and up to the CW regime. It is shown that whenever true CW organic lasing will be realized, significant thermal effects will have to be considered and properly managed.


Introduction
Organic Solid State Lasers (OSSLs) have recently been drawing much attention as low cost, compact and broadly tunable coherent sources covering the whole visible spectrum [1,2]. They have potential applications in the fields of spectroscopy [3], bio/chemo-sensing [4,5] or polymer fiber telecommunications [6]. In the past decade, various OSSL architectures have been developed based on thin-film gain media, realized with cost-effective techniques like spin coating, drop casting, or ink jet printing [7]. Lasing has been achieved with many optical resonator architectures, such as Distributed Feedback (DFB) resonators [8,9], Fabry-Perot waveguide lasers [10], microrings [11], vertical microcavities [12], or external cavity resonators [13]. In addition of their unique spectral flexibility in the visible range, OSSLs have specific properties compared to their inorganic counterparts: first, lasing in a continuous-wave (CW) regime has not been demonstrated yet, due to the piling up of triplet excitons which induce quenching of singlet states and additional losses due to triplet-triplet absorption [14]; second, all organic materials are prone to photodegradation under intense optical pumping [15,16]. Pulse energies that are produced from thin-film OSSLs are usually in the nJ range or below, with low repetition rates (< kHz) and single-spot lifetimes that are not exceeding ~10 6 pulses. These modest performances have long been a limit for the dissemination of organic solid-state laser technology into the marketplace [17]. However, OSSLs have proven to be excellent tools for absorption spectroscopy and Raman spectroscopy in biophotonics experiments [3], even though these demanding applications will keep requiring an ever increasing average power (longer pulses until CW, higher repetition rate) and high device lifetimes.
In the past few years, there have been important progresses towards higher average power and higher stability of OSSLs. Pulse energies above the µJ level and up to the mJ level are traditionally obtained, with pi-conjugated materials, from liquid dye lasers [18] or dyeimpregnated polymer bulk rods [19]; power scaling has been recently demonstrated in our group in a thin-film based solid-state laser architecture with a structure enabling the generation of pulse energies of several tens of µJ [13]. Furthermore, there is currently a strong interest, from both a fundamental and application-oriented perspective, towards the demonstration of a true Continuous-Wave (CW) organic laser. Long-pulse operation up to nearly 100 µs has been shown in an Alq3:DCM blend comprising a triplet manager [20]; M. Lenhardt et al. have demonstrated MHz repetition-rate operation in PFO with binaphtyl spacer groups (BN-PFO) [21]. In this latter publication, the reported performance at 1 MHz repetition rate corresponds to an average pump power of 2 mW. Taking data from [20], if a true CW laser is to be realized with the lowest-estimate announced threshold of 2.2 kW/cm 2 over the specified spot size, the laser would be pumped with ~1 Watt of CW power. In inorganic lasers, thermal effects are strongly affecting laser performance at this level of pump power. The question of their importance in OSSLs hence becomes relevant, given that thermal properties of organic films are known to be much poorer compared to inorganic crystals and semiconductors: for instance, the thermal conductivity of PMMA is only 0.19 W/m/K, while it is 14 W/m/K for undoped YAG and 55 W/m/K for GaAs. Importantly, these progresses towards CW laser action come along with recent improvements in device lifetime, realized thanks to encapsulation techniques, similar to those used for other organic optoelectronic devices, which help protecting the active gain layer against oxygen and moisture [16,22]. An improvement by a factor of 11 in device lifetime was for instance reported by Vannahme et al. [23].
There has been a large amount of literature about thermal effects in all kinds of solid-state laser technologies, in which they cause the most prominent limitation for average power scaling, loss of beam quality and polarization control [24]. As a basic requirement for laser action is the existence of distinct wavelengths for pump and laser fields, no laser can work without dissipation of some heat. The generated heat is at least equal to the quantum defect (the difference between pump photon and laser photon energy) but is generally higher as the quantum yield of the laser transition is not unity. In this paper and following the usual terminology, we hereafter call "thermal effects" all the phenomena that are due to the heat deposited into the gain medium by the pump. Thermal effects have not yet been experimentally investigated in OSSLs, to the best of our knowledge. Kozlov et. al have shown a temperature independent performance of a double heterostructure organic Alq 3 :DCM laser from 0 to 140 °C [25], which illustrates a very important difference between organic semiconductors and their inorganic counterparts; however this study focused on how the laser performance varied with the ambient temperature but did not give insights about (pumpinduced) thermal effects as they are usually understood.
For organic thin film lasers, thermal effects are expected to have consequences that will be for some part similar, and for most part different from what is seen in inorganic lasers. In a similar way, the pump distribution in the material creates a temperature gradient: because the refractive index varies with temperature, the resulting index gradient creates a thermal lens. This thermal lens modifies the stability regions in a laser based on a "vertical" cavity, that is either in a so-called OVCSEL (Organic Vertical Cavity Surface-Emitting Laser) or a VECSOL (Vertical External Cavity Surface-emitting Organic Laser.) This aspect will be shortly evaluated in OSSLs in the following. One might also expect that thermally-induced refractive index gradients contribute to index guiding and thus modify the spatial laser mode size, especially in thin-film waveguide lasers where the mode is laterally confined only by gain guiding; it is especially true in mirrorless waveguide lasers, often simply referred to as Amplified Spontaneous Emission (ASE) experiments. It is also the case in waveguide DFB lasers where the spatial extent of the mode in the lateral (in-plane) direction is defined by the size of the pump stripe.
In inorganic solid-state materials (crystals or glasses), temperature gradients also create stress and strain gradients which ultimately lead to catastrophic fracture [26]. In OSSLs, only organic crystals may be partly relevantly attached to this picture, but most OSSLs are actually based on polymeric materials (either conjugated polymers or small-molecular dyes dispersed into nonconductive polymers), or small-molecular organic semiconductor films. In these cases, the response of the thin film to a localized laser heating will be quite different from a catastrophic failure: at pump laser powers that are not high enough to locally reach the glass transition temperature, heating is essentially expected to speed up the thermally-activated photodegradation reactions, in addition of thermal-lensing effects related above. For higher heating, when the temperature comes to exceed the glass transition temperature, the increase in the polymer free volume allows the diffusion of active species over large distances, enhancing all non-fluorescent processes including bimolecular quenching, internal conversion and photobleaching [27,28]. At still higher temperatures, photodecomposition and ablation of the film can be expected, but this defines a domain where clearly no useful laser action can be envisioned any more. A comprehensive review of the influence of laser heating on polymer films can be found in [29].
The main difference while considering thermal effects in OSSLs compared to other laser technologies, is the obvious importance of photodegradation and the consideration of the operating lifetime as an important characteristic of the laser device. It is then of practical and fundamental interest to wonder whether the operating lifetime of an organic solid-state laser will be affected in some way by thermal effects. If so, heat management solutions (cooling, heat spreaders…) might be useful to increase OSSL lifetime and performance. Direct measurements of temperature maps onto a laser-pumped organic laser film are necessary to estimate the useful orders of magnitude of temperature rises and gradients.
In this paper we present the first (to the best of our knowledge) measurements of temperature maps in solid-state organic thin films during laser operation. The structure under study here is a Vertical External Cavity Surface Emitting Organic Laser (VECSOL). This laser design is well-suited to study thermal effects because its longitudinal pumping scheme allows well-defined and controlled energy deposition, and enables large-area modes (several hundreds of µm) which are compatible with the resolution attainable with thermal infrared microscopes, which is at best on the order of the infrared wavelength used for imaging, i.e. ca. 10 µm. Moreover, the VECSOL architecture enables power scaling through a simple increase of pump spot size [30] and is naturally suited for setting up heat management solutions, as the inorganic counterparts of VECSOLs, i.e. semiconductor VECSELs and thindisk crystalline lasers [31], have been indeed thought of and engineered precisely to address power scaling and thermal management issues.
In section 2, the temperature profiles, versus space coordinates and time, at the surface of the gain medium, are presented and discussed. Temperature maps have been recorded with a thermal infrared microscope [32].
In section 3, we show that the temperature variations can be accurately modeled with time-resolved finite-element thermal simulations. Once validated, this numerical model is used to provide useful insight into some regimes that cannot be easily studied experimentally: firstly, we investigate what is the temperature evolution at the nanosecond scale, which is the relevant timescale for short pump pulses. Secondly, in section 4, we use the model to investigate thermal limitations in a virtual high average power regime of VECSOLs. In section 5, two typical OSSL architectures taken from the literature (a microcavity laser and a DFB laser) are studied with our numerical model in order to evaluate the importance of thermal effects in those devices. Finally in section 6, we ask the question of thermal effects in the context of a future Continuous-Wave organic laser. Some guidelines that can be useful for future organic laser design are then proposed. The organic laser structure under investigation is a Vertical External Cavity Surface-emitting Organic Laser (VECSOL) as described in [13]. The gain medium consists of a 18-µm-thick film of PMMA (M w = 9.5 × 10 5 g·mol −1 ) doped by 1 wt. % of Rhodamine 640, spin coated directly onto a highly reflective plane dielectric mirror (R> 99.5% in the 600-660 nm range). A remote concave output coupler (radius-of-curvature of 200 mm and transmission of ~2% in the 600-680 nm range) closes the cavity [13]. In this work, we used a modified version of the genuine VECSOL (top-down view is shown in Fig. 1) in order to allow lasing during the recording of thermal infrared images. This configuration enables a determination of temperature in real lasing conditions, and in cases where the thermal load is different under lasing and nonlasing conditions, can be used to infer quantum efficiencies [26]. The modified VECSOL comprises a ZnSe plate, tilted at 45° relative to the front facet of VECSOL chip, coated in such a way that it transmits thermal radiation (T >90% @ 8-12µm) and reflects the pump and laser beams (R >99%). All experiments are performed at room temperature, in air, with no encapsulation. The pump laser source is a frequency-doubled Q-switched diode-pumped Nd:YAG emitting 20-ns pulses at 532 nm with an adjustable repetition rate (Harrier from Quantronix Inc.). The pulse duration was chosen in order to satisfy a trade-off between triplet piling up (which requires the use of short pulses) and good overall laser efficiency, which means in an external cavity that the population inversion must be maintained over a time longer than the oscillation buildup time [30]. The pump beam is focused to a 300-µm-in-diameter spot onto the dye doped PMMA layer, as shown in Fig. 2(a). The VECSOL chip absorbs 80% of the incident pump power. The thermal radiation is detected through the dichroic mirror with a FLIR A320 IR-camera, which captures thermal infrared radiation in the 8 -12 µm spectral range through a Germanium objective. A Germanium singlet with a focal length of 25 mm is added in order to form a simplified microscope.

Experimental setup
The spatial resolution of this thermal imaging system is measured to be around ~35 µm with a heated object observed through an 8-µm slit, hence considered here as a line source. The thermal image of the slit remains in a single pixel and < 10% of the energy is detected in the surrounding pixels. For comparison, the resolution in the object space determined from the size of the pixels (25 µm) and the magnification of the microscope (g = 1.4) is 35 µm, which means that no useful improvement in image quality would be obtained using an aberration-corrected Germanium objective instead of the singlet used here.
The IR-camera can operate at repetition rates up to ~7 frames per second and can consequently only give a time-averaged temperature profile of the facet of the VECSOL chip. In infrared thermography measurements, it is essential to know precisely the emissivity of the object under study to convert the infrared luminance information into a useful temperature. Infrared emissivity of the gain medium was measured by comparing its infrared luminance with that emitted by a reference blackbody. In order to avoid parasitic reflections of ambient thermal light by the gain chip, the latter was tilted by an angle of ~5° and both objects were disposed into an oven at 40°C. We measured a value of ε = 0.95 ± 0.01.
A typical temperature map is shown in Fig. 2(b), obtained for pump pulse energy of 40 µJ (peak pump intensity ~1.4 MW/cm 2 ) which is ~4 times above the laser threshold value of 11 µJ. The repetition rate of pump pulse is fixed at 1 kHz. The temperature profile in Fig. 2(c) shows the temperature map recorded at t = 10s after first exposure and shows an average temperature rise T of ~1.8 ± 0.1K. Comparison of the pump beam profile with the temperature profile (see inset of Fig. 2) shows lateral heat transport as the temperature profile is broader than the heat deposition zone. In Fig. 3(a), the evolution of the temperature rise at the center of the pumped zone is shown versus time, together with the evolution of laser output power and pump transmission. The decrease of temperature during laser operation appears to be clearly related to the reduction of absorption directly caused by photobleaching. The inset of Fig. 3(a) shows the measured emission spectrum. It is centered at ~650 nm and consists of several evenly spaced peaks, which corresponds to the free spectral range of the Fabry-Perot etalon formed by the thick active layer itself Each peak contains several closely-spaced external-cavity peaks that are not resolved here [13,30]. Figure 3(b) shows the transient temperature variations during the first pulses. With the time resolution attainable with the camera (~1/7s), the temperature variations appeared instantaneous at pump turn on as well as at pump turn off, and steady state was reached before the ~20th pulse (at 100 Hz). The transient temperature rise within the duration of one pulse, which is within nanosecond timescale, will be investigated in the simulation part in section 3. The laser efficiency in this case is small due to the long cavity length imposed by the presence of the dichroic ZnSe plate inside the cavity, and the losses added by the latter, and the output energy is ~4 µJ for 40 µJ of pump pulse energy. We noticed no detectable difference between the temperature measured under lasing and nonlasing conditions (at identical pump powers, with a beam blocker added inside the cavity to stop laser action); given the low measured temperature rises and the small laser conversion efficiency, this result cannot be used here to infer any value of nonradiative decay losses, as shown in [26]. The very small temperature rises measured here suggests a minor role played by thermal effects in the control of photodegradation rates. Degradation curves have been measured for different repetition rates at a given pump pulse energy so that only cumulative effects between pulses (due to long-lived states, typically triplets) or effects linked only to an increase of average power (typically, thermal effects) can have an influence when the device lifetime is expressed in terms of number of pulses.  The repetition rate was first fixed at 100 Hz, and the pulse energy was increased from 20 µJ to 60 µJ, and the temperature rise measured is shown in Fig. 4(a). In a second step, we fixed the pump pulse energy at 20 µJ (peak pump intensity ~0.7 MW/cm 2 ) and the repetition rate was increased from 50Hz to 200Hz by steps of 50Hz. Results are shown in Fig. 5. When increasing repetition rates, degradation is strongly accelerated and a higher average temperature rise is observed at the center of pump spot. The temperature rise at different repetition rates is shown in Fig. 4(b). However, the time-averaged measured temperature rises, on the order of a few Kelvins at most, can hardly explain this acceleration of photodegradation, as the glass transition temperature of PMMA is far from being reached. It is more likely that the behavior observed in Fig. 5 reflects the fact that degradation is mediated by long-lived triplet states that have a lifetime higher than the period between two pulses, inducing a cumulative effect.
However, in order to get a final conclusion on the responsibility of thermal effects in the photodegradation of the VECSOL laser, it is important to investigate the transient temperature at the timescale of the pump pulse, which is very difficult to measure with a thermal imaging system. We will then use numerical simulations to complete our understanding of the temperature spatial and temporal profiles in VECSOLs.

Numerical simulations
The differential equation describing the thermal effects is the heat transfer equation [33]: Where Q is the heat source per unit volume due to the absorbed laser power, T is the temperature field as a function of time and space, and ρ, C and k are the density, specific heat, and thermal conductivity of the material, respectively. r stands for the coordinate along radial direction, z represents the coordinate along longitudinal direction. t denotes time.
Since the pump beam has a Gaussian shape, the heat transfer equation will be solved in a circularly symmetric mode. The VECSOL chip is simplified into three parts: the doped PMMA, the dielectric distributed Bragg mirror (DBR) and BK7 substrate, as shown in Fig.  6(a). All the thermal conductivities are considered temperature-independent and equal to their values at 293 K, and internal interfaces are assumed to be perfectly conducting. The DBR consisting of a stack of TiO 2 /SiO 2 layers ensures high reflectivity at lasing wavelength: in order to take into account the layered structure of the DBR stack in the heat conduction, average thermal conductivities are calculated for radial (k r ) and longitudinal (k z ) axes according to [34]. The heat source term can be written as follows: Where R is the reflection of pump at bottom facet of VECSOL chip, E is the incident pump pulse energy, τ p is the pump pulse width and ω is the radius of the focused pump laser beam. α stands for the absorption coefficient of the pump beam. z = 0 is at the interface of BK7 substrate and air, r = 0 is the center of the laser beam. H (t) represents the time variation of the pump laser pulse. η h is the fraction of the absorbed pump power converted into heat, which in absence of laser field is equal to [26]: where Φ is the fluorescence quantum yield. To get realistic result in the simulation, the laser pulse shape H(t) is taken from the laser pump beam profile measured with a fast photodiode (DET10A from Thorlabs, risetime < 1ns) connected to a 1-GHz bandwidth oscilloscope.
As for the boundary conditions in radial direction, symmetry boundary conditions are used at the axis of rotation. Temperature at the edge of VECSOL chips is set equal to ambient temperature, i.e. ( , , ) 293 T r z t K → ∞ = .
In the longitudinal direction, the boundary condition at the top and bottom surface of the chip is given [26]: Where h is the convective heat transfer coefficient, σ is the Stefan-Boltzmann constant, ε is the emissivity and T amb is the ambient temperature. Equation (4) describes the heat flow occurring at the VECSOL chip top and bottom surfaces, through heat convection to the ambient air and thermal radiation. The material properties, laser parameters, heat transfer coefficients, and geometric parameters used in the model are presented in Table 1. The fraction of the pump power absorbed in DBR and substrate are neglected. The fraction of the pump power absorbed in the Rhodamine 640 doped PMMA that is converted to heat is 0.2, calculated from a quantum yield of ~0.96 in Rhodamine 640 and the quantum defect for the laser emitting at λ laser = 640 nm and pumped at λ pump = 532 nm [35,36]. Note that since laser action occurs close to the mean fluorescence wavelength, there is no need to take fluorescence into account to calculate the heat fraction [26]. As for the boundary conditions at the top surface of PMMA, the convective heat transfer coefficient is taken equal to a typical value of 10 W/(m 2 *K) [37]. The emissivity was measured experimentally, as related above, and is equal to 0.95. Figure 6(b) shows the evolution of temperature profile in PMMA layer along z-axis from 20 ns (end of one single pulse) to 1 ms. The PMMA behaves therefore as a heat source after absorption of the pump laser energy, and heat is transferred by conduction towards the DBR and the substrate within a few nanoseconds. The z-plane in which the maximum temperature is reached within the PMMA layer is shifted around 1 to 2 µm from the interface with the DBR mirror, depending on time. To validate our model, we will focus on the investigation of temperature onto the PMMA/air interface, in order to allow comparison with experimental results. The results presented in Fig. 7 show the heating effect onto the dye-doped PMMA/air interface. As shown in Fig. 7(a), each pump pulse induces a very short increase of temperature on a nanosecond timescale, followed by a slower temperature decay in the millisecond range. Figure 7(b) shows the temperature rise for a pump pulse energy of 20 µJ as a function of the number of pulses at different repetition rates. The temperature, averaged during a period during two pulses, first rises during the first pulses, as the temperature does not have enough time to relax to room temperature between pulses when the repetition rate is higher than typically 100 Hz. However, a quasi thermal "equilibrium", in which the averaged temperature does not vary any more, is reached after only a few tens of pulses, even at high repetition rates around 1 kHz, which confirms our experimental finding reported in section 2 that heating and cooling of the pumped zone occur almost instantaneously after turning on or off the pump, within a time window shorter than the image acquisition time of the IR camera. Another important conclusion that can be drawn from these simulations is that the fast temperature variations following each pulse are not significantly higher than the average temperature rise: hence, in the 1 kHz case represented in Fig. 7(b), the new "equilibrium" temperature is calculated to be only 6 K above ambient, with a minimum temperature of 5.5 K and a maximum temperature of 6.7 K. This steady state value can be treated as an average temperature rise at the surface of the gain layer, so that the temperatures measured by the IR camera do not underestimate significantly the peak temperature attained during pulsed pumping. In Fig. 4, the results of these simulations have been superimposed to the experimental results for comparison. In the simulations, the radius of pump spot of 150 ± 5µm and absorption in VECSOL chip of 80 ± 2% are used to estimate the uncertainties in temperature rise. Figure 4 shows the dependence of the averaged temperature rise on power density and repetition rate. It can be seen that experiments and simulations are matching very well, which validates the present model. There is no adjustable parameter in the simulation.
In conclusion of the two last sections, it is shown that the measured temperature rise in VECSOLs is only on the order of a few Kelvins under typical operating conditions. The numerical simulation, validated by a good match between predicted and measured temperature fields, shows that the temperature goes above the time-averaged temperature after each pulse, but only by about 1K. Such a small increase of temperature cannot account for the dramatic dependence of photodegradation with repetition rate reported in Fig. 5. The latter is most probably explained by the piling up of long-lived states, certainly triplet states, which play the role of mediators in the photodegradation process.

Thermal limitations in VECSOLs
For some applications OSSLs sometimes need to be operated at higher repetition rate (>kHz): for example, applying organic DFB lasers for Raman spectroscopy requires repetition rates up to 10 kHz [3]. In this section we investigate VECSOLs in a virtual high average power regime to question its limitations. It is uneasy to clearly establish at what point thermal effects will start being considered detrimental. An easy guess is to state that whenever the temperature inside the gain medium will exceed the glass transition temperature of the matrix, then lasing properties will be strongly affected, as exposed in the introduction. We firstly investigated VECSOLs with the same parameters as in sections 2 and 3 and virtually increase average power. The simulation results (Fig. 8) show that the temperature rise in PMMA layer can reach the glass transition temperature T g (~390K of PMMA, grey area in Fig. 8) at a pump pulse repetition rate of 30 kHz when the laser is operated at threshold. The results presented in Fig. 8(a) also show that temperature remains below T g for a wide range of pulse energies and for repetition rates below 1 kHz. Figure 8(b) shows the temperature rise in the dye-doped PMMA layer in a VECSOL versus average pump intensity, which is the only relevant parameter here. It is shown that T g is reached when the averaged power density exceeds ~400 W/cm 2 in this structure. As detailed in section 6, this is below the anticipated order of magnitude for a CW laser threshold. From an experimental point of view, the pump laser used in our experiments allows us working with repetition rates up to 50 kHz: however, our attempts to measure temperature maps at repetition rates > 1 kHz (or average power densities > a few tens of W/cm 2 ) failed as the material was destroyed in less than 1s, not letting enough time to measure any temperature profile. This confirms the conclusion drawn in the previous section that photochemical degradation, not directly linked to heating effects, limits the device lifetime much more effectively.
In addition of speeding up thermally-activated photochemical reactions, thermal effects may have important consequences on cavity stability through thermal lensing even for small gradients. From the measured temperature gradient between the center and the edge of the laser cavity mode, it is possible to simply evaluate the thermal lens (TL) focal length, under the simplifying assumptions that the temperature gradient follows a parabolic evolution inside the pumped region, meaning that the phase front distortion is also purely parabolic: the TL effect is then reduced to a change of the effective radius of curvature of the active mirror, without extra-losses (linked to the TL aberrations) for the fundamental cavity mode.
The optical path difference between a ray passing through the active medium of thickness e at the center of the pump spot (r = 0) and a ray passing at a radial distance r = ω is Note that the estimation of the optical path difference by a single dn/dT term is often inappropriate (especially when the measured dn/dT is negative) [26] and is only used here as a way to obtain a crude estimate.
The paraxial TL focal length will be: In the experimental conditions described in section 2, with ω = 150 µm, e = 18 µm, a measured ΔT ~1K between r = 0 and r = w, and with a dn/dT of PMMA taken to −10 −4 K −1 [39], the TL focal length is ~-6m, which will have negligible impact on resonator stability. In this case, even in the limit case evoked above (T g attained when pumping at 30 kHz repetition rate, at laser threshold), the TL focal length would be as long as 60 cm and would not modify cavity stability regions significantly.

Thermal effects in other typical Organic solid-state laser architectures: OVCSELs and DFB lasers
It is instructive to use the model to investigate thermal limitations in other OSSL architectures. We then looked at the maximum temperature rise in the active medium for two devices taken from recent literature, built with two archetypical structures: 1) an organic microcavity or OVCSEL (organic Vertical Cavity Surface Emitting Laser) and 2) a distributed feedback (DFB) waveguide laser. We took as a typical OVCSEL the demonstration by H. Sakata et al. of a 1-µm-thick C540A doped poly-N-vinylcarbazole (PVK) active layer between two DBR mirrors [12]. The simplified configuration of the laser is shown in Fig. 9(a), and the thickness and thermal properties of each layer can be found in Table 1. A quantum yield of 0.8 is taken into account for C540A/PVK in this simulation. In [12], a 3.3-ns pump pulse was focused onto a circular spot with a diameter of ~20 µm. In this simulation, we considered a peak pump intensity of 10 kW/cm 2 which is 10 times the pump threshold peak intensity. In [12], the laser was used at a repetition rate of 1 kHz: under these conditions, the temperature increase is only around 1 K. Organic micro-cavity laser (OVCSEL) with a peak pump intensity of 10 kW/cm 2 , identical to the structure used in [12] (b) Organic DFB laser with peak pump intensity of 1 kW/cm 2 , identical to the structure used in [41]. The arrow represents the repetition rate at which these lasers have been operated in [12,41]. The insets show the simplified device configuration used for modelling (thicknesses are reported in Table 1).
As a typical DFB organic laser we considered the work published by G. Tsiminis et al. [4,40]. This nanoimprinted organic laser used BBEHP-PPV as an active layer, spin-coated onto a photoresist grating on top of a silica substrate. A top cladding layer of CYTOP was deposited on BBEHP-PPV [40]. Here, we simplified the patterned polymeric layer into a single layer as shown in Fig. 9(b). The organic DFB laser was optically pumped with a peak pump density of 1 kW/cm 2 onto an area of 1.3mm × 1.3mm with a pulse duration of 47 ns. For the quantum yield of BBEHP-PPV, we took the value of 0.84 measured in [41]. The calculated maximum temperature rise in BBEHP-PPV is here negligible at repetition rates < 1MHz. Thermal effects are hence not effectively playing a role in these two devices.
Thermal lensing effects (and all related refractive index changes due to temperature) can be estimated in these structures too. In the OVCSEL laser, the TL focal length (10 times above threshold, 1 kHz repetition rate) is estimated to be ~500 mm, and would not modify the mode stability domains, which are more probably defined by gain guiding in such a case. In DFB lasers, TL is not relevant. However, one can expect changes in the resonant wavelength. The temperature dependent wavelength shift of DFB laser dλ/dT can be expressed with equation: Where the order of diffraction is described by m, n eff is the refractive index of the resonant mode and Λ is the corrugation period of DFB structure [42]. Here m = 2 and Λ~360 nm, the wavelength of the DFB laser is sensitive to laser temperature with a coefficient around ~0.04 nm/K assuming dn eff /dT is ~10 −4 K −1 . This implies that there is a negligible wavelength shift attributed to thermal effects in organic DFB lasers operated with repetition rates < MHz. The results exposed above suggest, from two archetypal examples taken from the literature, that thermal effects can be quite safely ignored in thin-film OSSLs working in a pulsed mode at low repetition rates.

Importance of thermal effects in future CW organic lasers
There is a growing interest towards the demonstration of continuous wave operation of OSSLs [38]. Y.F. Zhang and S. R. Forrest have recently demonstrated that introducing a triplet manager in an organic active medium can reduce the triplet-induced losses and enable OSSLs entering the CW regime [20]. A lasing duration of up to 100µs was shown, allegedly limited by photodegradation.
In [20], the OSSL active region consisted of a triplet manager, 9,10-di(naphtha-2yl)anthracene (ADN), codeposited with the conventional guest-host gain medium consisting of 2 vol% of the red emitting 4-(dicyanomethylene)-2-methyl-6-julolidyl-9-enyl-4H-pyran (DCM2) in tris(8-hydroxyquinoline)Al (Alq3). The 200-nm-thick active layer film was deposited on a 2-μm-thick SiO 2 -on-Si substrate onto which DFB gratings were previously etched [20]. The simplified device configuration used for the purposes of modelling is shown in Fig. 10(a). The estimated CW threshold in this device is announced to be 2.2 kW/cm 2 , and laser tests were carried out at 2.4 kW/cm 2 . We simulated this device in the CW regime with these parameters and results are shown in Fig. 10(a). The temperature in the active layers rises and reaches a steady value after ~100 seconds; this long rise time can be attributed to the high heat surface density deposited in the organic thin film owing to the large quantum defect (~1.2 kW/cm 2 ). Similar timescales and consistent temperature rises have been reported in high-intensity OLEDs operated under conditions where the deposited heat density is in a range of 200-600 W/cm 2 [43]. In Fig. 10(a), the calculated steady-state temperature rise ΔT is high, around ~100 K and can hence be expected to have a reasonable impact on both degradation and performance. It is however still below the glass transition temperature T g of Alq 3 (~460 K) [44], although the T g of the ADN/Alq 3 mixture is not known. The calculation indicates that after 100 µs, which is the maximum device lifetime achieved in [20], the temperature rise is about 50 K, as shown in the inset of Fig. 10(a). This significant heating cannot be ignored here and can play a role in speeding up photodegradation reactions, but the connection between the heating and the interruption of lasing after 100 µs cannot however be made. This simulation indicates that, whenever photodegradation issues will come to be solved (with this material or another), and true CW operation achieved, thermal effects will be the next issue to be addressed in order to guarantee stable laser performance. The temperatures reached in the CW regime are not negligible and can play a role in the pulse length limitation that should not be overlooked. Furthermore, this high temperature rise in organic DFB laser may lead to a shift in the resonance wavelength of about ~4 nm according to the temperature dependent wavelength shift coefficient in DFB Laser (dλ/dT) of ~0.04 nm/K. But although thermal effects can be problematic in CW OSSLs, there is room for improvement in such devices and many classical thermal management recipes can be applied [45]. It is for instance possible to cover the active region by a thermally conductive transparent cap. Since such a device will need encapsulation to be practically usable, this means that thin-film encapsulation techniques with a direct contact of the encapsulant with the active layer are preferable compared to a contact with inert gases or vacuum. The SiO 2 based grating layer is also responsible for part of the bad heat dissipation because of its low thermal conductivity of 1.4 W/(m*K) and acts as a thermal barrier. In Fig. 10(b), it is shown how the temperature rise ΔT in the active layer can be reduced down to 70 K by a slight increase of the thermal conductivity of this grating layer, up to a value of ca. 20 W/m/K, which is the order of magnitude of the thermal conductivity of a low-index transparent material like MgF 2 .

Summary
In this work we have investigated the role played by thermal effects (i.e. the effects of the heat produced by the pump energy not converted into light) on the photodegradation and overall performance of organic solid-state lasers, and Vertical External Cavity Surfaceemitting Organic Lasers in particular. Temperature maps were measured by a thermal infrared microscope in a working organic thin-film laser, after a proper calibration of the emissivity of the sample. The temperature rise in VECSOLs operating under typical low repetition rates (< 100 Hz) and pulse energies < 100 µJ (corresponding to an average power density < 15 mW/cm 2 ) is only a few Kelvins above ambient. Such a weak heating cannot account for the high dependence of photodegradation speed with repetition rate observed in Rhodamine 640:PMMA, which may be dominantly attributed to triplet piling up. Coupled with the measured thermal image, we have shown that the heating effect in VECSOL can be accurately modeled with time-resolved finite-element thermal simulations. The model allowed us to study temperature variations at the ns timescale, showing that the overheating after each pulse is not significant (of the order of a few K also). The model also validates the experimental finding that temperature transients at turn on are almost instantaneous at this level of average power density. After a quick transient of a few pulses, a new steady-state temperature is reached: from the model is could be estimated that an average power density higher than 400 W/cm 2 would be necessary to reach the glass transition temperature of PMMA. Thermal lensing has also been evaluated in VECSOLs and is shown to be negligible as it does not significantly affect the stability regions of the cavity. The validated model was applied to estimate the amplitude of thermal effects in two archetypal laser structures taken from the recent literature: an OVCSEL design and a DFB design. Within their typical range of pump average power density, the temperature rise is shown to be negligible, as well as the thermal lensing effect in the OVCSEL and the effect of the temperature-dependent wavelength shift in the DBR case. However, driven by the recent interest for developing CW organic lasers, we investigated thermal effects in this case, based on a recent demonstration of a quasi-CW organic laser based on a guest-host system mixed with a triplet manager. In this case, the temperature rise at laser threshold is significant (~100K) and underlines the importance of considering heat management in the design of OSSLs whenever true CW organic lasing will be demonstrated. The replacement of glass substrates and thin-film encapsulants by more thermally-conductive materials should then be envisioned.