Controlling the emission properties of solution-processed organic distributed feedback lasers through resonator design

Surface-emitting distributed feedback (DFB) lasers with both, resonator and active material based on solution-processable polymers, are attractive light sources for a variety of low-cost applications. Besides, the lasers should have competitive characteristics compared to devices based on high-quality inorganic resonators. Here, we report high performing all-solution-processed organic DFB lasers, consisting of water-processed photoresist layers with surface relief gratings located over the active films, whose emission properties can be finely tuned through resonator design. Their laser threshold and efficiency are simultaneously optimized by proper selection of residual resist thickness and grating depth, d. Lowest thresholds and largest efficiencies are obtained when there is no residual layer, while a trade-off between threshold and efficiency is found in relation to d, because both parameters decrease with decreasing d. This behaviour is successfully explained in terms of an overlap factor r, defined to quantify the interaction strength between the grating and the light emitted by the active film and traveling along it, via the evanescent field. It is found that optimal grating depths are in the range 100–130 nm (r ~ 0.5−0.4). Overall, this study provides comprehensive design rules towards an accurate control of the emission properties of the reported lasers.


Results and Discussion fabrication of DfB lasers: relationship between fabrication and geometrical resonator parameters.
The device structure (Scheme in Fig. 2a), includes as resonator a DCG photoresist layer with a 1D relief grating (s: thickness of the residual photoresist layer; d: grating modulation depth), deposited on top of an active film (h: thickness) of PS doped with perylene orange as laser dye.
All the DFB devices prepared in this work operate in the second order of diffraction, that is m = 2 in the Bragg condition (Equation 1) 1 where n eff is the effective refractive index of the waveguide (which depends on h, as well as on the refractive indexes of the film, substrate and cover) and Λ is the grating period. In second-order DFBs light is coupled out of the film mainly in a direction perpendicular to the film by first-order diffraction, at a wavelength λ DFB close to λ Bragg . Considering light traveling in a given waveguide mode, coupled mode theory 34 predicts that for pure index gratings (this is the case for the lasers prepared here, because h is uniform across the device and the grating is in a separated layer), the wavelength that exactly satisfies Eq. (1) cannot propagate in the film. So, a photonic stop-band centered at λ Bragg appears, and lasing oscillates on a pair of wavelengths, one at either edge of the dip. However, in the case of second-order devices, the peak with the lower wavelength has a larger threshold due to radiation losses 35 . Accordingly, single-mode emission at the peak of the longer wavelength is observed. The two geometrical resonator parameters analysed in this work (Fig. 2a), thickness of the residual layer (s) and grating modulation depth (d) depend on two fabrication parameters: the initial thickness of the DCG layer (s 0 ) and the development time (t D ).
For a given s 0 value, as t D increases, d grows and consequently the diffraction efficiency (η) of the grating. This is illustrated in Fig. 2b which shows the evolution of the diffracted intensity measured during the development process, as a function of t D for s 0 = 100 nm. Results for a film deposited directly over fused silica (instead of over an active film, as general for all the DFB devices) are also included in Fig. 2b. Their purpose is to provide a way to determine the development time at which the residual layer is eliminated (s = 0). This corresponds to that at which η no longer increases and reaches a plateau. Note that for the film deposited over the active film, η keeps increasing even after the residual layer has been eliminated. This is because the development process also affects the active film, so d keeps increasing because a grating is formed in the active film itself. Such situation would correspond to devices with a different architecture (i.e. with imprinted active films) [36][37][38] , in which the active film thickness would no longer be uniform across the device. Figure 2c,d show top and lateral field effect scanning electron microscope (FESEM) images, respectively, of one of the fabricated gratings (with d = 120 nm and s ∼ 260 nm). Remarkably, grating quality and morphology are similar to those of gratings fabricated in previous studies with a much more sophisticated development process than the one used in the present work 13 . The grainy texture of the surface is produced by gelatin fibres randomly distributed but oriented rather parallel to the substrate surface 39 . Such texture is observed independently on the Λ: period; s: residual layer) deposited over an active film (AF) (h: thickness) prepared over a fused silica (FS) substrate. (b) Development curves (diffracted intensity versus the development time, t D ) corresponding to a DCG PR layer coated over an AF (circles) and directly over FS (squares). Inset drawings illustrate different cases: grating with residual layer (at t D ~ 6 min), grating with no residual layer (at t D ~ 10.5 min) and grating imprinted on the active film (at t D ~ 13 min); (c,d) Top and lateral FESEM images, respectively, of a DCG grating with period Λ = 372 nm, depth d ∼ 120 nm, and residual layer thickness s ∼ 260 nm. type of development process. After developing, the grating profile is not sinusoidal, indicating that the development process is a nonlinear function of exposure. With this procedure the duty cycle for all the gratings fabricated is approximately 75:25 (hill:valley) so that a high feedback coupling coefficient, i.e. a low threshold, can be achieved 40,41 . DfB laser performance: dependence on the resonator geometrical parameters. In order to analyse the effect on the laser performance of s and d, we prepared four sets of DFB devices with s 0 values of 50, 100, 240 and 400 nm. By considering that the development selectivity is approximately 10, the maximum achievable d for each set, corresponding to s = 0 and with no grating engraved on the active film, would be around 45, 90, 216 and 360 nm, respectively.
A complete laser characterization was performed for all the prepared devices, obtaining their emission wavelength (λ DFB ), linewidth (FWHM), threshold (E th ) and laser slope efficiency (LSE). Results for one of them are shown in Fig. 3. Single mode emission with a linewidth < 0.1 nm was obtained in all cases. For all the DFB lasers prepared, it is seen that the emitted laser light is linearly polarized, in a direction parallel to the grating lines. This indicates that the laser mode is associated to the fundamental transverse electric waveguide mode TE 0 . Also, the beam divergence observed in a direction perpendicular to the grating lines is ~5 · 10 −3 rad.
Effect of varying s and d on the E th and LSE laser parameters. The influence of changing d and s on the threshold and LSE of all the prepared devices is analysed through Fig. 4a,b, respectively, in which data are plotted as a function of d. For a given set (each with a different s 0 value), s decreases as d increases, according to  www.nature.com/scientificreports www.nature.com/scientificreports/ s∼s 0 − (10/9) d. Data for the devices with no residual layer (s = 0) can be easily located by the vertical dashed lines shown.
With regards to the threshold (Fig. 4a), a similar behaviour is observed for the four series of experiments: the threshold decreases with increasing d (and therefore decreasing s), first at a high rate and then at a slower rate, reaching a minimum value when s = 0. By comparing the minimum thresholds for each series, the lowest values (~23 μJ/cm 2 ) correspond to those with smaller d (46 and 86 nm), whose s 0 values are 50 and 100 nm, respectively. Larger thresholds (46 and 63 μJ/cm 2 ) are obtained for devices with larger d and s 0 values (d = 216 nm and s 0 = 240 nm; and d = 367 nm and s 0 = 400 nm, respectively). Note that for some devices, i.e. those with s < 0, the development times were sufficiently long as to have the gratings imprinted directly on the active film. For such lasers, the thresholds are similar than those obtained when s = 0.
With respect to the effect of varying s and d on the LSE (Fig. 4b), it is seen that LSE increases with increasing d. Although this increase continues after the residual layer has been eliminated (after that, the grating starts getting imprinted on the active film), its rate diminishes for the two series of lasers with lower thresholds (those with lower s 0 , 50 and 100 nm, and therefore lower d, for s = 0; Fig. 4a). Note that among these two series, somewhat better efficiencies are obtained for the one with s 0 = 100 nm.
All the lasers prepared had gratings developed with a simple process, as explained in the methods section. In order to assess the importance of using this type of development process, in comparison to the more sophisticated one used in previous studies (an oxygen electron cyclotron resonance stream inside a high vacuum chamber), data for a laser with d = 220 nm and s = 0, prepared with this latter method, have been included in Fig. 4a,b (denoted as R-240). Considering the accuracy of measurements (~10%), no differences are observed in the LSE, while the threshold intensity is somewhat lower in the device prepared with the anisotropic method.
The threshold and LSE results are here analysed by considering the interaction between the grating and the evanescent wave of the light emitted by the active waveguide film and traveling along it. This aspect is more important in devices with the resonator located in a separated layer than in those with modulated active film thickness. This is because in the former type, the electric field intensity is lower inside the grating and it decreases rapidly from the top surface of the active layer. According to that, it is expected that the existence of a residual layer would be detrimental for the device performance 31 . Figure 5a shows the electric field intensity distribution of the TE 0 mode corresponding to s = 0 in the series of lasers with s 0 = 400 nm where these effects are more clear. Note that the DFB resonator provides the feedback for the in-plane light propagation, as well as the way to extract the light out of the device, and both mechanisms depend on the interaction between the evanescent wave of the light traveling along the active film and the grating. Thus, in order to get insights into this we have defined an www.nature.com/scientificreports www.nature.com/scientificreports/ overlap factor r for measuring the strength of this interaction. We define the overlap factor, r, as the ratio between the area A 1 under the curve in the grating corrugation region and the area A 0 of a rectangle of width equal to d and height equal to electric field intensity at the active layer surface (see Fig. 5b). Then where d eff is the effective grating depth. According to this definition, d eff is the width of the rectangle with a height equal to electric field intensity at the active layer surface, and area A 1 . The r and d eff parameters obtained for the devices with no residual layer for the four series of lasers prepared (devices located with a dashed line in Fig. 4) are listed in Table 1 and its dependence on the grating depth shown in Fig. 5c. Note that equation (2), applicable to devices with s = 0, can be easily generalized to treat lasers with s > 0 by simply replacing in such equation the parameter d, by the amount (d + s).
The relationship between d (and d eff ) with the laser threshold and with the LSE, for the devices (among the ones prepared) with no residual layer, is analysed through Fig. 5d,e, respectively. The laser threshold dependence on d in terms of the overlap factor r is rather complicated. This is because an increase of d increases external losses but also affects the feedback mechanism and, consequently, the net gain and the threshold. As observed in Fig. 5d, the threshold is maintained approximately constant in the lowest value (E th ~ 25 μJ/cm 2 ) for r > 0.4, which corresponds to grating depth values d < 130 nm (see Table 1 and Fig. 5c). Then, for r < 0.4 (d > 130 nm) the threshold increases rapidly. Literature about the influence of grating depth on the performance of DFB lasers is scarce and not conclusive because different device architectures are used. Huang et al. 42 compared two DFB lasers with top-layer resonators with grating depths of 130 and 60 nm, and found, at variance with the results obtained in the present study, the lowest threshold in the one with larger depth (80 μJ/cm 2 , versus 150 μJ/cm 2 ). There are more detailed studies with lasers based on resonators integrated in the active film. For example, in devices with gratings imprinted on fused silica and active films deposited on top, the lowest thresholds and larger laser efficiencies were obtained with the shallower grating depths 31,43 . More recently Doring et al. 32 Table 1. Parameters of DFB lasers with top-layer resonator architecture without residual layer (s = 0) and different grating depths (d). a Initial DCG layer thickness (error ± 5 nm); b Grating depth (error ± 5 nm); c DFB laser threshold (error ≈ 10%); d Output laser efficiency (error ≈ 10%); e Overlap factor, defined by considering the electric field intensity distribution corresponding to the grating as illustrated in Fig. 5b; f Effective grating depth, defined as the product of the overlap factor and the grating depth. is similar. Nevertheless, comparisons with these lasers should be taken with caution because for them, the active film thickness is modulated, so the variation of the grating depth implies a change in film thickness, which also has an influence on the threshold. The analysis of the grating depth dependence of the LSE is simpler (see Fig. 5e). As observed, the LSE increases linearly with d eff . Such dependency supports the suitability of the overlap factor definition, given that LSE is known to be proportional to the available η (represented by d eff ). Note that the LSE also increases with d, although non-linearly, first at high rate and then at slow rate presumably reaching a maximum value (see the curve linking data points for devices with s = 0 in Fig. 4b). A further increase of d appears to be useless, indicating that improving feedback seems to compensate the increasing out-coupling losses for small grating depths meanwhile out-coupling losses is the dominant mechanism for large grating depths. According to the previously discussed grating depth dependence of the laser threshold, for d ~ 130 nm (r ~ 0.4), which corresponds to approximate limiting d value to keep E th < 25 μJ/cm 2 , the LSE is around 80% of its maximum possible value (see Fig. 5c). By increasing d up to around 150 nm, the LSE could be improved (up to 88% of its maximum value), but this would be in detriment of the laser threshold, which would increase up to 35 μJ/cm 2 .

Effect of varying s and d on the laser wavelength.
The dependence of the experimental laser wavelength λ DFB on the grating depth d is analysed through the results shown in Fig. 6 for the series of devices with s 0 = 400 nm. A similar behaviour is observed for the other series (data for lasers with s 0 = 240 nm shown in Supplementary Fig. 1, Supporting Information). The observed decrease in λ DFB with increasing d is because the effective index n eff of the structure (values in the vertical right axis of Fig. 6) decreases, as a consequence of the DCG material loss during development.
In order to get insights on the physical mechanism contributing to lasing, we compare the experimental λ DFB values of the devices with residual layer s ≥ 0, to the corresponding resonant wavelengths λ Bragg (calculated through Eq. 1 with the n eff values obtained by simulation and plotted as a dashed line in Fig. 6). It is seen that in all cases emission occurs at a wavelength λ DFB , a few nm larger than λ Bragg . The observation of lasing at λ DFB values above λ Bragg is an expected result for top-layer resonator devices with s ≥ 0, because index coupling is the only mechanism responsible for the laser process 34,35 . Note that for DFB lasers with modulated active film thickness (i.e. devices with the active film deposited over a grating or with the grating directly imprinted on it, such as top-layer resonator DFB devices with s < 0), in addition to index coupling, there would be also a gain coupling contribution to lasing 31,44,45 . It is known that for a system with pure (or dominating) gain coupling, emission would occur at λ Bragg . The fact that in lasers with top-layer resonators with s ≥ 0 there is only one mechanism, makes them ideal systems to study the influence of the index coupling strength on the separation between λ Bragg and λ DFB . For the devices analysed in Fig. 6 the separation between λ DFB and λ Bragg varies from around 2.1 nm (for the lasers with smaller d) up to 2.7 nm, for the device with no residual layer (s = 0) whose d = 367 nm. The observed increase in the separation between λ DFB and λ Bragg as d increases is because the strength of the index coupling process (which is proportional to the ratio d/h) gets larger. This phenomenology was clearly observed in devices with gratings imprinted on the substrate, in which the ratio d/h varied in a wide range among the different devices (between 0.2 and 1.9) because film thickness was also varied 31 . In the present case, for a given series of devices (all with the same h), the separation between λ DFB and λ Bragg changes only slightly as d increases, because the variation of the amount d/h is small. This effect is also seen with the data of the series of devices with s 0 = 240 nm ( Supplementary Fig. 1, Supporting Information). In that case, for the laser with no residual layer (s = 0) and d = 216 nm, the amount (λ DFB − λ Bragg ) = 1.4 nm. This value is smaller than the one previously discussed for the device with s = 0 and d = 367 nm, corresponding to the series of s 0 = 400 nm, for which the amount (λ DFB − λ Bragg ) = 2.7 nm. This is in accordance with the strength of the index coupling mechanism (driven by d/h) for each series.

conclusions and perspectives
The emission properties of organic DFB lasers with both, active film and resonator based on solution-processed polymeric materials and with the resonator located on top of the active film, have been studied as a function of two resonator parameters: the thickness of the residual photoresist layer and the grating depth. It was found that a fine control of these parameters is crucial for the design and fabrication of devices with optimized performance. The lowest laser thresholds and largest efficiencies correspond to resonators without residual layer (s = 0). As for the grating depth, both the threshold and the laser efficiency increase with the grating modulation depth, and for the latter, above a certain d value, a further increase is inefficient. Results for lasers with s = 0 and different gratings depth have been successfully interpreted in terms of the overlap between the electric field intensity distribution and the grating, through the definition of an overlap factor r. The lasing threshold decreases rapidly when r increases and is maintained approximately constant in the lowest value (E th ∼ 25 μJ/cm 2 ) for r > 0.4, corresponding to grating depths d < 120 nm. On the other hand, the LSE increases with decreasing overlap factors, but at large grating depths, the growth rate diminishes, and the LSE reaches a maximum value. According to this trade-off for optimizing simultaneously the threshold and the efficiency through the grating depth, a reasonable criterium is to choose depths in the range 100-130 nm (r ~ 0.5−0.4). Such lasers would have thresholds E th < 25 μJ/cm 2 and LSE ∼ 80% of its maximum possible value.
From the point of view of the DCG resonator processing, the dry development step to obtain the relief gratings has been simplified considerably, with respect to methods previously used. Here it has been done with an inexpensive plasma cleaner machine, in contrast to a much more sophisticated methods previously used (an oxygen electron cyclotron resonance stream inside a high vacuum chamber). Despite the isotropy of the process used in this work, the gratings have sufficiently good quality. The method is simple and inexpensive and should be useful in mass production of organic DFB lasers.
www.nature.com/scientificreports www.nature.com/scientificreports/ Finally, it should be remarked that the knowledge achieved through this work might have an important impact for plastic optoelectronic in a broader sense than the one explored here related to organic lasers. Note that these relief gratings might be used for other active laser materials, not necessarily organic, with the only requirement to be insoluble in water; or for other optoelectronic devices, such as light emitting diodes 46 or solar cells 47 , with the purpose of improving their efficiency to extract or collect light. An example of a class of materials for which the resonators reported here might have applications are perovskites. Despite the great progress in the use of these materials for photovoltaic and LED applications [21][22][23]28 , the advances for lasing purposes, and more particularly in the form of DFB devices, has been more limited 25,26 . One of the reasons is the difficulty to prepare the perovskites as very thin (typically < 150 nm) optical waveguides with low scattering losses and low roughness and simultaneously keeping a high photoluminescence efficiency. Thus, it is key to optimize the synthesis for tight control of the grain size of the polycrystalline perovskite on the nanoscale, which requires synthetic methods rather different than the ones used with other kind of devices (e.g. solar cells) 25,26 . With regards to the potential use with perovskites of the DCG gratings reported here, a limitation of the top-layer configuration is the fact that the DCG layer is processed from water. This would require protection of the perovskite film, before depositing the DCG layer on top of it, for example by means of a protective polymer layer. On the other hand, the use of the DCG gratings in the configuration with the resist below the active film should be feasible, given that the DCG layer after development is water resistant. Ongoing work in these directions are presently being carried out in our laboratories.
Another research field in which the reported gratings might be of interest is that of two-dimensional (2D) materials. In recent years, the study of such systems in photonic devices of various kinds has aroused widespread attention due to their strong light-matter interaction 27,[48][49][50][51][52] . A variety of 2D materials, such as graphene-like systems 48 , Tellurium nanosheets 49 or perovskites nanosheets 27 , have demonstrated a good potential for non-linear optics devices. Particularly interesting for the purpose of the present work are recent reports of enhanced spontaneous emission and lasing on 2D Metal-chalcogenides [50][51][52] . Also promising is the use of nanographene nanosheets, whose use as DFB lasers with top-layer resonators has been just demonstrated 16 .

Methods
Device design and fabrication. Fabrication of 1D DFB lasers with the resonator on the top of the active layer consisted of the following steps: (1) Active film deposition: polystyrene (PS) films with the laser dye perylene orange (PDI-O) dispersed at 1.0 wt%, were deposited by spin-coating over commercial 2.5 × 2.5 cm 2 transparent fused silica substrates (i.e. quartz plates) from a toluene solution. (2) Photoresist deposition: layers of the negative photoresist DCG were spin-coated over the active films from a hot water solution (40 °C). The concentration of gelatine (Russelot, 200 bloom) in the solution was varied between 0.8 wt% and 7 wt% in order to obtain layers of thickness in the range 50-400 nm. The sensitizer (ammonium dichromate) was dissolved in a proportion 35 wt% of gelatine. (3) Grating recording: one dimensional gratings were recorded by HL with light from an Ar laser emitting at 364 nm in a simple and stable setup in which a mirror is attached with a 90° angle to the sample holder 53 . Intensities of the interfering beams were equal in order to achieve the maximum contrast. The average exposure was 45 mJ/cm 2 and an absorbent plate was attached to the back side of the substrate with an index matching liquid to avoid backward reflections. (4) Development: after desensitizing the DCG layer in a cool water bath (10 °C), surface-relief gratings were obtained by dry development in an oxygen plasma using the surface treatment machine Diener Zepto.
For the active film preparation, the amount of solvent was adjusted to obtain thickness of h ~ 600 nm, so the obtained waveguide supports one transversal electric mode (TE 0 ) which propagates with a high confinement factor, thus minimizing losses and optimizing the amplified spontaneous emission (ASE) performance 54 . The concentration of PDI-O was chosen to be 1 wt% because it was previously shown that the ASE performance is optimized with this proportion 55 , thus enabling to prepare DFB lasers with low thresholds and long lifetimes 7,13 .
The grating period value was chosen to have laser emission (λ DFB ) as closest as possible to the wavelength of maximum gain (i.e. that at which ASE occurs, λ ASE = 579 nm). This is known to be crucial to optimize the threshold 31,38 . The calculation of the proper Λ to obtain emission at a given wavelength (once film thickness h was decided to be 600 nm), was done by calculating n eff for the TE 0 waveguide mode traveling in the active film, and the corresponding λ Bragg value via eq. (1). Calculations of the n eff values, were performed by means of a free-access software program (1-D mode solver for dielectric multilayer slab waveguides) 56 . The DCG resonator was simulated by two layers: one of uniform thickness s and the refractive index of the DCG; and the other one, of thickness d, and a refractive index equal to the weighted average index of the two media at each side of the corrugated surface (air and DCG). The refractive index values used in the calculations (at λ = 580 nm) were: 1.55, for exposed and developed DCG; 1.592 for dye-doped PS, which corresponds to the value of non-doped PS; and 1.459 for fused silica. Since Λ values for the various devices are between 371 and 372 nm and the error in grating fabrication is of the order of 2 nm, we have considered that Λ = 372 nm in all cases.
Morphological characterization of the gratings. Grating periods were measured by comparing the corresponding diffraction pattern to those of calibrated reference gratings. The grating depth (d) and thickness of the residual layer (s) could be estimated from the initial thickness of the DCG layer (s 0 ), i.e. the thickness before grating fabrication; and from the selectivity of the process. The selectivity, defined as the ratio of the development rate of non-exposed to the exposed areas, at the illumination dose used (45 mJ/cm 2 ), was approximately 10. Grating profile studies were performed by means of FESEM (Carl Zeiss, model Merlin VP compact). Accurate determination of d variations was made by measuring the grating diffraction efficiency (η) and comparing it to results predicted by the coupled-wave theory taking into account the grating profile 57 . See data and details in Supplementary Fig. 2 www.nature.com/scientificreports www.nature.com/scientificreports/ optical characterization: refractive index and thickness. The refractive index and thickness of the active films and of the initial DCG layers have been determined by a modification of the envelope (or Swanepoel) method 58 . These methods are based on the analysis of interference fringes observed in the film transmission spectrum due to the light reflections in the film interfaces. The modified method used here allows to measure very thin films (thickness between 40 and 400 nm) in contrast to the standard envelope method, which is limited to values above 400 nm.

Laser characterization. Laser characterization was performed under excitation with a frequency-doubled
Neodimium Yttrium Aluminium Garnet, Nd:YAG laser (10 ns, 10 Hz,) emitting at 532 nm, as in previous studies 59 . The pump beam was linearly polarized parallel to the grating lines and incident at a 20° angle. The beam section over the sample was elliptical, with a minor axis of 1.1 mm. The emitted light was collected in reflectance, perpendicularly to the surface with an Ocean Optics USB2000 fiber spectrometer (resolution 1.3 nm) placed at about 1 cm from the sample. For spectral shape inspection a MAYA spectrometer (0.13 nm resolution) was used. The energy of the pulses was varied using neutral density filters.
The laser threshold (E th ) was estimated as the minimum intensity at which laser emission occurs. The accuracy of the determination was increased by considering the abrupt change of linewidth defined as the full width at half of the maximum (FWHM), which accompanies the phenomenon. The absolute laser efficiency (LSE), defined as the ratio between laser output energy and incident pump energy and usually expressed as a percentage, was determined from the slope of a linear fit of the representation of the output energy versus the pump energy. The setup was similar than the one described above, but here the pump and emitted energy were measured with high resolution energy detectors Ophir PD10-C and PD10-pJ-C (resolutions of 1 and 0.01 nJ, respectively).