1. Introduction

The first distributed feedback (DFB) laser was reported by Kogelnik and Shank in [1] and it was based on the organic dye Rhodamine 6G dissolved in gelatin as the gain material. Shortly afterwards, an inorganic GaAs based DFB laser was fabricated by Nakamura [2] which opened the path to numerous commercially available laser devices. Since then, a large number of studies have been performed on organic based DFB devices, using different active materials such as conjugated polymers, e.g. ladder-type poly(p-phenylene) [3], poly(paraphenylene vinylene)-based [4, 5], and polyfluorene in [6]. Host-guest systems using Alq3 as the host material [7, 8], dye-doped polymers [9], dye-doped metal oxide solgels [10] and others. Different aspects of DFB lasers have been investigated such as the influence of the excitation spot size [11], grating depth, and waveguide layer width [12], the effect of the duty cycle [13], and other emission properties [14]. The influence of dye concentration on the lasing threshold of an organic DFB and the impact of dye concentration on relative lasing efficiency above threshold are questions that have not been discussed extensively in the literature.

In general, a DFB laser consists of a waveguide layer which is modulated periodically in space either by index variation, by gain variation or by both. In such devices, light propagating in the waveguide layer is reflected from the periodic structure multiple times forming a photonic band gap for wavelengths satisfying the Bragg condition of [Eq. (1)]. In a second order DFB, when the waveguided light scatters from the grating, it is emitted in the normal direction relative to the plane of the waveguide. The distributed optical feedback mechanism together with optical gain in the waveguide layer make it possible to achieve lasing in such structures with relatively low threshold. Moreover, since light propagates within a thin layer of material, it is possible to reach high optical gain even for a small total volume of gain media.

In this work, we explore the behavior of an organic DFB laser as the concentration of gain material is varied over more than 2 orders of magnitude. The gain material we use is the laser dye 4-(Dicyanomethylene)-2-tert-butyl-6-(1,1,7,7-tetramethyljulolidin-9-enyl-vinyl)-4H-pyran (DCJTB) (see Fig. 1) incorporated into a poly(9-vinylcarbazole) (PVK) polymer matrix. In previous studies of similar systems [13], the concentration was fixed at 3 wt. %. Usually the concentration of gain material in a host matrix is of the same order of magnitude, namely a few percent, such as the 2.3% DCM doping in an Alq3 matrix [15], 3% DCM2 in Alq3 [16], and 0.5% for PDI-C6 doped into a PS film [12]. An example of a study using low gain concentration is the 0.05 wt.% of Rhodamine 6G reported in [17]. Since the laser dyes used in most organic DFB’s are 4-level laser systems, dye concentration is typically adjusted higher in order to minimize the lasing threshold in terms of incoming energy, with an upper limit of concentration being dictated by concentration quenching, which reduces the fluorescence quantum yield when the dye molecules are too close to each other.

 

Fig. 1 Absorption and emission spectra of the laser dye DCJTB when doped into a PVK host matrix at a concentration of 0.5% (ww). For the emission measurements, the sample was excited with a λ = 457 nm laser.

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2. Sample design and fabrication

Here we show the effects of changing the concentration of the laser dye DCJTB over the range between 5 wt.% to 0.025 wt.%. We chose the laser dye DCJTB because it is known to exhibit relatively low aggregation and hence low concentration quenching [18]. In the current work, the DCJTB is mixed with PVK, a high refractive index polymer (n = 1.69) that serves as the host matrix “core” for the asymmetric waveguide. The gratings for the DFB were fabricated to have a resonant wavelength near the peak of the fluorescence spectrum of DCJTB (Fig. 1), at about 600 nm. To construct a second order DFB, the grating periodicity must satisfy the Bragg condition:

We show numerical solution of this equations in Fig. 2(c). For the thicknesses under consideration, there are two possible solutions to the above set of waveguide equations, which correspond to the TE₀ and TM₀ modes. In addition, the lasing wavelength depends on nature of the grating modulation. For pure gain modulation, lasing occurs at the wavelength corresponding to the center of the bandgap, but at the long wavelength edge of the bandgap for pure refractive index modulation.

 

Fig. 2 (A) Schematic of the asymmetric DFB structure in cross-section from bottom to top: silicon subtract, 500 nm thick SiO₂ layer with 50 nm deep corrugation etched in, and waveguide core consisting a PVK host matrix doped with the laser dye DCJTB. (B) SEM image of the DFB grating. (C) The dependence of effective refractive index, n_eff, for the waveguide mode on the PVK:DCJTB layer thickness.

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The grating was fabricated via electron beam lithography. The sample consisted of a silicon substrate with a 1 μm thick layer of thermally grown SiO₂ on top. The electron beam resist, PMMA 950K A4, was spin coated on top of the substrate at 4000 rpm to form a layer of 200 nm in thickness, followed by baking at a temperature of 180°C for 90 sec. The grating was patterned over an area of 0.5 mm × 2 mm using the RAITH eLINE Plus electron beam lithography system. The grating was designed to have a period of 400 nm, with a line width of 190 nm and space width of 210 nm. The sample was exposed to the electron beam using Fixed Beam Moving Stage (FBMS) technology, in which the stage moves on a defined trajectory with a constant velocity while the electron beam does not change position, but just slightly deflects to expose the line and to achieve the desirable line width. This technique enabled us to achieve zero stitching error in the grating writing process. The accelerating voltage of the e-beam was 30KV, the beam current was 300 pA, the stage speed was 0.2 mm/sec. After developing the photoresist, a 20 nm thick film of Cr was deposited by e-beam evaporation which served as a hard mask for the etching process. After lift-off, inductively coupled plasma (SPTS, ICP) of CF₄ gas was used to etch the SiO₂ layer. The gas was flowed at 50 sccm, with a pressure of 10 mTorr, ICP power of 400W, and platten power of 50W. An etch time of 1 minute resulted in a 50 nm deep trench in the SiO₂ layer. The remaining Cr was removed via wet etch solution.

The gain layer was prepared by separately dissolving PVK and DCJTB in chlorobenzene and mixing them in different ratios in order to achieve different concentrations of dye in the host matrix. The concentration of PVK in chlorobenzene for the mix was kept constant, since the matrix concentration affects the viscosity and hence the thickness of the thin film formed during spin coating. To produce films of 200 nm, we used a concentration of 24 mg/ml of PVK in chlorobenzene, and the solution was spin coated on the grating at 1000 rpm. The film thickness corresponds to n_eff = 1.52 for TE₀ mode and a resonant wavelength of 608 nm. The actual center of the bandgap was at about 600 nm.

3. Characterization

The DFB structures were optically excited using 532 nm wavelength laser (Spectra-Physics, Explorer) that was configured to provide 8 ns pulses at a repetition rate of 1 Hz. The excitation spot was 300 μm in diameter and was formed by a 10× objective lens (NA = 0.3). In general, a bigger spot size can lead to a reduction of the DFB lasing threshold in terms of energy density, however the total energy in the pulse is limited by the excitation laser. In [11] it was found that for spot sizes with a diameter above 300 μm, any further reduction in threshold energy is very small. Emitted light was collected via the same objective lens and was separated from the excitation by a dichroic mirror and then routed into a spectrometer (Princeton Instruments SP-2500i) equipped with a cooled CCD. Fluorescence spectra were analyzed using a 150 g/mm for broadband measurements and a 1800 g/mm grating for high spectral resolution. The polarization of the incoming beam was adjusted to maximize the lasing output. The pulse energy was controlled by λ/2 waveplate and polarizer.

4. Results

Lasing from the devices was observed for the concentrations of DCJTB dye in PVK from 5% to 0.025%. It was manifest by threshold-like behavior of the output energy as a function of input energy (Fig. 3(a) and 3(c)) and the appearance of a narrow spectral line above threshold (Fig. 4(b)). The lasing was observed in the wavelength range between 605 nm to 610 nm, depending on the sample. The shift towards the longer wavelength edge of the DFB bandgap is typical for mixed gain and refractive index modulation.

 

Fig. 3 Output emission as a function of input energy density for different concentrations of the gain material DCJTB in the PVK host matrix, namely 5%, 2.5%, 1%, 0.5% 0.25%, 0.1%, 0.05% and 0.025%. Excitation and emission were both coupled normal to the plane of the structures.

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Fig. 4 (A) Emission spectra collected from DFB having 0.05% of dye in gain layer, as a function of excitation pulse energy. Note that the height of the lasing peak does not reflect the actual peak intensity since the linewidth is below the resolution of the spectrometer for this measurement which was performed with a 150 g/mm grating. (B) Emission spectrum of the DFB above threshold measured with higher resolution 1800 g/mm grating reveals an instrument limited linewidth of 0.1 nm. (C) Normalized fluorescence from short and long wavelength edges of the bandgap, at 572 nm and 625 nm respectively, are plotted in comparison to the laser line emission. It can be seen that above the threshold, the fluorescence intensity increases sub-linearly as a function of incoming energy, due to the preference for energy to flow into the lasing mode.

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As the concentration of DCJTB was reduced, the value of the energy fluence needed to achieve threshold rose according to the reduction of the light absorption in the gain layer (Fig. 5): A = I(1 − e^−αd), where α is the absorption coefficient, which is proportional to concentration of dye molecules. Nevertheless, the threshold absorbed energy density remains nearly constant from 0.025% up to 1%, as expected for lasing from organic dyes which typically behave as 4-level lasing systems. For dye ratios above 1%, the threshold excitation density rises because concentration quenching reduces the quantum yield of fluorescence.

 

Fig. 5 (A) Lasing threshold as function of DCJTB concentration in the PVK host matrix. The absorbed energy density for achieving threshold was derived from the measured energy fluence by calculating the absorption in the gain layer. (B) Relative slope efficiency of the lasing output above threshold as a function of dye concentration. Red curve is simulation which accounts for possible relaxation into charge separated states, while green curve is simulation with no such relaxation possible. (C) Relative number of charge separated (CS) states after excitation pulse, for pulse energy E = 2E_th.

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However, the relative slope efficiency, which we define as the slope efficiency of the device above and below lasing depends strongly on dye concentration (Fig. 5(b)). This dependence cannot be explained by gain saturation or absorption of excited states since the above threshold linearity of output energy to input energy extends at least up to 3E_th for doping ratio of 0.025% (Fig. 3). Triplet state absorption, which is a key factor in hindering CW lasing, cannot have a considerable influence on the system since it would require an unrealistically high triplet formation rate [19] as we will show further on. The possible change in the coupling factor - β, which can affect slope efficiency, is not compatible with our observation that the lasing threshold is nearly constant in terms of excitation density. Likewise, annihilation processes such as singlet-singlet, singlet-triplet, and triplet-triplet annihilation are only observed at high exciton density, while in our work we are far from this regime. The model for an ideal 4-level system predicts a small decrease in relative slope efficiency at low concentration, but it cannot explain the experimental data (Fig. 5(b)).

The observed results can be explained by considering charge separation of the excited DCJTB molecules. PVK is a known p-type material while DCJTB is n-type. It was observed in systems using a similar laser dye, DCM2 doped into the hole transport material TPD [20] that indeed excitons generated on the DCM2 molecules dissociate into separated electrons and holes at the dye-host matrix interface with electrons being trapped on the dye molecules. Geminate recombination [21] of such states typically occurs on the timescale of about 100 ns [22] as observed in organic photovoltaics. High hole mobility in PVK may further promote dissociation of the charges and thus lead to non-geminate recombination which can have lifetimes up to 1 μs [22]. In either case, recombination times of the separated charges are expected to be long compared to the spontaneous emission time - τ_sp and excitation pulse duration.

For our model, we derived rate equations that are similar to the formalism in [23] which describes lasing in the presence of electron transfer from excited singlet to triplet states. Here, focusing on the possibility of charge separation, we assume the DCJTB molecules, by themselves act as a 4-level lasing system. Namely, transitions from the excited state of absorption to the excited state of emission and likewise from the ground state of emission to the ground state of absorption occur fast enough to be considered as immediate. In addition, as we explained above, upon charge separation, the recombination time of the separated charges is much longer than the pulse duration, so no significant relaxation from these states is observed during the excitation pulse. We define N₀, N₃ as ground and excited states of the absorption transition and N₁, N₂ as ground and excited states of the emission transition. Since the transition from N₃ to N₂ as well as the transition from N₁ to N₀ is on picosecond scale, which is much faster when any other dynamics we can assume N₃ = N₁ = 0.

Solving the rate equations for different concentrations of dye molecules, we were able to describe reasonably well the experimental data using τ_CS/τ_sp = 0.79. This additional relaxation pathway can also be expected to reduce the fluorescence quantum yield in PVK, as it competes with spontaneous emission. Indeed, we evaluated the quantum yield of fluorescence for DCJTB in PVK compared to PMMA, Φ_PVK and Φ_PMMA, respectively. We found from fluorescence and absorption measurements that Φ_PVK/Φ_PMMA = 0.55. According to [18], the quantum yield of DCJTB in PMMA is Φ_DCJTB = 0.68 which gives Φ_PVK = 0.38. This reduction is consistent with our model that in PVK additional relaxation pathways are present that reduce the quantum yield.

It can be seen in Fig. 5(c) that the percentage of dye molecules trapped in the charge separated states becomes close to 100% for low concentrations of DCJTB. Charge separated states population mostly builds up during the lasing while it remains small before the lasing threshold is reached even for low concentrations of DCJTB. Hence the charge separation mechanism affects primarily the relative slope efficiency for lasing and not the threshold excitation density. Thus lasing occurs for dye concentrations that are as small as 0.025%, even though the slope efficiency has been reduced by charge separation. However, since the number of molecules needed to be excited is already about 50% of the total available molecules in the gain layer, it is hardly possible to see lasing at further reduced levels of dye doping.

Very recently, excitonic lasers utilizing monolayers of inorganic transition-metal dichalcogenides were reported in [24]. The concentration reached in this work suggests the possibility of a similar DFB architecture based on a monomolecular organic layer. In such a device, all of the active material would be confined into a single film, one molecular layer thick, inside of the waveguiding layer. For instance, if all of the DCJTB molecules in the 0.025% doped gain layer were concentrated in a single monolayer, the distance between them would be about 3.4 nm. This is the same spacing as for concentrations of about 2% of organic dye in a bulk host matrix. According to [18] at this distance, concentration quenching is small and quantum efficiency is close to its maximum value. Furthermore, since in the monomolecular layer, each molecule is surrounded by a lower number of neighboring dye molecules than in bulk, for the same distance between molecules, we can expect a lower non-radiative energy transfer rate. Hence, a lower degree of concentration quenching can be expected, which can enable efficient lasing even for higher local concentrations.

5. Conclusion

We investigated the lasing behavior in a DCJTB based DFB across two orders of dye concentration. The lasing threshold was found to be inversely proportional to the concentration of DCJTB, but nearly constant in terms of absorbed excitation density. Below a DCJTB concentration of 0.025%, lasing was not observed indicating a lower limit. Further dye molecules concentration reduction is not possible since the density of molecules becomes comparable to the excitation density at the lasing threshold. Varying the dye concentration had a significant impact on the relative slope efficiency for the DFB lasing output. We demonstrated that the decrease in efficiency as the gain concentration is lowered can be attributed to rapid charge separation that results in long lifetime charge separation states. Therefore, the influence of the electrical properties of the host and active materials, while sometimes not evident at high concentrations of gain, can have considerable impact on the lasing dynamics in the low concentration limit.