The coupling coefficients of various organic solid-state distributed feedback structures were calculated using an adapted Floquet matrix theory. Starting from these calculations, coupled mode theory is used to predict the performance of the various laser structures used within the course of this work. One important result is that the different surface texture of sublimed and evaporated structures gives rise to a different coupling mechanism. The transition from complex coupling to index coupling which is observed in 2nd order DFB lasers with increasing thickness of the Alq3:DCM film, was successfully modeled. Furthermore the gain
required to reach threshold can be reliably estimated. In summary, very good agreement between the predictions of the modeling and the experiments is found, even though some of the relevant material constants were not precisely known at the time the calculations were performed. Therefore these calculations are a powerful tool for the optimization of future organic DFB lasers. An example is outlined below.
Under continuous wave operation a certain longitudinal intensity distribution establishes inside the cavity of a DFB laser. This intensity distribution is a direct consequence of the
200 250 300 350 400 450 500 550 0 500 1000 1500 2000 2500 200 250 300 350 400 0 50 100 150 C oupl ing c ons ta nt κ (cm -1 ) Film Thickness (nm) Re (κ) Re (κ) Coup lin g C oef fic ient κ (c m -1 ) Film Thickness (nm) 0,00 0,02 0,04 0,06 0,08 0,10 G ai n c oupl in g co ef fic ient γ ' 0,00 0,01 0,02 0,03 0,04 G ai n C oupl ing C oef fic ien t γ ' Substrate m = 1 Evapor. film Substrate Spincasted film m = 1
Fig. 5.13: Calculated coupling coefficients for 1st order DFB structures with either a modulated
upper surface as in Alq3:DCM (left) or a flat upper surface as expected for a spincoated MeLPPP
film (right). The real part of the coupling coefficient is very weak in the Alq3:DCM structure,
64 5 Lasers with one-dimensional distributed feedback
excitation profile and the coupling strength κL, being the product of the coupling coefficient and the length of the device 134. For optimum performance the optical intensity distribution inside the cavity must be properly matched to the excitation distribution. Otherwise the excitation density is locally depleted (spatial hole burning) and the output power of the device exhibits strong fluctuations. If the excitation density is homogeneously distributed over the entire length of the device, so should be the optical intensity. This condition is reached if the value of κL is adjusted to 1.25 for an index coupled laser 223 or 1.6 for gain coupled device 224, respectively. On the other hand, the Gaussian excitation density distribution in optical experiments demands for a higher κL product, most likely in the order of 5-10 134. Since an infinite DFB structure does not have a well defined device length L it is the diameter of the excitation spot which has to be adjusted.
Due to the large modulation depth of the present DFB gratings, large coupling coefficients in the order of 500-1500 cm-1 are obtained in most of the structures. For optical excitation with a Gaussian excitation profile this implies an optimum spot diameter in the order of 100-200 µm, which is very convenient. In electrically driven devices, however, the distribution of excitation density is homogeneous and the large coupling coefficient implies an optimum device length in the order of only 10-20 µm. Such a short device requires a very high threshold gain (see equation 2-24). Therefore lower modulation depths are favorable for future electrically driven devices resulting in a reduced coupling coefficient, an increased optimum device lengths, and finally in a drastically reduced threshold gain. Due to the absence of surface emission losses, first order structures are the most promising candidates. Whereas up to now only dielectric gratings were considered, the Floquet-Bloch calculations can be extended to structures including metallic contacts 216,222.
65
In this chapter it is shown that two-dimensional distributed feedback can give rise to monomode laser operation with diffraction-limited surface emission. Excitation high above threshold results in multimode operation and enables a direct investigation of the two-dimensional photonic band structure.
Distributed feedback resonators based on nanopatterned substrates have shown to be a very promising method to fabricate organic semiconductor thin film lasers. One of their major drawbacks, however, is the presence of lateral modes leading to multimode laser operation. As seen in the previous chapter multimode operation is unfavorable due to the associated broadening of the laser spectrum and a large divergence. In order to concentrate the emission to a spectrally narrow line and to control the emission properties, it is crucial to reduce the number of lateral modes participating in the laser operation. The conventional way is the photolithographic definition of a lateral waveguide with a width of several microns. A more elegant method for mode selection is the use of two-dimensionally (2D) nanopatterned substrates giving rise to a 2D distributed feedback (2D-DFB) or in other words a 2D photonic band structure 140,141. Despite the early, promising results, there have only been very few experimental and theoretical 142-144,225 investigations until the recent renewed interest within the context of photonic crystal lasers 145.
6.1 Fabrication
The fabrication of the 2D-DFB lasers is very similar to the fabrication of the 1D-DFB lasers. As active laser material the conjugated polymer MeLPPP is used, which is spincast onto a mechanically flexible, nanopatterned substrate. The major difference to the 1D-DFB laser is in the form of the surface corrugation. Whereas a 1D sinusoidal corrugation with a periodicity of Λ =300 nm and a depth of h = 275 nm is used for 1D-DFB lasers, two perpendicular sinusoidal corrugations with a periodicity of Λz = Λx = 300 nm and a depth of hz = hx =
160 nm form the grating for the 2D-DFB laser. The maximum modulation depth is therefore similar for both structures, which is important when comparing the two structures. An AFM image of the resulting corrugation is displayed in the schematic setup of Fig. 6.1. The superior performance of our 2D-PBS lasers relies on phase locking of the modes established in the two perpendicular resonators. A particularly high grating quality is therefore compulsory, demanding that the deviation of the two periodicities Λz and Λx must not exceed the laser
66 6 Lasers with two-dimensional distributed feedback
PET with acrylic coating MeLPPP
Fig. 6.1: Schematic setup of a 2D-DFB laser. A film of MeLPPP is spincast onto a flexible, nanopatterned substrate. The surface of the substrate has a two-dimensional periodic corrugation shown by the AFM image. Laser emission is observed perpendicular to the substrate.
Gratings with sufficient quality can be fabricated by the soft lithography technique described in Section 5.1. As mentioned before, the corrugation is ultimately defined by the intensity pattern applied to a photoresist. Using a holographic exposure technique highly uniform 1D sinusoidal intensity profiles can be generated. 2D patterns are achieved if the sample is rotated between two subsequent exposures.