Determination of the Best Empiric Method to Quantify the Amplified Spontaneous Emission Threshold in Polymeric Active Waveguides

Amplified Spontaneous Emission (ASE) threshold represents a crucial parameter often used to establish if a material is a good candidate for applications to lasers. Even if the ASE properties of conjugated polymers have been widely investigated, the specific literature is characterized by several methods to determine the ASE threshold, making comparison among the obtained values impossible. We quantitatively compare 9 different methods employed in literature to determine the ASE threshold, in order to find out the best candidate to determine the most accurate estimate of it. The experiment has been performed on thin films of an homopolymer, a copolymer and a host:guest polymer blend, namely poly(9,9-dioctylfluorene) (PFO), poly(9,9-dioctylfluorene-cobenzothiadiazole) (F8BT) and F8BT:poly(3- hexylthiophene) (F8BT:rrP3HT), applying the Variable Pump Intensity (VPI) and the Variable Stripe Length (VSL) methods. We demonstrate that, among all the spectral features affected by the presence of ASE, the most sensitive is the spectral linewidth and that the best way to estimate the ASE threshold is to determine the excitation density at the beginning of the line narrowing. We also show that the methods most frequently used in literature always overestimate the threshold up to more than one order of magnitude.

the other two samples the vibronic peaks are not resolved, thus leading to higher values of the FWHM 23 at low excitation density. We anyway observe that this effect only affects the FHWM value below the  Figure S2. a: Example of the determination of the ASE integrated intensity for the PFO film. The ASE integrated intensity is evidenced by the region with horizontal red line pattern, while the contribution of the spontaneous emission to the total intensity is evidenced by the squared patterned region. b: Intensity increase with the stripe length for the PFO film (dots), the red line is the best fit function with Equation 1.
In order to determine the ASE integrated intensity at any given excitation density we plotted 28 the corresponding PL spectrum (see red line in Fig. S2 a) and we initially determined the integrated 29 emission intensity. We then separated the ASE contribution to the total integrated intensity by 30 exploiting the lack of excitation density dependence of the spontaneous emission lineshape. We thus 31 plotted a PL spectrum below the visual ASE threshold (blue line in Fig. S2 a) and we rescaled it in 32 order to match the intensity of the spontaneous emission contribution to the total spectrum (black line 33 in Fig. S2 a). We finally determined the total spontaneous emission intensity by numerical integration 34 of the rescaled spectrum below threshold, and the integrated ASE intensity as difference between the 35 total intensity and the spontaneous emission integrated intensity.

Working time estimate 48
In order to estimate the time required to obtain the threshold value with the different methods 49 we took into account the net time necessary for the measurements, for the data extraction and for the 50 fitting procedures (see Tab. S1).

51
In particular we considered that the visual determination of the threshold simply requires to 52 observe the PL spectra evolution while continuously increasing the excitation density, by running the 53 acquisition CCD in real time. This procedure can be completed in about 1 minute and we typically repeat it 4-5 times, in order to safely determine the minimum excitation density that leads to a lineshape 55 variation. We thus estimated that the determination of the visual threshold can take about 5 minutes.

56
For the other methods we first of all estimated the time to acquire each spectrum in about 1 minute, 57 considering that the integration time is typically of few seconds, and that every measurement just 58 needs to add the time for the setting of the acquisition parameter (excitation density in VPI experiments 59 and stripe length in VSL ones) and for the file saving. The methods based on the VPI methods thus 60 need about 25 minutes for the measurements. This limited time further evidences that the acquisition 61 of a high number of spectra has a very limited impact on the total experiment working time and thus, 62 on the contrary, there are not real reasons to limit the VPI experiment to the collection of a low number 63 of spectra, as often done in literature.

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The times for the VLS are instead much higher as we collected, at each excitation density, the PL to obtain the integrated ASE intensity. Overall this procedure can be completed in a bit more than 2 79 minutes.

80
On the contrary the extraction of the I peak value is much faster, as it simply requires to copy the 81 intensity value at the ASE peak wavelength for each spectrum (we estimated about 10 seconds).

82
A similar assumption was made for the time needed to have the PL intensity at a given wavelength 83 and stripe length in the VSL experiment.

84
Furthermore, we assumed that each best fit requires about 10 minutes. 85 We observe that the estimated time reported in the table for the VLS method corresponds to the 86 determination of the net gain dependence on the excitation density at a single wavelength. In our 87 experiment we determined the whole net gain spectrum by repeating the procedure for 75 different 88 wavelength, thus increasing of 75 times the real working time.

89
Finally, we highlight that the total times in the last column of the table represent only a lower 90 limit of the overall time taken by the experiment.