**1. Introduction**

Since their discovery [1,2], four decades of research has been performed on conjugated materials (polymers and oligomers) due to their captivating photophysical properties. The properties of these special materials, such as high quantum yield, high chromophore density, large Stokes shift, wavelength tunability, and large optical gain, have been studied in depth [3]. These extraordinary properties make these polymers ideal in many applications, such as in laser-active media [4–8] flexible FET (field-effect transistors) [9], photovoltaic devices [10], and photodiodes, as well as light-emitting diodes (LEDs) [9–11]. Both conjugated polymers (CPs) and conjugated oligomers (COs) are appealing laser materials and can produce lasing at proper concentrations in solid-state, thin-film, and liquid forms [12–16]. ASE is produced when the active medium is optically excited by an intense laser source. Moreover, the ASE feedback can be converted to a laser when an optical cavity is combined with the system [17]. In general, materials that can achieve ASE can produce lasing under an optical cavity. However, some materials produce lasing in the cavity but cannot produce ASE without a cavity.

Many CPs exhibit amplified spontaneous emission (ASE), mirrorless lasing with high intensity, spatial coherence, and low temporal coherence. CPs as active gain media have

**Citation:** Aljaafreh, M.J.; Prasad, S.; AlSalhi, M.S.; Alhandel, R.H.; Alsaigh, R.A. TD-DFT Simulation and Experimental Studies of a Mirrorless Lasing of Poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(1,4-diphenylenevinylene-2-methoxy-5-{2 ethylhexyloxy}-benzene)]. *Polymers* **2021**, *13*, 1430. https://doi.org/ 10.3390/polym13091430

Academic Editor: Asterios (Stergios) Pispas

Received: 10 March 2021 Accepted: 25 April 2021 Published: 29 April 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

produced ASE and lasing, which could be tunable over a wide range in the visible spectrum [18–20]. Broadband ASE is used as a light source, which benefits many applications such as fiber sensing and telecommunications. These polymers are highly efficient in energy transfer to other polymers, oligomers, and perovskite quantum dots.

The first report on ASE from CPs was presented by Moses et al. MEH-PPV produced ASE via optical pumping in solution and film. The quantum efficiency of MEH-PPV was compared to that of the conventional dye rhodamine 6G [21]. Another group reported laser emission from TOP-PPV in solution [22]. Another CP, poly(9,9-dioctylfluorene) (PFO), was also well studied and found to produce ASE at different wavelengths depending on the concentration in solution. Thin films of PFO produce ASE from the β-phase.

In 2007, Redmond's team studied the first incidence of single-nanowire lasing under optical pumping for CO PFO, in which nanowires were formed through the template wetting method and exhibited a single Fabry–Pérot mode [23]. The threshold energy was 100 nJ. Moreover, the M. S. AlSalhi group investigated the properties of a CP as an active laser medium and proved the presence of excimeric and dimeric states of the CP. They studied the spectral temporal profile as well as ASE from the CP under different concentrations, solvent types, temperatures, and laser energy excitations using a Princeton Instruments PI-MAX 4 ultrafast-gated emCCD with an Acton picosecond spectrograph [24]. R. H. Friend and his team organized an intensive research work on CP blend laser systems, especially with the Forster energy transfer (FRET) mechanism [25,26].

Copolymerization is a technique that enables existing monomers to be combined to achieve new bandgaps and emission properties. The ASE properties of copolymer PFO-copX were studied by S.A Alfahd et al. There have only been minimal studies carried out on copolymers with a combination of PFO and PPV derivatives.

However, in general, DFT simulation, optical, and laser studies of conjugated polymers are rare [27–31] and in particular, none are about PFO-co-PPV-MEHB. To the best of our knowledge, this work could be the first work on the TD-DFT calculation of CP PFOco-PPV-MEHB. We calculated electronic properties such as structure optimization; the EHOMO, ELUMO, EGap; the dipole moment; and the oscillator strength of PFO-co-PPV-MEHB for structures optimized under the three-monomer truncated-tail oligomer model using the DFT/Coulomb-attenuated method at the B3LYP (CAM-B3LYP)/6-31G(d,p) level by Gaussian 16 and other software. Furthermore, experimental studies of PFO-co-PPV-MEHB spectral and mirrorless laser properties in toluene under transverse excitation were performed. The pump source was the Nd: YAG laser of 355 nm. We demonstrate that under a suitable concentration and a low pump energy, CO PFO-co-PPV-MEHB can produce ASE at 508 in toluene. TRS studies display the ASE in 3D features, with the wavelength, spectral amplitude, and time as the X-, Y-, and Z-axes, correspondingly.
