## 2 Fundamental Principles
istic spectral features. When a photon is absorbed, electrons are excited from the HOMO to LUMO, creating a vibronic progression in the absorption spectrum due to coupling with molecular vibrations. Similarly, emission occurs when excited electrons return to the ground state, typically showing a Stokes shift due to geometric relaxation in the excited state. This vibronic structure leads to characteristic absorption and emission bands rather than sharp transitions, with the spectral shape influenced by both electronic and vibrational states. There are several known nonlinear optical effects in polymer organic semiconductors. In organic semiconductors, Second Harmonic Generation (SHG) arises from the non-centrosymmetric molecular structure and occurs when two photons combine to produce a single photon at twice the frequency [20; 21]. The efficiency of this process depends strongly on the molecular hyperpolarizability and the degree of polar ordering. Conjugated polymers with push-pull structures exhibit particularly strong SHG responses, making them valuable for frequency conversion applications in integrated photonic circuits. However, maintaining the non-centrosymmetric order in polymer films remains challenging and often requires special processing techniques. Electro-optic effects manifest as changes in refractive index under applied electric fields [22; 23]. In organic semiconductors, the effect primarily originates from molecular reorientation and electronic polarization. The fast response times (femtoseconds for electronic processes) make these materials particularly attractive for high-speed optical modulators and switches. Polymers with large dipole moments and extended \(\pi\)-conjugation typically show enhanced electro-optic coefficients, enabling efficient modulation at relatively low voltages [24]. Third Harmonic Generation (THG) in organic semiconductors converts three photons into one photon at triple the frequency. Unlike SHG, THG does not require non-centrosymmetric structures, making it more generally accessible in polymer systems [25; 26]. The effect scales with the third-order susceptibility \(\chi(3)\), which can be enhanced through extended conjugation and appropriate molecular design. THG finds applications in frequency conversion and optical signal processing, though thermal management can be challenging due to the high intensities required. Optical Kerr effect, this third-order nonlinear effect manifests as an intensity-dependent refractive index change. In conjugated polymers, the effect can be particularly strong due to the delocalized \(\pi\)-electron system [27]. The fast response time makes it useful for all-optical switching and signal processing. However, the same mechanism can lead to unwanted self-phase modulation in high-power applications, potentially distorting optical signals in waveguides. Two-Photon Absorption (TPA) occurs when two photons are simultaneously absorbed to excite an electron across an energy gap equivalent to the sum of their energies. In organic semiconductors, TPA can be enhanced through molecular design strategies that increase the two-photon cross-section [28]. While this effect can be detrimental in some applications by causing optical losses, it is deliberately exploited in others, such as 3D optical data storage, photodynamic therapy, and high-resolution imaging. The quadratic dependence on intensity provides inherent 3D selectivity in these applications [29]. These nonlinear optical phenomena are particularly interesting in organic semiconductors because their strength can be tuned through molecular design and processing conditions. The ability to engineer these properties at the molecular level, combined with solution processability, makes organic semiconductors versatile materials for photonic applications. However, practical implementation often requires careful consideration of trade-offs between nonlinear optical response, optical losses, and material stability.