## 1 Introduction  
Optical waveguides are one of the most important photonic components indispensable in many of today's technologies [1, 2]. The development of new materials and novel fabrication technologies for the realization of optical waveguides have attracted great attention. In particular, polymer-based waveguides are crucial soft photonic building blocks [3, 4, 5] for the development of complex multifunctional platforms, such as chip-to-chip interconnects in electronic systems [6, 7], lab-on-chips [8], optofluidic platforms [9], biomedical sensing [10, 11], wearable physiological monitoring [12], and optogenetics [13, 14, 15]. Single-mode optical waveguides have been fabricated through direct laser writing (DLW), soft lithography, and thermal curing methods using poly-siloxane and other commercially available polymer materials [16, 17, 18, 19]. polydimethylsiloxane (PDMS) is an elastomer of fundamental technological importance; because of its physical and chemical properties, and because of its easy handling. It is widely used for the realization of optical waveguides by combining hot embossing and standard soft lithography processes [20, 21, 22]. These methods are generally constrained to the fabrication of two-dimensional structures. However, the implementation of miniaturized photonic components with increased integration density calls for new, versatile fabrication technologies, which enable the formation of arbitrary submicron 3D shapes within a bulk material, such as two-photon DLW. Multi-photon polymerization (MPP) is one of the most important technological achievements for the microfabrication of fine structures in polymeric materials, because of its nonlinear feature resulting in a precisely localized and highly confined material modification [23]. Typically, polymer formulations for photopolymerization applications comprise a polymerizable component (the monomer) and a photosensitive component (the photoinitiator). Developments in these two-component materials are central to the field of MPP. We have recently shown the fabrication of sub-2 \(\upmu\)m waveguides in polydimethylsiloxane (PDMS) through multi-photon DLW without a photoinitiator (PI) [24]. The PI-free fabrication process using phenylacetylene as the monomer achieved an excellent refractive index contrast of 0.06 and a very low optical loss of 0.03 dB/cm in the 650-700 nm band. While the high refractive index contrast is clearly a result of a high degree of polymerization, the existence of long conjugated \(\uppi\)-bonds in the polymer result in very poor transmission in wavelengths shorter than 600 nm. Furthermore, this process was subject to defects in the fabrication of waveguides longer than one cm due to material damage, which is likely a result of the uncontrollable beam collapse caused by the self-focusing of light upon photopolymerization [25]. In a photoinduced polymerization process, the reaction probability of polymerization is proportional to a power function of the laser intensity depending on the order of the nonlinearity involved. This creates an intensity-dependent refractive index profile during the laser irradiation, which causes self-focusing and beam self-trapping. Different from nonlinear refractive indices of electronic and molecular origin, this chemically originated nonlinear refractive index reacts rather slow, possibly at the millisecond time scale as limited by the monomer diffusion time and is rather large in magnitude. This self-focusing process is a direct function of the refractive index change between the pre- and post-polymerization state, which is dependent on the degree of polymerization and the monomer concentration. The self-focusing that leads to beam collapse and material damage is an intrinsic effect that needs to be taken into consideration in the waveguide writing process. Motivated by the need to minimize self-focusing, we explored other monomer/PI combinations that can lead to different characteristics in PDMS.