## 1 Introduction  
Ultra-fast polymerization (3 s) with light curing units (LCUs) capable of producing a high radiantitance of 3000 mW/cm\({}^{2}\) can accelerate the clinical procedure of bonding [1, 2], making it more comfortable for the patient and saving time for the clinician. Today, the development of high-power light emitting diode (LED) chips has enabled progressively higher radiantitance (up to 3000 mW/cm\({}^{2}\)) in modern LCUs [1, 3]. LED technology is now the most used method for light curing of orthodontic adhesive systems for bracket bonding [1, 2]. Compared to halogen curing units, LED LCUs achieve successful clinical bonding in a shorter curing time [2, 4, 5]. Polymerization in light-cured dental resin composites depends on the total energy received [6; 7; 8]. Total energy, i.e., radiant exposure or energy density (J/cm\({}^{2}\)), is equal to radiantitance or power density (mW/cm\({}^{2}\)) multiplied by exposure time (s) [7; 9; 10]. The rapid polymerization protocol, using a very short (3 s) curing time, is based on the concept of \"exposure reciprocity,\" that is, the higher the light intensity of the LCU, the less time is needed for polymerization, given that the total delivered energy remains the same [1; 4; 5]. The higher the light intensity, the more photons are emitted, activating a higher amount of photoinitiator molecules and generating more free radicals, ensuring a faster polymerization reaction [11]. The degree of conversion (DC) is a measure of the efficiency of light curing, representing the percentage of monomer double bonds (C=C) that are converted into single bonds (C-C) during polymerization [12; 13; 14; 15; 16]. Higher DC values are associated with better mechanical and aesthetic properties as well as biocompatibility [14; 17], although the relationship is not always linear [12; 18]. Even though rapid high-intensity polymerization with modern LCUs enables delivering the same amount of total energy as with conventional curing by adjusting the curing unit output and curing time (the \"reciprocity law\"), previous studies [10; 19; 20; 21; 22] have demonstrated that at high radiant exitances (above 1000 mW/cm\({}^{2}\)), the polymerization reaction becomes qualitatively different, leading to different polymer structures, affecting chain length and crosslink density, compared to that formed under slower, more gradual polymerization [23]. The concept of rapid polymerization has been controversial and questioned for composites incorporating Norrish Type II photoinitiator systems like camphorquinone combined with a tertiary amine, and it was assumed to be achievable only for materials using Norrish Type I photoinitiators (e.g., Lucirin-TPO) [1]. Some material properties, like DC and other mechanical properties (like flexural strength and modulus), may be adversely affected by rapid polymerization [24]. Faster polymerization rates have been shown to hinder the propagation of the reaction, as a high number of activated free radicals terminate each other in the process called bimolecular termination, preventing further monomer activation [19; 25; 26]. This can result in lower final DC values, as well as a more heterogeneous polymer network with unreacted monomers trapped inside [27]. Although the adverse biological effects of orthodontic adhesive systems have not been as extensively investigated as those of restorative composites [28], prior studies investigating cytotoxicity of orthodontic adhesive systems [18; 27] showed that unreacted monomers could have adverse biological effects, especially considering the long exposure time over the duration of orthodontic therapy, which is typically 1.5-2 years. Inadequate polymerization of the orthodontic adhesive layer beneath brackets can facilitate the diffusion of cytotoxic components (resin components, like Bis-GMA and TEGDMA) into the enamel, dentin, and pulp tissues [18; 27]. There are some resin-based dental composites on the market that are advertised specifically for rapid high-intensity light curing [1].