# All-Optical Method of Determining Laser Power from the Photomechanical Effect
## 1 Introduction
The most common mechanism associated with the photomechanical effect is photothermal heating, where materials are heated upon absorbing light which increases their temperature [37, 38, 39, 40, 41, 42]. Photothermal heating can cause a reduction in the orientational order of mesogens in the previously mentioned liquid crystal polymers/elastomers which also results in a contraction along the director [43, 44, 45]. Materials expand volumetrically when heated [46, 47], where large coefficients of thermal expansion and small heat capacities offer the greatest photomechanical strains in isotropic materials. When small azobenzene dyes such as disperse red 1 are doped in amorphous polymers, a small portion of the linear strain has been attributed to molecular reorientation of dopant molecules [48, 49]. The type of photomechanical actuation exhibited by a material is determined by its shape and microscopic properties [50, 51, 52]. Uniaxial strain has been demonstrated in chromophore-doped polymer optical fibers, where bistable switches have been created using feedback from reflective ends [53, 54, 55, 56]. Asymmetric pumping of fibers and thin planar materials can result in photomechanical cantilevers [57, 58, 59]. Bilayer materials with mismatched photo-induced strains can also act as photomechanical cantilevers [60, 61, 62, 63, 64, 65, 66]. Photomechanical devices benefit from expansions, contractions, bends, twists, and other complex deformations of photomechanical materials [67, 68]. Many classes of photomechanical devices have been reported such as swimmers [69, 70], flyers [71], walkers [72, 73], tumblers [74], crawlers [75, 76], motors [77], energy harvesters [78, 79, 80, 81, 82, 83], microlens with tunable focal lengths [84], various biomimetic devices [85, 86, 87, 88, 89], and the photophone [90]. Photomechanical devices have also been shown to work as series [91, 92, 93] and parallel [94, 95] components of a photomechanical system. In this study, we investigate the photomechanical effect as a means of determining the power of a CW laser. A free-standing, dye-doped, polydimethylsiloxane (PDMS) layer with a surface relief grating expands after being heated by a pump laser, where the angle of a probe laser's diffracted beam can be used to determine the grating period as a function of time. The PDMS elastomer was chosen for several reasons. A transmission diffraction grating was embossed on the PDMS surface due to its excellent optical transparency, which is in contrast to opaque light scattering photomechanical materials such as liquid crystal elastomers. The photo-induced strain in PDMS is linearly dependent on the illumination intensity for isotropic materials like PDMS that thermally expand when heated. Materials such as liquid crystal elastomers have nonlinear strain responses to both heat and light caused by the change in orientational order of the mesogens [17]. Restricting the material to have a single mechanism for a strain response to light further increases the linearity of a device as opposed to allowing additional slower responses such as photoisomerization observed in some photochromic polymers [96, 97] and liquid crystal polymer networks [98]as well as reorientation effects from azobenzene-doped amorphous polymers [57]. Lastly, the coefficient of thermal expansion of PDMS is much greater than common thermoplastic polymers such as poly(methyl methacrylate) [99]. The cost of PDMS per unit volume is comparable with common plastic materials while have the formerly mentioned advantage, and it is easily cured in solvent-free formulations for soft-lithography applications.