# Microstructured Phononic Crystal Isolates from Ultrasonic Mechanical Vibrations  
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1 Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy; [EMAIL_ADDRESS] (V.Z. ); [EMAIL_ADDRESS] (A.C.)  
[PERSON]  
2 Istituto di Fotonice e Nanotecnologie (IFN), Consiglio Nazionale delle Ricerche (CNR), Piazza Leonardo da Vinci, 32-20133 Milano, Italy; [EMAIL_ADDRESS] (L.P.); [EMAIL_ADDRESS] (T.Z. ); [EMAIL_ADDRESS] (R.O.) [PERSON]  
2 Istituto di Fotonice e Nanotecnologie (IFN), Consiglio Nazionale delle Ricerche (CNR), Piazza Leonardo da Vinci, 32-20133 Milano, Italy; [EMAIL_ADDRESS] (L.P.); [EMAIL_ADDRESS] (T.Z. ); [EMAIL_ADDRESS] (R.O.) [PERSON]  
2 Istituto di Fotonice e Nanotecnologie (IFN), Consiglio Nazionale delle Ricerche (CNR), Piazza Leonardo da Vinci, 32-20133 Milano, Italy; [EMAIL_ADDRESS] (L.P.); [EMAIL_ADDRESS] (T.Z. ); [EMAIL_ADDRESS] (R.O.) [PERSON]  
1 Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy; [EMAIL_ADDRESS] (V.Z. ); [EMAIL_ADDRESS] (A.C.)  
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complete band gaps [22; 23; 24; 25; 26], whose properties do not rely exclusively on the intrinsic material properties, but mainly on their fine-scale structuring. Complete isolation, instead of vibration damping, can be obtained with attenuation factors that are orders of magnitude higher than those obtainable with a bulk material. The increasing interest on applications of phononic crystals in different contexts is testified by several recent works focused on the design and optimization of phononic crystals in terms of bandgap width, or on the miniaturization of such structures. Examples of topological optimization of phononic crystals [27], e.g., by using the SIMP approach and the MMA algorithm [28], genetic algorithms [29], the bidirectional evolutionary structural optimization (BESO) [30; 31] or the gradient-based approach [32], are indeed available. In parallel, examples of miniaturized phononic crystals are present in the recent literature [33; 34; 35; 36]. In this work, we take a step further with respect to the available literature by combining the ultra-wide bandgap property of an optimized phononic crystal with the very small dimensions, i.e., in the order of \(\upmu\)m, required by the MEMS world, thus opening the path to the possibility to integrate MEMS with metamaterials for vibration isolation purposes. The proposed prototype is studied, fabricated and tested to demonstrate its isolation properties. It is shown that attenuation factors of several orders of magnitude are obtained. The 2 PP technique, exploiting the nonlinearity of the absorption process and setting the intensity just above the threshold, can overcome the diffraction limit, obtaining resolutions down to hundreds of nanometres using a laser beam with wavelength of several hundreds of nanometers [37; 38; 39]. 2 PP-based manufacturing processes share with other additive manufacturing (AM) techniques, such as stereolithography, selective laser sintering, 3D printing, electron beam melting, and direct metal laser sintering, the ability to realize microarchitected materials with unlimited topological complexity, while increasing the resolution to the microscale [10; 40]. The limitations of the 2 PP technique are mainly related to the choice of building material. However, even though the resin usually employed has a relatively low elastic stiffness, the small dimensions of the microstructure that can be fabricated allow us to obtain phononic crystals with isolation properties in the range of interest to the MEMS applications targeted here (from hundreds of kHz to some MHz).