Chapter 1. Introduction 1 Chapter 2. Iron-based superconductors Ca10(Pt3As8)(Fe2As2)5 2.1 Crystals structure of Ca10(Pt3As8)(Fe2As2)5 and Ca10(Pt4As8)(Fe2As2)5 7 2.2 Crystal structure of La doped Ca10(Pt3As8)(Fe2As2)5 single crystal 9 2.3 Transport properties of Ca10(Pt3As8)(Fe2As2)5 2.3.1. Parent Ca10(Pt3As8)(Fe2As2)5 compound 14 2.3.2. Doping dependence of Ca10(Pt3As8)(Fe2As2)5 compound 15 2.4 Electronic structure of Ca10(Pt3As8)(Fe2As2)5 and Ca10(Pt4As8)(Fe2As2)5 17 2.5 Optical properties of iron-based superconductors 2.5.1. Optical properties of Pt doped Ca10(Pt3As8)(Fe2As2)5 compound 20 2.5.2. Psuedogap and electronic correlations in iron-based superconductor 23 References 28 Chapter 3. Experimental and Theoretical Methods 3.1. Synthesis methods of single crystal 3.1.1. Single crystals grown by vertical Bridgman method 32 3.1.2. Single crystal growth of La & Na doped Ca 10-3-8 compound 35 3.2. Transport measurement 3.2.1. Electrical resistivity measurement and measurement systems 37 3.2.2. Magnetoresistivity and Hall resistivity 39 3.3. Optical Spectroscopy 3.3.1. The principle of Fourier-transform spectroscopy 42 3.3.2. Fourier-transform infrared spectroscopy 45 3.3.3. Kramers-Kronig (K-K) relations for reflectivity analysis 50 3.3.4. Sum rules 52 3.3.5. Drude-Lorentz model 53 3.3.6. Superconducting gaps 55 References 57 Chapter 4. Results and Discussion 4.1 Superconducting-induced transfer of spectral weight due to microscopic coexistence of superconducting and magnetic correlation 58 References. 82 4.2 Optical properties in the hole-doped Ca8.5Na1.5(Pt3As8)(Fe2As2)5 single crystal with strong electron correlations 83 Referencee 111