Photonic Materials

Photonic Materials and Structures 2nd Semester 2025 Prof Christiano de Matos LIST OF EXERCISES 2 CONDUCTORS 1 Show that for a poor bad conductor 𝑘 𝑘 the real 𝑘 and imaginary 𝑘 parts of the wavevector can be written as page 23 of the book 𝑘 𝑛𝜔 𝑐 𝑘 𝜇𝜎𝑐 2𝑛 𝜎 2𝑛𝑐𝜀 2 Using Drudes model calculate the plasma frequencies of sodium and aluminum Compare the results with those shown in table 22 of the book Do the values agree for both materials Explain any observed discrepancies 3 Using the expression for the current density 𝐉 𝜎𝐄 and Drudes model show that the conductivity at a frequency 𝜔 is given by 𝜎𝜔 𝜀𝜔 𝛾 𝑚 𝑖𝜔 4 Draw graphs for the real and immaginary parts of the interband conductivity in graphene for photon energies 04 eV ℏ𝜔 16 eV Normalize the graphs by 𝜎 and assume 𝐸 04 eV Assume also τ 2 ps Describe in words what you see and explain the general observed behavior Photonic Materials and Structures 2nd Semester 2025 Prof Christiano de Matos LIST OF EXERCISES 1 BASICS 1 Given e find a b c 2 Given find a The magnitude of vector b The unit vector c The angles that does with the x y and z axes 3 Write the expressions of it in terms of the complex exponential ie 𝑖𝑡 𝐼𝑒 with the phases in radians and expressed in term of p a b 4 Given 𝑓𝑥 𝑦 𝑧 𝑥 𝑥𝑧 𝑠𝑖𝑛𝑦 and 𝑔𝑥 𝑦 𝑧 33𝑓 find a 𝑔𝑥 𝑦 𝑧 b 33 𝑔 c 33 𝑔 d 𝑓 e 𝑔 5 The 1550 nm wavelength is widely used for optical telecommunications Convert it to frequency in THz and to photon energy in eV 6 The complex refractive index of germanium at 400 nm wavelength is given by 𝑛6 414 2221𝑖 Determine a the phase velocity of light b the attenuation coefficient a z y x a a a A ˆ 2 ˆ 5ˆ z x a a B 4 ˆ 3ˆ B A B A AB q z y x a a a B 3ˆ 6 ˆ 2 ˆ B B aˆ B 30 0 cos t I i t w p w 20 0 sen t I i t Photonic Materials and Structures 2nd Semester 2025 Prof Christiano de Matos LIST OF EXERCISES 1 BASICS 1 Given A 5ax 2ay az and B 3ax 4az find a A B b A B c θAB 2 Given B 2ax 6ay 3az find a The magnitude of vector B b The unit vector âB c The angles that B does with the x y and z axes 3 Write the expressions of it in terms of the complex exponential ie it I0 ejωt θ0 with the phases in radians and expressed in term of π a it I0 cosωt 30 b it I0 senωt 02π 4 Given fxyz x2 xz siny and gxyz f find a xyz b g c d 2 f e 2 g 5 The 1550 nm wavelength is widely used for optical telecommunications Convert it to frequency in THz and to photon energy in eV 6 The complex refractive index of germanium at 400 nm wavelength is given by n 414 2221i Determine a the phase velocity of light b the attenuation coefficient α