第一章
1.10 Refractive index
(a) Consider light of free-space wavelength 1300 nm traveling in pure silica medium. Calculate the phase velocity and group velocity of light in this medium. Is the group velocity ever greater than the phase velocity?
(b) What is the Brewster angle(the polarization angle qp) and the critical angle(qc) for total internal reflection when the light wave traveling in this silica medium is incident on a silica/air interface. What happens at the polarization angle?
(c) What is the reflection coefficient and reflectance at normal incidence when the light beam traveling in the silica medium is incident on a silica/air interface?
(d) What is the reflection coefficient and reflectance at normal incidence when a light beam traveling in air is incident on an air/silica interface? How do these compare with part (c) and what is your conclusion?
1.18 Reflection at glass-glass and air-glass interface
A ray of light that is traveling in a glass medium of refractive index n1=1.460 becomes incident on a less dense glass medium of refractive index n2=1.430. Suppose that the free space wavelength of the light ray is 850 nm.
(a) What should the minimum incidence angle for TIR be?
(b) What is the phase change in the reflected wave when the angle of incidence qi =85°and when qi =90°?
(c) What is the penetration depth of the evanescent wave into medium 2 when qi =85° and when qi =90°?
(d) What is the reflection coefficient and reflection at normal incidence (qi =0 ° )when the light beam traveling in the glass medium (n=1.460) is incident on a glass-air interface?
(e) What is the reflection coefficient and reflectance at normal incidence when a light beam traveling in air is incident on an air/-glass interface (n=1.460)? How do these compare with part (d) and what is your conclusion?
1.20 TIR and polarization at water-air interface
(1) Given that the refractive index of water is about 1.33, what is the polarization angle for light traveling in air and reflected from the surface of the water?
(2) consider a diver in sea pointing a flashlight towards the surface of the water. What is the critical angle for the light beam to be reflected from the water surface?
1.22 phase changes on TIR
Consider a lightwave of wavelength 870nm traveling in a semiconductor medium (GaAs) of refractive index 3.6. It is incident on a different semiconductor medium (AlGaAs) of refractive index 3.4, and the angle of incidence is 80o. Will this result in total internal reflection? Calculate the phase change in the parallel and perpendicular components of the reflected electric field?
1.25 Goos-Haenchen phase shift
Aray of light that is traveling in a glass medium(1) of refractive index n1=1.460 becomes
incident on a less dense glass medium(2) of refractive index n2=1.430. Suppose that the free space wavelength of the light ray is 850nm.the angle of incidence θi=85°. Estimate the lateral Goos-Haenchen shift in the reflected wave for the perpendicular field component. Recalculate the Goos-Haenchen shift in the second medium has n2=1 (air). What is your conclusion?Assume that the virtual reflection occurs from a virtual plane in medium B at a distance d that is roughly the same as the penetration depth.Note that d actually depends on the polarization ,the direction of the field,but we will ignore this dependence.
第二章 作业习题： θ
2.7 Dielectric slab waveguide Consider a dielectric slab waveguide that has a thin GaAs layer of thickness 0.25μm between two AlGaAs layers. The refractive index of GaAs is 3.6 and that of the AlGaAs layers is 3.40. What is the cut-off wavelength beyond which only a single mode can propagate in the waveguide, assuming that the refractive index does not vary greatly with the wavelength? If a radiation of wavelength 860 nm (corresponding to bandgap radiation) is propagating in the GaAs layer, what is the penetration of the evanescent wave into the AlGaAs layer? What is the mode field width (MFW) of this radiation? Point out the effect of change of radiation wavelength (λ) on the MFW.
2.9 Dielectric slab waveguide Consider a planar dielectric waveguide with a core thickness 10μm, n1=1.4446, n2=1.4440. Calculate the V-number, the mode angle θm for m=0 (use a graphical solution, if necessary), penetration depth, and mode field distance (MFW=2α+2δ), for light wavelengths of 1.0μm and 5μm. What is your conclusion? Compare your MFW calculation with 2?0?2a?V?1?/V.The model angleθ0is given as θ0=88.85? for λ=1μm and θ0=88.72? for λ=1.5μm for the fundamental mode m=0.
2.10 A multimode fiber Consider a multimode fiber with a core diameter of 60μm, core refractive index of 1.47, and a cladding refractive index of 1.45 both at 870 nm. Consider operating this fiber at λ=870nm.
(a) Calculate the numerical aperture.
(b) Find out the normalized core-cladding index difference.
(c) Calculate the V-number for the fiber and estimate the number of guided modes. (d) Calculate the wavelength beyond which the fiber becomes single-mode. (e) Calculate the modal dispersion ??and hence the bit rate ?distance product .
2.12 Single mode fiber Consider a fiber with a SiO2-13.5%GeO2 core of diameter of 6?m and refractive index of 1.47 and a cladding refractive index of 1.46 both refractive indices at 1300 nm where the fiber is to be operated using a laser source with a half maximum width (FWHM) of 2 nm..
(a) Calculate the V-number for the fiver.
(b)what is the maximum allowed diameter of the core that maintains oprations in single-mode?
(c) Calculate the wavelength below which the fiber becomes multimode. (d) Calculate the numerical aperture.
(e) Calculate the maximum acceptance angle.
(f) Obtain the material dispersion and wavelength dispersion and hence estimate the bit rate
?distance product (B?L) of the fiber.
光电子学与光子学讲义-作业答案(第1、2章)13版
