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- Question : q1 - M axwell
- Question : q2 - Pr opagation in a medium of finite small conductivity An electromagnetic wave in an isotropic medium with a dielectric constant er and a finite conductivity s and traveling along z obeys the following equation for the variation of the electric field E perpendicular to z d2E dz2 - eoermo 02E 0t2 = mos 0E 0t (P1.1) Show that one possible solution is a plane wave whose amplitude decays exponentially with propagation along z, that is, E = Eo exp (-a?z) exp3j(vt - kz)4. Here exp (-a?z) causes the envelope of the amplitude to decay with
- Question : q3 - Po int light source What is the irradiance measured at a distance of 1 m and 2 m from a 1 W light point source?
- Question : q4 - G aussian beam Estimate the divergence and Rayleigh range of a Gaussian beam from a He-Ne Laser with l = 633 nm and a beam width of 1.00 nm at z = 0. After traversing 10 m through vacuum, what will the beam
- Question : q5 - G aussian beam in a cavity with spherical mirrors Consider an optical cavity formed by two aligned spheri- cal mirrors facing each other as shown in Figure 1.54. Such an optical cavity is called a spherical mirrorresonator, and is most commonly used in gas lasers. Sometimes, one of the reflectors is a plane mirror. The two spherical mirrors and the space between them form an optical resonator because only certain light waves with certain frequencies can exist in this optical cavity. The radiation inside a spherical mirror cavity is a Gaussian beam. The actual or particular Gaussian beam that fits into the cavity is that beam whose wavefronts at the mir- rors match the curvature of the mirrors. Consider the symmetric resonator shown in Figure 1.54 in which the mirrors have the same radius of curvature R. When a wave starts at A, its wavefront is the same as the curvature of A. In the middle of the cavity it has the minimum width and at B the wave again has the same curvature as B. Such a wave in the cavity can replicate itself (and hence exist in the cavity) as it travels between the mirrors provided that it has right beam characteristics, that is the right curvature at the mirrors. The radius of curvature R of a Gaussian beam wavefront at a distance z along its axis is given by Consider a confocal symmetric optical cavity in which the mirrors are separated by L = R. (a) Show that the cavity length L is 2zo, that is, it is the same as twice the Rayleigh range, which is the reason the latter is called the confocal length. (b) Show that the waist of the beam 2wo is fully determined only by the radius of curvature R of the mirrors, and given by 2wo = (2lR>p)1>2 (c) If the c avity length L = R = 50 cm, and l = 633 nm, what is the waist of the beam at the center and also at the mirrors?
- Question : q6 - Ca uchy dispersion equation Using the Cauchy coefficients and the general Cauchy equation, calculate refractive index of a silicon crystal at wavelengths of 200 o m and at 2 o m, over two orders of magnitude wave- length change. What is your conclusion?
- Question : q7 - Se llmeier dispersion equation Using the Sellmeier equation and the coefficients, obtain a graph of the refractive index of fused silica (SiO2) versus its wavelength in the range of 500 nm to 1550 nm.
- Question : q8 - Se llmeier dispersion equation The Sellmeier dispersion coefficient for pure silica (SiO2) and 86.5% SiO2-13.5% GeO2 are given in Table 1.2. Write a program on your computer or calculator, or use a math soft- ware package or even a spreadsheet program (e.g., Excel) to obtain the refractive index n as a function of l from 0.5 o m to 1.8 o m for both pure silica and 86.5% SiO2-13.5% GeO2. Obtain the group index, Ng, vs. wavelength for both materials and plot it on the same graph. Find the wavelength at which the material dispersion, defined as the derivative of the group velocity with respect to the wavelength, becomes zero in each material.
- Question : q9 - Th e Cauchy dispersion relation for zinc selenide ZnSe is a II
- Question : q10 - R efractive index, reflection, and the Brewster
- Question : q11 - S nell
- Question : q12 - S nell
- Question : q13 - S nell
- Question : q14 - F ermat
- Question : q15 - A ntireflection (AR) coating (a) A lase r beam of wavelength 1550 nm from air is launched to a single mode optical fiber with a core refrac- tive index n1 = 1.45. Estimate the refractive index and thickness of film required for an anti-reflecting coating on this fiber. (b) A Ge photodiode is designed to operate at 1550 nm, and it is required to have AR coatings to minimize reflected light. Two possible materials are available for AR coating: SiO2 with a refractive index of 1.46, and TiO2 with a refractive index of 2.2. Which would be better suited? What would be the thickness for the AR coating on this photodiode? The refractive index of Ge is about 4. (c) Consid er a Ge photodiode that is designed for operation around 1200 nm. What are the best AR coating refractive index and thickness if the refractive index of Ge is about 4.0?
- Question : q16 - S ingle- and double-layer antireflection V-coating For a single-layer AR coating of index n2 on a mate- rial with index n3( 7 n2 7 n1), as shown in Figure 1.57 (a), the minimum reflectance at normal incidence is given by Rmin = c n22 - n1n3 n22 + n1n3 d 2 when the reflections A, B, . . . all interfere as destructively as possible. Rmin = 0 when n2 = (n1n3)1>2. The choice of materials may not always be the best for a single-layer AR coating. Double-layer AR coatings, as shown inFigure 1.57 (b), can achieve lower and sharper reflectance at a specified wavelength as in Figure 1.57 (c). To reduce the reflection of light at the n1
- Question : q17 - ingle-, double-, and triple-layer antireflection coatings Figure 1.58 shows the reflectance of an uncoated glass, and glass that has a single- (1), double- (2) and triple- (3) layer AR coatings? The coating details are in the figure caption. Each layer in single- and double-layer AR coatings has a thickness of l>4, where l is the wavelength in the layer. The triple-layer AR layer has three coatings with thicknesses l>4, l>2, and l>4. Can you qualitatively explain the results by using interference? What applications would need single-, double-, and triple-layer coatings?
- Question : q18 - R eflection at glass
- Question : q19 - D ielectric mirror A dielectric mirror is made up of a quarter wave layer of GaAs with nH = 3.38 and AlAs with nL = 3.00 at around 1550 nm. The light is incident on the mirror from another semiconductor of refractive index n0 = 3.40. Find out the number of pairs of layers N needed to get 90% reflectance. Find out the band- width of the reflected light.
- Question : q20 - IR and polarization at water
- Question : q21 - R eflection and transmission at a semiconductor
- Question : q22 - P hase changes on TIR Consider a light wave of wavelength 870 nm traveling in a semiconductor medium (GaAs) of refractive index 3.60. It is incident on a different semiconductor medium (AlGaAs) of refractive index3.40, and the angle of incidence is 80
- Question : q23 - Fresnel
- Question : q24 - F resnel
- Question : q25 - oos-Haenchen phase shift A ray of light which 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 850 nm. The angle of incidence ui = 85
- Question : q26 - E vanescent wave Total internal reflection of a plane wave from a boundary between a more dense medium (1) n1 and a less dense medium (2) n2 is accompanied by an evanescent wave propagating in medium 2 near the boundary. Find the functional form of this wave and discuss how its magnitude varies with the distance into medium 2.
- Question : q27 - T IR and FTIR (a) By co nsidering the electric field component in medium B in Figure 1.21, explain how you can adjust the amount of transmitted light through a thin layer between two higher refractive index media. (b) What i s the critical angle at the hypotenuse face of a beam splitter cube made of glass with n1 = 1.6 and having a thin film of liquid with n2 = 1.3. Can you use 45
- Question : q28 - C omplex refractive index and dielectric constant The complex refractive index N = n - jK can be defined in terms of the complex relative permittivity er = er1 - jer2 as
- Question : q29 - C omplex refractive index Spectroscopic ellipsometry measurements on a germanium crystal at a photon energy of 1.5 eV show that the real and imaginary parts of the complex relative permittivity are 21.56 and 2.772, respectively. Find the complex refractive index. What is the reflectance and absorption coefficient at this wavelength? How do your calculations match with the experimental values of n = 4.653 and K = 0.298, R = 0.419 and a = 4.53 * 106 m-1?
- Question : q30 - omplex refractive index Figure 1.26 shows the infrared extinction coefficient K of CdTe. Calculate the absorption coefficient a and the reflectance R of CdTe at 60 o m and 80 o m.
- Question : q31 - Refractive index and attenuation in the infrared region
- Question : q32 - C oherence length A narrow band pass filter transmits wavelengths in the range 5000 { 0.5 A
- Question : q33 - S pectral widths and coherence (a) Suppo se that frequency spectrum of a radiation emitted from a source has a central frequency yo and a spec- tral width ?y. The spectrum of this radiation in terms of wavelength will have a central wavelength lo and a spectral width ?l. Clearly, lo = c>yo. Since ?l V lo and ?y V yo, using l = c>y, show that the line width ?l and hence the coherence length lc are(b) Calcul ate ?l for a lasing emission from a He-Ne laser that has lo = 632.8 nm and ?y ? 1.5 GHz. Find its coherence time and length.
- Question : q34 - oherence lengths Find the coherence length of the following light sources: (a) An LE D emitting at 1550 nm with a spectral width 150 nm; (b) A sem iconductor laser diode emitting at 1550 nm with a spectral width 3 nm; (c) A qua ntum well semiconductor laser diode emitting at 1550 nm with a spectral width of 0.1 nm; (d) A mul timode He-Ne laser with a spectral frequency width of 1.5 GHz; (e) A spec ially designed single mode and stabilized He-Ne laser with a spectral width of 100 MHz.
- Question : q35 - F abry
- Question : q36 - F abry
- Question : q37 - F abry
- Question : q38 - D iffraction A collimated beam of light of wavelength 632.8 nm is incident on a circular aperture of 250 o m. Find out the divergence of the transmitted beam. Obtain the diameter of the transmitted beam at a distance of 10 m. What would be the divergence if the aperture is a single slit of width 250 o m?
- Question : q39 - D iffraction intensity Consider diffraction from a uniformly illuminated circular aperture of diam eter D. The far field diffraction pattern is given by a Bessel function of the first kind and first order, J1, and the intensity at a point P on the angle ui with respect to the central axis through the aperture is I(g) = Ioa 2J1(g) g b 2 where Io is the maximum intensity, g = (1>2)kD sin u is a variable quantity that represents the a ngular position u on the screen as well as the wavelength (k = 2p>l) and the aperture diameter D. J1(g) can be calculated from J1(g) = 1 p L p 0 cos (a - g sin a)da where a is an integration variable. Using numerical integration, or a suitable mathematics software program, plot 3J1(g)>g4 vs. g for g = 0 - 8 and confirm that zero-crossings occur at g = 3.83, 7.02 and the maxima at g = 0, 5.14. What is the intensity ratio of the first bright ring (at g = 5.14) to that at the center of the Airy disk (g = 0)? (You can use a
- Question : q40 - B ragg diffraction A reflection grating is made on the surface of a semiconductor with a periodicity of 0.5 o m. If light of wavelength 1.55 o m is incident at an angle of 88
- Question : q41 - D iffraction grating for WDM Consider a transmission diffraction grating. Suppose that we wish to use this grating to separate out different wavelengths of information in a WDM signal at 1550
- Question : q42 - A monochromator Consider an incident beam on a reflection diffraction grating as in Figure 1.60. Each in- cident wavelength will result in a diffracted wave with a different diffraction angle. We can place a small slit and allow only one diffracted wave lm to pass through to the photodetector. The diffracted beam would con- sist of wavelengths in the incident beam separated (or fanned) out after diffraction. Only one wavelength lm will be diffracted favorably to pass through the slit and reach the photodetector. Suppose that the slit width is s = 0.1 mm, and the slit is at a distance R = 5 cm from the grating. Suppose that the slit is placed so that it is at right angles to the incident beam: ui + um = p>2. The grating has a corrugation periodicity of 1(a) What i s the range of wavelengths that can be captured by the photodetector when we rotate the grating from ui = 1
- Question : q43 - hin film optics Consider light incident on a thin film on a substrate, and assume normal incidence for simplicity. (a) Consid er a thin soap film in air, n1 = n3 = 1, n2 = 1.40. If the soap thickness d = 1 o m, plot the reflectance vs. wavelength from 0.35 o m to 0.75 o m, which includes the visible range. What is your conclusion? (b) MgF2 thin films are used on glass plates for the reduction of glare. Given that n1 = 1, n2 = 1.38, and n3 = 1.60 (n for glass depends on the type of glass but 1.6 is a reasonable value), plot the reflectance as a function of wavelength from 0.35 o m to 0.75 o m for a thin film of thickness 0.10 o m. What is your conclusion?
- Question : q44 - T hin film optics Consider a glass substrate with n3 = 165 that has been coated with a transparent opti- cal film (a dielectric film) with n2 = 2.50, n1 = 1 (air). If the film thickness is 500 nm, find the minimum and maximum reflectances and transmittances and their corresponding wavelengths in the visible range for normal incidence. (Assume normal incidence.) Note that the thin n2-film is not an AR coating, and for
- Question : q45 - T hin film optics Consider light incident on a thin film on a substrate, and assume normal incidence for sim- plicity. Plot the reflectance R and transmittance T as a function of the phase change f from f = -4p to +4p for the following cases (a) Thin s oap film in air, n1 = n3 = 1, n2 = 1.40. If the soap thickness d = 1 o m, what are the maxima and minima in the reflectance in the visible range? (b) A thin film of MgF2 on a glass plate for the reduction of glare, where n1 = 1, n2 = 1.38, and n3 = 1.70 (n for glass depends on the type of glass but 1.7 is a reasonable value.) What should be the thickness of MgF2 for minimum reflection at 550 nm? (c) A thin film of semiconductor on glass where n1 = 1, n2 = 3.5, and n3 = 1.55.
- Question : q46 - T ransmission through a plate Consider the transmittance of light through a partially transparent glass plate of index n in which light experiences attenuation (either by absorption or scattering). Suppose that the plate is in a medium of index no, the reflectance at each n
- Question : q47 - S cattering Consider Rayleigh scattering. If the incident light is unpolarized, the intensity Is of the scattered light a point at a distance r at an angle u to the original light beam is given by Is ? 1 - cos2 u r2 Plot a polar plot of the intensity Is at a fixed distance r from the scatter as we change the angle u around the scatterer. In a polar plot, the radial coordinate (OP in Figure 1.48 (b)) is Is. Construct a contour plot in the xy plane in which a contour represents a constant intensity. You need to vary r and u or x and y such that Is remains constant. Note x = r cos u and y = r sin u, u = arctan (y>x), r = (x2 + y2)1>2.
- Question : q48 - O ne-dimensional photonic crystal (a Bragg mirror) The 1D photonic crystal in Figure 1.50 (a), which is essentially a Bragg reflector, has the dispersion behavior shown in Figure 1.51 (a). The stop-band ?v for nor- mal incidence and for all polarizations of light is given by (R. H. Lipson and C. Lu, Eur. J. Phys., 30, S33, 2009) where ?v is the stop band, vo is the center frequency defined in Figure 1.51 and n2 and n1 are the high and low refractive indices. Calculate the lowest stop band in terms of photon energy in eV, and wavelength 1550 nm for a 1D photonic crystal structure with n1d1 = n2d2 = l>4, made up of: (i) Si (nSi = 3.5) and SiO2 (nSiO2 = 1.445) pairs, and (ii) Si3N4 (nSi3N4 = 2.0) and SiO2 pairs.
- Question : q49 - P hotonic crystals Concepts have been borrowed from crystallography, such as a unit cell, to d efine a pho- tonic crystal. What is the difference between a unit cell used in a photonic crystal and that used in a real crystal? What is the size limit on the unit cell of a photonic crystal? Is the refractive index a microscopic or a macro- scopic concept? What is the assumption on the refractive index?A scanning Fabry

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