1. Write out the third-order terms of the polarization for a single
beam described by a plane wave with amplitude E0 and frequency ω. What
frequencies appear in the polarization wave? Get solution
2. Write out the third-order terms of the polarization for two- beam interaction, where the beams are plane waves having amplitudes E01 and E02 and frequencies ω1 and ω2, respectively. What frequencies are radiated by the polarization wave? Get solution
3. Write out the second-order terms of the polarization for three-beam interaction, where the beams are plane waves having amplitudes E01 and E02, and E03 frequencies ω1, and ω2, and ω3, respectively. What frequencies are radiated by the polarization wave? Get solution
4. Arguing from Eq. (24-7), show that the linear electro-optic effect is found only in crystals lacking inversion symmetry. Get solution
5. a. Determine the coherence length for second harmonic generation in KDP when subjected to pulsed ruby laser light at λ0 = 694 nm. Appropriate refractive indices are n(694 nm) = 1.505 and n(347 nm) = 1.534.b. The measured coherence length of barium titanate at λ0 = 1.06 μm is 5.8 μm. Calculate the expected change in refractive index at λ = 0.53 μm. Get solution
6. Determine the half-wave voltage for a longitudinal Pockels cell made of ADP (ammonium dihydrogen phosphate) at λ = 546 nm. What is its length? Get solution
7. A longitudinal Pockels cell is made from lithium niobate. Determine the change in refractive index and the phase difference produced by an applied voltage of 426 V when the light beam is from a He-Ne laser at 632.8 nm. The length of the crystal is 1 cm. Get solution
8. Using Eq. (24-9), show that the transmittance of a Pockels cell can also be written as I = Imax sin2(Φ/2).a. At what values of V and Φ (greater than zero) is the transmittance zero?b. If the Pockels cell is preceded by an ordinary half-wave plate, what is the irradiance when V = 0 and when V = VHW? Get solution
9. In what kinds of media are both longitudinal Pockels and Kerr effects present? To get some idea of their relative strengths, compare them by calculating the ratio of retardations produced by an appropriately applied 10 kV. Derive an expression for this ratio. Then do a numerical calculation by assuming a hypothetical medium with “typical” values of r = 10 pm/V, K = 1 pm/V2, L = 2 cm, d = 1 cm, and n0 = 2. Take λ = 550 nm. Get solution
10. Calculate the length of a Kerr cell using carbon disulfide required to produce half-wave retardation for an applied voltage of 30 kV. The electrodes of the cell have a separation of 1.5 cm. Is this cell practical? Get solution
11. Show that Eq. (24-19) is equivalent to the Doppler effect for light. Use the fact that the Doppler frequency shift Δν for light reflected from a moving object is twice that of light emanating from a moving object, or Δν = 2νup/ν, where ν is the light frequency, υ its velocity in the medium, and up is the component of the object velocity parallel to the light wave’s propagation direction. Use the geometry of Figure 24-11 and the Bragg condition. Get solution
12. The speed of sound in glass is 3 km/s. For a sound wave having a width of 1 cm, calculate the advance of the sound wave while it is traversed by a light wave. Take n = 1.50 for the glass. What is the significance of this result? Get solution
13. a. Show that a small change in angle Δθ around the direction of the diffracted beam in Figure 24-11 can be expressed approximately by Δθ = ΔkS/k.b. Show that this result can be expressed as Δθ = (λ/υS) ΔυSwhere λ is the wavelength in the medium.c. The factor by which Δθ exceeds the beam divergence is a practically useful number N called “number of resolvable spots.” This serves as a figure of merit, giving the number of resolvable positions that can be addressed by the beam deflector. If the beam divergence is expressed by the diffraction angle θD = λ/D, with D the beam diameter, show that ...where τ is the time for the sound to cross the optical beam diameter.d. As a numerical example, consider modulation of the sound frequency in the range 80–120 MHz in fused quartz, where υS = 5.95 × 105 cm/s. If the beam diameter is 1 cm, determine the number of resolvable spots. Get solution
14. What acoustic frequency is required of a plane acoustic wave, launched in an acousto-optic crystal, so that a He-Ne laser beam is deflected by 1o? The speed of sound in the crystal is 2500 m/s and its refractive index at 632.8 nm is 1.6. Get solution
15. In Bragg’s equation (24-18), the wavelength of the light and the angle arc those measured within the medium. Show that, if the medium is isotropic and its sides are parallel to the direction of a plane acoustic wave, the equation also holds for the wavelength and angle of diffraction measured outside the medium. Get solution
16. Determine the difference in deflection angle for a He-Ne laser beam that is Bragg-scattered by an acoustic plane wave when the frequencies are 50 MHz and 80 MHz. The acoustic crystal is sapphire, with n = 1.76 and a sound speed of 11 km/s. Get solution
17. Design an optical isolator, as in Figure 24-10, that uses ZnS as the active medium. Let the magnetic field be produced by winding a solenoid directly onto the ZnS crystal at a turn density of 60 turns/cm. Assume λ = 589 nm. Get solution
18. A sample of SF57 glass with polished, parallel sides and 2.73 cm in length is placed between the tapered poles of an electromagnet. A small, central hole is drilled through the pole pieces to allow passage of a linearly polarized He-Ne laser beam through the sample and parallel to the magnetic field direction. The magnetic field is set at 5.098 kG.a. When red He-Ne laser light (632.8 nm) is used, the measured rotation is 900 min. Determine the Verdet constant for the glass.b. When green He-Ne laser light (543.5 nm) is used, the measured rotation is 1330 min. Determine the Verdet constant for the glass. Get solution
19. A 5-cm-long liquid cell is situated in a magnetic field of 4 kG. The cell is filled with carbon disulfide and linearly polarized sodium light is transmitted through the cell, along the B-field direction. Determine both the net rotation of the light and the circular dispersion of CS2 at this wavelength. Get solution
20. Sketch the shape of a nonsymmetrical pulse before and after reflection from an ordinary mirror and before and alter reflection from a PCM. In the latter case, assume that the PCM is “turned on” by initiating the pump beams at the instant the entire pulse has moved inside the PC medium. Show how this effect might be used to correct dispersion broadening in an optical fiber. (If necessary, consult Vladimir V. Shkunov, and Boris Ya. Zel’dovich, “Optical Phase Conjugation,” Scientific American, Dec. 1985: 54.) Get solution
21. Sketch an arrangement using a PCM to project a sharp, high-intensity image of a mask onto the photo-resist layer on a semiconducting chip without using lenses. This provides a means of doing photolithography without placing a mask in direct contact with the chip. (If necessary, consult Vladimir V. Shkunov, and Boris Ya. Zel’dovich, “Optical Phase Conjugation,” Scientific American, Dec. 1985: 54.) Get solution
2. Write out the third-order terms of the polarization for two- beam interaction, where the beams are plane waves having amplitudes E01 and E02 and frequencies ω1 and ω2, respectively. What frequencies are radiated by the polarization wave? Get solution
3. Write out the second-order terms of the polarization for three-beam interaction, where the beams are plane waves having amplitudes E01 and E02, and E03 frequencies ω1, and ω2, and ω3, respectively. What frequencies are radiated by the polarization wave? Get solution
4. Arguing from Eq. (24-7), show that the linear electro-optic effect is found only in crystals lacking inversion symmetry. Get solution
5. a. Determine the coherence length for second harmonic generation in KDP when subjected to pulsed ruby laser light at λ0 = 694 nm. Appropriate refractive indices are n(694 nm) = 1.505 and n(347 nm) = 1.534.b. The measured coherence length of barium titanate at λ0 = 1.06 μm is 5.8 μm. Calculate the expected change in refractive index at λ = 0.53 μm. Get solution
6. Determine the half-wave voltage for a longitudinal Pockels cell made of ADP (ammonium dihydrogen phosphate) at λ = 546 nm. What is its length? Get solution
7. A longitudinal Pockels cell is made from lithium niobate. Determine the change in refractive index and the phase difference produced by an applied voltage of 426 V when the light beam is from a He-Ne laser at 632.8 nm. The length of the crystal is 1 cm. Get solution
8. Using Eq. (24-9), show that the transmittance of a Pockels cell can also be written as I = Imax sin2(Φ/2).a. At what values of V and Φ (greater than zero) is the transmittance zero?b. If the Pockels cell is preceded by an ordinary half-wave plate, what is the irradiance when V = 0 and when V = VHW? Get solution
9. In what kinds of media are both longitudinal Pockels and Kerr effects present? To get some idea of their relative strengths, compare them by calculating the ratio of retardations produced by an appropriately applied 10 kV. Derive an expression for this ratio. Then do a numerical calculation by assuming a hypothetical medium with “typical” values of r = 10 pm/V, K = 1 pm/V2, L = 2 cm, d = 1 cm, and n0 = 2. Take λ = 550 nm. Get solution
10. Calculate the length of a Kerr cell using carbon disulfide required to produce half-wave retardation for an applied voltage of 30 kV. The electrodes of the cell have a separation of 1.5 cm. Is this cell practical? Get solution
11. Show that Eq. (24-19) is equivalent to the Doppler effect for light. Use the fact that the Doppler frequency shift Δν for light reflected from a moving object is twice that of light emanating from a moving object, or Δν = 2νup/ν, where ν is the light frequency, υ its velocity in the medium, and up is the component of the object velocity parallel to the light wave’s propagation direction. Use the geometry of Figure 24-11 and the Bragg condition. Get solution
12. The speed of sound in glass is 3 km/s. For a sound wave having a width of 1 cm, calculate the advance of the sound wave while it is traversed by a light wave. Take n = 1.50 for the glass. What is the significance of this result? Get solution
13. a. Show that a small change in angle Δθ around the direction of the diffracted beam in Figure 24-11 can be expressed approximately by Δθ = ΔkS/k.b. Show that this result can be expressed as Δθ = (λ/υS) ΔυSwhere λ is the wavelength in the medium.c. The factor by which Δθ exceeds the beam divergence is a practically useful number N called “number of resolvable spots.” This serves as a figure of merit, giving the number of resolvable positions that can be addressed by the beam deflector. If the beam divergence is expressed by the diffraction angle θD = λ/D, with D the beam diameter, show that ...where τ is the time for the sound to cross the optical beam diameter.d. As a numerical example, consider modulation of the sound frequency in the range 80–120 MHz in fused quartz, where υS = 5.95 × 105 cm/s. If the beam diameter is 1 cm, determine the number of resolvable spots. Get solution
14. What acoustic frequency is required of a plane acoustic wave, launched in an acousto-optic crystal, so that a He-Ne laser beam is deflected by 1o? The speed of sound in the crystal is 2500 m/s and its refractive index at 632.8 nm is 1.6. Get solution
15. In Bragg’s equation (24-18), the wavelength of the light and the angle arc those measured within the medium. Show that, if the medium is isotropic and its sides are parallel to the direction of a plane acoustic wave, the equation also holds for the wavelength and angle of diffraction measured outside the medium. Get solution
16. Determine the difference in deflection angle for a He-Ne laser beam that is Bragg-scattered by an acoustic plane wave when the frequencies are 50 MHz and 80 MHz. The acoustic crystal is sapphire, with n = 1.76 and a sound speed of 11 km/s. Get solution
17. Design an optical isolator, as in Figure 24-10, that uses ZnS as the active medium. Let the magnetic field be produced by winding a solenoid directly onto the ZnS crystal at a turn density of 60 turns/cm. Assume λ = 589 nm. Get solution
18. A sample of SF57 glass with polished, parallel sides and 2.73 cm in length is placed between the tapered poles of an electromagnet. A small, central hole is drilled through the pole pieces to allow passage of a linearly polarized He-Ne laser beam through the sample and parallel to the magnetic field direction. The magnetic field is set at 5.098 kG.a. When red He-Ne laser light (632.8 nm) is used, the measured rotation is 900 min. Determine the Verdet constant for the glass.b. When green He-Ne laser light (543.5 nm) is used, the measured rotation is 1330 min. Determine the Verdet constant for the glass. Get solution
19. A 5-cm-long liquid cell is situated in a magnetic field of 4 kG. The cell is filled with carbon disulfide and linearly polarized sodium light is transmitted through the cell, along the B-field direction. Determine both the net rotation of the light and the circular dispersion of CS2 at this wavelength. Get solution
20. Sketch the shape of a nonsymmetrical pulse before and after reflection from an ordinary mirror and before and alter reflection from a PCM. In the latter case, assume that the PCM is “turned on” by initiating the pump beams at the instant the entire pulse has moved inside the PC medium. Show how this effect might be used to correct dispersion broadening in an optical fiber. (If necessary, consult Vladimir V. Shkunov, and Boris Ya. Zel’dovich, “Optical Phase Conjugation,” Scientific American, Dec. 1985: 54.) Get solution
21. Sketch an arrangement using a PCM to project a sharp, high-intensity image of a mask onto the photo-resist layer on a semiconducting chip without using lenses. This provides a means of doing photolithography without placing a mask in direct contact with the chip. (If necessary, consult Vladimir V. Shkunov, and Boris Ya. Zel’dovich, “Optical Phase Conjugation,” Scientific American, Dec. 1985: 54.) Get solution
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