1. Derive the Jones matrix, Eq. (14-15), representing a linear
polarizer whose transmission axis is at an arbitrary angle θ with
respect to the horizontal. Get solution
2. Write the normalized Jones vectors for each of the following waves, and describe completely the state of polarization of each.a. ...b. ...c. ...d. ... Get solution
3. Describe as completely as possible amplitude, wave direction, and the state of polarization of each of the following waves.a. ...b. ...c. ... Get solution
4. Two linearly polarized beams are given by ...Determine the angle between their directions of polarization by (a) forming their Jones vectors and finding the vibration direction of each and (b) forming the dot product of their vector amplitudes. Get solution
5. Find the character of polarized light after passing in turn through (a) a half-wave plate with slow axis at 45°; (b) a linear polarizer with transmission axis at 45°; (c) a quarter-wave plate with slow axis horizontal. Assume the original light to be linearly polarized vertically. Use the matrix approach and analyze the final Jones vector to describe the product light. (Hint: First find the effect of the HWP alone on the incident light.) Get solution
6. Write the equations for the electric fields of the following waves in exponential form:a. A linearly polarized wave traveling in the x-direction.The ...-vector makes an angle of 30° relative to the y-axis.b. A right-elliptically polarized wave traveling in the y-direction.The major axis of the ellipse is in the z-direction and is twice the minor axis.c. A linearly polarized wave traveling in the x,y-plane in a direction making an angle of 45° relative to the x-axis. The direction of polarization is the z-direction. Get solution
7. Determine the conditions on the elements A, B, and C of the general Jones vector (Eq. 14-9), representing polarized light, that lead to the following special cases: (a) linearly polarized light; (b) elliptically polarized light with major axis aligned along a coordinate axis; (c) circularly polarized light. In each case, from the meanings of A, B, C, deduce the possible values of phase difference between component vibrations. Get solution
8. Write a computer program that will determine Ey,-values of elliptically polarized light from the equation for the ellipse, Eq. (14-12), with input constants A, B, and C and variable input parameter Ex. Plot the ellipse for the example given in the text, ... Get solution
9. Specify the polarization mode for each of the following Jones vectors:a. ...b. ...c. ...d. ...e. ...f. ...g. ... Get solution
10. Linearly polarized light with an electric field ... is inclined at +30° relative to the x-axis and is transmitted by a QWP with SA horizontal. Describe the polarization mode of the product light.Figure 1.... Get solution
11. Using the Jones calculus, show that the effect of a HWP on light linearly polarized at inclination angle α is to rotate the polarization through an angle of 2α. The HWP may be used in this way as a “laser-line rotator,” allowing the polarization of a laser beam to be rotated without having to rotate the laser. Get solution
12. An important application of the QWP is its use in an “isolator.” For example, to prevent feedback from interferometers into lasers by front-surface, back reflections, the beam is first allowed to pass through a combination of linear polarizer and QWP, with OA of the QWP at 45° to the TA of the polarizer. Consider what happens to such light after reflection from a plane surface and transmission back through this optical device. Get solution
13. Light linearly polarized with a horizontal transmission axis is sent through another linear polarizer with TA at 45° and then through a QWP with SA horizontal. Use the Jones matrix technique to determine and describe the product light.Figure 1.... Get solution
14. A light beam passes consecutively through (1) a linear polarizer with TA at 45° clockwise from vertical, (2) a QWP with SA vertical, (3) a linear polarizer with TA horizontal, (4) a HWP with FA horizontal, (5) a linear polarizer with TA vertical. What is the nature of the product light? Get solution
15. Unpolarized light passes through a linear polarizer with TA at 60° from the vertical, then through a QWP with SA horizontal, and finally through another linear polarizer with TA vertical. Determine, using Jones matrices, the character of the light after passing through (a) the QWP and (b) the final linear polarizer. Get solution
16. Determine the state of polarization of circularly polarized light after it is passed normally through (a) a QWP; (b) an eighth-wave plate. Use the matrix method to support your answer. Get solution
17. Show that the matrix ... represents a right-circular polarizer, converting any incident polarized light into right circularly-polarized light. What is the proper matrix to represent a left-circular polarizer? Get solution
18. Show that elliptical polarization can be regarded as a combination of circular and linear polarizations. Get solution
19. Derive the equation of the ellipse for polarized light given in Eq. (14-12). (Hint: Combine the Ex and Ey equations for the general case of elliptical polarization, eliminating the space and time dependence between them.) Get solution
20. a. Identify the state of polarization corresponding to the Jones vector ...and write it in the standard, normalized form of Table 14-1.b. Let this light be transmitted through an element that rotates linearly polarized light by +30°. Find the new, normalized form and describe the result. Get solution
21. Determine the nature of the polarization that results from Eq. (14-12) when (a) ε = π/2; (b) E0x = E0y = E0; (c) both (a) and (b); (d) ε = 0. Get solution
22. A quarter-wave plate is placed between crossed polarizers such that the angle between the polarizer TA of the first polarizer and the QWP fast axis is θ. How does the polarization of the emergent light vary as a function of θ? Get solution
2. Write the normalized Jones vectors for each of the following waves, and describe completely the state of polarization of each.a. ...b. ...c. ...d. ... Get solution
3. Describe as completely as possible amplitude, wave direction, and the state of polarization of each of the following waves.a. ...b. ...c. ... Get solution
4. Two linearly polarized beams are given by ...Determine the angle between their directions of polarization by (a) forming their Jones vectors and finding the vibration direction of each and (b) forming the dot product of their vector amplitudes. Get solution
5. Find the character of polarized light after passing in turn through (a) a half-wave plate with slow axis at 45°; (b) a linear polarizer with transmission axis at 45°; (c) a quarter-wave plate with slow axis horizontal. Assume the original light to be linearly polarized vertically. Use the matrix approach and analyze the final Jones vector to describe the product light. (Hint: First find the effect of the HWP alone on the incident light.) Get solution
6. Write the equations for the electric fields of the following waves in exponential form:a. A linearly polarized wave traveling in the x-direction.The ...-vector makes an angle of 30° relative to the y-axis.b. A right-elliptically polarized wave traveling in the y-direction.The major axis of the ellipse is in the z-direction and is twice the minor axis.c. A linearly polarized wave traveling in the x,y-plane in a direction making an angle of 45° relative to the x-axis. The direction of polarization is the z-direction. Get solution
7. Determine the conditions on the elements A, B, and C of the general Jones vector (Eq. 14-9), representing polarized light, that lead to the following special cases: (a) linearly polarized light; (b) elliptically polarized light with major axis aligned along a coordinate axis; (c) circularly polarized light. In each case, from the meanings of A, B, C, deduce the possible values of phase difference between component vibrations. Get solution
8. Write a computer program that will determine Ey,-values of elliptically polarized light from the equation for the ellipse, Eq. (14-12), with input constants A, B, and C and variable input parameter Ex. Plot the ellipse for the example given in the text, ... Get solution
9. Specify the polarization mode for each of the following Jones vectors:a. ...b. ...c. ...d. ...e. ...f. ...g. ... Get solution
10. Linearly polarized light with an electric field ... is inclined at +30° relative to the x-axis and is transmitted by a QWP with SA horizontal. Describe the polarization mode of the product light.Figure 1.... Get solution
11. Using the Jones calculus, show that the effect of a HWP on light linearly polarized at inclination angle α is to rotate the polarization through an angle of 2α. The HWP may be used in this way as a “laser-line rotator,” allowing the polarization of a laser beam to be rotated without having to rotate the laser. Get solution
12. An important application of the QWP is its use in an “isolator.” For example, to prevent feedback from interferometers into lasers by front-surface, back reflections, the beam is first allowed to pass through a combination of linear polarizer and QWP, with OA of the QWP at 45° to the TA of the polarizer. Consider what happens to such light after reflection from a plane surface and transmission back through this optical device. Get solution
13. Light linearly polarized with a horizontal transmission axis is sent through another linear polarizer with TA at 45° and then through a QWP with SA horizontal. Use the Jones matrix technique to determine and describe the product light.Figure 1.... Get solution
14. A light beam passes consecutively through (1) a linear polarizer with TA at 45° clockwise from vertical, (2) a QWP with SA vertical, (3) a linear polarizer with TA horizontal, (4) a HWP with FA horizontal, (5) a linear polarizer with TA vertical. What is the nature of the product light? Get solution
15. Unpolarized light passes through a linear polarizer with TA at 60° from the vertical, then through a QWP with SA horizontal, and finally through another linear polarizer with TA vertical. Determine, using Jones matrices, the character of the light after passing through (a) the QWP and (b) the final linear polarizer. Get solution
16. Determine the state of polarization of circularly polarized light after it is passed normally through (a) a QWP; (b) an eighth-wave plate. Use the matrix method to support your answer. Get solution
17. Show that the matrix ... represents a right-circular polarizer, converting any incident polarized light into right circularly-polarized light. What is the proper matrix to represent a left-circular polarizer? Get solution
18. Show that elliptical polarization can be regarded as a combination of circular and linear polarizations. Get solution
19. Derive the equation of the ellipse for polarized light given in Eq. (14-12). (Hint: Combine the Ex and Ey equations for the general case of elliptical polarization, eliminating the space and time dependence between them.) Get solution
20. a. Identify the state of polarization corresponding to the Jones vector ...and write it in the standard, normalized form of Table 14-1.b. Let this light be transmitted through an element that rotates linearly polarized light by +30°. Find the new, normalized form and describe the result. Get solution
21. Determine the nature of the polarization that results from Eq. (14-12) when (a) ε = π/2; (b) E0x = E0y = E0; (c) both (a) and (b); (d) ε = 0. Get solution
22. A quarter-wave plate is placed between crossed polarizers such that the angle between the polarizer TA of the first polarizer and the QWP fast axis is θ. How does the polarization of the emergent light vary as a function of θ? Get solution
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