Parameters of a Dielectric Waveguide. Light of free-space wavelength X, = 0.87 um is guided by a thin planar film of width d = 2 μm and refractive index n₁ = 1.6 surrounded by a medium of refractive index n₂ = 1.4. (a) Determine the critical angle 0, and its complement c, the numerical aperture NA, and the maximum acceptance angle for light originating in air (n = 1). (b) Determine the number of TE modes. (c) Determine the bounce angle and the group velocity v of the m= 0 TE mode.
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- Data are carried by pulses of light through long, transparent fibers—fiber-optic cables. Long lengths of fiber carry signals 100 km between amplifier stations. How long does it take a signal to travel this distance if the index ofrefraction of the fiber is 1.45?Light is incident from vacuum to crown glass; the light's vacuum wavelength is 500 nm, so the refractive index is 1.52 for crown glass. If the light is incident at an angle of 25.0o, what is the angle of light with respect to the normal once its has entered the crown glass? Answer in degrees.b) A Fabry-Perot device contains two parallel part-reflective surfaces, each with a power re- flection coefficient R = 0.92, separated by an air gap of 40 μm. The device is used at a small but non-zero angle of incidence, such that there is a transmission maximum at wavelength 589 nm. Calculate the coefficient of finesse, and the resolving power. If a sodium lamp emits 2 spectral lines at 589.0 and 589.6 nm respectively, comment on whether these two lines can be resolved by the device.
- A radio station has two antennas. The antennas are a distance d apart, where d equals half the broadcast wavelength. The antennas are driven in phase with each other. Let the x-axis be the line that runs through the two antennas. The angles are all measured counterclockwise from the +x-direction. (For the following, assume an observer is positioned a distance D far from the midpoint of the antennas, so that D ≫ d.) (a) In which directions is the strongest signal radiated? 0°, 180° 90°, 270° 0°, 90°, 180°, 270° 45°, 135°, 225°, 315° (b) In which directions is the weakest signal radiated? 0°, 180° 90°, 270° 0°, 90°, 180°, 270° 45°, 135°, 225°, 315°Light from a 100 mW laser with TE polarisation is incident at θI=60 degrees from air onto glass with refractive index nG=1.60 . Calculate the power transmitted into the glass. (Give your answer as power in mW, as a decimal with 1 d.p.)A light wave in air strikes the surface of a piece of sapphire (n = 1.77) at an angle of 24°. The incident light has component E-field amplitudes perpendicular and parallel to the plane-of-incidence of 25V/m and 14V/m, respectively. Determine the corresponding transmitted field amplitudes. Determine the corresponding transmitted field amplitudes.
- A beam splitter is an optical device that splits a beam of light - half of the incident light is transmitted through the beam splitter, and half is reflected. Supposed we could make a beam splitter that reflects only 35% and transmits the other 65% (rather than 50/50). A beam of laser light with wavelength 656 nm is incident on our imaginary 35/65 beam splitter, at an angle of 45°. The beam pulse lasts 1.50 ms, and has a diameter of 0.60 mm. The intensity of the transmitted beam is 3.25 kW/m2. Draw a clear physics diagram of the problem. What is the energy of a photon from this laser? Find the peak Electric field of the reflected beam. Find the peak Magnetic field of the incident beam. What color is the laser beam? What momentum is transferred to the beam splitter by the laser pulse?An astronaut on the International Space Station (ISS) is experimenting with a solid-state green laser communications system from on-orbit at 435 km altitude to the earth's surface with a wavelength of 532nm and beam divergence (width) of 10 radians or 5.73 x 10-150 << 1°. The indices of refraction in free space and the atmosphere are no = 1.00000 ..., and na = 1.000293. Although density in the atmosphere varies continuously from the thinness of the upper atmosphere (near p → 0) to higher density at the surface, refraction can be modeled as a “surface' mid-atmosphere just like classic Snell's Law calculations. (d) What is the refracted wavelength, and the speed of the laser beam in air? (e) If the communications bit rate is the inverse of the laser frequency period [s], what is this bit rate?A parallel beam of monochromatic light of wavelength 500nm passes through a slit of width 0. 5mm. Find the angular divergence in which most of the light is diffracted.
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