- Introduction In Some Lasers The Monochromatic Light Beam Within The System Has A Gaussian Intensity Irradiance Profil 1 (44.04 KiB) Viewed 23 times
- Introduction In Some Lasers The Monochromatic Light Beam Within The System Has A Gaussian Intensity Irradiance Profil 2 (51.91 KiB) Viewed 23 times
- Introduction In Some Lasers The Monochromatic Light Beam Within The System Has A Gaussian Intensity Irradiance Profil 3 (63.11 KiB) Viewed 23 times
- Introduction In Some Lasers The Monochromatic Light Beam Within The System Has A Gaussian Intensity Irradiance Profil 4 (42.82 KiB) Viewed 23 times
These are some important parameters that characterize the Gaussian beam: • Rayleigh range: z • Minimum beam waist (aka minimum spot size) at location z=0: w₁ • Beam waist at position z along the beam axis: w(2) 2 • Beam angular spread (radians): = 20, where = Note: is the beam wavelength Wo To make a functioning laser, curved mirrors are placed along the axis to create a resonant cavity that reflects the beam back and forth. If the two mirrors have radii of curvature R₁ and R2, respectively, they need to be placed at specific locations z1 and 22 along the axis to exactly match the wavefront's radii at those locations (Figure 3). L 1₁ ==0 Z₁ = Figure 3: Two-mirror resonant cavity³ Suppose you are given two mirrors with radii R₁ and R₂. They are to be placed a distance L apart. Where are the required mirror locations z, and z₂? The locations can be calculated from these equations: L(R₂-L) Z₂ = Z₁ + L R₁ + R₂-2L The Rayleigh length z is then: W₁ = R₂ L(R₂ - LXR, L)(R₁ + R₂ −L) (R₁ + R₂-2L)² Assuming index n = 1, the minimum beam waist w, is given by: LA 8,8: (1-818₂) (8₁ +8₂-28₁8₂). One mirror is fully reflective, while the other mirror is partially reflective, which allows the beam to be emitted from the resonator. L R₁ where =1- and 8₁ 82 = 1- L R₂
Primary Requirements Notes: • The PDR should mention which equations you implement in your program. • mm → millimeter, cm → centimeter, nm → nanometer, mi → mile (US customary) Write a complete C program that meets the following specifications: 1. Prompt the user to enter the following information in this order: • The curvature R₁ (in mm) of mirror 1 (located at plane position z.). • The curvature R₂ (in mm) of mirror 2 (located at plane position z₂). • The distance L (in cm) between the centers of the two mirrors. The wavelength λ (in nm) of light in the lasing medium. 2. Calculate and display the following values: Minimum spot size w, (in cm). • Position z, (in cm) of mirror 1. • Position z₂ (in cm) of mirror 2. • Beam angular spread Ⓒ (in radians). 3. Suppose the laser is pointed at a satellite in orbit around the earth at a distance N miles away. Calculate and display an estimate of the beam's waist (in km) at the satellite's location. . Additional Program Requirements • You will need to perform some unit conversions to work in a common unit (e.g., cm) • Declare floating point variables as type double for best accuracy. • Define a macro for the value of л. For consistency, use 3.141592654. • Display your calculated results to three (3) decimal places. Hint: To match the sample output, consider using the %g option. Save the program using this file name: hw2.c
Sample Run Enter radius of mirror 1 (mm): 250 Enter radius of mirror 2 (mm): 300 Enter distance between mirrors (cm): 15 Enter wavelength in the medium (nm): 1000 Enter distance to the satellite (mi): 1600 Laser system characteristics: z1 = -9 cm z2 = 6 cm we = 0.0195 cm Beam angular spread = 0.00326 radians Beam waist at satellite's location = 4.19 km Enter radius of mirror 1 (mm): 500 Enter radius of mirror 2 (mm): 1200 Enter distance between mirrors (cm): 30 Enter wavelength in the medium (nm): 632 Enter distance to the satellite (mi): 21000 Laser system characteristics: z1 = 24.5 cm z2 = 5.45 cm we 0.0224 cm Beam angular spread = 0.00179 radians Beam waist at satellite's location = 30.3 km