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Pulsed lasers have many applications, but are very complicated to construct. One problem is chromatic aberration, another is aligning the components. Commonly available laser systems can produce 1 fs (10-¹4 s) pulses. a) how far does light travel in 1 fs? b) If the energy per pulse is 100 mJ, what's the power per pulse (in Watts)? c) calculate the (minimum) spread of frequencies required to produce a 1 fs pulse.

Pulsed lasers have many applications, but are very complicated to construct. One problem is chromatic aberration, another is aligning the components. Commonly available laser systems can produce 1 fs (10-¹4 s) pulses. a) how far does light travel in 1 fs? b) If the energy per pulse is 100 mJ, what's the power per pulse (in Watts)? c) calculate the (minimum) spread of frequencies required to produce a 1 fs pulse.

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**Pulsed Lasers and Chromatic Aberration** Pulsed lasers have many applications, but they are very complicated to construct. One of the challenges is chromatic aberration, while another is aligning the components. Commonly available laser systems can produce 1 femtosecond (1 fs, \(10^{-14}\) s) pulses. **Questions:** a) How far does light travel in 1 femtosecond (fs)? b) If the energy per pulse is 100 millijoules (mJ), what’s the power per pulse (in Watts)? c) Calculate the (minimum) spread of frequencies required to produce a 1 fs pulse. d) If the center wavelength is 1 micrometer (µm), what is the range of wavelengths contained in a single pulse? e) Common varieties of optical glass have a dispersion \(\Delta n/\Delta \lambda = 0.025\) per micron. 1) If the index of refraction is 1.51 for \(\lambda = 1 \, \mu m\), what is the value of ‘n’ for the upper and lower wavelength? 2) The focal length of a lens is inversely proportional to the index of refraction: \(1/f \sim (n-1)\). What is the ratio of the focal lengths for the two extreme wavelengths? 3) How much longitudinal chromatic aberration (the difference in focal length between two colors) is there for a 100 mm focal length lens? How does this compare with (a)? What does this tell you?
Transcribed Image Text:**Pulsed Lasers and Chromatic Aberration** Pulsed lasers have many applications, but they are very complicated to construct. One of the challenges is chromatic aberration, while another is aligning the components. Commonly available laser systems can produce 1 femtosecond (1 fs, \(10^{-14}\) s) pulses. **Questions:** a) How far does light travel in 1 femtosecond (fs)? b) If the energy per pulse is 100 millijoules (mJ), what’s the power per pulse (in Watts)? c) Calculate the (minimum) spread of frequencies required to produce a 1 fs pulse. d) If the center wavelength is 1 micrometer (µm), what is the range of wavelengths contained in a single pulse? e) Common varieties of optical glass have a dispersion \(\Delta n/\Delta \lambda = 0.025\) per micron. 1) If the index of refraction is 1.51 for \(\lambda = 1 \, \mu m\), what is the value of ‘n’ for the upper and lower wavelength? 2) The focal length of a lens is inversely proportional to the index of refraction: \(1/f \sim (n-1)\). What is the ratio of the focal lengths for the two extreme wavelengths? 3) How much longitudinal chromatic aberration (the difference in focal length between two colors) is there for a 100 mm focal length lens? How does this compare with (a)? What does this tell you?
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