Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 1

Optical spectrum analyzers directly measure the wavelength of light in an air environment. However, most wavelength measurements are quoted in terms of wavelengths or optical frequencies in a vacuum. This can lead to errors, particularly in DWDM systems, since the index of refraction of air is a function of wavelength, temperature, pressure, and gas composition. The wavelength dependence of the index of refraction n air of standard dry air at 760 torr and 15°C is 64
where is measured in micrometers.
( a ) Given that vacuum = air n air , what is the error in wavelength measurement at 1550 nm if the effect of the index of refraction of air is ignored What impact would this have on 0.8-nm-spaced WDM channels in the 1550-nm window
( b ) To compensate for temperature and pressure effects on the value of n air , one can use the relationship
where P is measured in torr and T is in Celsius. How much does n (T, P) vary from n air when the pressure is 640 torr and the temperature is 0°C (which would be at a higher elevation and a lower temperature)