Question

I'm working with a Fabry Perot cavity with a length of 55 mm and an incident wavelength of 1550 nm. From theory the FSR of the FP cavity can be either computed using the equation

FSR = λ^2 / (2 n L)

where λ is the incident wavelength and L is the cavity length. Or, we can also compute the FSR if we know the positions of resonant dips and peaks from the resultant intensity pattern.

Considering the reflected intensity from the FP-cavity, and applying conditions for resonant dips, we can write the mth resonant dip as:

λm = 2 n L/ m

m being the order of interference.

FSR can now be calculated as λm - λ(m+1) which is equivalent to:

FSR = λm . λ(m+1) / (2 n L)

I expect the FSR from both equations gives more or less the same values. FSR calculated using incident wavelength value is 14.8 pm. But for the resonant dip-related equation I only get the expected FSR over a certain range of 'm'values.

From my understanding I expected the FSR to be same for all m values. I'm now confused about the concept of interference fringes. Is there a range of 'm' values to be considered? Or does the FSR of interference fringes actually change with m values?

Answer 1

The Fabry-Perot cavity is an interference device with two mirrors separated by a cavity length. The FSR can be calculated using either the incident wavelength or the positions of resonant dips and peaks. While the FSR should be the same for all m values, the resonant dip-related equation may only give the expected FSR for a certain range of m values.

Step-by-step explanation:

The Fabry-Perot cavity is an interference device that consists of two parallel reflecting surfaces, called mirrors, separated by a distance known as the cavity length. When light enters the cavity, it undergoes multiple reflections between the mirrors, creating interference patterns. These patterns are characterized by the Free Spectral Range (FSR), which represents the separation between adjacent resonant frequencies.

The FSR of the Fabry-Perot cavity can be calculated using the equation:

FSR = λ^2 / (2 n L)

Where λ is the incident wavelength, n is the refractive index of the medium between the mirrors, and L is the cavity length. This formula gives an estimate of the FSR based on the incident wavelength. However, when working with the positions of resonant dips and peaks, a different equation can be used:

FSR = λm . λ(m+1) / (2 n L)

Where λm represents the wavelength of the mth resonant dip, and m is the order of interference.

It is important to note that the FSR calculated using the incident wavelength value should be the same for all m values, as it is determined solely by the length of the cavity and the refractive index of the medium. However, when using the resonant dip-related equation, the range of m values that give the expected FSR may be limited. This is because the equation assumes ideal interference conditions, and certain values of m may result in non-resonant wavelengths that do not satisfy the conditions for resonant dips.