Single Mode to Multi-mode back to Single Mode

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The discussion focuses on the design of an interferometer that couples a laser into single-mode fiber (SMF) fused to multi-mode fiber (MMF). It highlights that if the fiber remains unperturbed, no interference pattern will be observed at the MMF output, but stretching the fiber could change the index of refraction and create an interference pattern. The output from the MMF will produce a speckle pattern due to the superposition of mode field patterns, which can change over time with varying modal group velocities. Measuring these changes in the speckle pattern, potentially through software or spatial correlators, is essential for detecting oscillatory deformations in the MMF. Understanding these dynamics is crucial for accurately interpreting the output from the SMF.
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Alright. I'm having a little trouble getting started on this design of an interferometer. Essentially what I want is to couple a laser into the single mode fiber (SMF), which is fusion spliced to a multi-mode fiber (MMF). Assuming the fiber is unperturbed, the modes will not mix and you will no interference pattern at the end of the MMF (or perhaps you will have an interference pattern characteristic of the 'unperturbed' state, I'm not really sure) . However, if the fiber is say, stretched, the index of refraction will change, causing an interference pattern. I'm wondering how I could measure this. If this were to be used to measure an oscillatory deformation of the MMF (lets pretend its change in length delta L is a sine function of some angular frequency omega), what would I see in terms of the output of the SMF. I'm pretty confused here...

Some more information. From wikipedia http://en.wikipedia.org/wiki/Speckle_pattern

"In the output of a multimode optical fiber, a speckle pattern results from a superposition of mode field patterns. If the relative modal group velocities change with time, the speckle pattern will also change with time. If differential mode attenuation occurs, modal noise results."
 
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Your 2nd MMF fiber will not support the single mode that is injected, IMO.
 
I think if you splice the SMF fibre to the MMF fibre, when you apply the laser the light entering the MMF will develop many modes. This will result in a speckle pattern on a screen near the output. If you now deform the MMF I think the speckle pattern will change.
So it is a matter of how to measure the changes in speckle pattern, which in these times I suppose will be done by software, subtracting one image from the other say. Or using some sort of spatial correlator.
 
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