# Should I use POP or Single Mode Coupling for my single-mode fiber coupling system?

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Userlevel 6
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• Zemax Staff
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It is common users ask which method they should use for their system or if the results are different, which one should they trust. To answer this question, let's first talk about the difference between the two methods.

When we calculate coupling efficiency, no matter with which method, what we do is the normalized overlap integral (more details in Help) between the beam amplitude, W(x,y), and fiber receiving mode, Fr(x,y). The overlap integral is like you compare the two complex-valued amplitude distribution. If they are same, the integrated value is 1. If they are not same, the result will be less then 1. For a single-mode fiber, it's a cylinder waveguide and the Fr(x,y) can be approximated by a Gaussian beam mode.

Now we can say, the main difference between POP and Single Mode Coupling is about mainly how we calculate the beam amplitude W(x,y). For POP, this is naturally the beam profile AFTER the image plane. Note the POP result is always shown as after refraction of the specified surface. On the other hand, the Single Mode Coupling basically uses the Huygens PSF when we check the "Use Huygens Integral". Note we assume users use Huygens in this discussion because it's more accurate than FFT PSF in most of cases. Therefore, to ask the difference of coupling efficiency calculated by POP and Single Mode Fiber methods is fundamentally same as to ask the difference of spot profile predicted by POP and Huygens PSF.

It is important we should not be surprised the calculated result is different between the two methods becuase they are based on different algorithms. It is possible the result is very different when the condition is far from assumptions of one method.

Both methods have their assumptions and limitations. Huygens PSF calculates the beam amplitude by tracing rays through the system and only considers the diffraction at final step. In contrast, POP propagate beams fully considering diffraction from the start to the end. Therefore, in most of cases, we would say POP is more trustable. Note that, however, POP needs more cares to make sure the result is correct. A surface by surface system check is always required.

However, POP has some algorithm assumptions, where the details can be found in Help file. When the system doesn't well meet the assumptions, it's suggested to switch to use Huygens. A typical case is when you have a laser source where divergence is faster than F/1. In that case, it's common we need to switch to use Huygens PSF. Practically, side-emitting type of laser diode usually has a large divergence and it's suggested to use Huygens PSF. And for VCSEL, it's possible the divergence angle is not too large and thus POP is adequate. When POP is adequate, it's should always be a better choice.

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Hi Michael,

Thanks for the explanation. Really helpful. Nevertheless, I still don't understand why here you recommend to use Huygens PSF, while in the help file to Single-Mode coupling it's written: 'The recommended approach is to leave this option unchecked. If the fast ray-based integration cannot be computed accurately, the fiber coupling will be zero and a warning will be printed which will recommend switching to the Huygens algorithm.'

So here is the question...when do we need to check Huygens and when we don't need to check it?

Userlevel 6
+2

Hi Nikolay,

To go from Maxwell equations to simpler forms like Huygens and FFT diffraction, we are making assumptions. These assumptions are well-described in the 'Introduction to Fourier Optics' by Joseph W. Goodman.

Both the Huygens PSF as well as the FFT PSF are based on the scalar diffraction theory. And in OpticStudio, we calculate both PSF from the wavefront information at the exit pupil.

Huygens

• The Huygens PSF is the coherent sum of wavelets orginating from secondary sources located at the wavefront at the exit pupil.

• The calculation is done at the image plane. So it works for a tilted image plane.

• But it may require a high sampling, and so be slower than the FFT calculation.

FFT

• The FFT is calculated by making a Fourier-transform of the wavefront amplitude at the pupil space.

• The FFT assumes that the image plane is in far-field (it is explained on chapter 4.2 in the Fourth edition of the book and also in our help file The Analyze Tab (sequential ui mode) > Image Quality Group > PSF > FFT PSF). This means the computed PSF is only accurate if the image surface is fairly close to the geometric focus for all rays; or put another way, that the transverse ray aberrations are not too large. There is no hard and fast limit, however if the transverse aberrations exceed a few hundred wavelengths, the computation is likely not accurate.

• The FFT is computed on an imaginary plane which is centered on and lies perpendicular to the incident chief ray at the reference wavelength.

I hope this clears things but do not hesitate if not.

Sandrine