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Returns the overlap and power coupling between two modes calculated by the FDE solver or recorded by frequency monitors from a varFDTD simulation. In FDTD, it calculates the overlap and power coupling between the field profiles (modes) recorded by two frequency monitors.
Overlap measures the fraction of electromagnetic fields that overlap between the two field profiles (modes). This is also the fraction of power from mode2 that can propagate in mode1 (for both forward and backward propagating fields). The absolute value of the entire formula is to ensure it is positive.
Note: Comparison with Mode expansion monitor This overlap calculation is similar to the calculations provided by the Expansion monitor, but it is designed for use in a slightly different situation.  The expansion monitor is intended for situations where the input file profile (mode2) is known within the same waveguide structure where mode1 exists.  The overlap calculation is intended for situations where the input field profile (mode2) is known in a different waveguide structure than the one where mode1 exists. For example, mode1 and mode2 are the fundamental modes of two different waveguide structures, and the overlap function is being used to estimate the efficiency of an endfire coupling arrangement between the two waveguides. The overlap calculation can provide accurate results in many situations, but it is worth noting that it is an approximate technique. One key assumption is that both mode1 and mode2 only contain fields that are propagating in a single direction.
The overlap calculation defined above can be written in terms of the quantities provided by the expansion monitor, as shown below. This represents the total power carried by the ith mode, including both the forward and backward propagating fields, normalized to the input power. See the online help for more information on Using Mode Expansion Monitors.
In the event that real(N) or real(P) is 0, the "real" can be replaced with "abs". 
Power Coupling measures the amount of power that can couple from mode2 into a forward propagating wave with the mode profile of mode1. The remaining power that can propagate in this mode will couple into the backwards propagating mode. Therefore, the power coupling is always less than or equal to the overlap. If the two modes have the same effective index, then the power coupling will be equal to the overlap.
A dielectric interface is a simple example. The modes (i.e. a plane wave) on each side of the interface have an overlap of 1, but the power coupling will be less than one. This is due to reflections caused by the index change at the interface.
These calculations are based on the methods described in Snyder and Love "Optical Waveguide Theory", Chapman & Hall, London, England, 1983.
Note: For an exact power coupling result at an interface, it is necessary to know the complete set of waveguide modes on both the input and output sides, and the MODE Solutions' EME solver can be used. See Overlap analysis for more information. 
Supported Product: FDTD, MODE 
Syntax 
Description 
out = overlap(mode2, mode1); 
•mode2, mode1: the mode names (in FDTD, use the names of the frequency monitors, "m1" and "m2" instead) •out(1): the mode overlap •out(2): the mode power coupling 
out = overlap(mode2, mode1, x, y,z); 
Mode alignment can be adjusted before overlap is calculated. •x offset •y offset •z offset The offset is applied to the second mode listed. 
Examples
This example shows how to use the overlap command to calculate the overlap and power coupling between two modes.
copydcard("mode1","test_mode1");
copydcard("mode2","test_mode2");
out = overlap("test_mode1","test_mode2");
?out(1); # overlap
?out(2); # power coupling
See Also
Measurements, copydcard, findmodes, coupling, bestoverlap, propagate, expand, expand2, optimizeposition