It serves no role for objects which do not overlap. The mesh order can be set at the material level (in the material database), or the object object level (in the object properties). Materials with a lower mesh order take priority over materials with a higher priority number (i.e. order 1 takes priority over 2). Areas which overlap are assigned the material properties of the higher priority material (see the following figure).
How to: Define structures with overlapping components (YouTube)
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In the figure above, there are two objects that partially overlap. Depending on their mesh orders, the object that is actually being simulated will be different. In the event that both overlapping materials have the same order, the mesh order will be inferred from the Object tree. Objects at the bottom of the tree will take priority over objects at the top of the tree. To ensure your simulation is well defined, it is recommended that you avoid situations where two different overlapping structure have the same mesh order. To set the mesh order using script, one can user setmaterial (material level), setnamed or set (object level).
For simulations using the conformal mesh, the mesh order property defines the material properties in the mesh cells where materials fully overlap one another. In the mesh cells which contain boundaries between two materials, the conformal mesh algorithm solves Maxwell's integral equations near these boundaries.
Tip: Use an index monitor to confirm that the structures are meshed as intended.
Note: The etch material in the default Material database
By default, most materials in the material database have a mesh order of 2. The only exception is the etch material, which has a mesh order of 1. The lower mesh order means that an object using the etch material will override other objects of a different material type.
The etch material has a refractive index of n=1. If you are using a different background index, you should modify the etch material to match the background index of your simulation.