Thank you for the reply!
I have tried to improve the simulation based on your suggestions. As you can see in the attached screenshot below, the span of the mode source is significantly increased and extended beyond the boundary of the varFDTD region. And the mode I selected in the mode source is just the fundamental TE mode. Unfornately, the output transmission is sometimes greater than the input one (since it becomes sinusoidal), alothough the difference is quite small.
I also check the field profile (see the figure below) at the input and output monitors and the fields look fine and not truncated.
And I found that increasing the distance between the boundary of varFDTD region and the output monitor at the right hand side will let shape of the output transmission spectrum less sinusoidal. So I am not sure if this indicates that the simualtion region should be much larger than that you suggested in point 2?