Why does the optical cloak use four refractions instead of three?

[Christofer Br]

https://www.researchgate.net/publication/273269952_A_Simple_Unidirectional_Optical_Invisibility_Cloak_Made_of_Water
Why did the authors of this cloak not choose a system with only three refractions for each light ray, so that the cloaked area would be a parallelogram? Is this impossible, or would it decrease the cloaking angle?

 

[Vanadium 50]

You could always write them and ask them, but I suspect the answer was simplicity. It's obvious how to do this with 4, and 4 breaks down to 2+2 so you can test half of it easily. It probably can be done with 3, but not so easily - the middle pice has to be just right: you need to make sure every ray spends an equal time in air and water, and that all the angles work out.

 

[Klystron]

Page 3 of the paper could use a fourth picture between pictures (1) background only and (2) 14 cm model that shows (2') background with device sans giraffe. Selection of background with hazy patterns and the large central tree figure directly behind the giraffe appear forced; designed to assist the illusion of continuity. The inexpensive nature of the device is intriguing.

Agree with simplicity as the answer to the OP. Minimal configuration that works ( and costs least).

 

[sophiecentaur]

I see the diagrams are 2 dimensional. Would it work in all planes? Prob some distortion.
I'm amazed that the idea could be 'new',

 

[Vanadium 50]

I'm amazed that the idea could be 'new',

It's been done with reflection for decades (centuries) by stage magicians. As they say "it's all done with mirrors".