The fundamental conception in physics of the propagation of the electromagnetic wave polarization in matter is newly understood as the cardinal keyword in free-space quantum communication technology and cosmology in astrophysics. Interactive visualization of the propagation mechanism of polarized electromagnetism in a medium with its helicity has accordingly received attention from scientists exploiting the protocol of quantum key distribution (QKD) to guarantee unconditional security in cryptography communication. We have provided a dynamic polarization platform for presenting the polarization modes of a transverse electromagnetic wave, converting the state of polarization through the arrangement of optical elements, using Jones vectors calculations in Methematica. The platform graphically simulates the mechanism of production and propagation of the polarized waves in a medium while satisfying Maxwell's equations.

1. INTRODUCTION
 2. MATHEMATICA SIMULATION FOR THE CONVERTING POLARIZATION MODES
  2.1 Electromagnetic waves in solids
  2.2  Polarization modes Mathematica simulation
  2.3 Helicity of the elliptically polarized wave
 3. DYNAMIC POLARIZATION PLATFORM WITH JONES VECTORS IN MATHEMATICA 
 4. SUMMARY 
 ACKNOWLEDGEMENT
 REFERENCES

• Yong-Dae Choi(Department of Microbial and Nanomaterials, Mokwon University)
• Bogyeong Kim(Department of Astronomy and Space Science, Chungnam National University)
• Hee-Joong Yun(Korean Institute of Science and Technology Information) Corresponding Author