Undergrad How to create the operator of unknown beamsplitter

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To calculate the operator of an unknown beamsplitter in quantum optics, it is essential to measure the properties of the reflected and transmitted beams, particularly focusing on their polarization states. The beamsplitter should have optically flat, parallel faces, and the Fresnel coefficients can help determine the splitting behavior. The Hong-Ou-Mandel experiment provides a foundational approach for constructing a unitary matrix representation of the beamsplitter. Additional resources, such as specific articles on interferometry, can offer more insights into the experimental design. Understanding these principles is crucial for accurately modeling the beamsplitter's operator.
Pattarasak
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Hello everyone, I'm undergraduate and my project is an experiment in the field of quantum optics. For now, I have an Unknown beamsplitter in my lab and I want to calculate the operator of this beamsplitter in matrix form (this BS is not perfected equipment because the reflected beam is not linear polarization ). Can anyone tell me how to design this experiment and what type of information that I have to measure to calculate the operator? thank you for the answer.
 
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What you are ultimately attempting may be more advanced than anything I have done, but for some more introductory material, I presume the beamsplitter has optically flat and very parallel faces, has a finite thickness, and has one side coated with an AR coating. All of the dielectric partial reflection is then assumed to occur from the uncoated face. The Fresnel coefficients can be used to calculate how the splitting occurs. See also the Insights article https://www.physicsforums.com/insights/fabry-perot-michelson-interferometry-fundamental-approach/ that I authored. ## \\ ## I specialize somewhat in Optics, but not Quantum Optics, so that you might be needing quite a bit more than this, but perhaps you might find this of some use.
 
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Hi Pattarasak,
If you do a google search for the Hong Ou Mandel experiment you will find many explanations of the way to construct a unitary matrix representation of the beam splitter in quantum optics.
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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