Your query is good. You are true that decomposition of light into polarized and unpolarized parts. However, this whole decomposition is explicitly dependent on your experimental and observational variables. When there is no case of polarization effect even when propagating through some medium, this decomposition becomes unfruitful. In the same note, the degree as well as type will creep in when the resultant output is monitored.

I don't think it's possible to characterize both unpolarized and polarized light simultaneously. Since the polarized light is of the same phase and the unpolarized light phase is different, the method of measuring polarized light is not suitable for measuring unpolarized light.

I agree, but if we characterising polarized part with some degree of polarization(partial ploarization) then remaining is unpolarized at same time. My question is about partial ploarization having its degree of ploarization only due to circular differs from liner or both are same?

As you state, it's possible to decompose a Stokes vector as the sum of an unpolarized Stokes vector plus a polarized Stokes vector. I don't believe it's possible to then decompose the polarized Stokes vector into the sum of a linearly polarized Stokes vector plus a circularly polarized Stokes vector. You can however determine the percentage of power in the linearly polarized and circularly polarized components of the field--the degree of linear polarization and degree of circular polarization, respectively. These are related to the "total" degree of polarization by P2 = (PLP)2 + (PCP)2.

Dear Milo Hyde , I believe symbol P denotes power, is it right?

As you mentioned, I agree, it is not possible to decompose total polarization as sum of two different types polarizations, but total field can be decomposed into polarized and unpolarized parts. My question is about the polarized part of decomposition either circular, linear or elliptical of same degree of polarization, is this decomposition of unpolarized and circular or unpolarized and linear or unpolarized and elliptical are give same properties on propagation ?

Because I wanted to know is it always a DOP or type of polarization also matters?

The P in my equation is the degree of polarization, PLP is the degree of linear polarization, and PCP is the degree of circular polarization. I'm having trouble understanding your question. When a Stokes vector is decomposed into an unpolarized Stokes vector plus a polarized Stokes vector, the polarized Stokes vector, in general, describes an elliptical state. This decomposition allows you to specify, for instance, that the beam is X% polarized, and the polarized state is elliptical with an angle of polarization $\psi$ and ellipticity angle $\chi$.

Dear Milo Hyde thank you for your answer. Yes, it is DOP and I confused by symbol P which is generally used in stokes parameters as S. I am working on a particular source which can emits CPL or LPL and studying its characteristics after some distance on propagation. I would like to study change in polarization characteristics for different polarization source.

As you mentioned " I don't believe it's possible to then decompose the polarized Stokes vector into the sum of a linearly polarized Stokes vector plus a circularly polarized Stokes vector", if stokes vector is (in column)[1 0 1/sqrt(2) 1/sqrt(2)]=[1 0 1/sqrt(2) 0]+[1 0 0 1/sqrt(2)] and LHS follows S2=S12+S22+S32. If is right it is possible to decompose and is it having any physical significance?

Please see the attachment. I got tired of trying to write symbols in this textbox.

Polarization remains one of most elementary concepts in Optics yet, speaking rigorously, not well understood commonly,. People confine their view to experiments based on measurement of intensities (coherence functions of order (1,1), which can be expressed in terms of Stokes parameters). Monochromatic unidirectional light having Stokes parameters (S0, S) can then be thought of being a superposition of polarized light having stokes parameters (|S|, S) and unpolarized light having stokes parameters (S0 - |S|, 0). Some other experts have stated to the effect that the state of polarization of the polarized component of given light is not arbitrary and is in fact given by the stokes vector S. This is true in the commonly understood sence (confined to discussing quantities ~ intensities (coherence functions of order (1,1).

Strictly speaking there are many polarization states of light (and not only two, polarized and unpolarized) and a general light beam cannot be said to be super position of polarized light and unpolarized light. If it were so, in the usual sense of "superposition", the characteristic function of light could have been written as product of characteristic functions of its polarized and unpolarizsed components. A very simple example of this is the light produced by parametric amplification of vacuum state in parametric amplification.

Also, the stokes parameters are inadequate to describe polarization properties in higher order coherence functions. e.g., in the simple example of . This was shown in one of our earlier papers,

Density operator of unpolarized radiation, H Prakash, N Chandra - Physical Review A, 796 (1971).

See also: Density operator of unpolarized radiation, H Prakash, N Chandra - Physical Review A, 1021(1971). Density operator for unpolarized radiation

H Prakash, N Chandra - Physics Letters A, 28(1971), UNPOLARIZED STATE OF LIGHT REVISITED, Report number: IC/81/3 5, Affiliation: INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS, TRIESTE, ITALY, Hari Prakash and NARESH CHANDRA, available on Researchgate.

Thank you very much for your reply Prof.Hari Prakash. I will go through the paper you recommended. The State of Stokes vector in polarized part of partial coherent partially polarized beam changes on propagation e.g., Gaussian schell model beams is well studied by Emil Wolf. Recently I have also read that polarized part is strictly being a single state of vibration in the sense that there should not be addition of two polarized components , it will results in unpolarization. Prof.A T Friberg( https://www.uef.fi/en/web/photonics/ari-t.-friberg ) and group doing research on unploarized light few of his papers cleared my doubt.

In regard of Stokes parameters are inadequate for higher order coherence functions, ( I am not sure) the two point Stokes parameters ( Article Generalized Stokes parameters of random electromagnetic beams

As mentioned in your affiliation ICTP Trieste, I have a plan to apply and attend the complex system course( http://indico.ictp.it/event/9024/ ), I would like to meet and discuss with you once if I selected for the same.