Skip to main content
SpringerLink
Log in

Generalized theory of interference, and its applications

Part I. Coherent pencils

  • Published:
Proceedings of the Indian Academy of Sciences - Section A Aims and scope Submit manuscript

Summary

The superposition of two coherent beams in different states of elliptic polarisation is discussed in a general manner. If A and B represent the states of polarisation of the given beams on the Poincaré sphere, and C that of the resultant beam, the result is simply expressed in terms of the sides,a, b, c of the spherical triangle ABC. The intensity I of the resultant beam is given by:

$$I = I_1 + I_2 + 2 \sqrt {I_1 I_2 } \cos \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} c cos \delta ;$$

the extent of mutual interference thus varies from a maximum for identically polarised beams (c = 0), to zero for oppositely polarised beams (c = π). The state of polarisation C of the resultant beam is located by sin2 1/2a = (I1/I) sin2 1/2c and sin2 1/2b = (I2/I) sin2 1/2c. The ‘phase difference’ δ is equal to the supplement of half the area of the triangle C′BA (where C′ is the point diametrically opposite to C). These results also apply to the converse problem of the decomposition of a polarised beam into two others.

The interference of two coherent beams after resolution into the same state of elliptic polarisation by an elliptic analyser or compensator is discussed; as also the interference (direct,and after resolution by an analyser) ofn coherent pencils in different states of polarisation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chandrasekhar, S.Radiative Transfer, Oxford, 1949.

  • Fano, U.J. Opt. Soc. Am., 1949,39, 859.

    Article  Google Scholar 

  • Jerrard, H. G. —, 1954,44, 634.

    Article  Google Scholar 

  • Mascart, E.Traite d’Optique, Paris, 1891,2.

  • M’Clelland, W. J. and Preston, T.A Treatise on Spherical Trigonometry with Applications to Spherical Geometry, 1897, PartsI andII, Macmillan.

  • Pancharatnam, S.Proc. Ind. Acad. Sci., 1955,42 A, 235.

    Google Scholar 

  • Perrin, F.J. Chem. Phys., 1942,10, 415.

    Article  Google Scholar 

  • Pockels, F.Lehrbuch der Kristalloptik, Teubner, 1906.

  • Ramachandran, G. N. and Ramaseshan, S.J. Opt. Soc. Am., 1952,42, 49.

    Article  Google Scholar 

  • Ramachandran, G. N.J. Madras Univ., 1952,22 B, 277.

    Google Scholar 

  • RayleighScientific Papers, Cambridge, 1902,3, 140.

    Google Scholar 

  • Stokes, G. G.Mathematical and Physical Papers, Cambridge, 1901,3, 233.

    Google Scholar 

  • Walker, J.Analytical Theory of Light, Cambridge, 1904.

Download references

Author information

Authors and Affiliations

  1. Memoir No. 88 of the Raman Research Institute, Bangalore-6

    S. Pancharatnam

Authors
  1. S. Pancharatnam
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Sir C. V. Raman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. 44, 247–262 (1956). https://doi.org/10.1007/BF03046050

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03046050

Keywords

Search

Navigation