Thakur’s Equation

Thakur's Equation

In what may come as a major achievement for India, it now stands established that the central equation of the 2014 Nobel document is from earlier works on nonlinear optics of the NRI scientist Professor Mrinal Thakur.


The Judge of an US court has referred to this equation (equation 3 of the Nobel document) as “Thakur’s Equation” which is Δ = λ/(2nsinα(1 + I/Is)1/2).


Earlier nominated for the Nobel Prize in Chemistry for 17 times, Professor Thakur currently is working as Director of Photonic Materials Research Laboratory of Auburn University in USA.


However, what violates the academic norms is the fact that though the “Thakur’s Equation” was officially announced, no credit was given to him in the 2014 Nobel Prize document.


The US court’s announcement of the “Thakur’s Equation” came in response to a case of plagiarism filed by the NRI scientist against the 2014 Nobel Laureates in Chemistry. The Judge ruled there is no law against plagiarism (despite the consequences) in California, USA.


Reacting to it, Professor Thakur demanded intervention of the Prime Ministers of Sweden and India: Lofven of Sweden and Prime Minister Narendra Modi took no action to resolve critical issues on the Nobel Prize raised multiple times earlier.

The 2000 Chemistry Nobel Prize Violates Academic Norms


The 2000 Chemistry Nobel Prize was awarded for the discovery of Conductive Polymers. The Royal Swedish Academy of Sciences gave the award only to those who discovered “Conjugated” conductive polymers and excluded Professor Thakur for his discovery of “Nonconjugated” conductive polymers.


The document preserved at the Nobel Foundation website for the 2000 Nobel Prize in chemistry is fundamentally incorrect. Alan Heeger, A.G. MacDiarmid and H. Shirakawa, recipients of the Nobel Prize for chemistry in 2000, made fundamentally incorrect (nonfactual) statements in their Nobel document that only conjugated polymers can be electrically conductive.


Legal communications involving US attorneys have recently established that these Nobel recipients have agreed at the legal-level that Professor Thakur’s experimental works and theory are fundamentally correct while theirs are fundamentally incorrect!


However, the following four critical issues have remained unresolved:


  • No credit to Professor Thakur in 2000 Nobel Prize and afterwards for his discovery of “Nonconjugated Conductive Polymers.”


  • The Royal Swedish Academy is yet to correct the document preserved at the Nobel Foundation website despite repeated requests. The document states a polymer must be conjugated to be electrically conductive – which is nonfactual and the corresponding theory as given is incorrect.


  • Professor Thakur’s research funding was abruptly stopped in 2003 as he brought up the incorrectness and inequity regarding the 2000 Nobel Prize in Chemistry.


  • Professor Thakur stakes claim to the 2014 Nobel Prize in Chemistry as well since “Super-resolved Fluorescence Microscopy” (2014 Nobel in Chemistry) is primarily based on earlier nonlinear optical experimental and theoretical studies performed by Professor Thakur and colleagues on organic materials.


Scientific Explanation of Thakur’s Equation

The 2014 Nobel Prize in Chemistry was awarded to Betzig, Hell and Moerner for their works on “Super-Resolved Fluorescence Microscopy.”

The nonlinear optical coefficients as a function of wavelength, excited-state lifetimes, two-photon absorption and the detailed saturation dynamics have all been measured using femtosecond-duration pulses and their theoretical interpretations have been established.

The excited state lifetime as measured is about 1.8 ps. In the off-resonant domain the response is instantaneous.

As discussed in such reports, (phase-space filling model applied to PTS-polydiacetylene crystal), the fractional change in oscillator strength, δf/f is related to the number fraction of electrons (excitons) involved in the transitions as given in the following:where Ns is the saturation density.

For organic materials, energy levels remain essentially unchanged when light is incident on it.

As it is well known, the gain constant, γ for downward transition (stimulated emission) involving two levels relates to the laser light intensity as follows:where Is is the intensity at which the gain (γo) reduces by a factor of 2.

Then, the fractional change in oscillator strength (downward transition),

The following equation (known as The Thakur’s Equation Δ = λ/(2nsinα(1 + I/Is)1/2), shows the line-width defined as the standard deviation as related to the number of electrons involved in the downward transitions (stimulated emission) due to the presence of the pump pulse:where Δo is the average line-width (= λ/(2nsinα) in the Abbe limit (1)Abbe, E. (1873) Archiv fur Mikroskopische Anatomy, 9: 413.

This is the central equation, Equation 3 given in page 5 of the 2014 Nobel document preserved at the Nobel Foundation website and is derived based on phase-space filling model and the statistics involved in the emission process. A derivation of this equation is not given in the literature.

In conclusion, super-resolved fluorescence microcopy, in particular stimulated emission depletion microscope essentially involves a femtosecond pump-probe measurement in third order optics of organic materials.

The mechanisms are adopted from earlier experimental and theoretical studies in third order optics involving well-defined materials such as polydiacetylene single-crystal films. The correlation between the line-width (resolution) and optical pulse intensity is developed using phase-space-filling model used in the case of PTS-polydiacetylene film.