Devin 2.0

The new Devin 2.0 evaluates model-independently the integrated low-frequency spectral weight (SW)

of an optical spectrum for which the real and imaginary parts, ε1(ω) and ε2(ω) = 4πσ1(ω) /ω, of the dielectric function are measured in a limited frequency range [ω_min,ω_max] with known error bars Δε1(ω) and Δε2(ω) .

The cutoff frequency ω_c must lie between ω_min and ω_max.

In order to use this web-interface you are kindly requested to upload the input file and provide the cutoff frequency. The input file must be in 5-columns format. Each line should correspond to one photon energy. The columns are

  1. Photon energy (frequency) ω
  2. Real part of the dielectric function
  3. Error bar of ε1
  4. Imaginary part of the dielectric function
  5. Error bar of ε2

The file should contain no empty lines, and no other information than the numbers in the five columns. The columns must be separates by SPACE symbols. The minimum number of lines (datapoints) is 10, the maximum – 200. The units of the photon energy ω can be chosen freely. The energy spacing between data points, as well as the order in which you put them, can be chosen freely.

The output SW is expressed using the units ω2.

Please fill in the file-upload form below

File to upload:
Cutoff Frequency:

to upload the file.

About Devin 2.0

At first glance, one might think that the problem of determination of SW, which requires the knowledge σ1(ω) of down to 0, cannot be solved. Or at least cannot be treated model-independently. Indeed, there is no model-independent way to extrapolate σ1(ω), taken alone, to the region below ω_min . However, one should not forget that ε1(ω) provides a crucial extra piece of information, as it is related to σ1(ω) at ALL FREQUENCIES via the Kramers-Kronig transform. Using ε1(ω) allows one to get an essentially model-independent answer, even though the problem remains ill-posed.

As it is the case for any ill-posed problem, the propagation of the error bars is the most important issue. One should mention that the determination of itself σ1(ω) below ω_min, using ε1(ω) as extra piece of information, would require extremely small, virtually prohibitive input error bars. Remarkably, in the case of SW, which is an integral of σ1(ω), the requirements on Δε1(ω) and Δε2(ω) are much more relaxed and often experimentally achievable. We recently developed an algorithm which minimizes the output error bars. It was successfully tested on a number of examples. Now it serves as an engine of Devin 2.0.

Technical remarks

  1. Providing correct input error bars is crucial to get a reliable answer. It is assumed that the input error bars are statistical, not frequency-to-frequency correlated and not systematic;
  2. The output error bar of SW is indicative. It takes into account both statistical noise of the input data and the numerical uncertainty of the algorithm itself;
  3. It is assumed that spectral resolution is the same as the energy difference between neighboring points. In other words, each point represents an average over the adjacent region
  4. It is recommended to fill the spectral range with points more or less uniformly avoiding big ‘holes’;
  5. The program assumes but does not check that the provided ε1(ω) and ε2(ω) are Kramers-Kronig consistent. If this is not the case, the output might be totally wrong but given with unrealistically small error bars.

Réalisation: Sur Mesure concept