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Measure of Time-frequency bandwidth relation: Experimental demonstration of Heisenberg Uncertainty Principle

OBJECTIVE: There is relationship between time width and frequency bandwidth in every spectroscopic experiments. This time width and frequency bandwidth relationship comes from uncertainty principle, which comes from Fourier Transformation. In daily experimental life, it is used in techniques like FTIR, FTNMR etc.

THEORY: The Heisenberg Uncertainty principle states that it is impossible to measure the two conjugate quantities (whose operators do not commute) simultaneously with arbitrary accuracy. As the laser pulse goes onto the shorter and shorter in time domain, it spectral bandwidth goes on increasing. The uncertainty in time and spectrum are related by

Where, ∆t is the time width and ∆ɷ is the spectral width. For the Gaussian shaped pulse, this relation becomes

Now, we cannot measure ∆ɷ directly from our spectrum, as there we have intensity vs. wavelength plot. Here, where, c is the velocity of light in vacuum, λ is the central wavelength.


1.      Laser switchable between CW and pulsed mode: Ti:Sapphire laser provides this unique facility.

2.      HR 2000 spectrometer.

3.      Multimode optical fiber.


1.      Ocean optics OOIBase32 for spectrum collection

2.      Origin pro for data plotting and analysis

Note: For user operation and usage no specific software needed.


1.      Turn on the laser.

2.      Measure the spectra of the CW laser using HR 2000 spectrometer. It has delta bandwidth.

3.      Turn on the ML switch to turn the laser in pulsed mode.

4.      Measure the spectrum of pulsed laser.

5.      Measure the pulse width of the laser (for femtosecond pulse, use autocorrelation technique, described in the other experiment).

6.      For measuring ∆t and ∆λ, get the FWHM (Full Width at Half Maximum) of the respective plots, which we take as the said parameters.

7.      Check for the validity of eqn. (1) or (2) (whichever is applicable).

Laser spectrum (left one: femto second pulsed, right one: CW laser)