Multiple Beam Interference
Finesse
Free Spectral Range
Visibility
Coherence length
Ideal & Real Fabry Perot
Stability Criterion
Spectral Analysis
Flat mirror
Confocal Cavity
Hemispherical cavity
Green DPSS single mode probe laser
Optional HeNe two mode probe laser
LM-0300 Fabry Perot Spectrum Analyzer
Topics:
LM-0300 Fabry Perot Spectrum Analyzer
This experiment shows the properties of optical resonators especially the „Fabry Perot“ (FP) resonator which is the most important of all stable laser resonators. The properties and behavior of such a resonator will be discussed and measured as well as the resonance condition, the free spectral range and finesse. The stability criteria of confocal, hemispherical and plane parallel resonator types are calculated and measured. Finally, the resonator will be used as a spectrum analyser, a so called scanning Fabry Perot. The mode spectra of the provided green single mode diode pumped solid state laser (DPSSL) and optional two mode HeNe laser is measured. The resonator mirrors are mounted in precision adjustment holders. One mirror is mounted on a low voltage piezoelectric transducer (PZT) which is controlled in amplitude and frequency by means of a voltage (0-150 V) controller. The other one is mounted into a precise translation element to achieve the perfect confocal match for curved mirror. The PZT periodically changes the length (0 to 10 µm) of the cavity sweeping over some resonances. The signal of the photodiode and the triangular PZT scanning amplitude are displayed on an oscilloscope showing the Airy function for some resonances. By using the known distance of the FP mirror, the free spectral range is determined and is used to calibrate the horizontal axis of the oscilloscope. The mode spectra of the DPSSL - Laser is measured and interpreted by this method. Surprisingly, the green emitting DPSSL emits a very pure single mode if the temperature and injection current are properly controlled. In addition, an optional two mode HeNe probe laser can be used to measure the mode spacing with the SFP. Some parts of this experiment can also be used in connection with the experimental HeNe-Laser, to demonstrate the single mode operation, when an etalon is used inside of its cavity. By tuning it, even the gain profile of the HeNe laser can be measured (see extension LE-0350).
A. Principle Fabry-Perot Set-ups
B. Typical SFP measurementThe static Airy function which describe the transmittance of a FP becomes now also a function of time t. The modulation of the length L(t) is usually done with a PZT. The length changes depending on the applied voltage. The transmission becomes maximum if L(t)=N·λ/2, whereby N is an integer number. The range for N → N+1 is the range between two consecutive transmission peaks and is called free spectral range (FSR). The FSR is a very important value as it allows the calibration of the time axis of the graph of Fig. B. The finesse F is determined as FSR/FWHM and its value is a parameter for the resolution of the FP. The finesse of a FP depends on the reflectivity of the mirror. However the flatness of the mirrors are even more important. In practice it turns out that the use of flat mirrors creates some disadvantages. Firstly, the alignment of absolute parallelism of both mirrors is hard to achieve and secondly the flatness of the mirror must be very accurate (better than λ/10). The case (B) of Fig. A shows the setup for such a plane mirror SFP. To reduce the limiting effect of the flatness imperfections, the beam of the probe laser is expanded (La and Lb). To dilute the high demand for precise alignment a SFP with spherical mirror is used. Due to the curved mirror the photons are redirected to stay inside the SFP. For a plane mirror already a small deviation of the parallel aligned mirrors lets the photons leave the cavity after a couple of round trips. In case (A) of Fig. A such a spherical SFP is shown. The best results are obtained if the mirror are positioned such that their distance L is =R (confocal). Since mirror M1 acts as concave lens the mode matching lens (L1) compensates this effect. As for all spherical cavities higher transverse modes can occur, thereby falsifying the measurement. The transverse modes vanish if the distance L is exactly aligned to R. For this purpose M1 is mounted onto a precise translation element which can be varied by a few mm.