Frequency Bistability in a Diode Laser
Using Diffraction Gratings
Forrest Smith1 , Weliton Soares2, Samuel Alves2, Itamar Vidal2, Marcos Oria2
1State University of New York at Geneseo, 2Federal University of Paraiba
Methods and Theory
- The cost and complexity of atomic cells make a mechanical alternative attractive.
- This project uses diffraction gratings, which disperse light at angles dependent on frequency: a feature which is analogous to atomic absorptive behavior.
To achieve and demonstrate frequency bistability in a diode laser system using entirely mechanical means, hopefully improving on the quality of previous successes.
- To ensure noticeably large feedback modulation, two diffraction gratings were used.
- The final change in output direction for some given feedback was theoretically modeled to discover dependencies and inform the placement of gratings in the experimental set up.
Final equation for angle change emerging from two diffraction gratings.
is the first angle of reflection , is the second angle of reflection, is the angle between the diffraction gratings , is the frequency in the laser caused by feedback , kis diffraction order (same for both) , is laser wavelength , c is the speed of light , and is the grating slit width for the second width.
- Bistability is a useful and important phenomenon exploited in experimental physics using diode lasers – Amplitude, Polarization, and Mode bistability are well established
- In 2005 Farias et al. demonstrated the first instance of frequency bistability at UFPB using orthogonal feedback modulated in frequency by atomic cells. 
Example of Atomic Absorption Intensity
Example of Diffraction Grating Transmission Intensity
-1 0 1
- First, theory was confirmed using a simplified system without feedback. Only two diffraction gratings, a 20 µm pinhole, and an intensity detector were used.
- The second diffraction grating face was approximately 35 cm away from the pinhole, which itself was close (~2 cm) from the detector to avoid diffraction.
- By modulating the diode\'s current in this simple system, feedback was emulated, and the laser underwent spatial oscillations along the face of the pinhole, which had a width of 20 µm.
- Pictured below, the green peaks represent the frequency of the laser beam without feedback. The sharp profile implied a very narrow distribution, and thus essentially a singular frequency
- The feedback of diode lasers are sensitive to both temperature, current, and feedback
- Great care was taken to control ambient temperature and cool the diode.
- Current and feedback are both dynamic quantities during this experiment. As such, the relationship between frequency and each value was plotted.
Oscilloscope image without feedback. Yellow line represents scanning cavity length, which causes green spikes where frequency is in resonance.
- With feedback, clearly defined and separated pairs of peaks were produced implying bistability, evolving over time as pictured below.
Oscilloscope image with feedback. Dual peaks where there were singular peaks implies successful oscillation between two frequencies.
- The wave with humps shows the intensity of laser signal passing through the pinhole over time.
- The distinct bumps, separated by long flat periods confirms that the laser is oscillating well past and back over the pinhole, confirming theory.
- The feedback power relationship is crucial for analyzing the dynamics which diffractive feedback produces as the feedback power is a measurable which informs the maximum and minimum dynamics
Conclusions & Prospectives
 B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oria, Physical Review Letters 94, 173902 (2005):
Frequency Bistability of a …
 C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oria, IEEE Journal of Quantum Electronics, Vol. 43, No. 3, March 2007:
Bistability in Semiconductor …
- Bistability appears to have been achieved, with this experiment achieving an oscillatory amplitude of approximately 18.2 MHz in frequency shift. This corresponds, in Eq. , to a value of 1.83x10-9 radians
- However, to confirm this result, a full mathematical model must be created, and predictions therein must be compared to this and replications of this experiment
- Further work can also be done to examine the time evolution of the frequencies in order to characterize the nature of the frequency oscillations.