Experimental study of stochastic phenomena in vertical cavity lasers

1
The vertical cavity laser (VCSEL)
Istituto Nazionale
Ottica Applicata
Largo Enrico Fermi 6
50125 Firenze (Italy)
www.inoa.it

• Giovanni Giacomelli (INOA), giacomelli_at_inoa.it
• COWORKERS
• Sylvain Barbay, LPN-CNRS, Marcoussis (France)
• Vyacheslav Chizhevsky, B.I. Stepanov Institute of
  Physics, Minsk (Belarus)
• Stefano Lepri, INFM, UdR Firenze (Italy)
• Francesco Marin, Physics Dept., Univ. of Firenze
  (Italy)
• Ivan Rabbiosi, ENS, Lyon (France)
• Alessandro Zavatta, Systems and Informatics
  Dept., Univ. of Firenze (Italy)

• Wavelength near IR (800 nm),.....
• Output power mW....
• Single longitudinal mode, multiple transverse
  modes (short and wide cavity High Fresnel
  number)
• TWO LINEAR polarizations emission (symmetrical
  cavity)
• GOOD beam quality
• High frequency modulation

Experimental study of stochastic phenomena in
vertical cavity lasers
Polarization bistability and noise driven
polarization dynamics
Polarization bistability in VCSELs
Experimental setup
2 polarization directions selected by the crystal
axis AND symmetrical cavity (circular,
rectangular) gt laser action on both
polarizations BUT impurities, inhomogeneities
ONE polarization lasing at threshold .....for
particular values of the pump current, the
symmetry can be restored POLARIZATION
BISTABILITY!
Remark very stable system (hour), fast
timescales (ms) gt GOOD STATISTICS
Reduction to two level residence time
distributions (Kramers statistics)
Kramers rates, changing the added noise power
Scanning the pump current across a bistable
point...
Average output frequency and effective diffusion
coefficient
Periodic modulation I stochastic resonance
Periodic modulation II phase synchronization
Time series SIN input

• Definition of phase f of a (real) signal x(t)
  with the Hilbert transform H
• X(t) x(t) i (Hx)(t) A(t) exp( if (t) )
• (in the case of sinusoidal signal, f Wt)
• Study of the phase difference f f OUT - f IN
• Feasible with experimental (or numerical...) time
  series

Noise increases from bottom to top. Inset at the
resonant noise value, for a small modulation
amplitude.
Response at the modulation frequency. Curve
linear response theory with experimentally
measured parameters

Time series (noise increases from bottom to top)
SIN filled symbols SQR empty symbols. ASQR
ASIN/sqrt(2)
ASR time series and in-out correlation
Vibrational resonance

Random modulation aperiodic stochastic resonance
Key references http//www.inoa.it/gianni
IDEA (partially....) replacing the white,
gaussian noise with high frequency modulation

• Polarization bistability Quantum Semiclass.
  Opt.
• 
  10, 469 (1998)
• Stochastic resonance - PRL 82, 675 (1999)
• - PRE 61, 157 (2000)
• Aperiodic SR - PRL 85, 4652 (2000)
• - PRE 63, 051110-1 (2001)
• Phase synchronization PRE 68, 020101(R) (2003)
• Vibrational resonance PRL 91, 220602 (2003)

• A different input signal? Bit-stream
• Random sequence of low (0) and high (1)
  level amplitudes, with a fixed rate (clock)
• Advantages
• Typical digital communication signal
  (applications...)
• Analytical evaluation of statistical indicators

Dots experimental correlations Boxes analytic
theory with experimentally measured
rates

Left laser response for increasing HF
modulation amplitude right increasing the added
noise power (SR)