Optically Injected Solid-State Lasers – Experiment

This experiment was performed at the University of Helsinki, Finland by Simo Valling, Thomas Fordell and Asa Lindberg [1,2]. The experimental setup of the optically injected Nd:YVO4 solid state laser system can be seen in Fig. 1. Two 1064 nm solid state Nd:YVO4 lasers were operated in a master-slave configuration. The Nd:YVO4 crystals (CASIX) are 1 mm thick with 1% Nd3+ atomic doping. The laser cavity was formed by HR coating on the front surface and 5% output coupling at the end facet. The laser crystals were pumped with 150 mW diode lasers (SDL) operating at 809 nm. The pump power was low enough to ensure single mode operation. Both the pump and laser polarization were along the c-axis of the crystal. Faraday isolators were used to block feedback to the pump lasers. The master laser crystal mount could be temperature controlled using a Peltier element. Interference filters removed excess pump light from the 1064 nm beams. Faraday isolators made the coupling between master and slave unidirectional and prevented unwanted feedback. Light from the master laser was injected into the slave via an acousto-optic modulator (AOM) and the relative injection power measured on the detector PD1. The beat frequency between the two lasers was measured on a 400 MHz detector (PD3).  The optical input (PD2) of a Tektronix CSA 7404 oscilloscope was used to measure the intensity time-series of the slave laser.

Fig. 1. Experimental setup: LD, laser diode; FI, Faraday isolator; TEC, temperature control; IF, interference filter; BS, beam splitter; AOM, acousto-optic modulator; FP, Fabry-Pérot interferometer; PD, photodetectors. Figure reproduced from [1].
Fig. 1. Experimental setup: LD, laser diode; FI, Faraday isolator; TEC, temperature control; IF, interference filter; BS, beam splitter; AOM, acousto-optic modulator; FP, Fabry-Pérot interferometer; PD, photodetectors. Figure reproduced from [1].

The power of the injected beam was modulated using the AOM and the temperature of the master laser was tuned with the Peltier element to control the frequency detuning between the lasers (Δω). The maximum range over which the frequency is shifted is approximately 32 MHz. This is very narrow compared to the mode spacing so no mode hopping occurs.

For a fixed detuning, long time-series data of the laser intensity were recorded as the injection strength (K) was slowly increased from zero until injection locking was achieved. This injection sweep was repeated at a large number of fixed frequency detuning values (Δω).

Analysis of this system has been communicated in a number of publications. Intensity maxima (Fig. 2a) were used to compare with theoretical bifurcation diagrams (Fig. 2b) [1].

Fig. 2. (a) Peak normalised intensity and (b) theoretical bifurcation diagram for the optically injected solid-state laser system for varying injection strength and frequency detuning.
Fig. 2. (a) Peak normalised intensity and (b) theoretical bifurcation diagram for the optically injected solid-state laser system for varying injection strength and frequency detuning.

Experimental bifurcation diagrams have also been generated based on the characteristics of the observed power time series [3].

Fig. 3. Experimental bifurcation diagram from the optically injected solid-state laser system for varying injection strength and frequency detuning [3].
Fig. 3. Experimental bifurcation diagram from the optically injected solid-state laser system for varying injection strength and frequency detuning [3].

An automated correlation dimension protocol has been implemented to map the complexity of the system state space [4].

Fig. 4. Correlation dimension map in the (K, Δω) plane for experimental data. Different dynamical region are identified as I: Locked (no data), II: Periodic (CD = 1), III: ‘Spiky’ Output (CD < 1), IV: Chaotic (CD > 2), V: Noisy (CD = ∞) [4]. Note that since this map was published an error in the automated process was discovered which meant that much of the black region V should actually should a CD ~ 1. The decreased SNR in this region caused the erroneous identification.
Fig. 4. Correlation dimension map in the (K, Δω) plane for experimental data. Different dynamical region are identified as I: Locked (no data), II: Periodic (CD = 1), III: ‘Spiky’ Output (CD < 1), IV: Chaotic (CD > 2), V: Noisy (CD = ∞) [4]. Note that since this map was published an error in the automated process was discovered which meant that much of the black region V should actually should a CD ~ 1. The decreased SNR in this region caused the erroneous identification.

 

Information about the data available

Experimental data can be downloaded here

Two 1064 nm solid state Nd:YVO4 lasers were operated in a master-slave configuration. The laser crystals were pumped with 150 mW diode lasers (SDL) operating at 809 nm. The pump power was low enough to ensure single mode operation. Light from the master laser was injected into the slave via an acousto-optic modulator (AOM) and the relative injection power measured on a detector. The temperature of the master laser was tuned with the Peltier element to control the frequency detuning between the lasers. The optical input of a Tektronix CSA 7404 oscilloscope was used to measure the intensity time-series of the slave laser under different combinations of injection strength and frequency detuning. This dataset consists of 55,440 files containing a single time series corresponding to a particular combination of injection strength and frequency detuning. The value of injection and detuning are specified in the file attributes ‘var1’ and ‘var2’. The filename also contains the detuning value and injection index.

 

 

References

[1] S. Valling, T. Fordell and A. M. Lindberg, “Maps of the dynamics of an optically injected solid-state laser”, Phys. Rev. A 72, 033810 (2005).
[2] S. Valling, T. Fordell and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser”, Optics Communications 254 (4-6), 282 (2005).
[3] S. Valling, B. Krauskopf, T. Fordell, A. M. Lindberg, “Experimental bifurcation diagram of a solid state laser with optical injection”, Optics Communications 271 (2), p.532 (2007).
[4] J. P. Toomey, D. M. Kane, S. Valling and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers”, Optics Express 17 (9), 7592–7608 (April 2009).