Observation of a Discrete Family of Dissipative Solitons in a Nonlinear Optical System

We report on the observation of a discrete family of spatial dissipative solitons in a simple optical pattern forming system, which is based on a modified single-mirror feedback arrangement. After a pitchfork bifurcation the system possesses two (nearly) equivalent coexisting states of different polarizations. The spatial solitons correspond to excursions from one of the two states serving as a background state towards the other one. The members of the soliton family differ in the number of high-amplitude radial oscillations. The observations are in good agreement with numerical simulations and general expectations for dissipative solitons.

Figure 1

Schematic experimental setup. $\lambda /8$: eighth-wave plate; M: mirror; PA: polarization analyzer; CCD: charge-coupled device camera.

Figure 2

Switching sequence of a solitary structure. Polarization analyzer aligned for suppression of the background beam in the detection branch: (a) background beam; (b) ignition of a soliton with circularly polarized addressing beam; (c) stable soliton with addressing beam switched off; (d) erasure of soliton with addressing beam of opposite circular polarization; (e) background beam. Parameters: mirror distance $d=120\mathrm{mm}$; buffer gas pressure $p_{N_2}=300\mathrm{mbar}$; cell temperature $T=321.8°\mathrm{C}$; laser detuning $\Delta =16.2\mathrm{GHz}$; laser power $P_{\mathrm{las}}=219\mathrm{mW}$; rotation of the slow axis of the eighth-wave plate with respect to input polarization $\Phi =4°{30}^{\prime }$.

Figure 3

Experimentally observed solitons. Parameters as in Fig. 2 with the exception of the replacements $T=327.3°\mathrm{C}$, $\Delta =14.6\mathrm{GHz}$, $P_{\mathrm{las}}=165\mathrm{mW}$, $\Phi =7°{00}^{\prime }$ in (b) to (d).

Figure 4

Numerically obtained structures. First column: Transmitted intensity in the field component orthogonal to the polarization of the background beam. Second column: Orientation distributions corresponding to first column. Orientation set to zero at a radius of 3 mm to simulate depolarization of the vapor at the cell walls in simulations with Gaussian beam input. Third column: Orientation distributions in simulations with plane wave input. Fourth column: Horizontal cuts through orientation distribution; ordinate scale extends from $-0.3$ to 0.3. First row: Slightly patterned state with negative orientation. Second to fifth rows: Solitons of different orders. Sixth row: Slightly patterned state with positive orientation. Parameters: $d=120\mathrm{mm}$, ground state relaxation rate $\gamma =200{\mathrm{s}}^{-1}$, relaxation rate of optical coherences ${\Gamma }_2=9.94\times {10}^9{\mathrm{s}}^{-1}$, $\Delta =11.9\mathrm{GHz}$, diffusion constant $D=255{\mathrm{mm}}^2{\mathrm{s}}^{-1}$, particle density $N=4.65\times {10}^{19}{\mathrm{m}}^{-3}$, length of heated zone $L=15\mathrm{mm}$, mirror reflectivity $R=99.5\%$. (a)–(l) pump rate in beam center $P_0=180\times {10}^3{\mathrm{s}}^{-1}$, beam radius $w_0=1.89\mathrm{mm}$ except (e),(k) $w_0=2.2\mathrm{mm}$, (m)–(x) $P_0=130\times {10}^3{\mathrm{s}}^{-1}$ except (n),(t) $P_0=150\times {10}^3{\mathrm{s}}^{-1}$; (a),(g),(c),(i),(f),(l) $\Phi =15°{30}^{\prime }$; (b),(h) $\Phi =19°{30}^{\prime }$; (d),(j),(e),(k) $\Phi =9°{30}^{\prime }$; (m),(s),(o),(u),(r),(x) $\Phi =13°{00}^{\prime }$; (n),(t) $\Phi =21°{00}^{\prime }$; (p),(v) $\Phi =8°{00}^{\prime }$; (q),(w) $\Phi =5°{00}^{\prime }$.