Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Time evolution of Nd:YAG laser-induced plasma from GdBa2Cu3O7 high-Tc superconductor

In order to characterise the laser ablation process from high-Tc superconductors, the time evolution of plasma produced by a Q-switching Nd:YAG laser from a GdBa2Cu3O7 superconducting sample has been studied using spectroscopic and ion-probe techniques. It has been observed that there is a fairly large delay for the onset of the emission from oxide species in comparison with those from atoms and ions of the constituent elements present in the plasma. Faster decay occurs for emission from oxides and ions compared with that from neutral atoms. These observations support the view that oxides are not directly produced from the target, but are formed by the recombination process while the plasma cools down. Plasma parameters such as temperature and velocity are also evaluated.

Hopf bifurcation in parallel polarized Nd:YAG laser

Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.

Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal

The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Influence of pulse repetition rate of Er : YAG laser and dentin depth on tensile bond strength of dentin-resin interface

The study evaluated the in vitro influence of pulse-repetition rate of Er:YAG laser and dentin depth on tensile bond strength of dentin-resin interface. Dentin surfaces of buccal or lingual surfaces from human third molars were submitted to tensile test in different depths (superficial, 1.0 and 1.5 mm) of the same dental area, using the same sample. Surface treatments were acid conditioning solely (control) and Er:YAG laser irradiation (80 mJ) followed by acid conditioning, with different pulse-repetition rates (1, 2, 3, or 4 Hz). Single bond/Z-250 system was used. The samples were stored in distilled water at 37 degrees C for 24 h, and then the first test (superficial dentine) was performed. The bond failures were analyzed. Following, the specimens were identified, grounded until 1.0- and 1.5-mm depths, submitted again to the treatments and to the second and, after that, to third-bond tests on a similar procedure and failure analysis. ANOVA and Tukey test demonstrated a significant difference (p < 0.001) for treatment and treatment X depth interaction (p < 0.05). The tested depths did not show influence (p > 0.05) on the bond strength of dentin-resin interface. It may be concluded that Er:YAG laser with 1, 2, 3, or 4 Hz combined with acid conditioning did not increase the resin tensile bond strength to dentin, regardless of dentin depth. (C) 2007 Wiley Periodicals, Inc.

Nitric oxide detection in cell culture exposed to LPS after Er:YAG laser irradiation

P>Aim To evaluate in vitro the effect of calcium hydroxide [Ca(OH)(2)] and Er:YAG laser on bacterial endotoxin [also known as lipopolysaccharide (LPS)] as determined by nitric oxide (NO) detection in J774 murine macrophage cell line culture. Methodology Samples of LPS solution (50 mu gmL-1), Ca(OH)(2) suspension (25 mg mL-1) and LPS suspension with Ca(OH)(2) were prepared. The studied groups were: I - LPS (control); II - LPS + Ca(OH)(2); III - LPS + Er:YAG laser (15 Hz 140 mJ); IV - LPS + Er:YAG laser (15 Hz 200 mJ); V - LPS + Er:YAG laser (15 Hz 250 mJ), VI - Pyrogen-free water; VII - Ca(OH)(2). Murine macrophage J774 cells were plated and 10 mu L of the samples were added to each well. The supernatants were collected for NO detection by the Griess reaction. Data were analysed statistically by one-way anova and Tukey`s test at 5% significance level. Results The mean and SE (in mu mol L-1) values of NO release were: I - 10.48 +/- 0.58, II - 6.41 +/- 0.90, III - 10.2 +/- 0.60, IV - 8.35 +/- 0.40, V - 10.40 +/- 0.53, VI - 3.75 +/- 0.70, VII - 6.44 +/- 0.60; and the values for the same experiment repeated after 1 week were: I - 21.20 +/- 1.50, II - 9.10 +/- 0.60, III - 19.50 +/- 1.00, IV - 18.50 +/- 0.60, V - 21.30 +/- 0.90, VI - 2.00 +/- 0.20, VII - 6.80 +/- 1.70. There was no significant difference (P > 0.05) between the control and the laser-treated groups (III, IV and V), or comparing groups II, VI and VII to each other (P > 0.05). Group I had significantly higher NO release than group II (P < 0.05). Groups II and VI had similar NO release (P > 0.05). Conclusions Calcium hydroxide inactivated the bacterial endotoxin (LPS) whereas none of the Er:YAG laser parameter settings had the same effectiveness.

SEM analysis of enamel surface treated by Er : YAG laser: Influence of irradiation distance

Background: Depending on the distance of laser tip to dental surface a specific morphological pattern should be expected. However, there have been limited reports that correlate the Er:YAG irradiation distance with dental morphology. Purpose: To assess the influence of Er:YAG laser irradiation distance on enamel morphology, by means of scanning electron microscopy (SEM). Methods: Sixty human third molars were employed to obtain discs (congruent to 1 mm thick) that were randomly assigned to six groups (n = 10). Five groups received Er:YAG laser irradiation (80 mJ/2 Hz) for 20 s, according to the irradiation distance: 11, 12, 14, 16, or 17 mm. and the control group was treated with 37% phosphoric acid for 15 s. The laser-irradiated discs were bisected. One hemi-disc was separated for superficial analysis without subsequent acid etching, and the other one, received the phosphoric acid for 15 s. Samples were prepared for SEM. Results: Laser irradiation at 11 and 12 min provided an evident ablation of enamel, with evident fissures and some fused areas. At 14, 16 and 17 mm the superficial topography was flatter than in the other distances. The subsequent acid etching on the lased-surface partially removed the disorganized tissue. Conclusions: Er:YAG laser in defocused mode promoted slight morphological alterations and seems more suitable for enamel conditioning than focused irradiation. The application of phosphoric acid on lased-enamel surface, regardless of the irradiation distance, decreased the superficial irregularities.

Influence of energy and pulse repetition rate of Er : YAG laser on enamel ablation ability and morphological analysis of the laser-irradiated surface

Objective: To assess the influence of energy and pulse repetition rate of Er:YAG laser on the enamel ablation ability and substrate morphology. Methods: Fifteen crowns of molars were sectioned in four fragments, providing 60 samples, which were ground to flatten the enamel surface. The initial mass was obtained by weighing the fragments. The specimens were hydrated for I h, fixed, and a 3-mm-diameter area was delimited. Twelve groups were randomly formed according to the combination of laser energies (200, 250, 300, or 350 mJ) and pulse repetition rates (2, 3, or 4 Hz). The final mass was obtained and mass loss was calculated by the difference between the initial and final mass. The specimens were prepared for SEM. Data were submitted to ANOVA and Scheffe test. Results: The 4 Hz frequency resulted in higher mass loss and was statistically different from 2 and 3 Hz (p < 0.05). The increase of frequency produced more melted areas, cracks, and unselective and deeper ablation. The 350 mJ energy promoted greater mass loss, similar to 300 mJ. Conclusions: The pulse repetition rate influenced more intensively the mass loss and morphological alteration. Among the tested parameters, 350 mJ/3 Hz improved the ability of enamel ablation with less surface morphological alterations. (C) 2007 Wiley Periodicals, Inc. J Biomed Mater Res.

Shear strength of the bond to primary dentin: influence of Er:YAG laser irradiation distance

The aim of this study was to assess in vitro the influence of Er:YAG laser irradiation distance on the shear strength of the bond between an adhesive restorative system and primary dentin. A total of 60 crowns of primary molars were embedded in acrylic resin and mechanically ground to expose a flat dentin surface and were randomly assigned to six groups (n = 10). The control group was etched with 37% phosphoric acid. The remaining five groups were irradiated (80 mJ, 2 Hz) at different irradiation distances (11, 12, 16, 17 and 20 mm), followed by acid etching. An adhesive agent (Single Bond) was applied to the bonding sites, and resin cylinders (Filtek Z250) were prepared. The shear bond strength tests were performed in a universal testing machine (0.5 mm/min). Data were submitted to statistical analysis using one-way ANOVA and the Kruskal-Wallis test (p < 0.05). The mean shear bond strengths were: 7.32 +/- 3.83, 5.07 +/- 2.62, 6.49 +/- 1.64, 7.71 +/- 0.66, 7.33 +/- 0.02, and 9.65 +/- 2.41 MPa in the control group and the groups irradiated at 11, 12, 16, 17, and 20 mm, respectively. The differences between the bond strengths in groups II and IV and between the bond strengths in groups II and VI were statistically significant (p < 0.05). Increasing the laser irradiation distance resulted in increasing shear strength of the bond to primary dentin.

Influence of water flow rate on shear bond strength of resin composite to Er : YAG cavity preparation

Purpose: To evaluate in vitro the influence of water flow rate on shear bond strength of a resin composite to enamel and dentin after Er:YAG cavity preparation. Methods: Ten bovine incisors were selected and roots removed. Crowns were sectioned in four pieces, resulting in 40 samples that were individually embedded in polyester resin (n=10), and ground to plane the enamel and expose the dentin. The bonding site was delimited and samples were randomly assigned according to cavity preparation: (1) Er:YAG/1.0 mL/minute; (2) Er:YAG/1.5 mL/minute; (3) Er:YAG/2.0 mL/minute and (4) High speed handpiece/bur (control group). Samples were fixed to a metallic device, where composite resin cylinders were prepared. Subsequently, they were stored for 24 hours and subjected to a shear bond strength test (500N at 0.5 mm/minute). Results: Means (MPa) were: enamel: 1: 12.8; 2: 16.8; 3: 17.5; 4: 36.0 and Dentin: 1: 13.6; 2: 18.7; 3: 12.1; 4: 21.3. Data were submitted to ANOVA and Tukey`s test. Adhesion to enamel was more efficient than for dentin. The cavities prepared with conventional bur (control) presented higher statistically significant bond strength values (P<0.05) than for Er:YAG laser for both enamel and dentin. No significant differences were observed between water flow rates employed during enamel ablation. For dentin, the shear bond strength of 2.0 mL/minute water flow rate was lower than for 1.5 mL/minute and 1.0 mL/minute rates. The Er:YAG laser adversely affected shear bond strength of resin composite to both enamel and dentin, regardless of the water flow rate used.

Adhesion to Er : YAG laser-prepared dentin after long-term water storage and thermocycling

This in vitro study evaluated the microtensile bond strength of a resin composite to Er:YAG-prepared dentin after long-term storage and thermocycling. Eighty bovine incisors were selected and their roots removed. The crowns were ground to expose superficial dentin. The samples were randomly divided according to cavity preparation method (I-Er:YAG laser and II-carbide bur). Subsequently, an etch & rinse adhesive system was applied and the samples were restored with a resin composite. The samples were subdivided according to time of water storage (WS)/number of thermocycles (TC) performed: A) 24 hours WS/no TC; B) 7 days WS/500 TC; C) 1 month WS/2,000 TC; D) 6 months WS/12,000 TC. The teeth were sectioned in sticks with a cross-sectional area of 1.0-mm(2), which were loaded in tension in a universal testing machine. The data were subjected to two-way ANOVA, Scheffe and Fisher`s tests at a 5% level. In general, the bur-prepared group displayed higher microtensile bond strength values than the laser-treated group. Based on one-month water storage and 2,000 thermocycles, the performance of the tested adhesive system to Er:YAG-laser irradiated dentin was negatively affected (Group IC), while adhesion of the bur-prepared group decreased only within six months of water storage combined with 12,000 thermocycles (Group IID). It may be concluded that adhesion to the Er:YAG laser cavity preparation was more affected by the methods used for simulating degradation of the adhesive interface.

Nd : YAG laser clinical assisted in class II furcation treatment

The Nd:YAG laser efficacy associated with conventional treatment for bacterial reduction has been investigated throughout literature. The purpose of this study was to evaluate the bacterial reduction after Nd:YAG laser irradiation associated with scaling and root planning in class II furcation defects in patients with chronic periodontitis. Thirty-four furcation lesions were selected from 17 subjects. The control group received conventional treatment, and the experimental group received the same treatment followed by Nd:YAG laser irradiation (100 mJ/pulse; 15 Hz; 1.5 W, 60 s, 141.5 J/cm(2)). Both treatments resulted in improvements of most clinical parameters. A significant reduction of colony forming unit (CFU) of total bacteria number was observed in both groups. The highest reduction was noted in the experimental group immediately after the treatment. The number of dark pigmented bacteria and the percentage of patients with Porphyromonas gingivalis, Prevotella intermedia, and Actinobacillus actinomycetemcomitans reduced immediately after the treatment and returned to values close to the initial ones 6 weeks after the baseline for both groups. The Nd:YAG laser associated with conventional treatment promoted significant bacterial reduction in class II furcation immediately after irradiation, although this reduction was not observed 6 weeks after the baseline.