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We study analytically the intensity phase coherence in a three-mode Fabry-Pérot laser. We consider in detail the case of a central mode with maximum gain and two side modes with smaller but equal gains. This laser is characterized by three relaxation oscillation frequencies ΩR″≳ΩL1″≳ΩL2″. In the framework of a linearized theory, the laser dynamics...
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... explore new features, we recall that if 1 the ratio ( ⍀ R Ј / ⍀ L Ј ) 2 varies between 7 and 5 for w increasing from 1 to infinity. However, if ␥ Ͻ 1 the ratios between the various frequencies may vary in a much larger range. The ratios A ϭ ( ⍀ R Љ / ⍀ L Љ 1 ) 2 , B ϭ ( ⍀ R Љ / ⍀ L Љ 2 ) 2 , and C ϭ ( ⍀ L Љ 1 / ⍀ L Љ 2 ) 2 are plotted in Fig. 2 as functions of ␥ for w Ϫ w 3 ϭ 1 ͑ solid curves ͒ and for w → ρ ͑ dashed curves ͒ . For ␥ → 1 we have C → 1; in addition, A → B → 5 for w → ρ while A → B → 7 for w → 1. For ␥ Ͻ 1, C is slightly greater than 1 but A and B can be made arbitrarily large by decreasing ␥ , as appears in Fig. 2. In Fig. 3 we draw ( ⍀ R Љ / ⍀ L Љ 1 ) 2 versus w Ϫ w 3 for different ␥ . For ␥ ϭ 1, the ratio ( ⍀ R Љ / ⍀ L Љ 1 ) 2 can vary only between 7 and 5 ͑ dashed line ͒ . For ␥ Ͻ 1 the range in which ( ⍀ R Љ / ⍀ L Љ 1 ) 2 varies is much wider and the value of ( ⍀ R Љ / ⍀ L Љ 1 ) 2 can be chosen by selecting appropriate values of w and ␥ . For instance, we find that ( ⍀ R Љ / ⍀ L Љ 1 ) 2 ϭ 9 for the parameters listed in Table I. When ⍀ R Љ ϭ 3 ⍀ L Љ 1 one may expect in experiments with external modulations a resonant effect such as a small amplitude modulation at ⍀ L Љ 1 leading to a large amplitude change at ⍀ R Љ due to third harmonic generation. Similar curves for ( ⍀ R Љ / ⍀ L Љ 2 ) 2 and ( ⍀ L Љ 1 / ⍀ L Љ 2 ) 2 are plotted in Figs. 4 and 5, respectively. We find, for instance, that ⍀ R Љ ϭ 3 ⍀ L Љ 2 for ͑␥ , w Ϫ w 3 ͒ ϭ ͑ 0.9, 1.3563 ͒ and ⍀ R Љ ϭ 4 ⍀ L Љ 2 for the parameters listed in Table II. For these pairs of pump and gain, a large amplitude response at ⍀ R Љ may be induced by a small amplitude periodic modulation at the lower frequency via harmonic generation. Let us empha- size that this kind of resonant response does not happen for ␥ ϭ 1 and hence is specific for the laser with nonequal gains. This analysis is easily completed by deriving the eigenvectors associated with the eigenvalues ͑ 30 ͒ – ͑ 32 ͒ . They are given ...
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Citations
... [9] The effects of hysteresis phenomena on the characteristics of pulses are also investigated in a passively mode-locked fiber laser. [10] Another important aspect of mode-locking is the formation of bifurcations which have commonly occurred in freerunning mode-locked lasers, [11,12] regenerative amplifiers, [13] and injection-locked laser amplifiers. [14,15] The different kinds of saddle-node (SN), Hopf, tongue, and pitchfork bifurcations (optical bistabilities) have vastly been exploited as high speed optical switches, [15,16] optical memories, [17] and flip-flop or optical logics. ...
... where D 0 /D 0 is the static population inversion ratio of threemode to single-mode lasers. [1] So far, we have introduced seven equations (6)- (12) for the motion of nine variables α L , α C , α R , x, D 1 , δ L , δ C , δ R , and δ D . If the complex conjugates of Eqs. ...
... In contrast to the former case, the Maxwell-Bloch equations of motion (8)- (14) now demonstrate the much complicated solutions in the form of bifurcations that are in complete agreement with the previous theoretical and experimental results. [11][12][13][14][15] The cavity electric field bifurcations originate from the atomic population inversion bifurcation. The fifteenth-order equation (25) is numerically solved to describe the motion of static population inversion component D 0 /D 0 in detail. ...
The random oscillations of many longitudinal modes are inevitable in both class −A and −B lasers due to their broadened atomic bandwidths. The destructive superposition of electric field components that are incoherently oscillating at the different longitudinal modes can be converted into a constructive one by using the mode-locking technique. Here, the Maxwell—Bloch equations of motion are solved for a three-mode class-B laser under the mode-locking conditions. The results indicate that the cavity oscillating modes are shifted by changing the laser pumping rate. On the other hand, the frequency components of cavity electric field simultaneously form the various bifurcations. These bifurcations satisfy the well-known mode-locking conditions as well. The atomic population inversion forms only one bifurcation, which is responsible for shaping the cavity electric field bifurcations.
We apply the multiple time scale method to perform a nonlinear analysis of the Tang, Statz, and deMars rate
equations, which describe an N-mode Fabry-Perot laser in which all modes have an equal gain and a large loss
rate. In addition to the two relaxation oscillation frequencies VL and VR known from the linearized analysis,
we find the four frequencies 2VL , VR6VL , and 2VR . The signature of antiphased dynamics for the new
frequencies is that there are no relaxation oscillations in the total intensity at VR6VL . The laser steady state
is shown to be stable, being characterized by damping rates derived explicitly. Relations among these damping
rates are obtained. We also study the role played by the initial condition in governing the manifestation of the
antiphase dynamics and the relative magnitude of the modal intensity power spectrum peak heights at the two
main frequencies VL and VR . Finally, we deal with the resonant case VR52VL . In this case, inphased
dynamics is shown to appear at 2VR , instead of at VR .
We generalize the reference model [Optics Comm. 107 (1994) 245] of a multimode laser to include an arbitrary loss rate k. As a result, the decay rates and the oscillation frequencies of the laser relaxation are both k-dependent. Perfect antiphased dynamics is shown to remain, no matter what value is assumed by k. However, depending on k, the oscillatory component of the dynamics may be quenched either partially or completely. For a given k, there exists a cut-off mode number and a set of critical laser parameters separating domains where oscillations occur from domains where there are no oscillations.
We present an asymptotic study of a three-mode Fabry - Perot laser with arbitrary relative modal gains in the rate equation limit. Dynamical modes are defined as the eigenvectors of the stability or Jacobian matrix. The associated eigenvalues are the decay rates and the relaxation oscillation frequencies. We show that if the modal gains are not equal, the ratio of the relaxation oscillation frequencies may display rational ratios which will lead to resonances. We classify the various states of the modal field intensities as in-phase, partial and perfect antiphase and find universal relations between the peak heights in the power spectra of the total and of the modal intensities at each of the relaxation oscillation frequencies. Our theoretical results are confirmed by numerical computation using the full rate equations. Experimental results obtained for the noise spectrum of an LNP microchip laser fully support our theoretical results. We also conjecture some properties of lasers operating in an arbitrary N-mode regime.
Quantum wires were formed in the 6-period InAs/In0.52Al0.48As structure on InP(0 0 1) grown by molecular beam epitaxy. The structure was characterized with transmission electron microscopy. It was found that the lateral periodic compositional modulation in the QWR array was in the direction and layer-ordered along the specific orientation deviating from the [0 0 1] growth direction by about 30°. This deviating angle is consistent with the calculation of the distribution of elastic distortion around quantum wires in the structure using the finite element technique.
We measure the power spectral densities, at relaxation oscillation frequencies, of the individual longitudinal modes and the total intensity of a Nd-doped yttrium aluminum garnet laser at low pumping rate. We then test relationships between these quantities that are derived from the modal rate equations theory. The theoretical relations for the two mode case are confirmed by the experiment. However, in the three-mode regime, theory and experiments do not agree well.
We discuss the problem of excess noise in lasers of different dynamical classes, as well as adequate models for the description of such noise. It is shown that the excess noise in lasers is caused by mode-mode coupling. The linear coupling leads to the phenomenon of excess noise in the narrow sense (Petermanns excess noise), while the nonlinear mode coupling is the universal mechanism for excess noise of dynamical nature. It is shown that the theory of excess noise in class-B lasers does not require new approaches and can be developed on the basis of models with adiabatically eliminated polarization obtained in a standard way.
Noise reduction in a multiwavelength distributed Bragg reflector fiber laser was demonstrated. A 20 dB reduction of in-phase intensity noise was achieved by using negative feedback to modulate the drive current of the laser pump diode. Strategies for reducing antiphase noise components are discussed.
