Theory of ultra-short laser pulses

Haken, Hermann; Ohno, Hajime

doi:10.1016/0030-4018(76)90218-2

Cited by 89 publications

(14 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[7]. This equation is similar to the results of Haken and Ohno [4,5], who interpret the right-hand side in terms of a potential V. Their coefficients are much more complex and do not make apparent the importance of the wave number in determining the direction of the bifurcation.…”

Section: The Simplified Amplitude Equationsupporting

confidence: 80%

See 1 more Smart Citation

Understanding the bifurcation to traveling waves in a class-Blaser using a degenerate Ginzburg-Landau equation

Carr

Erneux

1994

Phys. Rev. A

View full text Add to dashboard Cite

We analyze the Risken-Nummendal -Graham-Haken instability occurring in a homogeneously broadened two-level unidirectional ring laser modeled by the Maxwell-Bloch equations. We investigate the class-B limit of these equations and derive partial differential equations describing the evolution of traveling waves. In particular, we obtain a degenerate Ginzburg-Landau equation with higher-order nonlinearities. We then investigate this equation and determine periodic traveling wave solutions. We discuss their stability in terms of the laser parameters and predict unusual properties for the long-time behavior of the laser. PACS number(s): 42.50.p, 42.55.f, 42.60.MiAT=m, Azz+mzA+m3~A~A where A is the order parameter, T is a slow time, Z is a long space variable and the coe%cients m; are real.An important feature of our problem is the change of the direction of the bifurcation at the minimum of the neutral stability curve. As a result, we obtain a different and more complicated equation of the form

show abstract

Section: The Simplified Amplitude Equationsupporting

confidence: 80%

“…Haken and Ohno [4,5] obtained an equation for the critical bifurcating mode, and found a periodic solution coexisting with the stable steady state. They determine a bifurcation equation for the mode appearing at the Hopf bifurcation but the complexity of the coelcients prevents an analysis of the effects of the particular laser parameters.…”

mentioning

confidence: 99%

Understanding the bifurcation to traveling waves in a class-Blaser using a degenerate Ginzburg-Landau equation

Carr

Erneux

1994

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…The Maxwell-Bloch equations (MBE) in the rotating-wave approximation as a model for a multimode laser (MML) with a homogeneously broadened line were studied in the 1960s ; periodic self-pulsations (self-mode-locking) were then predicted [1][2][3] and more general instabilities were later discovered, including chaotic self-pulsations [4,5] . In the special case where spatial effects are neglected, these equations reduce to the single-mode laser model (SML), which is isomorphic to the Lorenz equations [6][7][8][9][10] .…”

Section: Introductionmentioning

confidence: 99%

Self-pulsing in a Laser Model with Discrete Gain and Loss

Zenteno

1989

Journal of Modern Optics

View full text Add to dashboard Cite

“…We follow the second option here, since this allows us to treat the system as an Ornstein-Uhlenbeck process [25], allowing for particularly easy calculation of the output spectral correlations. It is well known that a Hopf bifurcation exists at a critical pumping strength [26,27], above which the system enters the self-pulsing regime. A linearized fluctuation analysis can be performed below this critical point.…”

mentioning

confidence: 99%

Asymmetric Gaussian harmonic steering in second-harmonic generation

Olsen

2013

Phys. Rev. A

View full text Add to dashboard Cite

Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering. [3,4], is one of the central features which differentiates quantum mechanics from classical physics. It has previously been shown that SHG can be used to produce entangled fields at the two frequencies [5,6], later called "harmonic entanglement" by Grosse et al. [7].EPR expressed the original paradox in terms of position and momentum measurements. The essential step in their argument was to introduce correlated (entangled) states of at least two particles which persisted when the particles become spatially separated. According to EPR, depending on which property of one group of particles that was measured, a prediction with some certainty of the values of physical quantities of the other group of particles could be made. If these properties were represented by noncommuting operators (such as position and momentum), the Heisenberg uncertainty principle could seemingly be violated. The EPR conclusion was therefore that the description of physical reality given by quantum mechanics is not complete.In this Rapid Communication we use the continuousvariable (CV) characterization of EPR first put on a mathematical footing by Reid [8], using quadrature amplitudes, which have the same mathematical properti...

show abstract

Theory of ultra-short laser pulses

Cited by 89 publications

References 15 publications

Understanding the bifurcation to traveling waves in a class-Blaser using a degenerate Ginzburg-Landau equation

Understanding the bifurcation to traveling waves in a class-Blaser using a degenerate Ginzburg-Landau equation

Self-pulsing in a Laser Model with Discrete Gain and Loss

Asymmetric Gaussian harmonic steering in second-harmonic generation

Contact Info

Product

Resources

About