investigation of the resonance characteristics of the laser model in dipole
approximation.
Results of solution of symbolic equations for laser model in dipole approximation
at parametric variation of the resonator Q-factor are actual and original under action
of the high optical power, which passes into optical resonator of the laser active
medium. Such a process of Q-factor growth up to ultrahigh values in the optical
resonator (10
8
. . .10
12 ) is observed now in modern experimental QWLD investigations at utilization of disk resonators and on the base of Bragg optical lattices
described in Chaps. 2 and 3.
One of the analysis purposes in this chapter was determination of cause–effect
relations between critical values of Q-factor, at which single-frequency oscillation
stability is lost. These results of numerical calculation are obtained for linearhyperbolic, quadratic-hyperbolic and linear-cubic nonlinearities of the laser.
The investigation method is offered, which allows determination how the laser
AFCs are changed at growth of power level in the optical resonator or in the laser
active medium. We consider quadratic and cubic parametric variation of the resonator Q-factor. As the result of symbolic equation solution, we obtained that at
critical parameters, branches of stable and unstable operation “confluent” into the
single branch, which corresponds to disordered oscillating motions in the wide
frequency region. The determination of critical values of parameters is the significant
contribution in the theory of ultrahigh-Q disk resonators and Bragg resonators.
The main result OF Chap. 3, which is new in the laser analysis, is substantiation
and investigation of DE of fourth order of the laser model in dipole approximation in
quasi-stationary mode with high exceed of pumping over the threshold value. This
approach leads to the new glance, which is suitable for the laser engineer and the
expert in quantum electronics. The new glance at the quantum generator as the
generator with the nonlinear inertial property containing two resonance circuits in
the oscillating system, in contrast to traditional investigation of laser balance kinetic
equations, widens the scientific scope of scientist. During analysis of the quantum
generator, we reduced the complicate laser system with DE of fifth order, which in
the most cases is incomprehensible for students and young scientists, to DE of
second or third order, and we presented analog structures of the laser model.
Mentioned issues significantly facilitate the development of OEO theory, as the
reader will see from the following chapters.
References
1. H. Haken, Laser Theory, Encyclopedia of Physics, vol XXY/2c (Springer, Berlin, 1970)., 2nd
corr.ed., 1984
2. H. Haken, Introduction to lasers and masers (McGraw-Hill, New York, 1971)
3. H. Haken, H. Sauerman, Z. Phys. 173, 261 (1963).; 176, 47 (1963)
4. H. Haug, H. Haken, Theory of noise in semiconductor laser emission. Z. Physik 204,
262 (1967)
5. W.E. Lamb,Theory of optical masers, Jr., Phys. Rev. 134A, 1429 (1964)
200
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .
approximation.
Results of solution of symbolic equations for laser model in dipole approximation
at parametric variation of the resonator Q-factor are actual and original under action
of the high optical power, which passes into optical resonator of the laser active
medium. Such a process of Q-factor growth up to ultrahigh values in the optical
resonator (10
8
. . .10
12 ) is observed now in modern experimental QWLD investigations at utilization of disk resonators and on the base of Bragg optical lattices
described in Chaps. 2 and 3.
One of the analysis purposes in this chapter was determination of cause–effect
relations between critical values of Q-factor, at which single-frequency oscillation
stability is lost. These results of numerical calculation are obtained for linearhyperbolic, quadratic-hyperbolic and linear-cubic nonlinearities of the laser.
The investigation method is offered, which allows determination how the laser
AFCs are changed at growth of power level in the optical resonator or in the laser
active medium. We consider quadratic and cubic parametric variation of the resonator Q-factor. As the result of symbolic equation solution, we obtained that at
critical parameters, branches of stable and unstable operation “confluent” into the
single branch, which corresponds to disordered oscillating motions in the wide
frequency region. The determination of critical values of parameters is the significant
contribution in the theory of ultrahigh-Q disk resonators and Bragg resonators.
The main result OF Chap. 3, which is new in the laser analysis, is substantiation
and investigation of DE of fourth order of the laser model in dipole approximation in
quasi-stationary mode with high exceed of pumping over the threshold value. This
approach leads to the new glance, which is suitable for the laser engineer and the
expert in quantum electronics. The new glance at the quantum generator as the
generator with the nonlinear inertial property containing two resonance circuits in
the oscillating system, in contrast to traditional investigation of laser balance kinetic
equations, widens the scientific scope of scientist. During analysis of the quantum
generator, we reduced the complicate laser system with DE of fifth order, which in
the most cases is incomprehensible for students and young scientists, to DE of
second or third order, and we presented analog structures of the laser model.
Mentioned issues significantly facilitate the development of OEO theory, as the
reader will see from the following chapters.
References
1. H. Haken, Laser Theory, Encyclopedia of Physics, vol XXY/2c (Springer, Berlin, 1970)., 2nd
corr.ed., 1984
2. H. Haken, Introduction to lasers and masers (McGraw-Hill, New York, 1971)
3. H. Haken, H. Sauerman, Z. Phys. 173, 261 (1963).; 176, 47 (1963)
4. H. Haug, H. Haken, Theory of noise in semiconductor laser emission. Z. Physik 204,
262 (1967)
5. W.E. Lamb,Theory of optical masers, Jr., Phys. Rev. 134A, 1429 (1964)
200
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .