Abstract

The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two- and three-mode systems of differential equations coupled via quadratic χ2 type nonlinearity as well as two-mode systems coupled via cubic χ3 type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum- and difference-frequency generation, polarization dynamics, parity-time dynamics, and optical processing applications.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

5 November 2015: A correction was made to the funding section.


More Like This
Harmonic and supercontinuum generation in quadratic and cubic nonlinear optical media

S. Wabnitz and V. V. Kozlov
J. Opt. Soc. Am. B 27(9) 1707-1711 (2010)

Coupled-mode theory for microresonators with quadratic nonlinearity

Dmitry V. Skryabin
J. Opt. Soc. Am. B 37(9) 2604-2614 (2020)

Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

Tobias Hansson, François Leo, Miro Erkintalo, Jessienta Anthony, Stéphane Coen, Iolanda Ricciardi, Maurizio De Rosa, and Stefan Wabnitz
J. Opt. Soc. Am. B 33(6) 1207-1215 (2016)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (43)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription