Periods of Energy Exchange Under the Mutual Effects of Four-Wave Mixing, Self-Phase Modulation and Cross-Phase Modulation

Kasapeteva Z., Dakova-Mollova A., Dakova D., Kovachev K., Kovachev L., Biswas A.

Optics, cilt.7, sa.2, 2026 (ESCI, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/opt7020027
  • Dergi Adı: Optics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Directory of Open Access Journals
  • Anahtar Kelimeler: cross-phase modulation, four-wave mixing, nonlinear ordinary differential equations, periods of energy exchange, self-phase modulation
  • Karadeniz Teknik Üniversitesi Adresli: Hayır

Özet

In the present work a new regime of periodical energy exchange between pump, signal and idler waves, under the influence of the process of four-wave mixing (FWM), with additional consideration of the effects of self-phase modulation (SPM) and cross-phase modulation (XPM), is presented. In our previous papers a theoretical model which successfully describes the amplification and periodic energy exchange between the three optical waves in CW regime of laser source propagation (short-cut equations) was developed. Exact analytical solutions, describing the periodic changes in the intensities of pump, signal and idler waves, were found and expressed by the Jacobi elliptic functions. The period of the energy exchange between the waves can be presented by elliptic integral of the first kind. In the current research, the periods of energy exchange between the pump, signal and idler waves in the process of FWM, additionally taking into account the effects of SPM and XPM, are investigated. A comparison between the obtained results has been made. It is shown that the effects of self-phase modulation and cross-phase modulation increase the period of energy exchange.