### Abstract

Control of spatial light modulation is an important and useful technique in optical applications ranging from the manipulation of small particles to lithography. We show here that an input phase (amplitude) modulated beam can be effectively converted to an amplitude (phase) modulated output in a frequency converter such as the resonant optical parametric oscillator (OPO). This peculiar conversion property is, however, riot restricted to the OPO but applies to a wide variety of broad area nonlinear cavities. The slowly varying amplitudes of the pump A_{0}(x,t) and signal A_{1}(x,t) fields of a degenerate OPO at resonance, in the mean-field approximation, are described by: ∂_{t}A_{0} = Γ[-A_{0} + Ee ^{μcos(kx)} - A_{1}
^{2}] + i∂_{x} ^{2}A_{0} ∂_{t}A_{1} = -A_{1} + A_{0}A_{1}* + 2i∂_{x}
^{2}A _{1} (1) where Γ is the ratio of the pump and signal cavity decay rates, the parameter n is the (complex) amplitude of the input modulations and is such that |μ| < < 1, while E is the un-modulated amplitude of the external pump field. Perturbative calculations show that full phase (amplitude) to amplitude (phase) modulation conversion from the pump to the signal field is achieved for a modulation wavevector k_{c} given by k_{c} ^{2} = √Γ(E-1) (k_{c}
^{2} = √ΓE)

Original language | English |
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Title of host publication | EQEC '05. European Quantum Electronics Conference, 2005. |

Place of Publication | Piscataway, NJ |

Publisher | IEEE |

Number of pages | 1 |

ISBN (Print) | 0780389735, 9780780389731 |

DOIs | |

Publication status | Published - 10 Jan 2006 |

Event | 2005 European Quantum Electronics Conference, EQEC '05 - Munich, Germany Duration: 12 Jun 2005 → 17 Jun 2005 |

### Conference

Conference | 2005 European Quantum Electronics Conference, EQEC '05 |
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Country | Germany |

City | Munich |

Period | 12/06/05 → 17/06/05 |

### Keywords

- nput phase modulated beam
- amplitude modulated output
- frequency converter
- optical parametric oscillator (OPO)

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## Cite this

*EQEC '05. European Quantum Electronics Conference, 2005.*[1567242] Piscataway, NJ: IEEE. https://doi.org/10.1109/EQEC.2005.1567242