### 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)

Language | English |
---|---|

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 |
---|---|

Country | Germany |

City | Munich |

Period | 12/06/05 → 17/06/05 |

### Fingerprint

### Keywords

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

### Cite this

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

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*EQEC '05. European Quantum Electronics Conference, 2005..*, 1567242, IEEE, Piscataway, NJ, 2005 European Quantum Electronics Conference, EQEC '05, Munich, Germany, 12/06/05. https://doi.org/10.1109/EQEC.2005.1567242

**From phase to amplitude modulation in transverse nonlinear optics.** / Scroggie, A.J.; McCartney, G.; Jeffers, J.; Oppo, G.L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - From phase to amplitude modulation in transverse nonlinear optics

AU - Scroggie, A.J.

AU - McCartney, G.

AU - Jeffers, J.

AU - Oppo, G.L.

PY - 2006/1/10

Y1 - 2006/1/10

N2 - 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 A0(x,t) and signal A1(x,t) fields of a degenerate OPO at resonance, in the mean-field approximation, are described by: ∂tA0 = Γ[-A0 + Ee μcos(kx) - A1 2] + i∂x 2A0 ∂tA1 = -A1 + A0A1* + 2i∂x 2A 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 kc given by kc 2 = √Γ(E-1) (kc 2 = √ΓE)

AB - 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 A0(x,t) and signal A1(x,t) fields of a degenerate OPO at resonance, in the mean-field approximation, are described by: ∂tA0 = Γ[-A0 + Ee μcos(kx) - A1 2] + i∂x 2A0 ∂tA1 = -A1 + A0A1* + 2i∂x 2A 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 kc given by kc 2 = √Γ(E-1) (kc 2 = √ΓE)

KW - nput phase modulated beam

KW - amplitude modulated output

KW - frequency converter

KW - optical parametric oscillator (OPO)

UR - http://www.scopus.com/inward/record.url?scp=33847335169&partnerID=8YFLogxK

U2 - 10.1109/EQEC.2005.1567242

DO - 10.1109/EQEC.2005.1567242

M3 - Conference contribution book

SN - 0780389735

SN - 9780780389731

BT - EQEC '05. European Quantum Electronics Conference, 2005.

PB - IEEE

CY - Piscataway, NJ

ER -