Almost all transmission grating self-pumped phase-conjugate mirrors are equivalent

Area of Science:

• Nonlinear optics
• Photorefractive materials
• Laser physics

Background:

• Self-pumped phase-conjugate mirrors (SPPCMs) are crucial optical components.
• Transmission grating SPPCMs and double phase-conjugate mirrors (DPCMs) are distinct configurations.
• Understanding their equivalencies can simplify optical system design.

Purpose of the Study:

• To establish a formal equivalence between the photorefractive transmission grating ring SPPCM and the DPCM.
• To explore the topological relationships among various SPPCM configurations.
• To identify limitations in these equivalencies for different grating types.

Main Methods:

• Formal mathematical analysis of the photorefractive wave coupling equations.
• Comparison of the operational principles and boundary conditions of different SPPCM geometries.
• Topological analysis of the grating formation and beam propagation within the photorefractive media.

Main Results:

• The transmission grating ring SPPCM is formally equivalent to a DPCM with internal losses and equal-intensity inputs.
• This equivalence extends to a SPPCM using a photorefractive crystal with one highly reflecting face.
• All transmission grating SPPCMs, except the linear SPPCM, are topologically equivalent to a DPCM.
• No similar equivalence was found for the reflection grating ring phase conjugator.

Conclusions:

• The study reveals a significant topological equivalence between certain SPPCMs and DPCMs.
• This finding simplifies the understanding and potential design of photorefractive phase-conjugate mirrors.
• The equivalence is specific to transmission gratings, with reflection gratings exhibiting different behaviors.