Vector Soliton - History

History

In 1987 Menyuk first derived the nonlinear pulse propagation equation in SMF under weak birefringence. This seminal equation opened up the new field of "scalar" solitons to researchers. His equation concerns the nonlinear interaction (cross-phase modulation and coherent energy exchange) between the two orthogonal polarization components of the vector soliton. Researchers have obtained both analytical and numerical solutions of this equation under weak, moderate and even strong birefringence.

In 1988 Christodoulides and Joseph first theoretically predicted a novel form of phase-locked vector soliton in birefringent dispersive media, which is now known as a high-order phase-locked vector soliton in SMFs. It has two orthogonal polarization components with comparable intensity. Despite of the existence of birefringence, these two polarizations could propagate with the same group velocity as they shift their central frequencies.

In 2000, Cundiff and Akhmediev found that these two polarizations could form not only a so-called group-velocity-locked vector soliton but also a polarization-locked vector soliton. They reported that the intensity ratio of these two polarizations can be about 0.25–1.00.

However, recently, another type of vector soliton, "induced vector soliton" has been observed. Such a vector soliton is novel in that the intensity difference between the two orthogonal polarizations is extremely large (20dB). It seems that weak polarizations are ordinarily unable to form a component of a vector soliton. However, due to the cross-polarizaiton modulation between strong and weak polarization components, a "weak soliton" could also be formed. It thus demonstrates that the soliton obtained is not a "scalar" soliton with a linear polarization mode, but rather a vector soliton with a large ellipticity. This expands the scope of the vector soliton so that the intensity ratio between the strong and weak components of the vector soliton is not limited to 0.25–1.0 but can now extend to 20 dB.

Based on the classic work by Christodoulides and Joseph, which concerns a high-order phase-locked vector soliton in SMFs, a stable high-order phase-locked vector soliton has recently been created in a fiber laser. It has the characteristic that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile.

The following pictures show that, when the fiber birefringence is taken into consideration, a single nonlinear Schrödinger equation (NLSE) fails to describe the soliton dynamics but instead two coupled NLSEs are required. Then, solitons with two polarization modes can be numerically obtained.