Geometric-phase-induced arbitrary polarization and orbital angular momentum generation in helically twisted birefringent photonic crystal fiber
Takeshi Fujisawa, Kunimasa Saitoh
Abstract
The evolutions of polarization and orbital angular momentum (OAM) states of light in helically twisted birefringent photonic crystal fibers (TB-PCFs) are analyzed. It is shown that a circular polarization (CP) component ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> of a Stokes parameter) is periodically excited when usual linearly polarized (LP) modes of PCF are launched. The excitation originates from a geometric phase in TB-PCFs. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> excitation is larger for larger linear birefringence for a fixed twisting rate. If the linear birefringence is large enough, a CP filtering behavior can be seen in addition to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m3"> <mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> excitation. From the analytical consideration of the sign of the geometric phase, the TB-PCF with periodical inversion of twisting is proposed to generate arbitrary polarization state on the Poincaré sphere. Next, an OAM state generation in multimode TB-PCFs is shown for higher-order LP mode input. By observing a far-field interference pattern from TB-PCF mixed with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m4"> <mml:mrow> <mml:msub> <mml:mi>LP</mml:mi> <mml:mn>01</mml:mn> </mml:msub> </mml:mrow> </mml:math> mode, a vortex associated with the OAM state can be seen. Similar to the single-mode case, by using periodical twisting inversion, efficient OAM generation is possible. These results indicate that by simply launching fiber’s LP mode into TB-PCF, arbitrary polarization and OAM states can be generated, leading to a novel mechanism for the manipulation of the spatial state of light.