Patent ID: 6522818
Filing Date: 2003-02-18
Classification: G02B,G02F

Abstract:
A method for generating four-wave mixing in an optical fiber, in which probe light fs and pumping light fp, both set on a frequency axis on condition of fpâ‰ fs, are launched into the optical fiber to generate the four-wave mixing in the optical fiber,whereinallength z of said optical fiber is adapted to satisfy Lmin&lE;z&lE;Lmax, the Lmin and Lmax being determined by the following A and B; wherein,A: nonlinear ordinary differential equations for describing the four-wave mixing in an optical fiber are to be given by (dEp/dz)+(Â½)&agr;Ep=i&ggr;[(|Ep|2+2|Es|2+2|Ec|2)Ep+2E*pEsEc exp(i&Dgr;&bgr;z)]â€ƒâ€ƒ(2.1) (dEs/dz)+(Â½)&agr;Es=i&ggr;[(|Es|2+2|Ec|2+2|Ep|2)Es+E*cEp2 exp(âˆ’i&Dgr;&bgr;z)]â€ƒâ€ƒ(2.2) (dEc/dz)+(Â½)&agr;Ec=i&ggr;[(|Ec|2+2|Ep|2+2|Es|2)Es+E*sEp2 exp(i&Dgr;&bgr;z)]â€ƒâ€ƒ(2.3) â€ƒwhere E denotes an electric field, subscripts p, s, and c denote the pumping light, the signal light (the probe light), and wavelength converted light (idler light), &agr; denotes loss of the optical fiber per unit distance, &ggr; denotes a non-linear coefficient, &ggr; satisfyng a relationship among a pumping light wavelength &ggr;p, nonlinear refractive index n2, and effective area Aeff, &ggr;=(2&pgr;/&lgr;p)Â·(n2/Aeff)zâ€ƒâ€ƒ(3), &Dgr;&bgr; being phase mismatching of a propagation constant and satisfying a phase matching condition in terms of frequency given by 2&ohgr;p=&ohgr;s+&ohgr;câ€ƒâ€ƒ(4), where &ohgr; is an angular frequency, having a relationship of &ohgr;=2 &pgr;f with frequency f, and &Dgr;&bgr; also satisfying the following equation, &Dgr;&bgr;(&ohgr;s)=(&lgr;p2/2&pgr;c) D(&lgr;p)(&ohgr;sâˆ’&ohgr;p)2â€ƒâ€ƒ(5), where D is a chromatic dispersion coefficient of the optical fiber, the coefficient being normally expressed in ps/nmÂ·km unit, and c is the speed of light in vacuum, wherein,said differential equations are integrated over the entire length of the optical fiber L with respect to Es and Ec with accuracy of calculation of an error equal to or less than 0.1% along the coordinate z in the longitudinal direction of the fiber, and a resulting absolute value is squared to determine the corresponding optical power Ps(z) and Pc(z), using the solutions, conversion efficiency Gc of the idler light is calculated by a ratio of idler light intensity Pc(L) measured at an output end of the fiber to intensity Ps(0) of the probe light at an input end of the fiber, probe light gains Gs are calculated by a ratio of probe light intensity Ps(L) measured at the output end ofthe fiber to probe light intensity Ps(0) at the input end of the fiber, the Ps and Pc being the probe light intensity and the idler light intensity, respectively, which are expressed by functions with a distance from the input end of the fiber, L being an entire length of the fiber in question, the calculated probe light gains Gs are plotted with the horizontal axis representing distance z and the vertical axis representing the probe light gain or idler light conversion efficiency, Allowing z of a target quantity for calculation to take on a sufficiently large finite value that to cause variations in the longitudinal direction of the conversion efficiency of the idler light to oscillate periodically as a general property of the solutions letting z=Lm for the smallest value of z among the values of z by which the solutions take on maximal values due to periodic behavior, letting z=Lmax for a distance satisfying a condition of z>Lm and 10% longer than Lm, B: next, as for aforementioned equations (2.1)-(2.3), two different approximate solutions are known under appropriate conditions, idler light conversion efficiency Gc is given by a ratio of idler light intensity Pc(L) measured at the output end of the fiber to probe light intensity Ps(0) at the input end of the fiber, probe light gains Gs is given by a ratio of probe light intensity Ps(L) measured at the output end of the fiber to probe light intensity Ps(0) at the input end of the fiber, the Ps and Pc being the probe light intensity and the idler light intensity, respectively, which are expressed by functions with an argument of distance from the input end of the fiber, L being an entire length of the fiber in question, with only results being shown, signal light gain Gs and idler light generating efficiency Gc, which are obtained by respective approximate solutions, are expressed as follows, (a) First Solution (a.1) for 4&ggr;Pp>âˆ’&Dgr;&bgr;, Gs=1+&ggr;2Pp2(0)L2[(sin h ([gn]gaL)/gaL]2â€ƒâ€ƒ(6.1.1.a), Gc=&ggr;2Pp2(0)L2[(sin (gaL)/gaL]2â€ƒâ€ƒ(6.1.1.b), where ga=(Â½)[&Dgr;&bgr;(&Dgr;&bgr;+4&ggr;Pp)]Â½â€ƒâ€ƒ(6.1.2), next, (a.2) for 4&ggr;PpGs=1+&ggr;2Pp2(0)L2[(sin h (gbL)/gbL]2â€ƒâ€ƒ(6.2.1.a), Gc=&ggr;2Pp2(0)L2[(sin h (gbL)/gbL]2â€ƒâ€ƒ(6.2.1.b), where Gb=(Â½)[&Dgr;&bgr;(&Dgr;&bgr;, +4&ggr;Pp)]Â½â€ƒâ€ƒ(6.2.2), (b) Second solution; Gs=Ps(L)/Ps(0)=exp(âˆ’&agr;L)â€ƒâ€ƒ(7.1) Gc=Pc(L)/Ps(0)=&ggr;2Pp2(0)eâˆ’&agr;L{(1âˆ’eâˆ’&agr;L)2+eâˆ’&agr;L sin2 (&Dgr;&bgr;L/2)}/(&agr;2+&Dgr;&bgr;2) plotting the calculated results, with the horizontal axis representing distance z and the vertical axis representing Gc selecting the greatest value of distance z such that any of the solutions obtained by solving equations (2.1)-(2.3) numerically, the equations (6.1.1.a) and (6.1.1.b), the equations (6.2.1.a) and (6.2.1.b), and the equations 7.1 and 7.2 produce differences not less than 1% which are greater than the calculation error, and setting z=Lmin.