OPTICAL AMPLIFICATION AND RESHAPING BASED ON ROGUE WAVE IN THE FEMTOSECOND REGIME

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1 OPTICAL AMPLIFICATION AND RESHAPING BASED ON ROGUE WAVE IN THE FEMTOSECOND REGIME YAN WANG 1,2, LU LI 1 1 Institute of Theoretical Physics, Shanxi University, Taiyuan 36, China llz@sxu.edu.cn 2 College of Physics and Electronics Engineering, Shanxi University, Taiyuan 36, China Received January 11, 217 Abstract. Based on the higher order nonlinear Schrödinger equation, the amplification and the reshaping of ultrashort pulses are investigated. The numerical results show that the direct amplification of femtosecond pulses can be achieved by injecting a continuous wave (CW and filtering the CW at suitable positions in the presence of higher-order dispersion and nonlinear effects. The combination of continuous wave pump and spectral filter placed suitably in fiber plays the role of the amplifier, which can be used to long-haul transmission of pulses. As an example, long-haul transmission with four amplification periods is demonstrated. The effects of higher-order dispersion and Raman effect on the long-haul transmission of pulses are also discussed. Key words: Optical amplification and reshaping; Rogue wave. PACS: 2.65.Tg, 3.65.Ge, 11.3.Er. 1. INTRODUCTION In modern optical telecommunication systems, optical amplifiers have attracted much attention in recent years as an enabling technology for future long-haul highcapacity optical communications due to a range of practical and potential advantages. Communications with the aid of solitons have been possible since 19s and then the several schemes for the amplification and reshaping of solitons have been proposed theoretically [1 ] and can be realized by Erbium doped fiber amplifiers (EDFA [5], Raman amplifiers [6], parametric amplifiers [7] and semiconductor optical amplifiers [], in which EDFA and Raman amplifiers are commonly used by now. These optical amplifiers have their own limitations in practical applications. Particularly, it is difficult for both EDFA and Raman amplifiers to amplify ultrashort pulses in the picosecond-femtosecond range. The key of the picosecond-femtosecond pulse amplification based on EDFA is to use a shorter erbium fiber with a relatively high doping concentration between 1 ppm and 2 ppm [9]. For Raman amplifiers, the nonlinear stimulated Raman scattering can cause crosstalk that is harmful to the ultrashort pulse in the picosecond-femtosecond range [1, 11]. Besides, the competing nonlinear effects such as stimulated Brillouin scattering, self-phase modulation, Romanian Journal of Physics 62, 25 (217 v.2.* #6f1132b

2 Article no. 25 Yan Wang, Lu Li 2 and parametric four-wave interactions also affect the performance of the optical amplifier, especially for the pulses in the picosecond-femtosecond regime. Therefore the research in the area of optical amplifiers have attracted much attention over the past years [12 17]. Since the pioneering work on optical rogue wave (ORW in 27 [1], there has been much theoretical and experimental research on the existence conditions and key characteristics of ORWs [19 2]. Also, recent works on rogue waves in birefringent optical fibers [25, 26], on rogue-wave light bullets [27], on Peregrine soliton in PT-symmetric nonlinear couplers [2] and on rogue-wave formation in normaldispersion fiber lasers [29] have been investigated. In addition to the investigations of the formation mechanisms of rogue waves [3, 31], there are also attempts to search for their applications in different types of optical systems, for example, the supercontinuum generation [32, 33] and the generation and propagation of high power pulses and pulse trains [3 3], and in other physical contexts [39 3]. Recently, based on the Peregrine rogue wave, we have proposed a new scheme to amplify and reshape the optical pulses in long-haul transmission. The results have shown that the combination of continuous wave pump and spectral filter placed suitably in fiber plays the role of the amplifier, which can be used to amplification and reshaping of soliton. However, the pulse width of soliton is in the picosecond range []. From the point of view of the amplification mechanism, it should have in principle no relationship with the pulse width of the input pulse and pump wavelength or fiber parameters. Therefore, in this paper, we will investigate the amplification and reshaping of pulses based on rogue wave in the femtosecond regime. The paper is organized as follows. In Section 2, the amplification and the reshaping processes based on the higher-order nonlinear Schrödinger (NLS equation are introduced. In Section 3, the influence of higher-order dispersion and Raman effects on the long-haul transmission of pulse is discussed with four amplification periods as an example. Conclusions are made in the last Section. 2. AMPLIFICATION AND RESHAPING BASED ON THE HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION It is well known that the standard NLS equation is valid as the model for picosecond pulses with width 5 ps. When describing the propagation of pulses in the subpicosecond or femtosecond regime, we must consider some higher-order effects, such as third-order dispersion (TOD, self-steepening (SS, and self-frequency shift (SFS arising from the stimulated Raman scattering (SRS [5, 6]. In this case, we should consider the higher-order nonlinear Schrödinger (HNLS equation in the form (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

3 3 Optical amplification and reshaping in the femtosecond regime Article no. 25 [5] A z + α 2 A + iβ 2 2 A 2 T 2 β 3 3 A 6 T ( 3 = iγ A 2 A + i A 2 A T R A A 2. (1 ω T T Here A = A(z,T is the slowly varying envelope of the electric field, z is the propagation distance and T is the temporal coordinate in a frame of reference moving with the pulse at the group velocity v g (T = t z/v g. Coefficients β 2, β 3, γ, and T R account for the group-velocity dispersion (GVD, the TOD, the strength of the Kerr nonlinearity, the Raman time-delay constant, respectively, and α > is the fiber loss. In the case of β 2 <, and by means of rescaling, A(z,T P q(ξ,τ, τ T/T, and ξ = z/l D, with the temporal scale T = [ β 2 /(γp ] 1/2 and the nonlinear length L NL = (γp 1, Eq. (1 can be transformed into where q ξ = i +α ( q 2 q τ ( 1 2 q 2 τ 2 + q 2 q iα 5 q q 2 τ + α 3 3 q τ 3 α L q, (2 2 α 3 = β 3,α = 1,α 5 = T R,α 6 β 2 T ω T T L = L NL α, (3 which are related to the TOD, the self-steepening, and the Raman effect, and the fiber loss, respectively. In the absence of the higher-order dispersion and nonlinearity terms, i.e., α 3 = α = α 5 =, Eq. (2 can be reduced into the standard NLS equation with fiber loss. In this case, when an initial input pulse is injected into optical fiber, the pulse s power is decreased due to the presence of the loss and it evolves into a small amplitude pulse. There are different optical amplifiers which can be used to amplify the small amplitude pulse. Recently, based on the characteristic of the Peregrine rogue wave for the standard NLS equation, we investigated the amplification and the reshaping of the small amplitude pulse by injecting a continuous wave (CW and filtering the CW at suitable positions []. The results have demonstrated that the combination of a continuous-wave pump and a spectral filter placed suitably in fiber plays the role of the amplifier and can be used to long-haul transmission of solitons. It should be noted that the above results did not include the higher-order dispersion and nonlinearity terms and so are only valid for the picosecond pulses with width 5 ps. However, for the subpicosecond or femtosecond pulses, we must consider the higher-order dispersion and nonlinearity terms presented in Eq. (2. Here, (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

4 Article no. 25 Yan Wang, Lu Li Power (W Distance (km E ex (W.ps 6 (a Time (ps. (c.6. L max Time (ps 5 (e L max.3 Distance (km Power (W Power (W Power (W Time (ps Time (ps (b (d (f Time (ps Fig. 1 (Color online. The amplification and the reshaping of pulse in the presence of the TOD and Raman effects. (a The profile of the input pulse given by Eq. (; (b The profile of the small amplitude pulse after propagating for z = km; (c The evolution plot of the pulse intensity after injecting the CW background at z ; (d The red dashed curve is the maximally amplified pulse with zero-background and the blue solid curve is the input pulse to compare; (e The evolution of the energy exchange between the pulse and the CW; (f The red dashed curve is the reshaped pulse and the blue solid curve is the input pulse. our aim is to study the influence of these higher-order effects on the amplification and the reshaping of the small amplitude pulse. As in Ref. [], we take the initial condition as A(,T = 3 ( 3T P sech, ( and demonstrate the amplification and reshaping processes in the presence of the higher-order effects, as shown in Fig. 1, where the system parameters are adjusted to the high nonlinear fiber with β 2 = ps 2 km 1, β 3 = ps 2 km 1, γ = 1 W 1 km 1 around 155 nm, the fiber loss α = 1 db/km [2], and P =.7 W, T R = 1 fs. In this case, the normalized parameters are T =.3556 ps and L NL =.129 km, and the peak-power of the initial input given by Eq. ( is 6.3 W. And the parameters α 3, α, and α 5 given by Eq. (3 are.7,.23 and.2, respectively, which are considered as some small perturbations. Figure 1(a presents the distribution of the initial input given by Eq. (. After propagating for z = km (5 nonlinear lengths, it is evolved into a small amplitude pulse (which is also called attenuated pulse with the peak-power.22 W (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b T

5 5 Optical amplification and reshaping in the femtosecond regime Article no. 25 because of the fiber loss, as shown in Fig. 1(b. Note that the small amplitude pulse occurs a time shift due to the presence of the TOD and Raman effects. As in Ref. [], to amplify the small amplitude pulse, we inject a continuous wave with a specified power P by setting a continuous wave laser at the position z and construct a mixing form of the attenuated pulse and CW background, i.e., A(z,T + P. Thus, due to the interaction of the CW, the small amplitude pulse will be amplified until forming a maximally compressed pulse at the peak position L max =.2537 km, as shown in Fig. 1(c, which presents the evolution of the mixing pulse. From it one can see that the mixing pulse undergoes the strong temporal compression and peak-power increase and is split eventually [37]. Although the maximally compressed pulse that occurred at the peak position possesses a higher peak-power, it cannot directly travel with preserving its shape due to the presence of the CW background. To ensure its robust transmission, we need to set a spectral filter at the peak position L max to filter out the CW background. Thus we can acquire a zero-background pulse with the peak-power W (about 2.37 times of the original input pulse and the full width at half maximum (FWHM.12 ps, as shown in Fig. 1(d. Here the spectral filter filtered out the spectra around 155 nm (about a range of.2 nm by attenuating its spectral intensity by 1% []. Also, we computed the energy exchange between the attenuated pulse and the CW background by the expression E ex (z = + A(z,T A(z,± 2 dt, and the result is shown in Fig. 1(e. From it one can see that after injecting the continuous wave, the exchanged energy is always larger than the energy at position z. This means that the attenuated pulse gains the energy from the continuous wave so that it is amplified, as shown in Ref. []. Similarly, the energy exchange plot has an abrupt drop at the peak position L max. This indicates that the energy is lost, which is caused by eliminating the CW background. It should be noted that the exchanged energy loss is only about 7% for the high nonlinear fiber, which is less than that presented in Ref. [] even in the presence of the higher-order effects. Furthermore, from Fig. 1(d, one can see that the zero-background pulse extracted from the peak position L max is a maximally amplified pulse and has higher peak-power than the initial input. Thus, we can implement the reshaping of the zero background pulse to the initial pulse by choosing suitably the position of the spectral filter. The profile of the reshaped pulse extracted from L R =.1957 km is shown in Fig. 1(f, where the peak-power and the FWHM are W and.331 ps, respectively, which are almostly in agreement with that of the input pulse except for the slight asymmetry at the margin due to the presence of the higher-order effects. Note that the peak-power and the FWHM of the input pulse are 6.3 W and.291 ps, respectively. Here, it should be pointed that because the widths of the input pulse and the re- (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

6 Article no. 25 Yan Wang, Lu Li 6 Power (W Power (W Power (W Power (W (a (b 1 (c (a (b 2 (c (a (b 3 (c (a 1.2 (b (c Time (ps Time (ps 2 6 Time (ps Fig. 2 (Color online The long-haul transmission of pulses governed by Eq. (1 with four amplification periods. (a The initial input or the reshaped pulse; (b The small amplitude pulse after propagating z =.257 km; (c The reshaped pulse after pumping a CW at z and filtering the CW at L R, where the red dashed curves are the reshaped pulses and the blue solid curves are the input pulse. Here the subscripts indicate the number of periods. The system parameters are the same as in Fig. 1. shaped pulse or the maximally amplified pulse are in the femtosecond regime, HNLS equation is more suitable than the standard NLS equation for describing the propagation of the pulse. Also, the higher-order effects in HNLS equation will cause the shift of the reshaped pulse or the maximally amplified pulse in temporal domain. In spite of this, even in the presence of the higher-order dispersion and Raman effects, we can implement the amplification and reshaping of the pulse by injecting a CW and filtering the CW at suitable positions. 3. THE LONG-HAUL TRANSMISSION OF PULSES IN THE FEMTOSECOND REGIME In this Section, based on the HNLS equation (1, we will perform the long-haul transmission of pulses in the femtosecond regime, which can be achieved by periodically pumping and filtering a CW, as shown in the above Section. As an example, Fig. 2 presents the results of the long-haul transmission with four amplification periods, where the amplification period is taken as z =.257 km (3 nonlinear lengths and the input pulse is given by Eq. (. Figures 2(a 1 -(a present the distributions of the input pulse and the reshaped (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

7 7 Optical amplification and reshaping in the femtosecond regime Article no. 25 Power (W Power (W Power (W Power (W (a (b 1 (c (a (a (a 2 6 Time (ps (b 2 (c (b 3 (c (b Time (ps 2 6 (c 2 6 Time (ps Fig. 3 (Color online. The long-haul transmission of pulse with four amplification periods, where 1% random noise is added to the input pulse. Here, the system parameters are the same as in Fig. 2. pulses, respectively. After propagating for the distance z =.257 km (3 nonlinear lengths, each of the pulses is evolved into the small amplitude pulse due to the presence of fiber loss, as shown in Figs. 2(b 1 -(b, respectively. And then, by pumping a CW at z and filtering the CW at L R (note that the realistic position is z + L R, the small amplitude pulses are amplified and reshaped to the input pulse when the reshaped positions L R are chosen as L R =.726 km,.517 km,.566 km,.57 km, respectively, and the results are shown in Figs. 2(c 1 -(c, where the peak-powers and the FWHMs of the reshaped pulses are W, W, W, 6.33 W and.2692 ps,.255 ps,.252 ps,.2617 ps, respectively, which are almostly in agreement with those of the input pulse given by Eq. (. The results show that the combination of continuous wave pump and spectral filter placed suitably in fiber plays the role of the amplifier, and can be used to long-haul transmission of the femtosecond pulses governed by HNLS equation (1 including the higher-order dispersion and Raman effects. Comparing our results with those reported in Ref. [], the difference is that the pulses are shifted in temporal domain due to the presence of higher-order effects, and the longer the transmission distance is, the larger the shift is, as shown in Figs. 2(c 1 -(c. Finally, we consider the influence of the noise on the long-haul transmission of pulses, for example, 1% random noise is added to the input pulse. The corresponding (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

8 Article no. 25 Yan Wang, Lu Li results are shown in Fig. 3, in which the peak-powers and FWHMs of the reshaped pulses are W, 6.2 W, 6.1 W, 6.1 W and.267 ps,.2 ps,.257 ps,.29 ps when the reshaped positions are chosen as L R =.721 km,.511 km,.577 km, and.5 km, respectively. Similarly, the input pulse is well reshaped in long-haul transmission with four amplification periods except the pulses are shifted in the temporal domain.. CONCLUSIONS In summary, based on HNLS equation, the amplification and the reshaping of pulses in the femtosecond regime have been studied. The numerical results have shown that the direct amplification of femtosecond pulses can be achieved by injecting a continuous wave and filtering the continuous wave at suitable positions even in the presence of higher-order dispersion and nonlinear effects. Thus, the combination of the continuous wave pump and spectral filter placed suitably in fiber plays the role of the optical amplifier, which can be used to long-haul transmission of pulse. The numerical results have shown that this procedure is feasible. The amplification and the reshaping processes can be easily implemented and the principle we have revealed can be applied to higher-order models, to fibers with other parameters, and to input pulses with different profiles. Acknowledgements. This research is supported by the National Natural Science Foundation of China grant and the Shanxi Scholarship Council of China grant REFERENCES 1. A. Hasegawa and Y. Kodama, Amplification and reshaping of optical solitons in glass fiber-i, Opt. Lett. 7, ( Y. Kodama and A. Hasegawa, Amplification and reshaping of optical solitons in glass fiber-ii, Opt. Lett. 7, ( Y. Kodama and A. Hasegawa, Amplification and reshaping of optical solitons in galss fiber-iii. Amplifiers with random gain, Opt. Lett., 32 3 (193.. A. Hasegawa, Amplification and reshaping of optical solitons in a galss fiber-iv: Use of the stimulated Raman process, Opt. Lett., ( R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, Low-noise erbium-doped fiber amplifier operating at 1.5 µm, Electron. Lett. 23, ( L. F. Mollenauer and K. Smith, Demonstration of soliton transmission over more than km in fiber with loss periodically compensated by Raman gain, Opt. Lett. 13, ( R. H. Stolen and J. E. Bjorkholm, Parametric Amplification and Frequency Conversion in Optical Fibers, IEEE J. Quantum Electron. QE-1, (192.. M. J. O Mahony, Semiconductor optical amplifiers for use in future systems, J. Lightwave Technol. 6, (19. (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

9 9 Optical amplification and reshaping in the femtosecond regime Article no M. Nakazawa, Propagation and Amplification of Ultrashort Optical Soliton Pulses in Erbium- Doped Fibers for Very High Speed Communication, Springer Series in Chemical Physics, 53 Ultrafast Phenomena VII, pp ( T. Yamamoto and S. Norimatsu, Statistical Analysis on Stimulated Raman Crosstalk in Dispersion- Managed Fiber Links, J. Lightwave Technol. 21, ( A. S. L. Gomes, V. L. da Silva, and J. R. Taylor, Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method, J. Opt. Soc. Am. B5, ( B. A. Malomed, G. D. Peng, and P. L. Chu, Nonlinear-optical amplifier based on a dual-core fiber, Opt. Lett. 21, ( S. Singh and R. S. Kaler, Power transient and its control in Raman-erbium doped fiber amplifier hybrid optical amplifier subject to multi-channel bursty traffic, J. Opt. Technol. 1, ( G. Sobon, J. Sotor, A. Przewolka, I. Pasternak, W. Strupinski, and K. Abramski, Amplification of noise-like pulses generated from a graphene-based Tm-doped all-fiber laser, Opt. Express 2, ( N. A. Naderi, A. Flores, B. M. Anderson, and I. Dajani, Beam combinable, kilowatt, all-fiber amplifier based on phase-modulated laser gain competition, Opt. Lett. 1, ( V. V. Slabko, A. K. Popov, V. A. Tkachenko, and S. A. Myslivets, Three-wave mixing of ordinary and backward electromagnetic waves: extraordinary transients in the nonlinear reflectivity and parametric amplification, Opt. Lett. 1, ( C. Gaida, M. Gebhardt, F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, Thulium-doped fiber chirped-pulse amplification system with 2 GW of peak power, Opt. Lett. 1, ( D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature 5, ( N. Akhmediev et al., Roadmap on optical rogue waves and extreme events, J. Opt. 1, 631 ( S. Toenge, T. Gdin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and M. Dudley, Emergent rogue wave structures and statistics in spontaneous modulation instability, Sci. Rep. 5, 13 ( M. Liu, A. P. Luo, W. C. Xu, and Z. C. Luo, Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser, Opt. Lett. 1, ( B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, The Peregrine soliton in nonlinear fibre optics, Nature Phys. 6, ( B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Observation of Kuznetsov-Ma soliton dynamics in optical fibre, Sci. Rep. 2, ( K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Peregrine soliton generation and breakup in standard telecommunications fiber, Opt. Lett. 36, ( S. H. Chen and D. Mihalache, Vector rogue waves in the Manakov system: diversity and compossibility, J. Phys. A, ( D. Mihalache, Localized structures in nonlinear optical media: a selection of recent studies, Rom. Rep. Phys. 67, ( S. H. Chen, J. M. Soto-Crespo, F. Baronio, P. Grelu, and D. Mihalache, Rogue-wave bullets in a composite (2+1D nonlinear medium, Opt. Express 2, ( C. Q. Dai and Y. Y. Wang, Controllable combined Peregrine soliton and Kuznetsov-Ma soliton in PT-symmetric nonlinear couplers with gain and loss, Nonlinear Dyn., (215. (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b

10 Article no. 25 Yan Wang, Lu Li Z. W. Liu, S. M. Zhang, and F. W. Wise, Rogue waves in a normal-dispersion fiber laser, Opt. Lett., ( C. Kharif and E. Pelinovsky, Physical mechanisms of the rogue wave phenomenon, Eur. J. Mech. B/Fluids 22, ( A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, Rogue waves and rational solutions of the Hirota equation, Phys. Rev. E 1, 662 ( J. M. Dudley, G. Genty, and B. Eggleton, Harnessing and control of optical rogue waves in supercontinuum generation, Opt. Express 16, ( D. R. Solli, C. Ropers, and B. Jalali, Active control of rogue waves for stimulated supercontinuum generation, Phys. Rev. Lett. 11, (2. 3. G. Y. Yang, L. Li, S. T. Jia, and D. Mihalache, High power pulses extracted from the Peregrine rogue wave, Rom. Rep. Phys. 65, 391 ( G. Y. Yang, L. Li, S. T. Jia, and D. Mihalache, Controlling high power pulses extracted from maximally compressed pulse in a nonlinear optical fiber, Rom. Rep. Phys. 65, ( G. Y. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, Breatherlike solitons extracted from the Peregrine rogue wave, Phys. Rev. E 9, 6299 ( G. Y. Yang, L. Li, and S. T. Jia, Peregrine rogue waves induced by the interaction between a continuous wave and a soliton, Phys. Rev. E 5, 66 ( Y. Wang, L. J. Song, L. Li, and A. B. Malomed, High-power pulse trains excited by modulated continuous waves, J. Opt. Soc. Am. B 32, ( D. Mihalache, Localized optical structures: An overview of recent theoretical and experimental developments, Proc. Romanian Acad. A 16, (215.. Y. B. Liu, A. S. Fokas, D. Mihalache, and J. S. He, Parallel line rogue waves of the third-type Davey-Stewartson equation, Rom. Rep. Phys. 6, ( S. W. Xu, K. Porsezian, J. S. He, and Y. Cheng, Multi-optical rogue waves of the Maxwell-Bloch equations, Rom. Rep. Phys. 6, ( S. H. Chen, P. Grelu, D. Mihalache, and F. Baronio, Families of rational soliton solutions of the Kadomtsev-Petviashvili equation, Rom. Rep. Phys. 6, ( F. Yuan, J. G. Rao, K. Porsezian, D. Mihalache, and J. S. He, Various exact rational solutions of the two-dimensional Maccari s system, Rom. J. Phys. 61, (216.. Y. Wang, L. J. Song, and L. Li, Optical amplification and reshaping based on the Peregrine rogue wave, Appl. Opt. 55, ( G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, New York, Y. Kodama and A. Hasegawa, Nonlinear pulse propagation in a monomode dielectric guide, IEEE J. Quantum Electron. 23, (197. (c RJP 62(Nos. 3-, id:25-1 (217 v.2.* #6f1132b