We demonstrate that optical solitons can exist in dispersion-inverted highly-nonlinear AlGaAs nanowires. This is accomplished by strongly reversing the dispersion of these nano-structures to anomalous over a broad frequency range. These self-localized waves are possible at very low power levels and can form in millimeter long nanowire structures. The intensity and spectral evolution of solitons propagating in such AlGaAs nanowaveguides is investigated in the presence of loss, multiphoton absorption and higher-order dispersion

Christodoulides, D. N.

El-Ganainy, R.

Makris, K. G.

Mokhov, S.

Morandotti, R.

English

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 2000s Faculty Bibliography 1-1-2006 Solitons in dispersion-inverted AlGaAs nanowires R. El-Ganainy University of Central Florida S. Mokhov University of Central Florida K. G. Makris University of Central Florida D. N. Christodoulides University of Central Florida R. Morandotti Find similar works at: https://stars.library.ucf.edu/facultybib2000 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2000s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation El-Ganainy, R.; Mokhov, S.; Makris, K. G.; Christodoulides, D. N.; and Morandotti, R., "Solitons in dispersion-inverted AlGaAs nanowires" (2006). Faculty Bibliography 2000s. 6114. https://stars.library.ucf.edu/facultybib2000/6114 Solitons in dispersion-inverted AlGaAs nanowires   R. El-Ganainy, S. Mokhov, K. G. Makris, and D. N. Christodoulides College of Optics & Photonics-CREOL & FPCE, University of Central Florida, Orlando, Florida, 32816  R. Morandotti Institut national de la recherché scientifique, Université du Québec, Varennes, Québec, Canada J3X 1S2  Abstract:  We demonstrate that optical solitons can exist in dispersion-inverted highly-nonlinear AlGaAs nanowires. This is accomplished by strongly reversing the dispersion of these nano-structures to anomalous over a broad frequency range. These self-localized waves are possible at very low power levels and can form in millimeter long nanowire structures. The intensity and spectral evolution of solitons propagating in such AlGaAs nanowaveguides is investigated in the presence of loss, multiphoton absorption and higher-order dispersion.                 ©2006 Optical Society of America                   OCIS codes: (190.5530) pulse propagation and solitons, (190.4370) Nonlinear optics, fibers,       (260.2030) Dispersion.  References and links 1. P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York 2004).  2. S. G. Leon-Saval,  T. A. Birks,  W. J. Wadsworth,  P. St. J. Russell, and M. W. Mason, "Supercontinuum generation in submicron fibre waveguides," Opt. Express 12, 2864-2869 (2004). 3. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “ Subwavelength-diameter silica wires for low-loss optical wave guiding”, Nature 426, 816-819, (2003). 4. J.C.Knight, J. Arriaga, T.A Briks, A. Ortigosa-Blanch, W.J. Wadsworth and P. St. J. Russell, “ Anomalous Dispersion in Photonic Crystal Fiber”, IEEE  Photonics Technology Letters 12, 807-809, (2000). 5. M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13, 6848-6855 (2005). 6. G. Brambilla, F. Koizumi, V. Finazzi, and D. J. Richardson, "Supercontinuum generation in tapered bismuth silicate fibres", Electron. Lett. 41, 795-797 (2005). 7. H. Ebendorff-Heidepriem,  P. Petropoulos,  S. Asimakis,  V. Finazzi,  R. C. Moore,  K. Frampton,  F. Koizumi,  D. J. Richardson, and T. M. Monro, "Bismuth glass holey fibers with high nonlinearity", Opt. Express 12, 5082-5087 (2004). 8. G. Brambilla, F. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires", Electron. Lett. 41, 400-402 (2005). 9. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi and S. Itabashi, “Four-wave mixing in silicon wire waveguide”, Opt. Express, 13, 4629-4635, (2005). 10. Y. K. Lizé,  E. C. Mägi,  V. G. Ta'eed,  J. A. Bolger,  P. Steinvurzel, and B. J. Eggleton, "Microstructured optical fiber photonic wires with subwavelength core diameter", Opt. Express 12, 3209-3217 (2004). 11. V. Kumar, A. George, J. C. Knight, and P. St. J. Russell, "Tellurite photonic crystal fiber", Opt. Express 11, 2641-2645 (2003). 12. J. C. Knight, “Photonic Crystal fibers”, Nature 424, 847-851 (2003). 13. G.I. Stegeman, A. Villeneuve, J. Kang, J.S. Aitchison, C.N. Ironside, K. Al-hemyari, C.C. Yang, C-H. Lin, H-H. Lin, G.T. Kennedy, R.S. Grant and W. Sibbett, "AlGaAs Below Half Bandgap: The Silicon of Nonlinear Optical Materials", Int. J. of Nonlinear Optical Physics, 3, 347-371 (1994). 14. J. E. Heebner, N. N. Lepeshkin, A. Schweinsberg, G. W. Wicks, R. W. Boyd, R. Grover and P.-T. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators”, Opt. Lett. 29, 769-771, (2004). 15. R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, F. Pozzi, C. R. Stanley, and M. Sorel, “Enhanced Third-Order Nonlinear Effects in Optical AlGaAs Nanowires”, post-deadline paper PDP7, Nonlinear Guided Waves and Their Applications, OSA Topical Meeting, Dresden, Germany, Sep. 6-9, 2005. #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  227716. U. Peschel , T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission”, Appl. Phys. Lett. 67 ,  2111-2113 (1995). 17. C.J. Hamilton, B. Vogele, J.S. Aitchison, G.T. Kennedy, W. Sibbett, W. Biehlig, U. Peschel, T. Peschel, F. Lederer, “Bright Solitary pulses in AlGaAs waveguides at half the band gap”, Opt. Lett. 21, 1226-1228, (1996). 18. S.Gehrsitz, F.K. Reinhart, C. Gourgon, A. Vonlanthen and H. Sigg, “The refractive index of AlxGa1-xAs below the band gap: Accurate determination and empirical modeling” J. Appl. Phys, 87,7825-7837 (2000). 19. J. U. Kang, A. Villeneuve, M. Sheik-Bahae, George I. Stegeman, K. Al-hemyari, J. S. Aitchison, C. N. Ironside, “ Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap”, Appl. Phys. Lett. 65, 147-149 (1994). 20. K. Okamoto, Fundamental of Optical Waveguides, (Academic Press, San Diego 2000). 21. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon waveguides”, Opt. Express 12,1025-1035 (2004). 22. A.L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers”Opt. Lett. 27, 924-926 (2002).  1. Introduction The interaction of light with matter on a nanometer scale opens up new opportunities which may have far reaching implications in telecommunications, computation, biophotonics, and sensing technologies [1]. Lately, single-mode sub-wavelength waveguides or nanowires have been realized in several material systems [2-11]. Such optical nanowire structures are capable of providing superior light confinement and are thus ideal for nonlinear optics applications [12]. Clearly, of interest will be to fabricate such nanowires using high contrast, highly nonlinear materials, such as AlGaAs-known to exhibit a nonlinearity that is three orders of magnitude higher than that of silica glass [13,14]. Apart from being highly nonlinear, AlGaAs nanowires are also highly promising in terms of applications since they can be integrated with other optoelectronic components on the same wafer and thus can serve as information conduits among miniaturized devices.  Quite recently, enhanced spectral broadening or SPM has been observed for the first time in 700μm long AlGaAs nanowires [15]. An important question associated with this particular system is whether optical solitons are possible in AlGaAs nanowaveguides. This is of relevance since solitons can be used to either overcome dispersion effects or to achieve pulse compression in such nanostructures. We note that so far, optical solitons have only been observed in multi-layer AlGaAs structures in which the dispersion can be engineered [16,17]. Yet, in primitive weakly guiding AlGaAs waveguides such solutions are not possible since this material system exhibits appreciable normal dispersion in the spectral region of interest [18], i.e. for mm μλμ 7.11.1 << .  Here we theoretically demonstrate, that, because of high contrast, the dispersion of an air-clad AlGaAs nanowire can become strongly anomalous (becomes inverted), thus overcoming material dispersion limitations. This in turn may allow optical soliton formation in millimeter long structures. These solitons are possible at very low power levels (at ~5 W) in spite of the fact that the AlGaAs nanowires can exhibit anomalous dispersion that is a thousand times higher than that of silica glass. The intensity and spectral evolution of these solitons is investigated in AlGaAs nanowaveguides in the presence of loss, multi-photon absorption, and higher-order dispersive and nonlinear effects. 2. AlGaAs Nanowire dispersion properties To analyze the dispersion properties of AlGaAs  nanowires, let us consider for example an AsGaAl 8.02.0 nanorod of core radius a  as shown in Fig.1(a).  This particular composition ( AsGaAl 8.02.0 ) is deliberately chosen since in the neighborhood of mμλ 55.1=  it is known to exhibit relatively low two-photon absorption [19]. In addition, we assume that the nanowire is air-cladded. We note that even though completely air-clad structures are rather difficult to develop these days, it is yet possible to fabricate waveguides that are mostly surrounded by air, with characteristics very similar to the one analyzed here. At this wavelength the #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  2278refractive index of AsGaAl 8.02.0  is approximately 3.27, and the nanorod is operated at or close to the single-mode regime. In general, the nanowire dispersion relation is given by [20]:            ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛+=⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+⎥⎦⎤⎢⎣⎡+ 22222221111)()(')()(')()(')()('wnnuwumwwKwKnnuuJuJwwKwKuuJuJcorecladmmcorecladmmmmmm      . (1) In Eq.(1) )(uJm is a Bessel function of the first kind and of order m  and  similarly )(wK m  is a modified Bessel function, and primes represent derivatives with respect to the argument. 22effcoreo nnaku −= , 22 cladeffo nnakw −=  where λπ /20 =k  is the free space wavevector and effn  is the effective refractive index of the mode [20]. coren  is the core index and 1=cladn  since the exterior medium is air. The wavelength dependence of the refractive index is accounted by using the Sellmeier expansion of AsGaAl xx −1 , i.e  [18]:                2211222/1),()(/1),()(),(),,(λλλ−+−+=TxExCTxExCTxATxnoocore      . (2)                            In general, the constants A , 0C , 1C , 0E  and 1E  depend on the Al  composition )(x , the temperature T , and  the free space wavelength λ . Here all calculations were carried out at room temperature. The dispersion properties of the fundamental mode 11HE of such a nano-structure are obtained by numerically solving Eq. (1) for 1=m , with the core index evaluated at each frequency step from Eq. (2). The dispersion coefficient 22" / ωββ dd=  of an AsGaAl 8.02.0  nanowire is shown in Fig.1(b) in units of mps /2  for different core radii. In this same figure, the bulk AsGaAl 8.02.0  dispersion is also included for comparison.                          Fig. 1. (a) a nanowire structure; (b) group velocity dispersion "β  of an  Al0.2 Ga 0.8 As  nanowire when its radius    is (A) 160, (B) 175 and (C) 193 nm. Bulk dispersion of Al0.2 Ga 0.8 As  is also shown.  It is important to note that because of the strong index contrast of the AlGaAs  nanowaveguide and the resulting field confinement, the waveguide dispersion dominates and as a result the dispersion can become inverted and strongly anomalous [4,21]. In fact for nma 193= , the dispersion of such a nanorod can reach very high values, as high as mps /12 2− , which is 310 times higher than that of a standard silica fiber at 1.55 mμ .  #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  2279     Parenthetically, we would like to point out that these same structures can also lead to very high normal dispersion. Figure 2(a) depicts the total dispersion of an AsGaAl 8.02.0  nanorod when its radius is nma 160= . As one can see, the anomalous dispersion of this structure (also shown in Fig. 1(b) for mμλ 4.1≤ )  is followed by a region of strong normal dispersion especially at 1.55 mμ . In fact around 1.55 mμ  the dispersion is approximately mps /80 2" =β . Thus the dispersion of a cm2  long AlGaAs  nanorod will be sufficient to cancel that arising from a km25.1  long anomalously dispersive fiber with group velocity dispersion nmkmpsD ./1= . In addition Fig. 2(b) shows the group index gg cn υ/= and the effective index effn  of an AsGaAl 8.02.0  nanowire of radius nma 175=  as a function of wavelength. Note that the group index in this case can be as high as 52.5≈gn  around 1.55 mμ , which indicates “slow” light transport (because of waveguide dispersion) in spite of the fact that  bulk index is 3.27 and 56.1=effn  .              Fig. 2. (a) group velocity dispersion "β when nma 160= , (b) group and effective refractive indices of an  AsGaAl 8.02.0   nanowire when  nma 175= .           For the subsequent discussion, we chose two operating points based on the designs (C) and (B) shown in Fig. 1(b).  In particular the design (C) is used at 1.55 mμ  where the third-order dispersion is very small whereas design (B) is used at 1.5 mμ  where cubic dispersive effects become appreciable. The nanowire of case (C) is single-moded for mμλ 57.1≥ whereas that of (B) is monomode for mμλ 42.1≥ .  3. Soliton effects in AlGaAs nanowires Nonlinear pulse propagation in such nanowire structures is modeled using the evolution equation [22]:         ( )02!43222222)(=++⎥⎥⎦⎤⎢⎢⎣⎡∂∂++∂∂++∂∂∑∞=ϕϕαϕϕαϕϕωϕϕωϕβαϕϕ iiTicnTmiizim oommmm      .   (3) In Eq.(3),ϕ  represents the pulse envelope, gztT υ/−= ,α is the linear loss coefficient, mmm ωββ ∂∂= /)( is the thm  order dispersion coefficient evaluated at the carrier angular frequency λπω /20 c= , )2/()( 22 onnn η =  where Wcmn /103.1 2132 −×=   is the #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  2280nonlinear Kerr coefficient and n is the linear refractive index of AlGaAs ( oη is the free space wave impedance). 2152 /105.6 Vm−×=α and 43313 /1063.5 Vm−×=α are the two-photon and three-photon absorption coefficients respectively at mμλ 55.1≈ [19]. In all cases, the dispersion curve is incorporated in Eq.(3) using a dispersion Taylor series over a broad spectral range (greatly exceeding the pulse spectrum). Here the linear loss for the field is taken to be 125. −= cmα .      Figure 3(a) shows the intensity evolution of a fs200 (FWHM) hyperbolic secant optical pulse when is launched into a mm5  long AsGaAl 8.02.0  nanowire of core radius nma 193=  (corresponding to curve (C) of Fig.1(b)) at mμ55.1 . For this design, the quadratic dispersion ( mps /12 2'' −=β ) dominates the propagation process (the higher-order dispersion terms are negligible) and the dispersion length is mm5.1≈ , i.e., is very small. The pulse peak power in this case is approximately W5.5  (with a 75% confinement factor), corresponding to the fundamental soliton in this nanowire structure.  As Fig. 3(a) clearly indicates, this soliton can be sustained over approximately 3-4 dispersion lengths, i.e. up to a distance that is ultimately determined by the linear loss of the system. Fig. 3(b) on the other hand depicts soliton compression under similar conditions when the input power of the pulse is 8 W.  For this power level, at 2 dispersion lengths, the FWHM pulsewidth becomes fs175 . Figure 3(c) and (d) demonstrate similar results when an AlGaAs nanowire corresponding to curve (B) of Fig.1(b), is used at mμ5.1 . Even in this case, in spite of appreciable third-order dispersion effects and multi-photon absorption, a fs200  soliton forms at W2 , as shown in Fig. 3(c). Soliton compression is also shown for this case in Fig. 3(d) when the input power is W8.2 . It is important to note that in all cases ultrashort solitons in these nanowires can form within millimeters and at very low power levels.                        Fig. 3 Intensity evolution of a 200 fs soliton propagating in a 193 nm (radius) AlGaAs nanowire when the peak power is (a) 5.5 and (b) 8 W. Similarly, (c) and (d) depict soliton propagation and compression in a nanowire of radius 175 nm when the peak power is 2 and 2.8 W respectively. #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  2281Figure 4 depicts the power spectra that may result in an AsGaAl 8.02.0 nanowaveguide of radius nma 193=  when is excited at mμ55.1  with a 200fs FWHM optical pulse. When the input peak power is enough to establish an optical soliton (5.5 W) the power spectrum remains essentially invariant during propagation as shown in Fig. 4(a). At a higher power (8W) the pulse undergoes compressions and thus its spectrum broadens (Fig. 4(b)). Figures 4(c) and (d) on the other hand depict the expected spectra and intensity profile of a higher order soliton at mmL 5≈ . In this latter case, the peak power is 50 W and thus corresponds to an 3=N  higher order soliton solution. The splitting behavior observed in Fig. 4(d) is attributed to multi-photon absorption.                                      Fig. 4. (a)  Input and output soliton power spectra corresponding to the case shown in (a)  Fig.3 (a) ; (b) Fig.3.(b) ;     (c) and (d) spectral generation and intensity profile for an 3=N  soliton (50 W peak power) at mmL 5≈   In conclusion we have shown that optical solitons can exist in dispersion-inverted highly-nonlinear AlGaAs  nanowires. These soliton waves are possible at very low power levels in spite of strong dispersion and can form in millimeter long nanowire structures. The intensity and spectral evolution of solitons propagating in such AlGaAs  nanowaveguides was investigated in the presence of loss, multiphoton absorption and higher-order dispersion.       #67969 - $15.00 USD Received 10 February 2006; revised 10 March 2006; accepted 11 March 2006(C) 2006 OSA 20 March 2006 / Vol. 14,  No. 6 / OPTICS EXPRESS  2282

Solitons in dispersion-inverted AlGaAs nanowires

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Solitons in dispersion-inverted AlGaAs nanowires

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