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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11584–11590
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On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses

Lin Zhang, Yan Yan, Yang Yue, Qiang Lin, Oskar Painter, Raymond G. Beausoleil, and Alan E. Willner  »View Author Affiliations


Optics Express, Vol. 19, Issue 12, pp. 11584-11590 (2011)
http://dx.doi.org/10.1364/OE.19.011584


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Abstract

Dramatic advances in supercontinuum generation have been made recently using photonic crystal fibers, but it is quite challenging to obtain an octave-spanning supercontinuum on a chip, partially because of strong dispersion in high-index-contrast nonlinear integrated waveguides. We show by simulation that extremely flat and low dispersion can be achieved in silicon nitride slot waveguides over a wavelength band of 500 nm. Different from most of previously reported supercontinua that were generated either by higher-order soliton fission in anomalous dispersion regime or by self-phase modulation in normal dispersion regime, a two-octave supercontinuum from 630 to 2650 nm (360 THz in total) can be generated by enhancing self-steepening in pulse propagation in nearly zero dispersion regime, when an optical shock as short as 3 fs is formed.

© 2011 OSA

1. Introduction

One basic building block in nonlinear optics is a supercontinuum generator, which has experienced a revolutionary development after its realization using photonic crystal fibers (PCFs) [1

1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000). [CrossRef]

,2

2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

]. Supercontinua of a few octaves in width have been reported [3

3. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25(19), 1415–1417 (2000). [CrossRef]

,4

4. G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28 μm in a fluoride fiber,” Appl. Phys. Lett. 95(16), 161103 (2009). [CrossRef]

] for numerous applications such as frequency metrology, optical coherence tomography, pulse compression, microscopy and spectroscopy, telecommunication, and sensing. A key figure of merit is the width of a supercontinuum, which is greatly affected by the spectral profile of the dispersion in a nonlinear medium. The success of PCF-based supercontinuum generation is partially attributed to advanced dispersion engineering allowed by design freedom of the 2D lattice in the fiber cladding [2

2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

,5

5. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424(6948), 511–515 (2003). [CrossRef] [PubMed]

]. Generally, the dispersion engineering is aimed at desirable zero-dispersion wavelengths and low dispersion over a wide spectral band. Flat dispersion of ± 2 ps/(nm·km) over a 1000-nm-wide wavelength range was proposed [6

6. M. L. V. Tse, P. Horak, F. Poletti, N. G. Broderick, J. H. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]

,7

7. W.-Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009). [CrossRef]

].

Highly nonlinear integrated waveguides and photonic wires with high index contrast have generated much excitement in recent years [8

8. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]

,9

9. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011). [CrossRef]

], forming the backbone of compact devices in a photonic-integrated-circuit platform. However, to the best of our knowledge, demonstrated on-chip supercontinua have a spectral range of ~400 nm [10

10. Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004). [CrossRef] [PubMed]

14

14. D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express 18(2), 923–930 (2010). [CrossRef] [PubMed]

], far less than one octave, which is partially because of insufficient capability to engineer the dispersion of nonlinear waveguides. Recently, the dispersion profile of a silicon waveguide was made 20 times flatter by introducing a nano-scale slot structure [15

15. L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18(19), 20529–20534 (2010). [CrossRef] [PubMed]

], but this is still not sufficient to support more than one octave spectral broadening of femtosecond optical pulses.

Here, we propose a silicon nitride slot waveguide, which exhibits further improvement in dispersion flatness by 30 times, compared with that reported in Ref [15

15. L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18(19), 20529–20534 (2010). [CrossRef] [PubMed]

]. In our simulation, a two-octave supercontinuum can be obtained on a chip by enhancing pulse self-steepening and forming an optical shock as short as 3 fs. The supercontinuum can be ‘transferred’ to third-harmonic spectral range by phase-locked pulse trapping effect. On-chip supercontinuum generation is believed to be a key enabler for building portable imaging, sensing, and frequency-metrology-based positioning systems. We expect that the advanced dispersion engineering technique in integrated waveguides opens the door to combine ultrafast optics and nano-photonics and to apply ultra-wideband optical information technologies ubiquitously.

2. Flat all-normal dispersion in silicon nitride slot waveguide

The proposed silicon nitride (Si3N4) slot waveguide is shown in Fig. 1
Fig. 1 Silicon nitride slot waveguide for dispersion flattening and supercontinuum generation. A horizontal silica slot is between two silicon nitride layers.
. A horizontal silica slot is formed between two Si3N4 layers. The substrate is 2-μm-thick SiO2. The waveguide parameters are: width W = 980 nm, upper height Hu = 497 nm, lower height Hl = 880 nm, and slot height Hs = 120.5 nm. Material dispersions of Si3N4 and SiO2 are considered. The waveguide has a single fundamental mode at the vertical polarization beyond 1800 nm.

3. Supercontinuum generation by enhanced nonlinear self-steepening effect

We use a generalized nonlinear envelope equation (GNEE) [17

17. G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15(9), 5382–5387 (2007). [CrossRef] [PubMed]

,18

18. S. Wabnitz and V. V. Kozlov, “Harmonic and supercontinuum generation in quadratic and cubic nonlinear optical media,” J. Opt. Soc. Am. B 27(9), 1707–1711 (2010). [CrossRef]

], with third harmonic generation considered, to model supercontinuum generation. It has been confirmed that the simulation of even sub-cycle pulse propagations using this envelope equation is quite accurate [17

17. G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15(9), 5382–5387 (2007). [CrossRef] [PubMed]

20

20. P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81(1), 013819 (2010). [CrossRef]

], which is in excellent quantitative agreement with numerical integration of accurate Maxwell's equations [21

21. J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52(7), 973–986 (2005). [CrossRef]

]. We use split-step Fourier method [22

22. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

] to solve the following GNEE:
(z+α2+im=2(i)mβmm!mtm)A=[NKerr(A)+NRaman(A)]
where
NKerr(A)=iγe(1iτKerrt)(|A|2A+13A3e2iω0t)  andNRaman(A)=iγR(1iτRamant)(AthR(tt')(|A|2+13A2e2iω0t')dt').
We denote A = A(z,t) as the complex amplitude of an optical pulse. Its Fourier transform is A˜(z,ω)=(1/2π)A(z,t)exp(iωt)dt. The terms |A|2A and (1/3)A3exp(2iω0t) describe the self-phase modulation and third-harmonic generation, respectively. α is the propagation loss, and βm is the mth-order dispersion coefficient. The nonlinear coefficient γe of the waveguide is obtained using a full-vectorial model. The shock times τKerr and τRaman for Kerr and Raman nonlinearities are calculated with consideration on wavelength-dependent effective mode area and nonlinear index n2. hR(t) is the Raman response function.

A chirp-free hyperbolic secant pulse spectrally centered at 2200-nm wavelength, with a full width at half-maximum (FWHM) of 120 fs and a peak power of 6 kW (pulse energy of 0.8 nJ), is launched into the proposed Si3N4 slot waveguide. Figure 3(a)
Fig. 3 Two-octave supercontinuum generation in the dispersion-flattened slot waveguide. (a) The input 120-fs pulse is centered at 2200-nm wavelength. A supercontinuum is generated from 630 to 2650 nm mainly due to self-steepening of the pulse. (b) In time domain, an optical shock as short as 3 fs (see the inset) is formed, as the pulse travels 5 mm.
shows that, along the waveguide, the pulse generates significantly blue-shifted spectral components down to 800 nm wavelength mainly due to self-steepening [22

22. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

,27

27. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]

]. In our case, the flattened dispersion reduces walk-off of newly generated spectral components, which facilitates the formation of an optical shock at the pulse falling edge that is as short as 3 fs (see Fig. 3(b)), as it travels 5 mm. The optical shock induces so much spectral blue shift that it reaches a short-wavelength region where third harmonics are generated. The blue part of the spectrum becomes stable at a propagation distance of 15 mm and shows a small power fluctuation of 3 dB over a 754-nm-wide wavelength range from 847 to 1601 nm at 20 mm. The high-power part of the spectrum is red-shifted and extended to 2650 nm, due to self-phase modulation and Raman self-frequency shift [22

22. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

]. The supercontinuum is formed from 630 to 2650 nm (that is, 360 THz in total) at –35 dB, covering a two-octave bandwidth.

Spectral evolution along the waveguide length is illustrated in Fig. 4
Fig. 4 Spectral evolution in the slot waveguides. Low dispersion causes dramatic spectral broadening and optical shock formation, from A to B. Then, accumulated dispersion makes the pulse falling edge less steep and improves spectral flatness, from B to C. Self-phase modulation produces blue-shifted frequencies near the carrier frequency, from A to D.
. A few nonlinear interactive processes responsible for the formation of the supercontinuum can be seen. First, self-steepening of the optical pulse, associated with intensity-dependent group velocity [22

22. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

], causes a sharp falling edge of the pulse. On the other hand, self-phase modulation produces blue-shifted spectral components at the falling edge, which walk-off very little relative to the edge, due to the low dispersion. Together with the self-steepening effect, these high-frequency components in turn help form a shaper edge, resulting in bluer shifts. Therefore, the flat and low dispersion triggers this positive feedback mechanism for optical shock formation and spectral broadening, which follows from A to B as shown in Fig. 4. Such a steep pulse edge transfers energy to a frequency range near 370 THz, ~230 THz away from the pulse carrier frequency. Second, tracking from B to C in Fig. 4, we note that, with accumulated dispersion, the falling edge becomes less steep, and newly generated blue-shifted frequencies are closer to the carrier, which improves the spectral flatness of the supercontinuum. Another effect of the dispersion is that the blue-shifted components walk away from the steep edge and overlap with the pulse tail, forming a beating pattern as shown in Fig. 3(b). Third, the pulse waveform in Fig. 3(b) has a high-power 'shoulder' at the beginning of its falling edge before the optical shock, which generates blue-shifted frequencies near the carrier following from A to D in Fig. 4. Fourth, third-harmonic generation occurs at 408 THz, and some frequency-resolved fringes are observed mainly due to cross-phase modulation by the input pulse [22

22. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

]. The third-harmonic pulse sees a larger group delay and escapes from the envelope of the input pulse. This is why the third-harmonic spectrum becomes stable after a distance of ~1 mm.

The dynamics of the self-steepening-induced supercontinuum generation, corresponding to Fig. 4, can be intuitively represented using spectrograms generated by the cross-correlation frequency-resolved optical gating (X-FROG) technique [2

2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

], in which an optical pulse is characterized simultaneously in time and frequency domains. As explained above, the fundamental pulse experiences dramatic self-steepening and spectral broadening in its propagation from 0 to 4 mm. Due to frequency-dependent group delay, the blue part of the edge walks off relative to the pulse, as seen at a distance of 10 mm, which forms a hockey-stick-like pattern in the spectrogram shown in Fig. 5
Fig. 5 Spectrogram evolution of the pulse. Strong self-steepening and spectral broadening occur in the pulse propagation from 0 to 4 mm. At 10 mm, the blue part of the pulse falling edge walks off due to dispersion. This forms a hockey-stick-like pattern in the spectrogram. A third-harmonic pulse trapped by the fundamental pulse due to a nonlinear phase locking also has a hockey-stick-like spectrogram, though stretched 3 times in the frequency domain.
.

The third-harmonic pulse exhibits more complex dynamics, and its evolution is significantly affected by group delay and pulse trapping induced by third harmonic generation [28

28. N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett. 89(14), 143901 (2002). [CrossRef] [PubMed]

,29

29. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007). [CrossRef]

]. As shown in Fig. 5, the third-harmonic pulse is generated and cross-phase modulated at the beginning of propagation. From 1 mm to 2 mm, the tail of the third-harmonic pulse, which is after the steep edge of the fundamental pulse, walks away quickly, since its frequency is not located in the dispersion-flattened spectral range. The rest part of the pulse that coincides with the peak of the fundamental pulse is split into two parts. First, the low-frequency part travels slowly, and after it arrives at the steep edge of the fundamental pulse, it is blue-shifted due to cross-phase modulation and then escapes from the envelope of the fundamental pulse. Second, the high-frequency part is trapped by the fundamental pulse due to a nonlinear phase locking mechanism [28

28. N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett. 89(14), 143901 (2002). [CrossRef] [PubMed]

] and carries the dispersion property impressed by the fundamental pulse [28

28. N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett. 89(14), 143901 (2002). [CrossRef] [PubMed]

,29

29. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007). [CrossRef]

], which is why its pattern in the spectrogram is also hockey-stick-like, although stretched 3 times in the frequency domain. As seen in Fig. 5, such phase-locked pulse trapping enables us to up-convert a 200-THz-wide supercontinuum that can be 2000 nm wide in wavelength, across a few-hundred-THz spectral region, to where a supercontinuum cannot be efficiently formed with an optical pulse at a local frequency, with flattened dispersion hardly achievable near material bandgap wavelength in practice.

4. Discussion and conclusion

Different from most of previously investigated supercontinua that were generated mainly due to either self-phase modulation in normal dispersion regime or high-order soliton fission and dispersion wave generation in anomalous dispersion regime [2

2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

], the reported supercontinuum features a highly asymmetric spectrum caused mainly by pulse self-steepening. Moreover, using a silicon nitride waveguide, one can have high output power and extended spectral range that are difficult to obtain in silicon waveguides.

In summary, we presented a dispersion tailoring technique that allows us to improve dispersion flatness by 30 times in integrated high-index-contrast waveguides. Benefiting from this, one can generate a two-octave supercontinuum on a chip by enhancing pulse self-steepening, which paves the way for ultrafast and ultra-wideband applications on an integrated nano-photonics platform. We believe that the on-chip supercontinuum generation would serve as a key enabler for building portable imaging, sensing, and positioning systems.

Acknowledgments

The authors would thank Jacob Levy at Cornell University for helpful discussions. This work is supported by HP Labs.

References and links

1.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000). [CrossRef]

2.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

3.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25(19), 1415–1417 (2000). [CrossRef]

4.

G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28 μm in a fluoride fiber,” Appl. Phys. Lett. 95(16), 161103 (2009). [CrossRef]

5.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424(6948), 511–515 (2003). [CrossRef] [PubMed]

6.

M. L. V. Tse, P. Horak, F. Poletti, N. G. Broderick, J. H. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]

7.

W.-Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009). [CrossRef]

8.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]

9.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011). [CrossRef]

10.

Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004). [CrossRef] [PubMed]

11.

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007). [CrossRef] [PubMed]

12.

I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007). [CrossRef] [PubMed]

13.

M. R. E. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As2S3) chalcogenide planar waveguide,” Opt. Express 16(19), 14938–14944 (2008). [CrossRef] [PubMed]

14.

D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express 18(2), 923–930 (2010). [CrossRef] [PubMed]

15.

L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18(19), 20529–20534 (2010). [CrossRef] [PubMed]

16.

A. M. Heidt, “Pulse preserving flat-top supercontinuum generation in all-normal dispersion photonic crystal fibers,” J. Opt. Soc. Am. B 27(3), 550–559 (2010). [CrossRef]

17.

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15(9), 5382–5387 (2007). [CrossRef] [PubMed]

18.

S. Wabnitz and V. V. Kozlov, “Harmonic and supercontinuum generation in quadratic and cubic nonlinear optical media,” J. Opt. Soc. Am. B 27(9), 1707–1711 (2010). [CrossRef]

19.

G. Genty, B. Kibler, P. Kinsler, and J. M. Dudley, “Harmonic extended supercontinuum generation and carrier envelope phase dependent spectral broadening in silica nanowires,” Opt. Express 16(15), 10886–10893 (2008). [CrossRef] [PubMed]

20.

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81(1), 013819 (2010). [CrossRef]

21.

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52(7), 973–986 (2005). [CrossRef]

22.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

23.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]

24.

K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express 16(17), 12987–12994 (2008). [CrossRef] [PubMed]

25.

S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17(4), 2298–2318 (2009). [CrossRef] [PubMed]

26.

Y. Wang, R. Yue, H. Han, and X. Liao, “Raman study of structural order of a-SiNx:H and its change upon thermal annealing,” J. Non-Cryst. Solids 291(1-2), 107–112 (2001). [CrossRef]

27.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]

28.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett. 89(14), 143901 (2002). [CrossRef] [PubMed]

29.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007). [CrossRef]

OCIS Codes
(130.3060) Integrated optics : Infrared
(130.3120) Integrated optics : Integrated optics devices
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Integrated Optics

History
Original Manuscript: April 20, 2011
Manuscript Accepted: May 26, 2011
Published: May 31, 2011

Citation
Lin Zhang, Yan Yan, Yang Yue, Qiang Lin, Oskar Painter, Raymond G. Beausoleil, and Alan E. Willner, "On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses," Opt. Express 19, 11584-11590 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11584


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References

  1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000). [CrossRef]
  2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
  3. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25(19), 1415–1417 (2000). [CrossRef]
  4. G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28 μm in a fluoride fiber,” Appl. Phys. Lett. 95(16), 161103 (2009). [CrossRef]
  5. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424(6948), 511–515 (2003). [CrossRef] [PubMed]
  6. M. L. V. Tse, P. Horak, F. Poletti, N. G. Broderick, J. H. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]
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