Abstract

Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.

© 2007 Optical Society of America

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2007 (5)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Phot. 1, 449–458 (2007).
[Crossref]

A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref] [PubMed]

P. Bermel, A. Rodriguez, J. D. Joannopoulos, and M. Soljacic, “Tailoring optical nonlinearities via the Purcell effect,” Phys. Rev. Lett. 99, 053601 (2007).
[Crossref] [PubMed]

J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25, 2539–2546 (2007).
[Crossref]

H. Shinojima, “Optical nonlinearity in CdSSe microcrystallites embedded in glasses,” IEICE Trans. Electron. E90-C, 127–134 (2007).
[Crossref]

2006 (6)

2005 (7)

2004 (6)

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[Crossref]

M. G. Martemyanov, E. M. Kim, T. V. Dolgova, A. A. Fedyanin, O. A. Aktsipetrov, and G. Marowsky, “Third-harmonic generation in silicon photonic crystals and microcavities,” Phys. Rev. B 70, 073311 (2004).
[Crossref]

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[Crossref]

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92, 083903 (2004).
[Crossref] [PubMed]

P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Phys. Rev. B 69, 035316 (2004).
[Crossref]

X. Brokmann, L. Coolen, M. Dahan, and J. P. Hermier, “Measurement of the radiative and nonradiative decay rates of single CdSe nanocrystals through a controlled modification of their spontaneous emission,” Phys. Rev. Lett. 93, 107403 (2004).
[Crossref] [PubMed]

2003 (11)

A. H. Norton and C. M. de Sterke, “Optimal poling of nonlinear photonic crystals for frequency conversion,” Opt. Lett. 28, 188–190 (2003).
[Crossref] [PubMed]

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzetti, L. C. Andreani, F. Romanato, L. Businaro, E. Di Fabrizio, A. Passaseo, and M. De Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161306 (2003).
[Crossref]

H. Y. Ryu and M. Notomi, “Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity,” Opt. Lett. 28, 2390–2392 (2003).
[Crossref] [PubMed]

A. R. Cowan and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003).
[Crossref]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[Crossref] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, “Optical bistability in axially modulated OmniGuide fibers,” Opt. Lett. 28, 516–518 (2003).
[Crossref] [PubMed]

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506–2508 (2003).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 83, 1512–1514 (2003).
[Crossref]

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[Crossref]

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003).
[Crossref]

2002 (9)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2002).
[Crossref]

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2001 (8)

D. V. Talapin, A. L. Rogach, A. Kornowski, M. Haase, and H. Weller, “Highly luminescent monodisperse CdSe and CdSe/ZnS nanocrystals synthesized in a hexadecylamine-trioctylphosphine oxide-trioctylphospine mixture,” Nano Lett. 1, 207–211 (2001).
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2000 (4)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
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1999 (3)

1998 (1)

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1996 (2)

1995 (3)

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1994 (1)

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
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1993 (1)

1991 (1)

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1990 (1)

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1989 (1)

1982 (1)

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1981 (2)

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1980 (1)

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1977 (1)

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1970 (1)

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1966 (1)

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1962 (1)

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G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609 (2001).
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X. Brokmann, L. Coolen, M. Dahan, and J. P. Hermier, “Measurement of the radiative and nonradiative decay rates of single CdSe nanocrystals through a controlled modification of their spontaneous emission,” Phys. Rev. Lett. 93, 107403 (2004).
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Yu, X.

Zhang, B.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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Appl. Phys. Lett. (9)

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T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
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M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
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IEEE J. Quantum Electron. (4)

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Figures (7)

Fig. 1.
Fig. 1.

Sketch of a system composed by an optical resonator coupled symmetrically to both an input and output ports. ωc is the corresponding resonant frequency and Γ is the width of the resonance. Pin and Pout label the incoming and outgoing powers through the structure, respectively. Inset shows the typical linear transmission spectrum corresponding to this system.

Fig. 2.
Fig. 2.

(a) Evolution of the transmission spectra through the system sketched in Fig. 1 when the refractive index of the resonator is increased by δn. As can be seen in this panel, δn shifts the original resonant frequency of the cavity ωc (dashed line) towards the frequency of the external illumination ωp (blue dashed line). (b) Dependence of Pout/Pin as a function of the outgoing power for Δ=3 (see text for details on this magnitude). (c) Same function as (b) but this time Pout is plotted as a function of Pin for several values of Δ. Dotted lines display the unstable branches of the hysteresis loop for each case.

Fig. 3.
Fig. 3.

(a) Photonic crystal implementation of the system sketched in Fig. 1. The PhC is made by a periodic two dimensional distribution of high dielectric rods (εH =12.25, yellow regions in the figure) in a low-ε background (εL =2.25). The rods have a radius of r=0.25a. A point defect, introduced by increasing the radius of the central rod to r=0.33a, is symmetrically coupled to two single mode PhC waveguides on the left and right. The electric field pointing into the page is depicted with positive (negative) values in red (blue). (b) Computed dependence of the output power (Pout ) as a function of the input power (Pin ) for the structure shown in panel (a) when the central rod is assumed to be made by a nonlinear Kerr-like material. Green line displays the results obtained from a perturbation theory analysis while the blue dots correspond to the result of a nonlinear FDTD simulation. Dashed lines represent the unstable branch of the bistable loop.

Fig. 4.
Fig. 4.

Schematic diagram of waveguide-cavity system. Input light from a waveguide (left) at one frequency ω 1 is coupled to a doubly-resonant cavity (with resonances at ω 1 and ω 2, with respective lifetimes Q 1 and Q 2) and converted to a cavity mode at another frequency ω 2 by a χ (2) process. The converted light is radiated back into the waveguide at both frequencies.

Fig. 5.
Fig. 5.

Plot of conversion efficiency Pω2out/Pin (black), and reflection Pω1out/Pin vs. P in for the schematic geometry in Fig. 4 (Here in/out denotes input/output power at frequency ω). The maximum conversion efficiency is achieved at the expected critical power P 0. To compute this figure, we have chosen conservative modal parameters ω 1=0.3 2πc/a, Q 1=104, Q 2=2Q1, 1/VHG ≈10-5a-3 (where a is the characteristic length scale of the system, see Ref. [35] for further details on this calculation).

Fig. 6.
Fig. 6.

A 7×7 square lattice of dielectric rods (ε=12.25) in air, with a single defect rod in the middle. On top of the dielectric structure outlined in black, the Ez field is plotted, with positive (negative) values in red (blue). A small region of nonlinear material, e.g., a CdSe nanocrystal, with transition frequency ωelec , is placed in the defect rod.

Fig. 7.
Fig. 7.

(a) Numerical calculation of the enhancement of SE for the set-up in Fig. 6, given by the ratio of the rate of emission in the PhC, T -1 1,purcell, divided by the emission rate in vacuum, T -1 1,vac. (b) Kerr enhancement η≡Reχ(3) purcell /Reχ (3) vac as a function of electronic transition frequency (ω elec) for a system of dielectric rods in air, with the parameter values listed in the text.

Equations (4)

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P out P in = 1 1 + ( ( ω ω c ) Γ ) 2
P out P in = 1 1 + ( P out P 0 Δ ) 2
χ ( 3 ) = 4 3 N μ 4 T 1 T 2 2 ( Δ T 2 i ) h ¯ 3 ( 1 + Δ 2 T 2 2 ) 2 ,
Re χ ( 3 ) 4 3 N μ 4 ( 1 h ¯ Δ ) 3 T 1 T 2 .

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