## Overcoming phase mismatch in nonlinear metamaterials [Invited] |

Optical Materials Express, Vol. 1, Issue 7, pp. 1232-1243 (2011)

http://dx.doi.org/10.1364/OME.1.001232

Acrobat PDF (943 KB)

### Abstract

Nonlinear metamaterials have potentially interesting applications in highly efficient wave-mixing and parametric processes, owing to their ability to combine enhanced nonlinearities with exotic and configurable linear properties. However, the strong dispersion and unconventional configurations typically associated with metamaterials place strong demands on phase matching in such structures. In this paper, we present an overview of potential phase matching solutions for wave-mixing processes in nonlinear metamaterials. Broadly speaking, we divide the phase matching solutions into conventional techniques (anomalous dispersion, birefringence, and quasi-phase matching) and metamaterial-inspired techniques (negative-index and index-near-zero phase matching), offering numerical and experimental examples where possible. We find that not only is phase matching feasible in metamaterials, but metamaterials can support a wide range of phase matching configurations that are otherwise impossible in natural materials. These configurations have their most compelling applications in those devices where at least one of the interacting waves is counter-propagating, such as the mirror-less optical parametric oscillator and the nonlinear optical mirror.

© 2011 OSA

## 1. Introduction

1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. **7**, 118–119 (1961). [CrossRef]

3. I. Shoji, T. Kondo, and R. Ito, “Second-order nonlinear susceptibilities of various dielectric and semiconductor materials,” Opt. Quantum Electron. **34**, 797–833 (2002). [CrossRef]

4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. **127**, 1918–1939 (1962). [CrossRef]

5. P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. **35**, 23–39 (1963). [CrossRef]

7. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. **9**, 114–166 (1966). [CrossRef]

11. C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasi-phase-matched second-harmonic generation,” Opt. Lett. **24**, 1139–1141 (1999). [CrossRef]

12. J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO_{3},” Opt. Lett. **22**, 862–864 (1997). [CrossRef] [PubMed]

13. C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics **1**, 459–462 (2007). [CrossRef]

14. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science **292**, 77–79 (2001). [CrossRef] [PubMed]

15. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

16. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. **91**, 037401 (2003). [CrossRef] [PubMed]

17. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science **313**, 502–504 (2006). [CrossRef] [PubMed]

19. D. Huang, A. Rose, E. Poutrina, S. Larouche, and D. R. Smith, “Wave mixing in nonlinear magnetic metacrystal,” Appl. Phys. Lett. **98**, 204102 (2011). [CrossRef]

20. M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, “Amplification and squeezing of quantum noise with a tunable josephson metamaterial,” Nat. Phys. **4**, 929–931 (2008). [CrossRef]

21. D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. **91**, 144107 (2007). [CrossRef]

22. D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. **96**, 104104 (2010). [CrossRef]

## 2. Wave-mixing and phase mismatch: an overview

*ω*

_{1}≤

*ω*

_{2}≤

*ω*

_{3}. These equations apply to all three-wave mixing processes, such as difference frequency generation, sum frequency generation, and optical parametric amplification and oscillation. For the wave-mixing process to be efficient, both Eqs. (1) and (2) must be satisfied to within the uncertainties given by the system’s finite spatial and temporal extents [24

24. A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase-matching of momentum and energy in nonlinear optical processes,” Nat. Photonics **4**, 570–575 (2010). [CrossRef]

*k*= |

*k⃗*

_{1}+

*k⃗*

_{2}–

*k⃗*

_{3}|. The physical meaning of the phase mismatch can be understood by considering the coherence length

*z*-axis, we can write

*z*-direction. We summarize the four possible co-linear phase matching configurations in Table 1. In labeling these configurations, we borrow the conventional notation of birefringent phase matching, such that Type I refers to like-propagating lower-frequency waves, and Type II refers to unlike-propagating lower-frequency waves. While most nonlinear devices to date are based on the parallel-I configuration, the anti-parallel configurations are crucial to several highly intriguing and advantageous devices, such as the mirror-less optical parametric oscillator (MOPO) [7

7. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. **9**, 114–166 (1966). [CrossRef]

10. Y. Ding, J. Kang, and J. Khurgin, “Theory of backward second-harmonic and third-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear medium,” IEEE J. Quantum Electron. **34**, 966–974 (1998). [CrossRef]

27. A. Popov and V. Shalaev, “Negative-index metamaterials: second-harmonic generation, manley-rowe relations and parametric amplification,” Appl. Phys. B **84**, 131–137 (2006). [CrossRef]

*n*> 0, the anti-parallel configurations require rather extreme techniques to overcome phase mismatch [25].

26. E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. **12**, 093010 (2010). [CrossRef]

## 3. Anomalous dispersion phase matching

28. T. C. Kowalczyk, K. D. Singer, and P. A. Cahill, “Anomalous-dispersion phase-matched second-harmonic generation in a polymer waveguide,” Opt. Lett. **20**, 2273–2275 (1995). [CrossRef] [PubMed]

29. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. **47**, 2075–2084 (1999). [CrossRef]

26. E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. **12**, 093010 (2010). [CrossRef]

*F*is the oscillator strength,

*ω*

_{0}is the resonance frequency, and

*γ*is the damping coefficient. If we assume the nearly degnerate case

*ω*

_{1}≈

*ω*

_{2}and take the limit as

*γ*→ 0, the phase matching condition can be simplified to where we have taken

*ɛ*is the permittivity seen by the

_{i}*i*

^{th}wave. Assuming the metamaterial contains no electrically resonant elements at these frequencies and neglecting the effects of spatial dispersion, it follows that the permittivity must display normal dispersion and thus the right hand side will be greater than 1. To meet the phase matching condition, the frequencies must therefore satisfy

*ω*

_{1}<

*ω*

_{0}<

*ω*

_{3}. Furthermore, if, to avoid losses, the frequencies are equally detuned from resonance such that

*δɛ*∼ 0.1, phase matching would require

*F*∼ 0.01. While anomalous dispersion phase matching applies naturally to resonant metamaterials, residual absorption in the transparency windows will tend to limit its applicability.

## 4. Birefringence phase matching

*θ*is the angle between the optical axis and the direction of propagation. Thus, provided the birefringence is large enough, the phase matching condition can be met by selecting the polarizations of each wave and tuning

*θ*through rotation of the crystal. As an example, let us consider Type I-(

*eeo*) phase matching in the nearly degenerate case,

*ω*

_{1}≈

*ω*

_{2}. For this configuration, phase matching can be achieved in a nonlinear crystal if the maximum birefringence,

*θ*≠ 0°, 180°, ±90°, walk-off between the ordinary and extraordinary beams imposes a limit on the maximum interaction length [2].

*eoo*) birefringent phase matching in the anti-parallel-IIa configuration for the nearly degenerate case,

*ω*

_{1}≈

*ω*

_{2}, where wave 1 is anti-parallel to waves 2 and 3. Invoking (

*eoo*) polarizations in the refractive indices of Table 1, phase matching in this case requires a birefringence of

*ω*

_{1}<<

*ω*

_{2}, this constraint is relaxed, leading to speculation that birefringent phase matching for backward wave oscillation will likely only be achievable with a signal frequency in the mid- or far-infrared spectrum, while the idler and pump are near-infrared or higher frequency waves [7

7. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. **9**, 114–166 (1966). [CrossRef]

30. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. **90**, 077405 (2003). [CrossRef] [PubMed]

31. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature **470**, 366–371 (2011). [CrossRef]

*μ*m, immersed in a hypothetical nonlinear dielectric with

*ɛ*= 2

_{d}*ɛ*

_{0}and

*d*

_{11}= 10 pm/V. Such a structure is easily fabricated by existing techniques, with a frequency range of operation that includes the far-infrared wavelength of 10.6

*μ*m, corresponding to the output of a CO

_{2}laser. Labeling the crystal axes as in Fig. 1(b), this metamaterial supports coupling between the structure and the incident fields only for electric fields polarized in the

*Z*-direction. Furthermore, the fields coupled into the structure naturally localize in the capactive gaps between overlapping bars, with a dominant electric field component in the

*X*-direction. The symmetry of the metamaterial prevents linear coupling between these polarizations, and thus the metamaterial is strongly biaxial with effective linear susceptibility tensors that are diagonal in the

*XYZ*basis. The resulting nonlinear tensors, however, are not diagonal. Considering Type-I(eeo) and propagation in the

*YZ*-plane, there is significant overlap of the

*X*-components of the electric fields of the three modes in the capacitive gaps, and the metamaterial thus supports a non-zero

*d*

_{35}nonlinear coefficient. This artificially engineered nonlinearity, combined with the massive anisotropy, can support birefringence phase matched oscillations without a mirror, with distinct benefits compared to alternate implementations.

33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

32. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E **71**, 036617 (2005). [CrossRef]

*YZ*plane, the metamaterial is positive uniaxial to within simulation error, with extraordinary and ordinary waves corresponding to TM and TE polarizations, respectively. The principal values of the extraordinary and ordinary indices are shown in Fig. 1(c), displaying anomalously large birefringence, as expected. Furthermore, we perform Type-I(eeo) difference frequency generation simulations using the techniques outlined in Ref. [23], using an ordinary-polarized 10.6

*μ*m pump wave as wave 3, and sweeping the frequencies of waves 1 and 2. We use the results of these simulations in the transfer matrix-based nonlinear retrieval method to determine the

*d*

_{35}nonlinear coefficient [34

34. A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E **82**, 036608 (2010). [CrossRef]

*d*

_{35}coefficient that is both non-zero and several times larger than the

*d*

_{11}in the background dielectric, owing to the field localization enhancement effect [23]. Renaming waves 1, 2 and 3 to signal, idler, and pump, these results are immediately applicable to the nonlinear process of optical parametric oscillation. Indeed, the anisotropy is large enough to support birefringent phase matching of a counter-propagating signal wave, corresponding to the anti-parallel-IIa configuration. By rotating the direction of propagation

*z*relative to the optical axis

*Z*, depicted in Fig. 1(a), the anti-parallel-IIa phase matching condition can be satisfied for signal and idler frequency pairs over a wide frequency range, as shown in Fig. 1(d). Thus, for pumping with a CO

_{2}laser, this metamaterial can be expected to support mirror-less oscillations, generating a tunable signal wave with a frequency ranging from 1 to 8 THz. Moreover, the natural material chosen as the embedding dielectric does not require significant birefringence nor nonlinear cross-terms, allowing for high flexibility in the choice of embedding material, and, consequently, the potential achievement of competitively-low oscillation thresholds. We note that the large anisotropy, however, is accompanied by proportionately large walk-off, except near

*θ*= 90°, corresponding to

*ω*

_{1}≈ 2

*π*× 8.18 THz and

*ω*

_{2}≈ 2

*π*× 20.10 THz. Similarly, walk-off can be eliminated at any single signal-idler frequency pair by redesigning the anisotropy of this metamaterial to ensure that the principal values of the refractive indices satisfy the phase matching condition.

## 5. Quasi-phase matching

4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. **127**, 1918–1939 (1962). [CrossRef]

5. P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. **35**, 23–39 (1963). [CrossRef]

35. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. **28**, 2631–2654 (1992). [CrossRef]

*k*=

*mG⃗*, or equivalently Λ =

*mL*

_{coh}, where

*m*is any integer. As such, the possible frequencies for phase matching are strictly limited by the choice of poling period, with small associated tuning bandwidths [35

35. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. **28**, 2631–2654 (1992). [CrossRef]

*π*in the case of first-order QPM [6].

12. J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO_{3},” Opt. Lett. **22**, 862–864 (1997). [CrossRef] [PubMed]

13. C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics **1**, 459–462 (2007). [CrossRef]

15. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

36. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E **71**, 036609 (2005). [CrossRef]

37. A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. **107**, 063902 (2011). [CrossRef] [PubMed]

38. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature **444**, 597–600 (2006). [CrossRef] [PubMed]

41. T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science **325**, 1518–1521 (2009). [CrossRef] [PubMed]

42. A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A **84**, 013823 (2011). [CrossRef]

## 6. Negative-index phase matching

*ɛ*] < 0 and Re[

*μ*] < 0 in a certain frequency band [14

14. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science **292**, 77–79 (2001). [CrossRef] [PubMed]

43. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**, 4184–4187 (2000). [CrossRef] [PubMed]

27. A. Popov and V. Shalaev, “Negative-index metamaterials: second-harmonic generation, manley-rowe relations and parametric amplification,” Appl. Phys. B **84**, 131–137 (2006). [CrossRef]

44. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B **69**, 165112 (2004). [CrossRef]

45. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B **23**, 529–534 (2006). [CrossRef]

*z*-direction supports a positvely-directed wavevector. In particular, there were two processes that proved highly intriguing from a theoretical viewpoint: mirror-less optical parametric amplification and oscillation, and the nonlinear optical mirror effect.

27. A. Popov and V. Shalaev, “Negative-index metamaterials: second-harmonic generation, manley-rowe relations and parametric amplification,” Appl. Phys. B **84**, 131–137 (2006). [CrossRef]

*n*

_{1}= −

*n*

_{3}and requires either the fundamental or second-harmonic wave to propagate in a negative-index band and the other in a positive-index band. Such a device has been demonstrated at microwave frequencies, shown schematically in Fig. 3(b) [37

37. A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. **107**, 063902 (2011). [CrossRef] [PubMed]

*F*= 0.22,

*ω*

_{0}= 2

*π*× 608 MHz,

*γ*= 2

*π*× 14 MHz,

*ɛ*= 2.2

_{b}*ɛ*

_{0}, and

*ω*= 2

_{c}*π*× 674 MHz. The corresponding index of refraction and coherence lengths are plotted in Fig. 3(a), showing a dramatic rise in the coherence length of the anti-parallel-I configuration as the fundamental wave is tuned through the negative-index band. Thus, owing to negative-index phase matching, second-harmonic generation in the anti-parallel-I configuration was shown to be far more efficient than in the parallel-I configuration [37

37. A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. **107**, 063902 (2011). [CrossRef] [PubMed]

46. A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. **31**, 2169–2171 (2006). [CrossRef] [PubMed]

47. N. M. Litchinitser and V. Shalaev, “Metamaterials: Loss as a route to transparency,” Nat. Photonics **3**, 75 (2009). [CrossRef]

## 7. Index-near-zero phase matching

48. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E **70**, 046608 (2004). [CrossRef]

49. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using *ɛ*-near-zero materials,” Phys. Rev. Lett. **97**, 157403 (2006). [CrossRef] [PubMed]

*n*

_{3}= 0, the anti-parallel-IIa and anti-parallel-IIb configurations are both satisfied by

*n*

_{1}

*ω*

_{1}=

*n*

_{2}

*ω*

_{2}. This characteristic of index-near-zero materials can be used to achieve simultaneous phase or QPM of two or more configurations, opening avenues to a wide range of simultaneous and/or cascaded nonlinear processes.

*ω*

_{1}=

*ω*

_{2}) parallel-I and anti-parallel-I configurations has been achieved at microwave frequencies, using the same metamaterial described above by Eqs. (7) and (8), but in the region where

*n*

_{1}≈ 0 [37

**107**, 063902 (2011). [CrossRef] [PubMed]

*k*≈ |

*k*

_{3}| for both configurations, so that an incident fundamental wave was able to simultaneously generate second-harmonic waves in the positive and negative

*z*-directions, shown schematically in Fig. 3(c).

## 8. Conclusion

_{2}laser.

## Acknowledgments

## References and links

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22. | D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. |

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31. | M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature |

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36. | D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E |

37. | A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. |

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42. | A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A |

43. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

44. | V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B |

45. | I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B |

46. | A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. |

47. | N. M. Litchinitser and V. Shalaev, “Metamaterials: Loss as a route to transparency,” Nat. Photonics |

48. | R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E |

49. | M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using |

50. | M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second and third harmonic generation in a |

**OCIS Codes**

(160.3380) Materials : Laser materials

(290.4210) Scattering : Multiple scattering

**ToC Category:**

Metamaterials

**History**

Original Manuscript: September 12, 2011

Manuscript Accepted: October 5, 2011

Published: October 13, 2011

**Virtual Issues**

Nonlinear Optics (2011) *Optical Materials Express*

(2011) *Advances in Optics and Photonics*

**Citation**

Alec Rose and David R. Smith, "Overcoming phase mismatch in nonlinear metamaterials [Invited]," Opt. Mater. Express **1**, 1232-1243 (2011)

http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-7-1232

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