## Subdiffraction focusing of scanning beams by a negative-refraction layer combined with a nonlinear layer

Optics Express, Vol. 14, Issue 23, pp. 11194-11203 (2006)

http://dx.doi.org/10.1364/OE.14.011194

Acrobat PDF (213 KB)

### Abstract

We evaluate the possibility to focus scanning light beams below the diffraction limit by using the combination of a nonlinear material with a Kerr-type nonlinearity or two-photon absorption to create seed evanescent components of the beam and a negative-refraction material to enhance them. Superfocusing to spots with a FWHM in the range of 0.2λ is theoretically predicted both in the context of the effective-medium theory and by the direct numerical solution of Maxwell equations for an inhomogeneous photonic crystal. The evolution of the transverse spectrum and the dependence of superfocusing on the parameters of the negative-refraction material are also studied. We show that the use of a Kerr-type nonlinear layer for the creation of seed evanescent components yields focused spots with a higher intensity compared with those obtained by the application of a saturable absorber.

© 2006 Optical Society of America

## 1. Introduction

1. A. KK. Wong, *Resolution enhancement techniques in optical lithography* (SPIE Press, Bellingham, Washington, 2001). [CrossRef]

*π*/λ (evanescent components) are lost during propagation. Near-field optical methods can overcome this limitation due to the creation and interaction of evanescent components with the sample. One of the most common ways is the use tapered or etched optical fibers [3

3. E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science **251**, 1468–1450 (1991). [CrossRef] [PubMed]

4. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. **57**, 2615–2626 (1990). [CrossRef]

23. A. Husakou and J. Herrmann, “Superfocusing of light below the diffraction limit by photonic crystals with negative refraction,” Opt. Express **12**, 6491–6497 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-26-6491. [CrossRef] [PubMed]

23. A. Husakou and J. Herrmann, “Superfocusing of light below the diffraction limit by photonic crystals with negative refraction,” Opt. Express **12**, 6491–6497 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-26-6491. [CrossRef] [PubMed]

24. A. Husakou and J. Herrmann, “Focusing of Scanning Light Beams below the Diffraction Limit without Near-Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material,” Phys. Rev. Lett. **96**, 013902 (2006). [CrossRef] [PubMed]

^{-2}–10

^{-1}of the input intensity.

*E*

_{evan}by a Kerr medium (KM) and its amplification by a NRM is schematically shown. The phases of both propagating and evanescent components are almost matched for optimized parameters, which allows constructive interference of all components and the formation of a subwavelength spot. Subdiffraction focusing is described both in the context of the effective-medium description for quasi-homogeneous NRMs, such as metamaterials, and by direct numerical solution of Maxwell equations in a periodic medium for a NRM implemented by a photonic crystal. We show that in order to avoid loss of the evanescent components and diffraction of the input beam it is necessary to choose a nonlinear material with a high linear refractive index. Additionally, we investigate the dependence of subdiffraction focusing on the deviations of the NRM parameters from the ideal

*ε*=

*μ*=-1 case and determine the parameters which most sensitively influence the focusing. We have also studied a system with a nonlinearity provided by a two-photon absorber instead of a Kerr medium, which allows to lower intensity requirements. We note that in contrast to results of Ref. [24

24. A. Husakou and J. Herrmann, “Focusing of Scanning Light Beams below the Diffraction Limit without Near-Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material,” Phys. Rev. Lett. **96**, 013902 (2006). [CrossRef] [PubMed]

## 2. The effective-medium-theory description of NRM

*ω*

_{0}is the frequency of the field,

*P*

_{NL}(

*k*

_{x},

*k*

_{y},

*z*) denotes the Fourier transform of the nonlinear polarization

*P*

_{NL}(

*x*,

*y*,

*z*)=

*ε*

_{0}

*χ*

_{3}

*E*(

*x*,

*y*,

*z*)

^{3},

*χ*

_{3}=(4/3)

*c*ε

_{0}

*n*

_{2}is the nonlinear susceptibility. In the perturbation-theory approach the solution can be found in the form

*z*<

*L*where

*L*is the thickness of the nonlinear layer. The first term in the square brackets corresponds to the forward-propagating waves, and the second to the backward-propagating waves which is zero for

*z*>

*L*. It can be shown that the forward-propagating part satisfies a simpler first-order equation:

25. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E **70**, 036604 (2004). [CrossRef]

*k*

_{z}=0 in the Fourier domain, but after Fourier transform to the space the field

*E*(

*x*,

*y*,

*z*) remains finite. Besides, Fourier components with

*k*

_{z}=0 are very weak and do not contribute to the formation of the spot in our calculation. Equation (3) was solved by the split-step Fourier method.

*L*and effective parameters

*ε*and

*μ*is described by the transfer functions

*T*

_{s,p}(

*k*

_{x},

*k*

_{y})

_{s}=

*μk*

_{z}/

*q*

_{z}+

*q*

_{z}/(

*μk*

_{z}) for S-polarized and κ

_{p}=

*εk*

_{z}/

*q*

_{z}+

*q*

_{z}/(

*εk*

_{z}) for P-polarized components with

*s*and

*p*denote correspondingly

*S-*and

*P-*polarization. These transfer functions relate the output field

**E**

_{s,p}(

*k*

_{x},

*k*

_{y},

*L*) with the input field

**E**

_{s,p}(

*k*

_{x},

*k*

_{y},0). The spatial structure of the field at the output of the system is then found by the backward Fourier transformation. The back-reflection from the Kerr medium is neglected. The field

**E**

_{s,p}(

*k*

_{x},

*k*

_{y}, 0) at the input surface of the NRM is given by the field after the slab of a nonlinear Kerr-type medium positioned immediately before the slab, as shown in Fig. 1.

*n*

_{0}around unity, the evanescent components are lost over the distance λ/2

*π*, and therefore the effective length over which they are generated is of the same order. That means that to achieve significant (of about

*π*/2) phase modification necessary to generate seed evanescent components of sufficient intensity, over such a short distance, the maximum nonlinear contribution to the refractive index should be around unity. Since materials with such high nonlinear modification of the refractive index are not available, we cannot use a nonlinear film with

*n*

_{0}~1 and thickness around λ/2

*π*as the nonlinear layer. Instead, we considered in Fig. 2 a nonlinear layer with relatively high linear refractive index

*n*

_{0}=3.0 and thickness of about λ, which allows to preserve and accumulate the evanescent components with

*k*

_{0}is the

*vacuum*wavenumber. In this case the effective length of the nonlinear layer is limited only by the gradual increase of the spot size due to diffraction, which occurs after a propagation distance of several λ, and a relative nonlinear modification of the refractive index in the order of 0.03 is sufficient. There exist a large number of natural and artificial materials with strong optical nonlinearities. To give a few examples, the nonlinear refractive index of different semiconductors can have

*n*

_{2}values in the order of 10

^{-12}W/cm

^{2}. Due to near-resonant processes in the vicinity of the bandgap, the values in the range of 10

^{-8}W/cm

^{2}can be achieved, for example in ZnSe in the wavelength range from 440 to 460 nm[26

26. Y. J. Ding, C. L. Guo, G. A. Swartzlander, Jr., J. B. Khurgin, and A. E. Kaplan, “Spectral measurement of the nonlinear refractive index in ZnSe using self-bending of a pulsed laser beam,” Opt. Lett. **15**, 1431–1433 (1990). [CrossRef] [PubMed]

*n*

_{2}in the order of |

*n*

_{2}|=7×10

^{-8}W/cm

^{2}[27

27. R. S. Bennink, Y.-K. Yoon, and R. W. Boyd, “Acessing the optical nonlinearity of metals with metal-dielectric photonic bandgap structures,” Opt. Lett. **24**, 1416–1418 (1999). [CrossRef]

*n*

_{2}~10

^{0}-10

^{3}W/cm

^{2}can be achieved in thin dye-doped liquid-crystal layers[28

28. L. Lucchetti, M. Gentili, and F. Simoni, “Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase,” Appl. Phys. Lett. **86**, 151117 (2005). [CrossRef]

*T*

_{res}the effective nonlinear refractive index is given by

*n*

_{2}

*τ*/

*t*

_{res}where

*τ*is the pulse duration. Depending on the chosen nonlinear material, the parameter Δ

*n*

_{0}=

*n*

_{2}

*I*/

*n*

_{0}=0.03 which is assumed in Fig. 2 can be achieved with intensities in the order of 10

^{7}–10

^{12}W/cm

^{2}.

*z*~1λ, one can see that evanescent components start to appear, and after the nonlinear layer they possess a notable amplitude. Note also that during the propagation in the NRM layer the optimum spot is achieved not at the position when the spectrum is broadest (

*z*=2.4λ), but at the position

*z*=2.6λ where the spectrum is flat and the phases (not shown) imply constructive interference.With further propagation, the spectrum becomes narrower due to the assumed deviations of

*ε*and

*μ*from the ideal case

*ε*=

*μ*=-1.

*n*

_{0}=3.3%. It is, fortunately, not an absolute prerequisite of superfocusing, and significantly lower values can be used, albeit with tradeoff of the spot size. In Fig. 4 the superfocusing is illustrated for a one order of magnitude lower nonlinear modification of the refractive index Δ

*n*

_{0}=3×10

^{-3}, which can be achieved even by a fast Kerr nonlinearity. The transverse spectrum is narrower than in Fig. 2 due to a lower amplitude of the seed evanescent components, and the output spot is larger with a FWHM of 0.38λ/0.25λ, but still exhibits focusing below the diffraction limit.

## 3. Superfocusing by a nonlinear layer and a photonic crystal with negative refraction

^{7}) number of planar waves, including the reflected and transmitted plane waves outside the slab, as detailed in Ref. [30]. The periodic boundaries of the structure determine the coupling between these waves, resulting in a large-order system of linear equations which is solved numerically. We consider the parameter region with all-angle negative refraction of a hexagonal lattice of circular holes in the material like Si with parameters and geometry as indicated in Fig. 6(a). In Fig. 6(b), the transmission into the 0th Bragg order is presented in dependence on the transverse wavenumber of the incoming wave, which shows several peaks for evanescent components with

*k*

_{⊥}>2

*π*/λ with a transmission up to 10

^{3}.

^{-2}–10

^{-1}, and somewhat larger spot sizes [24

24. A. Husakou and J. Herrmann, “Focusing of Scanning Light Beams below the Diffraction Limit without Near-Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material,” Phys. Rev. Lett. **96**, 013902 (2006). [CrossRef] [PubMed]

**96**, 013902 (2006). [CrossRef] [PubMed]

## 5. Conclusion

*ε*and

*μ*from -1 in the effective medium theory does not arise for photonic crystals and superfocusing is even possible in the range of so-called all-angle negative refraction where an effective index can not be defined. The physical mechanism here is that wide transmission peaks for evanescent components due to resonances with bound photon modes yield a sufficient amplification of the evanescent components which allow superfocusing. This means that not the negative index is the main physical requirement for the predicted effect, but the existence of wide transmission peaks much larger than unity for evanescent components.

## References and links

1. | A. KK. Wong, |

2. | T. W. McDaniel, |

3. | E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science |

4. | S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. |

5. | M. A. Paesler and P. J. Moyer, |

6. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of |

7. | J. B. Pendry, “Negative refraction makes perfect lens,” Phys. Rev. Lett. |

8. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science |

9. | M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B |

10. | E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: Negative refraction by photonic crystals,” Nature |

11. | G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett |

12. | V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett |

13. | N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature |

14. | Q. Thommen and P. Mandel, “Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media”, Phys. Rev. Lett. |

15. | C. Luo, S.G. Johnson, J.D. Joannopoulos, and J.B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B |

16. | N. Fang, H. Lee, C. Sun, and X. Zhang, “SubDiffraction-Limited Optical Imaging with a Silver Superlens,” Science |

17. | D. Melville and R. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express |

18. | C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. |

19. | A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, “Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. |

20. | Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, “Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies,” Phys. Rev. Lett. |

21. | P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature |

22. | E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, “Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens,” Phys. Rev. Lett. |

23. | A. Husakou and J. Herrmann, “Superfocusing of light below the diffraction limit by photonic crystals with negative refraction,” Opt. Express |

24. | A. Husakou and J. Herrmann, “Focusing of Scanning Light Beams below the Diffraction Limit without Near-Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material,” Phys. Rev. Lett. |

25. | M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E |

26. | Y. J. Ding, C. L. Guo, G. A. Swartzlander, Jr., J. B. Khurgin, and A. E. Kaplan, “Spectral measurement of the nonlinear refractive index in ZnSe using self-bending of a pulsed laser beam,” Opt. Lett. |

27. | R. S. Bennink, Y.-K. Yoon, and R. W. Boyd, “Acessing the optical nonlinearity of metals with metal-dielectric photonic bandgap structures,” Opt. Lett. |

28. | L. Lucchetti, M. Gentili, and F. Simoni, “Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase,” Appl. Phys. Lett. |

29. | D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. |

30. | K. Sakoda, |

31. | C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B |

32. | G. M. Gale and A. Mysyrowicz, “Direct creation of excitonic molecules in CuCl by giant two-photon absorption,” Phys. Rev. Lett. |

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(220.2560) Optical design and fabrication : Propagating methods

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 26, 2006

Revised Manuscript: September 27, 2006

Manuscript Accepted: September 27, 2006

Published: November 13, 2006

**Citation**

A. Husakou and J. Herrmann, "Subdiffraction focusing of scanning beams by a negative-refraction layer
combined with a nonlinear layer," Opt. Express **14**, 11194-11203 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11194

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### References

- A. KK. Wong, Resolution enhancement techniques in optical lithography (SPIE Press, Bellingham, Washington, 2001). [CrossRef]
- T. W. McDaniel, Handbook of magneto-optical data recording: materials, subsystems, techniques (Noyes publishing, Westwood, 1997).
- E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991). [CrossRef] [PubMed]
- S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2626 (1990). [CrossRef]
- M. A. Paesler and P. J. Moyer, Near-field optics: theory, instrumentation and applications, John Wiley and Sons, New York (1996).
- V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ∑ and ," Soviet Phys. Usp. 10, 509-518 (1968) [Usp. Fiz. Nauk 92, 517-526 (1967).]. [CrossRef]
- J. B. Pendry, "Negative refraction makes perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
- M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000). [CrossRef]
- E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003). [CrossRef] [PubMed]
- G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005). [CrossRef] [PubMed]
- V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005). [CrossRef]
- N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005). [CrossRef] [PubMed]
- Q. Thommen and P. Mandel, "Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media", Phys. Rev. Lett. 96, 053601 (2006). [CrossRef] [PubMed]
- C. Luo, S.G. Johnson, J.D. Joannopoulos, and J.B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002). [CrossRef]
- N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005). [CrossRef] [PubMed]
- D. Melville and R. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005) [CrossRef] [PubMed]
- C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005). [CrossRef] [PubMed]
- A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004). [CrossRef] [PubMed]
- Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005). [CrossRef] [PubMed]
- P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003). [CrossRef] [PubMed]
- E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003). [CrossRef] [PubMed]
- A. Husakou and J. Herrmann, "Superfocusing of light below the diffraction limit by photonic crystals with negative refraction," Opt. Express 12, 6491-6497 (2004) [CrossRef] [PubMed]
- A. Husakou and J. Herrmann, "Focusing of Scanning Light Beams below the Diffraction Limit without Near- Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material," Phys. Rev. Lett. 96, 013902 (2006). [CrossRef] [PubMed]
- M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004). [CrossRef]
- Y. J. Ding, C. L. Guo, G. A. Swartzlander,Jr., J. B. Khurgin, and A. E. Kaplan, "Spectral measurement of the nonlinear refractive index in ZnSe using self-bending of a pulsed laser beam," Opt. Lett. 15, 1431-1433 (1990). [CrossRef] [PubMed]
- R. S. Bennink, Y.-K. Yoon, and R. W. Boyd, "Acessing the optical nonlinearity of metals with metal-dielectric photonic bandgap structures," Opt. Lett. 24, 1416-1418 (1999). [CrossRef]
- L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005). [CrossRef]
- D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003). [CrossRef]
- K. Sakoda, Optical properties of photonic crystals, Springer, 2001.
- C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003). [CrossRef]
- G. M. Gale and A. Mysyrowicz, "Direct creation of excitonic molecules in CuCl by giant two-photon absorption," Phys. Rev. Lett. 32, 737-740 (1974). [CrossRef]

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