Abstract

Generation of third-harmonic radiation, visible to the naked eye as a collimated green beam, is obtained via femtosecond excitation of the optical surface modes (SMs) propagating along a one-dimensional (1D) photonic crystal (PC) for $s$- and $p$-polarizations separately. For both polarizations, the PC SMs exist at the fundamental and third-harmonic frequencies, which allows efficient nonlinear conversion at the phase-matching points. The pattern of the third-harmonic surface wave scattering is detected and modeled, and it is shown that this pattern reveals the mode structure of the PC. Applications of the studied 1D PC structure for the experimental testing of 2D nonlinear materials are discussed.

© 2019 Optical Society of America

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2019 (1)

S. Yamashita, “Nonlinear optics in carbon nanotube, graphene, and related 2d materials,” APL Photon. 4, 034301 (2019).
[Crossref]

2018 (1)

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

2017 (2)

S. A. Mikhailov, “Comment on ‘Graphene–a rather ordinary nonlinear optical material’,” Appl. Phys. Lett. 111, 106101 (2017).
[Crossref]

J. B. Khurgin, “Response to ‘Comment on Graphene–a rather ordinary nonlinear optical material’,” Appl. Phys. Lett. 111, 106102 (2017).
[Crossref]

2016 (2)

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

V. Agranovich and G. La Rocca, “Organic–inorganic heterostructures for nonlinear optics,” J. Lumin. 169, 422–425 (2016).
[Crossref]

2015 (2)

S. Sederberg and A. Elezzabi, “Coherent visible-light-generation enhancement in silicon-based nanoplasmonic waveguides via third-harmonic conversion,” Phys. Rev. Lett. 114, 227401 (2015).
[Crossref]

I. Degli-Eredi, J. Sipe, and N. Vermeulen, “TE-polarized graphene modes sustained by photonic crystal structures,” Opt. Lett. 40, 2076–2079 (2015).
[Crossref]

2014 (1)

J. Khurgin, “Graphene–a rather ordinary nonlinear optical material,” Appl. Phys. Lett. 104, 161116 (2014).
[Crossref]

2013 (1)

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

2012 (1)

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

2011 (2)

Y. Shen, “Surface nonlinear optics,” J. Opt. Soc. Am. B 28, A56–A66 (2011).
[Crossref]

V. Agranovich, Y. N. Gartstein, and M. Litinskaya, “Hybrid resonant organic-inorganic nanostructures for optoelectronic applications,” Chem. Rev. 111, 5179–5214 (2011).
[Crossref]

2009 (1)

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

2007 (1)

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79, 4729–4735 (2007).
[Crossref]

2006 (1)

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[Crossref]

2004 (1)

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]

1999 (1)

1975 (1)

D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B 12, 4036–4046 (1975).
[Crossref]

Agranovich, V.

V. Agranovich and G. La Rocca, “Organic–inorganic heterostructures for nonlinear optics,” J. Lumin. 169, 422–425 (2016).
[Crossref]

V. Agranovich, Y. N. Gartstein, and M. Litinskaya, “Hybrid resonant organic-inorganic nanostructures for optoelectronic applications,” Chem. Rev. 111, 5179–5214 (2011).
[Crossref]

Agranovich, V. M.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

Alieva, E.

Alieva, E. V.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79, 4729–4735 (2007).
[Crossref]

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[Crossref]

Alyatkin, S. Y.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

Belyanin, A.

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

Bourelle, S. A.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Boyd, R. W.

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]

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Celebrano, M.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Cerullo, G.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Chekalin, S. V.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Dadap, J. I.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Dal Conte, S.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

De Fazio, D.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Degli-Eredi, I.

Eggleton, B.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Elezzabi, A.

S. Sederberg and A. Elezzabi, “Coherent visible-light-generation enhancement in silicon-based nanoplasmonic waveguides via third-harmonic conversion,” Phys. Rev. Lett. 114, 227401 (2015).
[Crossref]

Eliel, E.

Ferrar, A. C.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Gartstein, Y. N.

V. Agranovich, Y. N. Gartstein, and M. Litinskaya, “Hybrid resonant organic-inorganic nanostructures for optoelectronic applications,” Chem. Rev. 111, 5179–5214 (2011).
[Crossref]

Goykhman, I.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Grillet, C.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Hone, J.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Hong, S.-Y.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Khurgin, J.

J. Khurgin, “Graphene–a rather ordinary nonlinear optical material,” Appl. Phys. Lett. 104, 161116 (2014).
[Crossref]

Khurgin, J. B.

J. B. Khurgin, “Response to ‘Comment on Graphene–a rather ordinary nonlinear optical material’,” Appl. Phys. Lett. 111, 106102 (2017).
[Crossref]

Konopsky, V. N.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79, 4729–4735 (2007).
[Crossref]

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[Crossref]

Krauss, T.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Kuzik, L.

La Rocca, G.

V. Agranovich and G. La Rocca, “Organic–inorganic heterostructures for nonlinear optics,” J. Lumin. 169, 422–425 (2016).
[Crossref]

Lepeshkin, N. N.

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]

Litinskaya, M.

V. Agranovich, Y. N. Gartstein, and M. Litinskaya, “Hybrid resonant organic-inorganic nanostructures for optoelectronic applications,” Chem. Rev. 111, 5179–5214 (2011).
[Crossref]

Luo, B.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Ma, T.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Markowicz, P. P.

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]

Melnikov, A. A.

V. N. Konopsky, E. V. Alieva, S. Y. Alyatkin, A. A. Melnikov, S. V. Chekalin, and V. M. Agranovich, “Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals,” Light Sci. Appl. 5, e16168 (2016).
[Crossref]

Mikhailov, S. A.

S. A. Mikhailov, “Comment on ‘Graphene–a rather ordinary nonlinear optical material’,” Appl. Phys. Lett. 111, 106101 (2017).
[Crossref]

Mills, D. L.

D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B 12, 4036–4046 (1975).
[Crossref]

Monat, C.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Moss, D.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Muench, J. E.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

O’Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Osgood, R. M.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Ott, A. K.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Petrone, N.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Petrov, J.

Polini, M.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Prasad, P. N.

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]

Pudavar, H.

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]

Purdie, D. G.

G. Soavi, G. Wang, H. Rostami, D. G. Purdie, D. De Fazio, T. Ma, B. Luo, J. Wang, A. K. Ott, D. Yoon, S. A. Bourelle, J. E. Muench, I. Goykhman, S. Dal Conte, M. Celebrano, A. Tomadin, M. Polini, G. Cerullo, and A. C. Ferrar, “Broadband, electrically tunable third-harmonic generation in graphene,” Nat. Nanotechnol. 13, 583–588 (2018).
[Crossref]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Vol. 111 of Springer Tracts in Modern Physics (Springer, 1988).

Rostami, H.

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Figures (7)

Fig. 1.
Fig. 1. Layout of the experiment. In the color inset, a photograph of the reflected beams of the first and third harmonics is presented (s-polarization).
Fig. 2.
Fig. 2. Calculated dispersions of the 1D PC structure for (a)  $p$ -polarization and (b) s-polarization. Phase-matching points are indicated by white pentagrams and are connected by white dotted lines.
Fig. 3.
Fig. 3. TH spectra for (a)  $p$ - and (b) s-polarizations.
Fig. 4.
Fig. 4. Pump power dependence of THG (s-polarization). Unfilled circles: experimental data; solid line: linear fit in logarithmic scale, with a slope $ 3.1 \pm 0.5 $ .
Fig. 5.
Fig. 5. Scattering pattern of TH at 516 nm.(a) Ordinary scattering and (b) increased scattering after breathing onto the surface. (c) Simulated angular spectrum of the intensity of the optical field at the external surface of the 1D PC. (d) TH scattering lines when the TH is the sum of three unscattered FH wavevectors and when it is the sum of two unscattered and one scattered wavevector of the FH.
Fig. 6.
Fig. 6. Illustration of the model used for the simulation of refraction of the reradiated wave, which is formed after surface scattering of the third harmonic outside the plane of incidence of the first harmonic.
Fig. 7.
Fig. 7. (a) Simulated angular pattern of the scattered and refracted waves. (b) Superimposed simulated and experimental angular patterns.

Equations (11)

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x N ( α ) = R tan ( δ 1 ) cos ( γ ) ,
y N ( α ) = R tan ( δ 1 ) sin ( γ ) ,
δ 1 = arcsin ( n 0 sin ( δ 0 ) ) ,
δ 0 = arctan ( 2 | A S | sin ( β ) sin ( γ ) a ) ,
γ = arctan ( sin ( β ) cos ( β ) a 2 | A S | ) ,
β = arctan ( 2 2 tan ( α ) ) ,
| A S | = a 2 sin ( θ N ) 2 sin ( θ N + φ ) ,
φ = arctan ( ( cos ( α ) ) 1 ) ,
θ N = arcsin ( ρ N / n 0 ) ,
α = arctan ( sin ( α 1 ) 2 + cos ( α 1 ) ) ,
θ [ s c + 2 ] = arcsin ( 5 + 4 cos ( α 1 ) 3 sin ( arcsin ( ρ S M ( s ) / n 0 ) ) ) .

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