Abstract

The transformation of the polarization distribution of a laser beam from linear to radial and azimuthal by means of a subwavelength binary corrugation etched in a high-index substrate faces fabrication difficulties and an inherent contradiction preventing the achievement of both conditions of 100% transmission and of π phase difference between polarization components. The contradiction is solved by resorting to an easily fabricable high-index corrugation on a low-index substrate where a larger period gives rise to grating-mode reflection/transmission phases that permit the fulfillment of both conditions with a depth-minimized corrugation. From the principle of the solution, a targeted numerical search gives the complete set of the corresponding shallow structures, achieving polarization rotation in a fitting analytical form versus normalized variables.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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  15. T. Kämpfe and O. Parriaux, “Parameter-tolerant binary gratings,” J. Opt. Soc. Am. A 27, 2660–2669 (2010).
    [CrossRef]
  16. MC Grating by N. Lyndin, http://www.mcgrating.com.

2010

2008

T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33, 122–124 (2008).
[CrossRef] [PubMed]

G. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm,” Opt. Lett. 33, 2782–2784 (2008).
[CrossRef] [PubMed]

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

2007

2005

2004

2003

D. Biss and T. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28, 923–925 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

1996

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1950 (1996).
[CrossRef] [PubMed]

1995

S. Chou and W. Deng, “Subwavelength amorphous silicon transmission gratings and applications in polarizers and waveplates,” Appl. Phys. Lett. 67, 742–744 (1995).
[CrossRef]

Ahmed, M.

Biss, D.

Brown, T.

Chou, S.

S. Chou and W. Deng, “Subwavelength amorphous silicon transmission gratings and applications in polarizers and waveplates,” Appl. Phys. Lett. 67, 742–744 (1995).
[CrossRef]

Clausnitzer, T.

Deng, W.

S. Chou and W. Deng, “Subwavelength amorphous silicon transmission gratings and applications in polarizers and waveplates,” Appl. Phys. Lett. 67, 742–744 (1995).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Fainman, Y.

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[CrossRef]

Graf, T.

Heckenberg, N.

Jackel, S.

Kämpfe, T.

Kley, E. B.

Lai, K.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Lai, W.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Lalanne, P.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lerman, G.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Levy, U.

Lim, Y.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Lumer, Y.

Machavariani, G.

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[CrossRef]

Meir, A.

Moshe, I.

Nieminen, T.

Pang, L.

Parriaux, O.

Peschel, U.

Phua, P.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Pommier, J.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[CrossRef]

Rubinsztein-Dunlop, H.

Schadt, M.

Schulz, J.

Stalder, M.

Tan, B.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Tan, H.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Tishchenko, A.

Tsai, C.

Tünnermann, A.

Voss, A.

Wu, R.

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

Appl. Phys. A

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[CrossRef]

Appl. Phys. Lett.

S. Chou and W. Deng, “Subwavelength amorphous silicon transmission gratings and applications in polarizers and waveplates,” Appl. Phys. Lett. 67, 742–744 (1995).
[CrossRef]

J. Mod. Opt.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
[CrossRef]

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Other

P. Phua, W. Lai, Y. Lim, B. Tan, R. Wu, K. Lai, and H. Tan, “High power radial polarization conversion using photonic crystal segmented half-wave-plate,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMO4.
[PubMed]

MC Grating by N. Lyndin, http://www.mcgrating.com.

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of spatially constant and spatially varying polarization distributions.

Fig. 2
Fig. 2

Cross section of the binary grating with definition of the normalized parameters.

Fig. 3
Fig. 3

Sketch of the grating line directions for transforming linearly to radially or azimuthally polarized light and the realization as a segmented constant-period grating.

Fig. 4
Fig. 4

Effective index of the TE and TM polarizations within the effective medium theory for n r = 3.5 and n c = 1.0 .

Fig. 5
Fig. 5

(a) Parameters of a polarization rotating grating for λ = 1064 nm etched into a high-index substrate [9] and (b) height dependency of the transmission amplitude for TE and TM polarizations. The indicated, optimized grating height achieves a π phase shift between polarizations.

Fig. 6
Fig. 6

Definition of the reflection and transmission coefficients for a zeroth-order grating mode.

Fig. 7
Fig. 7

Effective index of the TE 0 and TM 0 modes versus the corrugation duty cycle with indication of values chosen in the example.

Fig. 8
Fig. 8

(a) Parameters of a polarization rotating grating for λ = 1064 nm etched into a high-index layer on a low-index substrate and (b) height dependency of the transmission amplitude for TE and TM polarizations. The indicated optimized grating height achieves a π phase shift between polarizations.

Fig. 9
Fig. 9

Diagrams of the grating parameters of the depth-minimized polarization rotating gratings and their achieved performance versus the chosen ridge and substrate refractive indices.

Tables (1)

Tables Icon

Table 1 Coefficients of the Polynomial Approximation Defined in Eq. (18), Allowing the Calculation of the Parameters of a Polarization Rotating Grating and Its Performance for a Chosen Combination of n s and n r

Equations (18)

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Λ < λ n s ,
n eff TE = d n r 2 + ( 1 d ) n g 2 , n eff TM = 1 / ( d n r 2 + ( 1 d ) n g 2 ) .
r c = n c n eff n c + n eff ; r s = n eff n s n eff + n s .
T max = ( 1 r c ) ( 1 r s ) ( 1 r c r s ) 2 ,
T max = 4 n c n s ( n eff + n c n s / n eff ) 2 .
n eff = n c n s
T max = 4 n c n s ( n c + n s ) 2 .
φ r TE arg ( r 00 , c TE ) + arg ( r 00 , s TE ) ; φ t TE arg ( t c , 0 TE ) + arg ( t 0 , s TE ) ,
φ r TM arg ( r 00 , c TM ) + arg ( r 00 , s TM ) ; φ t TM arg ( t c , 0 TM ) + arg ( t 0 , s TM ) .
φ RT TE = φ r TE + 2 2 π λ n eff TE h .
φ out TE = φ t TE + 2 π λ n eff TE 0 h , φ out TM = φ t TM + 2 π λ n eff TM 0 h ,
Δ φ out = φ out TE φ out TM .
φ RT TE = m FP 2 π ,
Δ φ out = ( 2 m dif 1 ) π ,
h FP = λ 2 π n eff TE ( π 1 / 2 φ r TE ) ; h dif = λ 2 π ( n eff TE n eff TM ) ( π φ t TE ) .
1.5 n r 4.5 , 1.2 n s 2.3.
n s < 0.381 n r 4 3.638 n r 3 + 13.102 n r 2 20.653 n r + 13.206.
f ( n r , n s ) c 00 + c 10 n r + c 01 n s + c 20 n r 2 + c 11 n r n s + c 12 n s 2 + c 30 n r 3 + c 21 n r 2 n s + c 12 n r n s 2 + c 03 n s 3 +

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