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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    [CrossRef]
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  13. A. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
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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 (1)

2008 (3)

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]

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]

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 (3)

2005 (2)

2004 (1)

2003 (2)

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

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

1996 (2)

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]

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

1995 (1)

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 (1)

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. (1)

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. (1)

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 (1)

Opt. Express (1)

Opt. Lett. (7)

Opt. Quantum Electron. (1)

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. (1)

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

Other (2)

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

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]

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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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