## Broadband antireflective structures applied to high resistive float zone silicon in the THz spectral range

Optics Express, Vol. 17, Issue 5, pp. 3063-3077 (2009)

http://dx.doi.org/10.1364/OE.17.003063

Acrobat PDF (1491 KB)

### Abstract

The optimal structural parameters for an antireflective structure in high resistive float zone silicon are deduced for a rectangular and a hexagonal structure. For this the dependence of the effective index from the filling factor was calculated for both grating types. The structures were manufactured by the Bosch®-process. The required structural parameters for a continuous profile require an adaption of the fabrication process. Challenges are the depth and the slight positive slope of the structures. Starting point for the realization of the antireflective structures was the manufacturing of deep binary gratings. A rectangular structure and a hexagonal structure with period 50 μm and depth 500 μm were realized. Measurements with a THz time domain spectroscopy setup show an increase of the electric field amplitude of 15.2% for the rectangular grating and 21.76% for the hexagonal grating. The spectral analysis shows that the bandwidth of the hexagonal grating reaches from 0.1 to 2 THz.

© 2009 Optical Society of America

## 1. Introduction

1. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am . B **7**, 2006–2015 (1990). [CrossRef]

^{-1}for the range of 0.2-2 THz. A very precise measurement of the refractive index and absorption coefficient is given in [2

2. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am . B **21**, 1379–1386 (2004). [CrossRef]

2. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am . B **21**, 1379–1386 (2004). [CrossRef]

3. M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Terahertz beam propagation measured through three-dimensional amplitude profile determination,” J. Opt. Soc. Am . B **20**, 2215–2225 (2003). [CrossRef]

1. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am . B **7**, 2006–2015 (1990). [CrossRef]

4. C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tünnermann, “Design and evaluation of a THz time domain imaging system using standard optical design software,” Appl. Opt . **47**, 4994–5006 (2008). [CrossRef] [PubMed]

5. C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tϼnnermann, “Design and analysis of quasioptical THz time domain imaging systems,” Proc. SPIE **7100**, 71000S (2008). [CrossRef]

6. A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, “An anti-reflection coating for silicon optics at terahertz frequencies,” IEEE Microwave Guided Wave Lett . **10**, 264–266 (2000). [CrossRef]

7. I. Hosako, “Multilayer optical thin films for use at terahertz frequencies: method of fabrication,” Appl. Opt . **44**, 3769–3773 (2005). [CrossRef] [PubMed]

8. J. Kröll, J. Darmo, and K. Unterrainer, “Metallic wave-impedance matching layers for broadband terahertz optical systems,” Opt. Express **15**, 6552–6560 (2007). [CrossRef] [PubMed]

9. W. Withayachumnankul, B. M. Fischer, S. P. Mickan, and D. Abbott, “Retrofittable antireflection coatings for T-rays,” Microwave Opt. Technol. Lett . **49**, 2267–2270 (2007). [CrossRef]

10. P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘Moth Eye” principle,” Nature **244**, 281–282 (1973). [CrossRef]

11. A. Gombert, B. Bläsi, C. Bühler, and P. Nitz, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng . **43**, 2525–2533 (2004). [CrossRef]

12. C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, and A. Tünnermann, “Broadband antireflective surface-relief structure for THz optics,” Opt. Express **15**, 779–789 (2007). [CrossRef] [PubMed]

## 2. Theory

### 2.1 Grating period

_{y}→ ∞).

_{x}= Λ

_{y}) are

**a**

_{1}= (Λ,0,0)

^{T}and

**a**

_{2}= (0,Λ,0)

^{T}. The corresponding basis vectors of the reciprocal grating are

**g**

_{1}= (2

*π*/Λ)

**u**

_{x}and

**g**

_{2}= (2

*π*/Λ)

**u**

_{y}, with

**u**

_{x},

**u**

_{y}- unit vectors in x-and y-direction. The basis vectors of the hexagonal grating are

**a**

_{1}= (Λ,0,0)

^{T}and

**a**

_{2}= Λ·(0.5,sin(60°)0,0)

^{T}. The corresponding basis vectors of the reciprocal grating are:

**g**

_{1}= 2

*π*/(Λ sin(60°)) · (sin(60°),-0.5,0)

^{T}and

**g**

_{2}= 2

*π*/(Λ sin(60°))

**u**

_{y}. The basis vectors of the reciprocal grating are drawn in Fig. 1(c) and (d) for the rectangular and the hexagonal grating, respectively. The reciprocal grating of the rectangular grating is again a rectangular grating with same axes alignment. The reciprocal grating of the hexagonal grating is again a hexagonal grating but with the axes rotated -30° about the z-axis (Fig. 1(d), red dots). The condition for constructive interference at a certain angle of incidence is:

**k**

_{i,xy}- the projection of the incident wave vector onto the xy-plane,

**k**

_{uv,xy}- the projection of the diffracted wave vector onto the xy-plane, and

**g**

_{uv}=

*u*

**g**

_{1}+

*v*

**g**

_{2}- the grating vector belonging to the diffraction order

*u,v*. From Eq. (1) a condition can be deduced such that the z-component of the diffracted wave vector is imaginary, i.e. the diffracted wave is evanescent. For a zeroth-diffraction-order grating following condition must hold:

*λ*– wavelength in vacuum,

*n*

_{1}– refractive index of the incident medium (air),

*n*

_{2}– refractive index of the substrate,

*θ*- the polar angle of incidence and

_{i}*φ*- the azimuthal angle of incidence. The factor

*f*depends on the grating type. For the rectangular grating the factor is

_{g}*f*= 1, and for the hexagonal grating the it is:

_{g}*f*= 1/sin(60°) = 1/0.866 = 1.155. The phase angle

_{g}*δ*is the angle between a vector of the reciprocal grating and the basis vector

_{i}**g**

_{1}. For the rectangular grating, the phase angles for the two basis vectors are

*δ*

_{1}= 0° and δ

_{2}= 90°. For the hexagonal grating, the phase angles are δ

_{1}= 0° and δ

_{2}= 120°. For a linear grating, only one basis vector of the reciprocal grating exists with

*δ*

_{1}= 0°.

*λ*, depends on the angle of incidence, the refractive index and the grating type.

*θ*= 0°), it holds:

*θ*= 90°), it holds:

*θ*independent of the azimuthal angle

*φ*the maximum ratio appears for (

*φ*-

*δ*) = 0:

_{i}*λ*is given for several angles of incidence. The cutoff wavelength

*λ*is the wavelength for which condition (2) is just obeyed. The relation between the cutoff wavelength at a hexagonal grating and at a rectangular grating is:

_{c}### 2.2 Effective index

14. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am . A **12**, 333–339 (1995). [CrossRef]

*λ*[15

15. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am . A **11**, 2695–2703 (1994). [CrossRef]

*d*/

*λ*[16

16. P. Lalanne and D. Lemercier-Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am . A **14**, 450–458 (1997). [CrossRef]

*λ*→ 0) can be determined:

*n*

_{eff,⊥}

^{(0)}. – the zeroth-order effective index perpendicular to the grating vector,

*n*

_{eff,∥}

^{(0)}– the zeroth-order effective index parallel to the grating vector. The effective medium theory of second-order takes the normalized grating period Λ/

*λ*, with the second potency into account:

*n*

_{eff,⊥}– the second-order effective index perpendicular to the grating vector,

*n*

_{eff,∥}

^{(2)}– the second-order effective index parallel to the grating vector. With these effective indices a 1D grating can be described as a uniaxial medium with the extraordinary axis parallel to the grating vector.

15. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am . A **11**, 2695–2703 (1994). [CrossRef]

**a**

_{1}and

**a**

_{2}) have the same length (Λ

_{x}= Λ

_{y}) the 2D rectangular structure becomes a uniaxial structure with the optic axis perpendicular to the surface, i.e.

*n*=

_{eff,x}*n*(Fig. 1(c)). A hexagonal grating can also be described as a rectangular grating with two different grating periods in x and y direction (Fig. 1(d)). Although the grating vectors

_{eff,y}**a**

_{1}and

**a**

_{2}

^{*}have a different length, the effective indices in x and y direction are also equal. Thus, the hexagonal structure works also as a uniaxial medium with the optic axis perpendicular to the surface.

15. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am . A **11**, 2695–2703 (1994). [CrossRef]

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

19. H. Kikuta, Y. Ohira, H. Kubo, and K. Iwata, “Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit,” J. Opt. Soc. Am . A **15**, 1577–1585 (1998). [CrossRef]

*f*=

_{i}*w*/Λ

_{i}_{i}- with

*i*= {

*x,y*} (Fig. 1(c)). For cylinders in a rectangular grating with same period in x- and y-direction, the filling factor is the diameter of the pillars to the grating period

*f*=

*D*/Λ. For cylinders in a hexagonal grating, the filling factor is the ratio of the diameter of the pillars to the grating period in x direction

*f*=

*D*/Λ

_{x}(Fig. 1(d)). Here, a filling factor of one means hexagonal densest packing.

**11**, 2695–2703 (1994). [CrossRef]

*n*= √

*n*

_{1}

*n*

_{2}and

*d*=

*λ*/4

*n*must hold. Thus, the thickness for a quarter-wave layer is 50.694 μm. This thickness was constant at the calculations. For smaller depths, reflectance would not reach zero. For greater depths, there would be several minima such that the curve cannot be used for a definite determination. At the optimal refractive index of 1.85, reflectance is zero.

*f*= 0 and

*f*= 1, reflectance is that of the uncoated boundary. At a certain filling factor (here

*f*= 0.8), reflectance is zero. This filling factor corresponds to the optimal refractive index for a quarter-wave layer (

*n*= 1.85). By comparison of both curves, the filling factor can be assigned to the refractive index with the same reflectivity because the effective index is the one that has the same effect like a homogeneous medium.

**11**, 2695–2703 (1994). [CrossRef]

*λ*= 0.001 the grating is in the quasi-static limit and for Λ/

*λ*= 0.2 the zeroth-order condition is just obeyed. Figure 3(b) shows the dependence of the effective index on the filling factor for different 2D gratings in the quasi-static limit (Λ/

*λ*= 0.001). Figure 3(b) shows that in the quasi-static limit, the filling factor that corresponds to the optimal for a quarter-wave layer is 0.8 for square cuboids in a rectangular grating, 0.84 for cylinders in a hexagonal grating, and 0.9 for cylinders in a rectangular grating. It turned out that for the optimal refractive index, the area filling factors are nearly the same for all grating types: 0.64 for square cuboids in rectangular grating, 0.64 for cylinders in hexagonal grating, and 0.636 the cylinders in rectangular grating. These curves can be used as syntheses curves for a certain refractive index.

*λ*was 0.2. The curves show that the high refractive index of silicon causes extreme polarization dependence. This is why 2D structures are preferred as antireflective structures for HRFZ silicon.

### 2.3 Continuous structures

14. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am . A **12**, 333–339 (1995). [CrossRef]

*f*= 0) to the substrate material (

*f*= 1).

*d*/

*λ*. For

*d*/

*λ*≥ 0.3, reflectance is below 7.1% for cones in a rectangular grating reflectance, below 5.6% for cones in a hexagonal grating reflectance, and below 4.3% for pyramids. Because of the index step a remaining reflectance of about 2% occurs for cones in a rectangular grating and about 0.5% for cones in a hexagonal grating. The minimum normalized grating depth of 0.3 applied to the long-wavelength end (3000 μm) yields a minimum structural depth of 900 μm.

### 2.4 Starting point: deep binary structures

2. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am . B **21**, 1379–1386 (2004). [CrossRef]

_{1}d

_{1}), with c – velocity of light in vacuum, n

_{1}– the refractive index of the layer, and d

_{1}– the layer thickness. Thus, for a lower refractive index than the optimal, the fundamental frequency is higher, and the distance of the odd multiples of this frequency is larger than at the optimal refractive index. Above the quasi-static limit the modulation is higher, transmittance of 100 percent is reached several times within in range of 1.3-1.7 THz, and for frequencies above 0.5 THz transmittance does not drop to the value of the uncoated surface. This behavior cannot be achieved with a homogeneous layer, as well. Thus, the behavior of deep binary structures can only be predicted in the quasi-static limit by effective media theory. Above the behavior can only be predicted by RCWA, i.e. it is not possible to assign a certain refractive index to those deep structures.

## 3. Manufacturing of the structures by deep reactive ion etching (DRIE)

## 4. Measurements and results

*t*= ∆

*n*·

*d*/

*c*= (3.42-1.85)·500

*μm*/3.10

^{8}

*m*/

*s*= 2.62 ps, with ∆

*n*– change of the refractive index,

*d*– layer depth, and

*c*– velocity of light in vacuum. This is a first indicator that the intended structural parameters are realized. The curve of the unstructured sample shows pulse echoes at 39.13 ps and 60.93 ps. These are due to Fresnel reflections within the silicon sample. The small pulse echo around 23.3 ps (5.9 ps after the main pulse) is due to the alignment of the THz system and appeared also without any sample in the setup. The inset in Fig. 9(a) shows the theoretical delay times of the secondary pulses for the structured sample, if the structured layer has an effective index of 1.85. The secondary pulses should appear at 6.2 ps, 11.4 ps, and 17.6 ps. The second pulse at the structured sample is and overlay of the pulse copy caused by internal reflections and the amplified pulse present in the system 5.9 ps after the main pulse. The maximum of the second pulse appears 4.42 ps after the main pulse. This pulse maximum has a negative sign, because of the phase shift of 180° on reflection from an optical denser medium. Further pulse copies appear at 11.8 ps and 16.44 ps after the main pulse (measured from the position of the pulse maximum). Additionally to the pulse copies, the rising edge of the main pulse shows fast oscillations (see arrow in Fig. 9). These are due to little index steps within the structured region. The index steps are due to the breaks in the etching process (see Fig. 6 and Fig. 7). The pulse maximum at the sample with the rectangular structure increases by 15.2% with respect to the unstructured sample.

## 5. Conclusion

## Acknowledgment

## References and links

1. | D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am . B |

2. | J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am . B |

3. | M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Terahertz beam propagation measured through three-dimensional amplitude profile determination,” J. Opt. Soc. Am . B |

4. | C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tünnermann, “Design and evaluation of a THz time domain imaging system using standard optical design software,” Appl. Opt . |

5. | C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tϼnnermann, “Design and analysis of quasioptical THz time domain imaging systems,” Proc. SPIE |

6. | A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, “An anti-reflection coating for silicon optics at terahertz frequencies,” IEEE Microwave Guided Wave Lett . |

7. | I. Hosako, “Multilayer optical thin films for use at terahertz frequencies: method of fabrication,” Appl. Opt . |

8. | J. Kröll, J. Darmo, and K. Unterrainer, “Metallic wave-impedance matching layers for broadband terahertz optical systems,” Opt. Express |

9. | W. Withayachumnankul, B. M. Fischer, S. P. Mickan, and D. Abbott, “Retrofittable antireflection coatings for T-rays,” Microwave Opt. Technol. Lett . |

10. | P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘Moth Eye” principle,” Nature |

11. | A. Gombert, B. Bläsi, C. Bühler, and P. Nitz, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng . |

12. | C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, and A. Tünnermann, “Broadband antireflective surface-relief structure for THz optics,” Opt. Express |

13. | H. Ibach and H. Lüth, |

14. | E. B. Grann, M. G. Moharam, and D. A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am . A |

15. | E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am . A |

16. | P. Lalanne and D. Lemercier-Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am . A |

17. | S. Rytov, “Electromagnetic Properties of a Finely Stratified Medium,” Soviet Physics JETP |

18. | P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt . |

19. | H. Kikuta, Y. Ohira, H. Kubo, and K. Iwata, “Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit,” J. Opt. Soc. Am . A |

20. | H. A. Macleod |

21. | J. Bischoff and R. Brunner, “Numerical investigation of the resolution in solid immersion lens systems,” Proc. SPIE |

**OCIS Codes**

(310.1210) Thin films : Antireflection coatings

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: November 13, 2008

Revised Manuscript: December 15, 2008

Manuscript Accepted: January 14, 2009

Published: February 17, 2009

**Citation**

Claudia Brückner, Thomas Käsebier, Boris Pradarutti, Stefan Riehemann, Gunther Notni, Ernst-Bernhard Kley, and Andreas Tünnermann, "Broadband antireflective structures applied to
high resistive float zone silicon in the THz
spectral range," Opt. Express **17**, 3063-3077 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3063

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### References

- D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2015 (1990). [CrossRef]
- J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004). [CrossRef]
- M. T. Reiten, S. A. Harmon, and R. A. Cheville, "Terahertz beam propagation measured through three-dimensional amplitude profile determination," J. Opt. Soc. Am. B 20, 2215-2225 (2003). [CrossRef]
- C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tünnermann, "Design and evaluation of a THz time domain imaging system using standard optical design software," Appl. Opt. 47, 4994-5006 (2008). [CrossRef] [PubMed]
- C. Brückner, B. Pradarutti, R. Müller, S. Riehemann, G. Notni, and A. Tünnermann, "Design and analysis of quasioptical THz time domain imaging systems," Proc. SPIE 7100, 71000S (2008). [CrossRef]
- A. J. Gatesman, J. Waldman, M. Ji, C. Musante, and S. Yngvesson, "An anti-reflection coating for silicon optics at terahertz frequencies," IEEE Microwave Guided Wave Lett. 10, 264-266 (2000). [CrossRef]
- I. Hosako, "Multilayer optical thin films for use at terahertz frequencies: method of fabrication," Appl. Opt. 44, 3769-3773 (2005). [CrossRef] [PubMed]
- J. Kröll, J. Darmo, and K. Unterrainer, "Metallic wave-impedance matching layers for broadband terahertz optical systems," Opt. Express 15, 6552-6560 (2007). [CrossRef] [PubMed]
- W. Withayachumnankul, B. M. Fischer, S. P. Mickan, and D. Abbott, "Retrofittable antireflection coatings for T-rays," Microwave Opt. Technol. Lett. 49, 2267-2270 (2007). [CrossRef]
- P. B. Clapham and M. C. Hutley, "Reduction of lens reflection by the 'Moth Eye' principle," Nature 244, 281-282 (1973). [CrossRef]
- A. Gombert, B. Bläsi, C. Bühler, and P. Nitz, "Some application cases and related manufacturing techniques for optically functional microstructures on large areas," Opt. Eng. 43, 2525-2533 (2004). [CrossRef]
- C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, and A. Tünnermann, "Broadband antireflective surface-relief structure for THz optics," Opt. Express 15, 779-789 (2007). [CrossRef] [PubMed]
- H. Ibach and H. Lüth, Festkörperphysik (Springer, 2002).
- E. B. Grann, M. G. Moharam, and D. A. Pommet, "Optimal design for antireflective tapered two-dimensional subwavelength grating structures," J. Opt. Soc. Am. A 12, 333-339 (1995). [CrossRef]
- E. B. Grann, M. G. Moharam, and D. A. Pommet, "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A 11, 2695-2703 (1994). [CrossRef]
- P. Lalanne, and D. Lemercier-Lalanne, "Depth dependence of the effective properties of subwavelength gratings," J. Opt. Soc. Am. A 14, 450-458 (1997). [CrossRef]
- S. Rytov, "Electromagnetic Properties of a Finely Stratified Medium," Soviet Physics JETP 2, 466-475 (1956).
- P. Lalanne and D. Lemercier-Lalanne, "On the effective medium theory of subwavelength periodic structures," J. Mod. Opt. 43, 2063-2085 (1996). [CrossRef]
- H. Kikuta, Y. Ohira, H. Kubo, and K. Iwata, "Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit," J. Opt. Soc. Am. A 15, 1577-1585 (1998). [CrossRef]
- H. A. Macleod, Thin-film optical filters (Institute of Physics Publ, 2002).
- J. Bischoff and R. Brunner, "Numerical investigation of the resolution in solid immersion lens systems," Proc. SPIE 4099, 1-11 (2000).

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