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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 4 — Feb. 19, 2007
  • pp: 1415–1427
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Polarization independent enhanced optical transmission in one-dimensional gratings and device applications

David Crouse and Pavan Keshavareddy  »View Author Affiliations


Optics Express, Vol. 15, Issue 4, pp. 1415-1427 (2007)
http://dx.doi.org/10.1364/OE.15.001415


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Abstract

A review and analysis is performed of various resonance effects associated with subwavelength one-dimensional (1-D) metal gratings for transverse electric (TE) and transverse magnetic (TM) polarized incident radiation. It is shown that by tuning the structural geometry (especially the groove width) and material composition of the 1-D gratings, polarization independent enhanced optical transmission (EOT) can be achieved. Three different cases of EOT have been studied for 1-D metal gratings: a) EOT for TM-polarized incident radiation b) EOT for TE-polarized incident radiation, and most importantly c) EOT for un-polarized incident light. Potential uses of these results in the design and improvement of various optoelectronic devices, such as polarizers, photodetectors and wavelength filters are discussed.

© 2007 Optical Society of America

1. Introduction

One-dimensional (1-D) reflection and transmission gratings have been researched for decades because of their interesting and “anomalous” optical characteristics and potential applications in various fields (reference [1

1. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostrucutred metals,” Phys. Rev. B 66,155412(1) –155412(10) (2002) [CrossRef]

] and references therein), including beam splitting polarizers, photodetectors, Raman scattering and super lenses [1–21

1. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostrucutred metals,” Phys. Rev. B 66,155412(1) –155412(10) (2002) [CrossRef]

]. These anomalous optical characteristics of 1-D gratings are explained by individual optical and electromagnetic resonance modes (and combinations or hybrids of these modes) that exist in these structures. Figure 1 shows the electromagnetic fields of three different types of resonances that are usually associated with the grating anomalies in 1-D gratings: 1) Wood-Rayleigh anomalies (WRs): WRs occur when one diffraction order grazes the surface of the grating as it changes from an evanescently decaying surface-confined mode to a radiating diffracted mode as the wavelength of the incident beam is decreased. 2) Surface plasmons (SPs): SPs are surface charge oscillations and their associated electromagnetic fields at a metal/dielectric interface. In one of the earliest papers addressing optical anomalies in 1-D gratings, Fano proposed that SPs were responsible for some of these optical anomalies [5

5. U. Fano, “The theory of anomalous diffraction gratings and quasi-stationary waves on metallic surfaces,” J. Opt. Soc. Am. 31,213–222 (1941). [CrossRef]

]. 3) Cavity modes (CM): CMs are resonantly excited modes within the groove of the grating. Only a TM-polarized incident beam (i.e., a beam with the magnetic field oriented parallel to the metal wires (see Appendix)) has a nonzero electric field component in the same direction as an electric field component of an SP mode in a lamellar grating and therefore only TM-polarized light can couple with and excite SPs [1

1. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostrucutred metals,” Phys. Rev. B 66,155412(1) –155412(10) (2002) [CrossRef]

,6

6. D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley and Sons, Belfast, 1982), pp.661-724.

]. In contrast, WRs and CMs occur for both TE-polarized and TM-polarized incident light.

Fig. 1. (a) The effective electromagnetic energy density for the 1.11eV horizontally oriented surface plasmons (HSPs). This energy profile illustrates typical HSP characteristics. The magnetic field intensities for (b) 1.16eV WR and (c) 0.73eV CM. For the WR and CM modes, the structure has a Si substrate and Au contacts with d = 0.3μm, c = 0.15μm and h = 0.4μm and grooves filled with air. For the CM mode, the structure is altered to increase the aspect ratio of the groove by having c = 0.075μm and h = 0.57μm; all other dimensions remain the same. In all cases, a TM-polarized beam is incident on the structure from above (i.e., the air layer).

It is the purpose of this paper to describe the optical properties of subwavelength metal gratings and the various optical and electromagnetic resonance effects associated with them, determine the geometrical and compositional dependencies of (and ability to independently tune) TE-polarization EOT and TM-polarization EOT, and determine if a practical grating structure can be designed that exhibits simultaneous EOT for TE-polarized light and TM-polarized light (i.e., EOT for both polarizations occurring at the same wavelength and angle of incidence). For the sake of completeness, we describe three different cases of EOT in subwavelength metal transmission gratings (see Fig. 2): (a) Case 1 - EOT of TM-polarized incident radiation, (b) Case 2 - EOT of TE-polarized incident radiation, (c) Case 3 - EOT of un-polarized (TE+TM) incident radiation. Case 1 has been studied extensively and it has been shown that subwavelength metal gratings can achieve EOT for TM-polarized radiation, with CMs playing a significant role in EOT. A more detailed review of Case 1 can be found in reference [13

13. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 20,7760–7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760 [CrossRef]

]. On the other hand, Case 2 has received very little attention, primarily due to the inability of TE-polarized light to excite SPs, which were initially considered to be the modes primarily responsible for EOT. Case 3, to our knowledge, has never been studied. It will be shown in this paper that EOT can be achieved simultaneously for TE-polarized and TM-polarized incident light for a simple and realizable classical 1-D metal grating (i.e., a device with realistic structural dimensions and material parameters). The result is of great importance from both a theoretical point of view and for its use in optoelectronic devices. In fact, our present study was motivated by the need to improve the performance of metal-semiconductor-metal photodetectors (MSM-PDs), a structure that is essentially a 1-D metal grating on top of a semiconductor substrate. We have previously demonstrated that the performance of MSM-PDs can be greatly improved for TM-polarized incident light by tapping into a specific combination of resonance effects associated with EOT [14–17

14. D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

]. However, in order for the idea to gain practical significance it was necessary to design a 1-D grating structure that exhibits EOT for both TE-polarized and TM-polarized light. With the results of polarization independent EOT described in this work, along with the use of the light localization techniques described in references [14–17

14. D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

], it is expected that high performance (i.e., high responsivity and high bandwidth) MSM-PDs can be developed. More generally, the ability to tune and achieve enhanced or suppressed transmission for both TE-polarized and TM-polarized light at a particular wavelength by changing a grating’s structural geometry and/or material composition can be used in developing novel, or improving the performance of existing, optoelectronic devices such as TM selective polarizers (Case 1), TE selective polarizers (Case 2), and wavelength filters (Case 3).

Fig. 2. The three different cases of EOT in 1-D metal gratings that are described in this paper.

2. Polarization independent enhanced optical transmission

Figure 3 shows the location of the peak of transmission for TM-polarized and TE-polarized light as a function of groove width (with groove width varying from 0.35μm to 0.66μm) for a structure with period d = 1.75μm, groove height h = 1μm, and silicon inside the groove with a ε = 11.9. As can be seen from Fig. 3, the peak at which EOT occurs moves to higher energies for TM-polarized light and lower energies for TE-polarized light and that for an energy of 0.5eV (λ = 2.5 μm) and the point of intersection of the two curves produces a device design where simultaneous EOT can be achieved for TE and TM polarization. Figure 4(a) and 4(b) shows the reflectance and transmittance as a function of energy for TE-polarized and TM-polarized light for the above structure with the groove widths being 0.45μm for 0.615μm respectively. From Fig. 4(b), it can be concluded that for unpolarized incident light with an equal contribution from both polarization states (50% TM, 50% TE), as high as 94% of the incident light can be transmitted into the substrate. This result will have the potential to effect significant design improvements in a variety of optoelectronic devices, which are typically operated using polarization-independent radiation.

By plotting the peaks of transmission for TM-polarized light and the dips of transmission for TE-polarized light as a function of groove width, we can find the optimum groove width (point of intersection of the two curves ) for a design for a TM polarization transmitter and TE polarization reflector (Case 1). Case 1 is a well-known result and is used in designing polarizers, which separate the TE and TM polarization states. On the other hand, Case 2, in which TE-polarized light is transmitted and TM-polarized light is reflected, is equally important and has not been studied before. Using the same analysis, namely plotting the peaks of transmission of TE-polarized light and dips of transmission of TM-polarized light as a function of groove width, we can find the optimum groove width for the design of a TE-polarization transmitter and a TM polarization reflector.

Fig. 3. The dependence of the peaks in transmission for the first three order modes for TE-polarized and TM-polarized light. It is seen that the CMs for TE-polarized light have a strong dependence on groove width that can be exploited to align these modes with TM-polarization CMs.
Fig. 4. (a)Left: Reflectance (black) and Zero-order transmission (red) coefficients for the structure with d = 1.75μ, c = 0.45μm, h = 1μm, εgroove=11.9, showing optical characteristics consistent with Case 1 at 0.333eV and Case 2 at 0.415eV. Right (b): Reflectance (black) and Zero-order transmission (red) coefficients for the structure with d = 1.75μm, c = 0.615μm, h = 1 μm, εgroove=11.9, exhibiting aligned TE and TM polarization EOT (Case 3). In both the left-hand and right-hand plots, solid lines correspond to TM polarization and dotted lines correspond to TE polarization results.

Figure 4a shows one possible structure, which acts both as a TM polarization transmitter (TE reflector) and a TE polarization transmitter (TM reflector) at λ = 3.729μm (ħω = 0.333eV) and λ = 2.992μm (ħω = 0.415eV) respectively. Even though the line-widths of the peak transmission are different for Case 1 and Case 2 for the structure shown, it is possible to design narrow or broad peaks by changing the groove aspect ratio (i.e., groove height divided by groove width) depending on the application of interest. For example, photodetectors generally require a broad transmission peak, while wavelength filters may require narrow or broad transmission peaks depending on if they are being used as wavelength selectors or band-pass filters. Also, the phase of the reflected and transmitted beams have not been explicitly stated in this work, and while they may not be important for polarizers or optical transmission gratings, it can be important in other sensor applications.

To further understand the light channeling characteristics of these subwavelength gratings that exhibit simultaneous TE and TM polarization EOT, the electric and magnetic fields are plotted in Fig. 5 and the Poynting vector plotted in Fig. 6 for the above structure, which achieves EOT for 0.5eV TE-polarized and TM-polarized light. As mentioned before, the electromagnetic fields for TM-polarized light are more concentrated on the groove walls (this will be more prominent for wider grooves) compared to TE-polarized light in which the electromagnetic fields are positioned towards the center of the groove. Also, it can be seen that the resonant excitation of CMs is associated with significantly more field enhancement for TM as compared to TE, with a field enhancement for TM reaching as high as ~11 and a field enhancement for TE at ~4 (corresponding to intensity enhancements of ~121 and ~16 respectively) for this device geometry and specific CMs. A similar behavior has been previously reported for reflection gratings, where in it was shown that anomalous absorption of reflection gratings for TE is not accompanied by significant field enhancement, in contradistinction to anomalous absorption in TM polarization [21

21. E. Popov and L. Tsonev, “Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light,” Surf. Science. Lett. 271,L378–L382 (1992). [CrossRef]

]. The Poynting vector shows that the grooves act as light funnels, collecting and channeling the incident light through the grooves. However, the channeling is distinctly different for TE-polarized and TM-polarized light. For TM-polarized light, the channeling of energy occurs close to metal contacts and for TE-polarized light, channeling occurs more towards the center of the groove.

Two additional differences between the characteristics of TE-polarized and TM-polarized light incident on these lamellar grating structures are worth noting. First, the two polarization states have different cut-off frequencies at which a CM, and therefore EOT, occurs due to the different electromagnetic boundary conditions of the two polarization states at metal/dielectric interfaces. More specifically, there is no cut-off frequency for TM-polarization but there is for TE-polarization. Second, for TM-polarized light the energy of the peak of transmission and amount of transmission may be strongly dependent on the metal wire width and period due to the interactions between CMs and SPs if these two resonances have similar energies [13

13. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 20,7760–7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760 [CrossRef]

]. For TE-polarized light however, no SPs are present and the location of peak transmission and the amount of transmission is almost independent of the metal wire width and hence independent of the period for a fixed groove opening.

Fig. 5. Left: The magnitude of the z-component of the magnetic field produced by TM polarized 0.5eV normal incident light. Right: The magnitude of the z-component of the electric field produced by TE polarized 0.5eV normal incident light.
Fig. 6. Left: The Poynting vector for TM polarized 0.5eV normal incident light. Right: The Poynting vector for TE polarized 0.5eV normal incident light.

3. Device applications

The ability to independently control TE polarization and TM polarization EOT, as well as align EOT for both polarization states, can be applied to many optoelectronic devices, both active devices and passive devices. We have shown previously that the light channeling described in this paper, and light localization techniques described in references [14–17

14. D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

], for TM polarization can be used to improve the performance of metal-semiconductor-metal photodetectors (MSM-PDs). The results of this paper will allow for the performance of MSM-PDs for a TE polarized incident beam, as well as an un-polarized incident beam, to be optimized as well. The use of the independent control of TE polarization EOT and TM polarization EOT in the development of two types of passive devices is described below.

3.1 Polarizers

3.2 Wavelength Filters

Optical wavelength filters are important components for optical communication systems where they serve, for example, as wavelength-selective elements in optical receivers or as noise filters in optical amplifiers [27

27. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32,2606–2613 (1993) [CrossRef] [PubMed]

, 28

28. Guido Niederer, Wataru Nakagawa, Hans Peter Herzig, and Hans Thiele, “Design and characterization of a tunable polarization-independent resonant grating filter,” Opt. Express 13,2196–2200 (2005). [CrossRef] [PubMed]

]. In particular, there is great interest in filters that are fabricated on semiconductor materials, since they may be directly integrated with semiconductor optical amplifiers and detectors. For applications in fiber-optic networks, however, it is essential that these filters be independent of the state of polarization of the incident light. Typically, optical wavelength filters are designed with waveguides with Bragg gratings containing grating lines perpendicular to the propagation direction. In this paper, we show that by carefully designing the structural geometry of a classical 1-D metal grating, polarization independent wavelength filters can be achieved. A very important design consideration for wavelength filters is the line-width of transmission peak. For a given geometry, the linewidth of the peak of transmission for TM-polarized light can be changed by changing the groove aspect ratio, with high aspect ratios producing broader peaks and vice-versa. On the other hand, for TE-polarized light, the peaks are typically very narrow. Using the tuning techniques described in this paper, we have designed a 1-D metal grating (on top of SiO2) to act as a polarization independent wavelength filter at the communication wavelength. Figure 7 shows the optical response of this 1-D grating filter, which has peak transmission of 86% at 1550nm and FWHM of the transmission equal to 41nm. The present design is not only highly efficient in transmitting light for a particular wavelength, but also can be easily integrated with various other optical components.

Fig. 7. Reflectance (black) and Zero-Order transmittance (red) for a un-polarized (50%TM, 50%TE) light incident on 1-D grating with d = 690nm, c = 287.5nm, h = 1193.7nm, with silicon inside the groove and SiO2 (ε = 2) as the substrate. This is an example of a polarization-independent wavelength filter that can be achieved using the tuning techniques mentioned in this paper at 1550nm with a peak transmission for un-polarized light at 86% and FWHM of transmission equal to 41nm.

4. Conclusion

We have shown that EOT can be achieved for both TM-polarized and TE-polarized light, both separately and simultaneously (in terms of wavelength and angle of incidence). It has been shown that the groove width is a very important design parameter in tuning the peak of EOT in TE and TM polarized light. The results of EOT are discussed in relation to improvements in, or the development of, novel optoelectronic devices including MSM-PDs, metal grating polarizers that can transmit TE and TM radiation and optical wavelength filter at 1550nm.

5. Appendix

The optical and electromagnetic characteristics of lamellar gratings are modeled in this work using a coupled mode algorithm that uses the surface impedance boundary condition (SIBC) approximation. This method is described in detail in references [14

14. D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

, 20

20. H. Lochbihler and R. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32,3459–3465 (1993). [CrossRef] [PubMed]

] and only summarized below. This method uses the following approximation relating the tangential components of the electric and magnetic fields at a dielectric/metal interface:[14

14. D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

] [20

20. H. Lochbihler and R. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32,3459–3465 (1993). [CrossRef] [PubMed]

]

E=Zn̂×H
(A1)

where Z = 1/nmetal, with nmetal being the complex index of refraction of the metal. This approximation is valid if the dielectric constant of the metal is much larger than the neighboring dielectric (which is largely true in the infrared and visible spectral regions).

Fig. 8. The figure defines the coordinate system used in the calculation. Only one period of the grating is shown. In the calculations, the top layer is assumed to be air (ε = 1).

The electromagnetic fields are expressed as a linear combination of orthogonal modes as follows:

fair(x,y)=exp(i(αoxβo(yh2)))+n=Rnexp(i(αnx+βn(yh2)))
(A2)
fgroove(x,y)=n=0Φn(x,y)
(A3)
fsubstrate(x,y)=n=Tnexp(i(αnxβ˜n(y+h2)))
(A4)

Φn(x,y)=Xn(x)Yn(y)
(A5)
Xn(x)=dnsin(μnx)+cos(μnx)
(A6)
Yn(y)=anexp(iυny)+bnexp(iυny)
(A7)

where the terms μn and υn obey the relation:

μn2+υn2=εgrooveko2
(A8)

Applying the SIBC condition to the left-hand and right hand sides of the grooves results in the following equations (respectively):

dn=ηgrooveμn
(A9)
tan(cμn)=2ηgrooveμnμn2η22
(A10)

where c is the width of the groove and ηgroove = koεgrooveZ/i for TM polarization and ηgroove = ko/iZ for TE polarization. An important step in the above method is the solution to Eq. (A10). We have used the technique described by Tayeb and Petit [29

29. G. Tayeb and R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Optica Acta 31,1361–1365 (1984). [CrossRef]

], which is shown to be very effective and computationally less demanding. In this method the roots of Eq. (A10) are found by integration starting from an initial value. We have performed the integration using the Runge-Kutta method.

Applying boundary conditions equating the tangential field components and the SIBC conditions at the metal/dielectric interfaces at y = h/2 and y = -h/2 yields the following equations.

n=(In+Rn)eiαnx=mXm(x)(φmam+φm1bm)0xc
(A11)
in=βn(In+Rn)eiαnx={iγairγgroovemX(x)υm(φmamφm1bm)0xcηairn=(In+Rn)eiαnxcxd
(A12)
n=Tqneiαnx=mX(x)(φm1am+φmbm)0xc
(A13)
in=β˜nTneiαnx={iγsubstrateγgroovemXm(x)υm(φm1amφmbm)0xcηsubstraten=Tneiαnxcxd
(A14)

where γair = εair = 1, γgroove = εgroove, γsubstrate = εsubstrate, ηair = koZ/i and ηsubstrate = koεsubstrateZ/i for the TM polarization and γair = γgroove = γsubstrate = 1, ηair = ηsubstrate = ko/iZ for the TE polarization and φm = e mh/2.

Then multiplying Eqs. (A11) and (A13) by Xm(x) and integrating over the region 0≤xc and multiplying Eqs. (A12) and (A14) by e qx/d and integrating over the region 0≤xd yields the following matrix equations that are used to determine the unknown coefficients Rn, Tn, an and bn:

MΨ=Ω
(A15)

with

M=(GNφ10ηairJiγairγgrooveKυφiγairγgrooveφ100Nφ1G0iγsubstrateγgrooveφ1iγsubstrateγgrooveKυφiβ˜+ηsubstrateJ)
(A16)
Ψ=RabTandΩ=GI(+ηairJ)I00
(A17-A18)

where the matrices φ, β, υ are square matrices with nonzero components along the main diagonal given by φm, βn, υm that have been previously defined; G, N, J, K are matrices with components given by:

Gmn=0cXm(x)exp(iαnx)dx
(A19)
Knm=1d0cXm(x)exp(iαnx)dx
(A20)
Jqn=1dcdexp(i(αnαq)x)dx
(A21)
Nmn=0cXm(x)Xn(x)dx=δmn[((ηgrooveμm)2+1)c2+ηgrooveμm2]
(A22)

The number of modes used in the electromagnetic field expansions were large and the solutions were convergent. The results obtained using the above approach were checked using another method that assumes that the walls of the grooves are perfectly conducting. These results yield practically identical results indicating that even though the convergence of TE polarization solutions using the SIBC approximation is worse than the convergence of TM polarization solutions, the main results showing EOT for both TM and TE polarizations will hold true when more accurate methods are used for the calculations.

Once Eq. (A15) is used to find all of the unknown coefficients, the reflectance (i = air in Eq. A23), transmittance and diffraction efficiencies (i = substrate in Eq. A23) can be calculated as the ratio of the ŷ -component of the Poynting vector for an outward propagating mode and the ŷ -component of the incident beam (assuming a normalized incident beam and a top layer being air):

Sy,nSy,incident=εiγicosθoutward,ncosθincidentΨoutward,n2
(A23)

where Ψ outward,n is either Rn or Tn and θoutput,n is the angle of the outward propagating mode.

Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. 0539541. Also part of the work is performed at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation.

References and links

1.

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostrucutred metals,” Phys. Rev. B 66,155412(1) –155412(10) (2002) [CrossRef]

2.

E. Popov and L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69,193–198 (1989). [CrossRef]

3.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phil. Mag. 4,396–408 (1902).

4.

A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4,1275–1297 (1965). [CrossRef]

5.

U. Fano, “The theory of anomalous diffraction gratings and quasi-stationary waves on metallic surfaces,” J. Opt. Soc. Am. 31,213–222 (1941). [CrossRef]

6.

D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley and Sons, Belfast, 1982), pp.661-724.

7.

U. Schroeter and D. Heitmann “Surface plasmons enhanced transmission thorough metallic gratings,” Phys. Rev. B 58,15419–15421 (1998) [CrossRef]

8.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phy. Rev. B 66,161403(1)–161403(4) (2002) [CrossRef]

9.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83,2845–2848 (1999) [CrossRef]

10.

Qing Cao and Philippe Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88,057403(1) –057403(4) (2002). [CrossRef]

11.

M.M.J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66,195105–195116 (2002) [CrossRef]

12.

A. G Borisov, F. J. Garcia de Abajo, and S. V. Shabanov, “Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,” Phys. Rev. B 71,075408(1) –075408(7) (2005). [CrossRef]

13.

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 20,7760–7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760 [CrossRef]

14.

D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52,2365–2373 (2005). [CrossRef]

15.

D. Crouse, M. Arend, J. Zou, and P. Keshavareddy, “Numerical modeling of electromagnetic resonance enhanced silicon metal-semiconductor-metal photodetectors,” Opt. Express 14,2047–2061 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2047 [CrossRef] [PubMed]

16.

D. Crouse and Ravina Solomon, “Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes,” Solid-State Electronics 49,1697–1701 (2005). [CrossRef]

17.

D. Crouse and P. Keshavareddy, “Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors,” J. Opt. A: Pure Appl. Opt. 8,175–181 (2006). [CrossRef]

18.

Stephane Collin, Fabrice Pardo, and Jean-Luc Pelouard, “Resonant-cavity-enhanced subwavelength metal-semiconductor-metal photodetector,” Appl. Phys. Lett. 83,1521–1523 (2003). [CrossRef]

19.

Stéphane Collin, Fabrice Pardo, Roland Teissier, and Jean-Luc Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85,194–196 (2004). [CrossRef]

20.

H. Lochbihler and R. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32,3459–3465 (1993). [CrossRef] [PubMed]

21.

E. Popov and L. Tsonev, “Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light,” Surf. Science. Lett. 271,L378–L382 (1992). [CrossRef]

22.

David R. Lide, Handbook of Chemistry and Physics (CRC Press, London, 1992–1993).

23.

H. Ichikawa, “Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method,” J. Opt. Soc. Amer. A 15,152–157 (1998) [CrossRef]

24.

M. G. Moharam, Pommet D. A., E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous couple-wave analysis for surface relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12,1077–1086 (1995) [CrossRef]

25.

Hitoshi Tamada, Tohru Doumuki, Takashi Yamaguchi, and Shuichi Matsumoto, “Al wire -grid polarizer using the s-polarization resonance effect at the 0.8μm wavelength band,” Opt. Lett. 22,419–421 (1997). [CrossRef] [PubMed]

26.

Donghyun Kim, “Polarization characteristics of a wire-grid polarizer in a rotating platform,” Appl. Opt. 44,1366–1371 (2005). [CrossRef] [PubMed]

27.

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32,2606–2613 (1993) [CrossRef] [PubMed]

28.

Guido Niederer, Wataru Nakagawa, Hans Peter Herzig, and Hans Thiele, “Design and characterization of a tunable polarization-independent resonant grating filter,” Opt. Express 13,2196–2200 (2005). [CrossRef] [PubMed]

29.

G. Tayeb and R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Optica Acta 31,1361–1365 (1984). [CrossRef]

OCIS Codes
(040.5160) Detectors : Photodetectors
(050.1950) Diffraction and gratings : Diffraction gratings
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Diffraction and Gratings

History
Original Manuscript: October 6, 2006
Revised Manuscript: November 7, 2006
Manuscript Accepted: November 7, 2006
Published: February 19, 2007

Citation
David Crouse and Pavan Keshavareddy, "Polarization independent enhanced optical transmission in one-dimensional gratings and device applications," Opt. Express 15, 1415-1427 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1415


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References

  1. F. J. Garcia-Vidal and L. Martin-Moreno, " Transmission and focusing of light in one-dimensional periodically nanostrucutred metals," Phys. Rev. B 66, 155412(1) -1554121(0) (2002) [CrossRef]
  2. E. Popov and L. Tsonev, "Electromagnetic field enhancement in deep metallic gratings," Opt. Commun. 69, 193-198 (1989). [CrossRef]
  3. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-408 (1902).
  4. A. Hessel and A. A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965). [CrossRef]
  5. U. Fano, "The theory of anomalous diffraction gratings and quasi-stationary waves on metallic surfaces," J. Opt. Soc. Am. 31, 213-222 (1941). [CrossRef]
  6. D. Maystre, "General study of grating anomalies from electromagnetic surface modes," in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley and Sons, Belfast, 1982), pp. 661-724.
  7. U. Schroeter, D. Heitmann " Surface plasmons enhanced transmission thorough metallic gratings," Phys. Rev. B 58, 15419-15421 (1998) [CrossRef]
  8. A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phy. Rev. B 66, 161403(1)- 161403(4_ (2002). [CrossRef]
  9. J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999) [CrossRef]
  10. Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403(1) - 057403(4) (2002). [CrossRef]
  11. M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-195116 (2002) [CrossRef]
  12. A. G Borisov, F. J. Garcia de Abajo, S. V. Shabanov, "Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials," Phys. Rev. B 71, 075408(1) - 075408(7) (2005). [CrossRef]
  13. D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 20, 7760-7771 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7760 [CrossRef]
  14. D. Crouse, "Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications," IEEE Trans. Electron Devices 52, 2365-2373 (2005). [CrossRef]
  15. D. Crouse, M. Arend, J. Zou, and P. Keshavareddy, "Numerical modeling of electromagnetic resonance enhanced silicon metal-semiconductor-metal photodetectors," Opt. Express 14, 2047-2061 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2047 [CrossRef] [PubMed]
  16. D. Crouse and R. Solomon, "Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes," Solid-State Electronics 49, 1697-1701 (2005). [CrossRef]
  17. D. Crouse and P. Keshavareddy, "Electromagnetic Resonance Enhanced Silicon-on-Insulator Metal-Semiconductor-Metal Photodetectors," J. Opt. A: Pure Appl. Opt. 8, 175-181 (2006). [CrossRef]
  18. Stephane Collin,Fabrice Pardo, and Jean-Luc Pelouard, "Resonant-cavity-enhanced subwavelength metal-semiconductor-metal photodetector," Appl. Phys. Lett. 83, 1521-1523 (2003). [CrossRef]
  19. Stéphane Collin,Fabrice Pardo,Roland Teissier,and Jean-Luc Pelouard, " Efficient light absorption in metal-semiconductor-metal nanostructures," Appl. Phys. Lett. 85, 194-196 (2004). [CrossRef]
  20. Lochbihler, H.  and R. Depine, "Highly conducting wire gratings in the resonance region," Appl. Opt. 32, 3459-3465 (1993). [CrossRef] [PubMed]
  21. E. Popov, L. Tsonev, "Resonant electric field enhancement in vicinity of a bare metallic grating exposed to s-polarize light," Surf. Science. Lett. 271, L378-L382 (1992). [CrossRef]
  22. David R. Lide, Handbook of Chemistry and Physics (CRC Press, London, 1992-1993).
  23. H. Ichikawa, "Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method," J. Opt. Soc. Amer. A 15, 152-157 (1998) [CrossRef]
  24. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous couple-wave analysis for surface relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995) [CrossRef]
  25. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, "Al wire -grid polarizer using the s-polarization resonance effect at the 0.8μm wavelength band," Opt. Lett. 22, 419-421 (1997). [CrossRef] [PubMed]
  26. D. Kim, "Polarization characteristics of a wire-grid polarizer in a rotating platform," Appl. Opt. 44, 1366-1371 (2005). [CrossRef] [PubMed]
  27. S. S. Wang, R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32, 2606-2613 (1993) [CrossRef] [PubMed]
  28. G. Niederer, W. Nakagawa, H. P. Herzig, H. Thiele, "Design and characterization of a tunable polarization-independent resonant grating filter, " Opt. Express 13, 2196-2200 (2005). [CrossRef] [PubMed]
  29. G. Tayeb and R. Petit, "On the numerical study of deep conducting lamellar diffraction gratings," Optica Acta 31, 1361-1365 (1984). [CrossRef]

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