## Analysis of optical waveguides with ultra-thin metal film based on the multidomain pseudospectral frequency-domain method |

Optics Express, Vol. 19, Issue 5, pp. 4324-4336 (2011)

http://dx.doi.org/10.1364/OE.19.004324

Acrobat PDF (2262 KB)

### Abstract

Analysis of optical waveguides with thin metal films is studied by the multidomain pseudospectral frequency-domain (PSFD) method. Calculated results for both guiding and leaky modes are precise by means of the PSFD based on Chebyshev-Lagrange interpolating polynomials with modified perfectly matched layer (MPML). By introducing a suitable boundary condition for the dielectric-metallic interface, the stability and the spectrum convergence characteristic of the PSFD-MPML method can be sustained. The comparison of exact solutions of highly sensitive surface plasmon modes in 1D dielectric-metal waveguides and those calculated by our PSFD-MPML demonstrates the validity and usefulness of the proposed method. We also apply the method to calculate the effective refractive indices of an integrated optical waveguide with deposition of the finite gold metal layer which induces the hybrid surface plasmon modes. Furthermore, the 2-D optical structures with gold films are investigated to exhibit hybrid surface plasmon modes of wide variations. We then apply hybrid surface plasmon modes to design novel optical components–mode selective devices and the polarizing beam splitter.

© 2011 OSA

## 1. Introduction

1. M. Faraday, “Experimental relations of gold (and other metals) to light,” Philos. Trans. R. Soc. Lond. **147**(0), 145–181 (1857). [CrossRef]

7. R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B Chem. **10**(3), 209–217 (1993). [CrossRef]

15. D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90 ° bends in sub-wavelength metallic slot waveguides,” Opt. Express **18**(15), 16139–16145 (2010). [CrossRef] [PubMed]

12. J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express **16**(19), 14902–14909 (2008). [CrossRef] [PubMed]

15. D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90 ° bends in sub-wavelength metallic slot waveguides,” Opt. Express **18**(15), 16139–16145 (2010). [CrossRef] [PubMed]

16. S. J. Al-Bader and M. Imtaar, “Optical fiber hybrid-surface plasmon polaritons,” J. Opt. Soc. Am. B **10**(1), 83–88 (1993). [CrossRef]

17. Y. C. Lu, L. Yang, W. P. Huang, and S. S. Jian, “Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry,” J. Lightwave Technol. **26**(13), 1868–1876 (2008). [CrossRef]

8. R. Weisser, B. Menges, and S. Mittler-Neher, “Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. **56**(3), 189–197 (1999). [CrossRef]

13. M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express **16**(25), 20227–20240 (2008). [CrossRef] [PubMed]

16. S. J. Al-Bader and M. Imtaar, “Optical fiber hybrid-surface plasmon polaritons,” J. Opt. Soc. Am. B **10**(1), 83–88 (1993). [CrossRef]

19. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. **18**(5), 737–743 (2000). [CrossRef]

28. S. Guo, F. Wu, S. Albin, H. Tai, and R. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express **12**(15), 3341–3352 (2004). [CrossRef] [PubMed]

29. Q. H. Liu, “A pseudospectral frequency-domain (PSFD) method for computational electromagnetics,” IEEE Antennas Wirel. Propag. Lett. **1**(1), 131–134 (2002). [CrossRef]

35. P. J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. **22**(12), 908–910 (2010). [CrossRef]

33. P. J. Chiang, C. P. Yu, and H. C. Chang, “Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(2), 026703 (2007). [CrossRef] [PubMed]

34. P. J. Chiang, C. L. Wu, C. H. Teng, C. S. Yang, and H. C. Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron. **44**(1), 56–66 (2008). [CrossRef]

35. P. J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. **22**(12), 908–910 (2010). [CrossRef]

35. P. J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. **22**(12), 908–910 (2010). [CrossRef]

*n*

_{eff}of the SP and the HSP modes in this work. However, the core waveguide structures treated in this paper consist of dielectric-metallic interfaces and it is noticeable that the boundary condition significantly influences the convergence behavior while solving optical waveguide problems by numerical methods. Compared with the dielectric-dielectric interfaces in [35

**22**(12), 908–910 (2010). [CrossRef]

36. T. Baba and Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expression,” IEEE J. Quantum Electron. **28**(7), 1689–1700 (1992). [CrossRef]

37. Y.-T. Huang, C.-H. Jang, S.-H. Hsu, and J.-J. Deng, “Antiresonant reflecting optical waveguides polariza-tion beam splitters,” J. Lightwave Technol. **24**(9), 3553–3560 (2006). [CrossRef]

37. Y.-T. Huang, C.-H. Jang, S.-H. Hsu, and J.-J. Deng, “Antiresonant reflecting optical waveguides polariza-tion beam splitters,” J. Lightwave Technol. **24**(9), 3553–3560 (2006). [CrossRef]

39. I. Hodgkinson, Q. H. Wu, M. Arnold, L. De Silva, G. Beydaghyan, K. Kaminska, and K. Robbie, “Biaxial thin-film coated-plate polarizing beam splitters,” Appl. Opt. **45**(7), 1563–1568 (2006). [CrossRef] [PubMed]

8. R. Weisser, B. Menges, and S. Mittler-Neher, “Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. **56**(3), 189–197 (1999). [CrossRef]

## 2. Numerical examples and discussion

### 2.1 Dielectric-metal waveguide

_{0}and piecewise uniform refractive indices

*n*=

*n*and

_{a}*n*=

*n*for dielectric and metal, respectively, where dielectric

_{b}*n*is a real number and metallic

_{a}*n*is a complex number. In the dielectric-metal waveguide, the fields of the TM mode (

_{b}*E*, 0,

_{x}*E*},

_{z}*H*, 0}) propagate toward the

_{y}*z*-direction and the magnetic field can be expressed as

*γ*is the propagation constant,

*k*

_{0}=

*ω*/

*c*is the free-space wave number, in which

*ω*is the angular frequency, and

*c*is the velocity of light in vacuum.

*x*- and

*z*-directions. Accordingly, the solutions of the field in Eq. (2) satisfying such characteristics can be expressed asDue to phase matching, we can obtain

*γ*and the effective index

*n*

_{eff}from Eq. (3) aswhere

*n*

_{eff}is in general a complex number. Besides of the analytic solution in Eq. (4), we may employ the PSFD-MPML introduced in [35

**22**(12), 908–910 (2010). [CrossRef]

**22**(12), 908–910 (2010). [CrossRef]

*n*(a complex number) and the dielectric

_{b}*n*(a complex number), we derive the following boundary conditions by Maxwell’s curl equationswhere

_{a}*θ*is equal to

*n*= 1.52, the metal is gold, and it is operated at wavelengths

_{a}*λ*= 0.532 μm to

*λ*= 1.55 μm. The index

*n*of gold at different wavelengths is referred to [40

_{b}40. E. D. Palik, *Handbook of Optical Constants of Solids* (Academic Press, Inc., 1988), http://refractiveindex.info/.

*k*

_{1}

*and*

_{x}*k*

_{2}

*of Eq. (3) are complex numbers, i.e., there are propagating and evanescent components in the*

_{x}*x*direction. Hence, our PSFD-MPML is an appropriate method for analyzing such a structure.

*d*

_{3}= 0.1 μm is imposed and the thicknesses of metallic and dielectric layers are

*d*

_{1}=

*d*

_{2}= 0.3 μm, respectively. Figure 2(b) shows the calculated magnetic fields at

*λ*= 1.55 μm and it is observed that the results by adopting our PSFD-MPML agree with the exact solutions very well. Table 1 lists the calculated effective indices (

*n*

_{eff}) of the SP mode by using Dirichlet, PML, and the MPML boundary conditions in the same computational window size as shown if Fig. 2(a). It can be seen that the results of using MPML agree with the exact

*n*

_{eff}up to 9 significant digits as the degree

*N*is larger than 22, while the results by using both Dirichlet and PML can even not converge. Hence, the MPML has been demonstrated the capability of modeling unbound areas in such cases and it will be adopted in the subsequent studies.Furthermore, to demonstrate the superiority of the PSFD-MPML for solving the SP and HSP modes over other methods, we reconsider the structure shown in Fig. 2(a) and adopt the thicknesses of gold and dielectric layers as

*d*

_{1}= 0.5μm and

*d*

_{2}= 1.42μm, respectively, with

*λ*= 0.5μm. We solve this problem by using our PSFD-MPML method and the improved finite-difference mode solver (FDMS) proposed in [21

21. Y.-P. Chiou, Y.-C. Chiang, and H.-C. Chang, “Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices,” J. Lightwave Technol. **18**(2), 243–251 (2000). [CrossRef]

*O*(

*h*

^{2}) and

*O*(

*h*

^{4}), respectively, where

*h*is the grid size and corresponds to (

*d*

_{1}+

*d*

_{2})/

*h*total unknowns. And for the PSFD-MPML, only two sub- domains are adopted with the same degree

*N*, corresponding to

*n*

_{eff}) with respect to the number of unknowns for using

*O*(

*h*

^{2})-FDMS,

*O*(

*h*

^{4})-FDMS, and PSFD-MPML, respectively. The relative error in

*n*

_{eff}is defined as

*n*

_{eff}for each method is also shown in Fig. 3(b). As indicated in [21

21. Y.-P. Chiou, Y.-C. Chiang, and H.-C. Chang, “Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices,” J. Lightwave Technol. **18**(2), 243–251 (2000). [CrossRef]

22. Y.-C. Chiang, Y.-P. Chiou, and H.-C. Chang, “Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles,” J. Lightwave Technol. **20**(8), 1609–1618 (2002). [CrossRef]

*O*(

*h*

^{2})-FDMS and

*O*(

*h*

^{4})-FDMS is very sparse. However, the memory required for the PSFD-MPML to obtain the same accuracy is dramatically smaller than the improved FDMS because of the spectrum convergence of the PSFD-MPML. Accordingly, we again demonstrate that the PSFD-MPML is very suitable to model the dielectric-metallic structures supporting the SP and/or HSP modes. Note that the structures shown in Figs. 1(a) or 2(a) are simple exercises with the SP mode and then the subsequent practical components with ultra

**-**thin metal films are complicated structures with both the SP and HSP modes, which is very difficult to accurately analyze their

*n*

_{eff}using the uniform-grid and low-order numerical methods.

### 2.2 Mode selective waveguide

8. R. Weisser, B. Menges, and S. Mittler-Neher, “Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. **56**(3), 189–197 (1999). [CrossRef]

*n*

_{sub}= 1.5195, a glass waveguide core with

*n*

_{core}= 1.5595 and

*d*= 2 μm, a SiO

_{c}_{x}buffer layer with

*n*

_{buf}= 1.520 and

*d*= 0.5μm, a gold film with

_{b}*n*

_{Au}= 0.463 +

*j*2.4 and

*n*= 1.333. The operation wavelength was chosen to be

*λ*= 0.532 μm. In order to compare the attenuation behavior of different modes, the imaginary part of effective indices Im(

*n*

_{eff}) (which is denoted as

*κ*in [8

**56**(3), 189–197 (1999). [CrossRef]

*N*= 12. The solid lines are the results from the commercially available program TRAMAX [8

**56**(3), 189–197 (1999). [CrossRef]

*n*

_{eff}for theTM

_{1}HSP mode and the corresponding numbers of degrees

*N*in Table 2 . It is seen that a relative error smaller than the order of 10

^{−12}can be achieved by using degree

*N*= 18 in gold thickness

*d*= 1.9 μm, and let the core thickness

_{b}*d*varying from 0.9 μm to 1.6 μm. Figures 5(a) and 5(b) show the calculated Re(

_{c}*n*

_{eff}) and Im(

*n*

_{eff}) for the TM

_{0}and the TM

_{1}HSP modes, respectively, versus the core thickness

*d*. It can be observed that the gap of Im(

_{c}*n*

_{eff}) between the TM

_{0}and the TM

_{1}HSP modes becomes larger as

*d*decreases. Thus the TM

_{c}_{1}HSP mode can be facilely eliminated with

*d*= 0.9 μm in the waveguide while the TM

_{c}_{0}HSP mode sustains a relative smaller attenuation.

*d*= 3.6 μm, the gold thickness

_{c}*n*

_{1}= 1.5595, and the cladding index

*n*

_{2}= 1.5195. There are eight modes (four TM modes and four TE modes) in the multimode waveguide for absence of the gold layer at wavelength

*λ*= 0.532 μm. The gold film can be set at the location where the amplitude of the field profile for a certain mode is close to zero and thus minimize Im(

*n*

_{eff}) of this mode. Accordingly, the gold film is chosen to be located between 0.68 μm and 0.685 μm for minimizing Im(

*n*

_{eff}) of the TE

_{2}mode. Table 3 lists the results of the corresponding

*n*

_{eff}for seven modes of this waveguide. According to Table 3, significant changes in the imaginary part of

*n*

_{eff}can be investigated as the gold film is included. The TE

_{2}mode has the lowest leaky power than other modes and its real part of

*n*

_{eff}is close to 1.5473738447 which is

*n*

_{eff}of the original waveguide without the gold film. Although the TM

_{2}mode also has a small amplitude between 0.68 μm and 0.685 μm, it can induce the HSP mode and its Im(

*n*

_{eff}) is in the order close to other modes. Accordingly, we may connect waveguides with and without the metal film and the TE

_{2}mode will be passed while other modes will be attenuated in the section with the metal film. By properly setting the location of the metal thin film, different modes can be selected through such devices. Note that

*n*

_{eff}of the TM

_{0}mode is absent in Table 3, because the TM

_{0}mode will induce the SP mode and its Im(

*n*

_{eff}) is the largest one among these modes.

### 2.3 Mode selective coupler and polarizing beam splitter

*n*

_{core}= 1.46 and its radius is

*r*= 2 μm, which is surrounded by the cladding with index

*n*

_{2}= 1.456 and the aspect ratio

*d*/

*r*equals 5. Due to the geometrical symmetry, we only take a quarter of the original area, which is

*λ*= 0.6 μm and calculated

*n*

_{eff}of the first four even and odd modes with respect to different thickness

*n*

_{eff}) and Im(

*n*

_{eff}), respectively, versus

*N*= 14. Figure 10 shows the Im(

*n*

_{eff}) curves of these modes with respect to

*λ*under

*d*= 6 nm. Because the

_{g}*n*

_{eff}) is lowest among these modes as shown in Figs. 9(b) and 10. Hence, if we properly design the geometry of the coupler, other modes may be attenuated to a negligible level and left only the

*N*. Obviously, numerical results with five digits of accuracy can be obtained by using only a degree

*N*= 10 and convergence up to the order of 10

^{−8}can be achieved by using high-order degrees. Note that there is a peak in the curves of the

*i*polarized modes,

*C*(

_{i}*i*=

*x*or

*y*), which is defined as

*i*polarization modes. Figure 12 shows

*C*and

_{x}*C*versus wavelengths

_{y}*λ*at metal film thickness

*C*and

_{x}*C*can be effectively separated with the help of the inserted gold film. Therefore, when beams of both

_{y}*x*- and

*y*- polarization magnetic fields are injected into left facet of the structure, only

*y*-polarization magnetic fields can be transferred and propagated into the other side of the waveguide due to the factor of

*C*>>

_{y}*C*. Thus it functions as a polarizing beam splitter. It is as a result of the

_{x}*y*-polarization magnetic fields strongly interacting by inducing the surface plasmon. The efficiency of this polarizing beam splitter will be discussed in detail by our future work.

## 3. Conclusion

**56**(3), 189–197 (1999). [CrossRef]

## Acknowledgments

## References and links

1. | M. Faraday, “Experimental relations of gold (and other metals) to light,” Philos. Trans. R. Soc. Lond. |

2. | U. Kreibig, and M. Vollmer, |

3. | N. W. Ashcroft, and N. D. Mermin, |

4. | H. Raether, |

5. | H. Raether, |

6. | M. I. Stockman, “Electromagnetic Theory of SERS,” in |

7. | R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B Chem. |

8. | R. Weisser, B. Menges, and S. Mittler-Neher, “Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. |

9. | T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. |

10. | J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propaga-tion with subwavelength-scale localization,” Phys. Rev. B |

11. | R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A |

12. | J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express |

13. | M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express |

14. | A. Hassani and M. Skorobogatiy, “Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics,” Opt. Express |

15. | D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90 ° bends in sub-wavelength metallic slot waveguides,” Opt. Express |

16. | S. J. Al-Bader and M. Imtaar, “Optical fiber hybrid-surface plasmon polaritons,” J. Opt. Soc. Am. B |

17. | Y. C. Lu, L. Yang, W. P. Huang, and S. S. Jian, “Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry,” J. Lightwave Technol. |

18. | H. J. M. Kreuwel, P. V. Lambeck, J. M. N. Beltman, and T. J. A. Popma, “Mode-coupling in multilayer structures applied to a chemical sensor and a wavelength selective directional coupler,” in |

19. | M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. |

20. | Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. |

21. | Y.-P. Chiou, Y.-C. Chiang, and H.-C. Chang, “Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices,” J. Lightwave Technol. |

22. | Y.-C. Chiang, Y.-P. Chiou, and H.-C. Chang, “Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles,” J. Lightwave Technol. |

23. | Y.-P. Chiou, Y.-C. Chiang, C.-H. Lai, C.-H. Du, and H.-C. Chang, “Finite-difference modeling of dielectric waveguides with corners and slanted facets,” J. Lightwave Technol. |

24. | S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microw. Guid. Wave Lett. |

25. | N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonators with curved surfaces,” IEEE Trans. Microw. Theory Tech. |

26. | K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microw. Theory Tech. |

27. | Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express |

28. | S. Guo, F. Wu, S. Albin, H. Tai, and R. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express |

29. | Q. H. Liu, “A pseudospectral frequency-domain (PSFD) method for computational electromagnetics,” IEEE Antennas Wirel. Propag. Lett. |

30. | B. Yang, D. Gottlieb, and J. S. Hesthaven, “Spectral simulations of electromagnetic wave scattering,” J. Comput. Phys. |

31. | B. Yang and J. S. Hesthaven, “A pseudospectral method for time-domain computation of electromagnetic scattering by bodies of revolution,” IEEE Trans. Antenn. Propag. |

32. | J. S. Hesthaven, P. G. Dinesen, and J. P. Lynovy, “Spectral collocation time-domain modeling of diffractive optical elements,” J. Comput. Phys. |

33. | P. J. Chiang, C. P. Yu, and H. C. Chang, “Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

34. | P. J. Chiang, C. L. Wu, C. H. Teng, C. S. Yang, and H. C. Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron. |

35. | P. J. Chiang and Y.-C. Chiang, “Pseudospectral frequency-domain formulae based on modified perfectly matched layers for calculating both guided and leaky modes,” IEEE Photon. Technol. Lett. |

36. | T. Baba and Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expression,” IEEE J. Quantum Electron. |

37. | Y.-T. Huang, C.-H. Jang, S.-H. Hsu, and J.-J. Deng, “Antiresonant reflecting optical waveguides polariza-tion beam splitters,” J. Lightwave Technol. |

38. | M. Elshazly-Zaghloul and R. M. Azzam, “Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties,” J. Opt. Soc. Am. |

39. | I. Hodgkinson, Q. H. Wu, M. Arnold, L. De Silva, G. Beydaghyan, K. Kaminska, and K. Robbie, “Biaxial thin-film coated-plate polarizing beam splitters,” Appl. Opt. |

40. | E. D. Palik, |

**OCIS Codes**

(230.4000) Optical devices : Microstructure fabrication

(260.2110) Physical optics : Electromagnetic optics

(130.5440) Integrated optics : Polarization-selective devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: December 22, 2010

Revised Manuscript: February 9, 2011

Manuscript Accepted: February 10, 2011

Published: February 18, 2011

**Citation**

Po-Jui Chiang, Yen-Chung Chiang, Nai-Hsiang Sun, and Shi-Xi Hong, "Analysis of optical waveguides with ultra-thin metal film based on the multidomain pseudospectral frequency-domain method," Opt. Express **19**, 4324-4336 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4324

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### References

- M. Faraday, “Experimental relations of gold (and other metals) to light,” Philos. Trans. R. Soc. Lond. 147(0), 145–181 (1857). [CrossRef]
- U. Kreibig, and M. Vollmer, Optical Properties of Metal Clusters, (Springer-Verlag, 1996).
- N. W. Ashcroft, and N. D. Mermin, Solid State Physics, (Harcount, 1976).
- H. Raether, Surface Plasmons, (Springer-Verlag, 1988).
- H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1998).
- M. I. Stockman, “Electromagnetic Theory of SERS,” in Springer Series Topics in Applied Physics–Surface Enhanced Raman Scattering Physics and Applications, K. Kneipp, M. Moskovits, and H. Kneipp, ed. (Springer-Verlag, 2006).
- R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B Chem. 10(3), 209–217 (1993). [CrossRef]
- R. Weisser, B. Menges, and S. Mittler-Neher, “Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. 56(3), 189–197 (1999). [CrossRef]
- T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84(6), 852–854 (2004). [CrossRef]
- J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propaga-tion with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
- R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef]
- J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16(19), 14902–14909 (2008). [CrossRef] [PubMed]
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