Abstract

Analytical techniques known in the literature are used to (i) identify all the planar waveguide modes in four top-emitting organic light-emitting diode (OLED) structures over the visible spectrum, and (ii) compute both TM and TE power spectra for classically radiating dipoles in the emissive layers of these OLED structures. Peaks in the computed power spectra are identified with the waveguide modes in the OLED devices, and areas associated with these peaks are used to estimate the excitation probability of the waveguide modes. In cases where ambiguities arise because of overlapping peaks, it is shown that computed power spectra can be approximated as sums of Lorentzian line shapes. It is found that for all four structures, the dipoles couple almost 80% of their radiant energy into TM modes with only about 20% going into TE modes. Furthermore, except for a narrow spectral band, the excited TM modes are primarily short-range surface plasmon polaritons. Excitations in the narrow spectral band correspond to TM and TE Fabry–Perot microcavity modes. Finally, the analysis shows that, in the absence of grating couplers, only light in the microcavity modes escapes into the air cover.

© 2006 Optical Society of America

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References

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  1. L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
    [CrossRef]
  2. R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp.1-65.
    [CrossRef]
  3. H. Kuhn, "Classical aspects of energy transfer in molecular systems," J. Chem. Phys. 53, 101-108 (1970).
    [CrossRef]
  4. K. G. Sullivan and D. G. Hall, "Enhancement and inhibition of electromagnetic radiation in plane-layered media. I. Plane-wave spectrum approach to modeling classical effects," J. Opt. Soc. Am. B 14, 1149-1159 (1997).
    [CrossRef]
  5. K. G. Sullivan and D. G. Hall, "Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors," J. Opt. Soc. Am. B 14, 1160-1166 (1997).
    [CrossRef]
  6. W. L. Barnes, "Topical review fluorescence near interfaces: the role of the photonic mode density," J. Mod. Opt. 45, 661-699 (1988).
    [CrossRef]
  7. J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission form planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
    [CrossRef]
  8. W. H. Weber and C. F. Eagan, "Energy transfer from an excited dye molecule to the surface plasmons of an adjacent metal," Opt. Lett. 4, 236-238 (1979).
    [CrossRef] [PubMed]
  9. J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
    [CrossRef]
  10. R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
    [CrossRef]
  11. Justification for this assumption is based on computations carried out for a series of OLED structures in which (i) the imaginary part of the index of refraction of the ETL was allowed to be nonzero, and (ii) an additional layer was introduced between the ETL and the HTL. The additional layer was assumed to have an index of refraction equal to that of the real part of the ETL, and the emitting dipoles were assumed to be in the middle of this layer. It was found that as the thickness of the additional layer decreased, a new peak emerged in the power spectrum for large values of u (i.e., u > 10), and the area under this peak increased as d−3 where d is the thickness of the additional layer. This new channel is presumably due to dipole-dipole energy transfer and is known in the literature as the Förster transfer, as has been confirmed by numerically comparing the results obtained to Eq. (2.52a) of Ref. 2. Given that virtually all of the dipole energy goes to Förster transfer energy as d approaches zero, almost no light could be extracted from OLED devices if this channel were a nonradiative loss. Because this is not seen experimentally, it is assumed that the dipole-dipole transfer energy is not lost and that the imaginary part of the medium in which the dipoles are embedded is best treated as being effectively zero.
  12. H. Kogelnik, "Theory of dielectric waveguides," in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, 1988), Chap. 2.
  13. The abruptness of these transitions may be an artifact due to the failure of the root search algorithm to find TM-D1A and TM-D1B modes at wavelengths very close to the degeneracy wavelengths.
  14. See, for example, R. W. Gruhlke, "Optical Emission from Surface Waves Supported in Thin Metal Films," Ph.D. dissertation (University of Rochester, 1987).
  15. D. K. Gifford and D. G. Hall, "Emission through one of two metal electrodes of an organic light-emitting diode via surface-plasmon cross coupling," Appl. Phys. Lett. 81, 4315-4317 (2002).
    [CrossRef]
  16. R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
    [CrossRef] [PubMed]
  17. See, for example, C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, 1967), pp. 257-265.

2005

J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
[CrossRef]

2004

L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

2002

D. K. Gifford and D. G. Hall, "Emission through one of two metal electrodes of an organic light-emitting diode via surface-plasmon cross coupling," Appl. Phys. Lett. 81, 4315-4317 (2002).
[CrossRef]

2000

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission form planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

1997

1992

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
[CrossRef]

1988

W. L. Barnes, "Topical review fluorescence near interfaces: the role of the photonic mode density," J. Mod. Opt. 45, 661-699 (1988).
[CrossRef]

1986

R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

1979

1970

H. Kuhn, "Classical aspects of energy transfer in molecular systems," J. Chem. Phys. 53, 101-108 (1970).
[CrossRef]

Barnes, W. L.

L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission form planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

W. L. Barnes, "Topical review fluorescence near interfaces: the role of the photonic mode density," J. Mod. Opt. 45, 661-699 (1988).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp.1-65.
[CrossRef]

Eagan, C. F.

Forbes, G. W.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
[CrossRef]

Gifford, D. K.

D. K. Gifford and D. G. Hall, "Emission through one of two metal electrodes of an organic light-emitting diode via surface-plasmon cross coupling," Appl. Phys. Lett. 81, 4315-4317 (2002).
[CrossRef]

Gruhlke, R. W.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Hall, D. G.

D. K. Gifford and D. G. Hall, "Emission through one of two metal electrodes of an organic light-emitting diode via surface-plasmon cross coupling," Appl. Phys. Lett. 81, 4315-4317 (2002).
[CrossRef]

K. G. Sullivan and D. G. Hall, "Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors," J. Opt. Soc. Am. B 14, 1160-1166 (1997).
[CrossRef]

K. G. Sullivan and D. G. Hall, "Enhancement and inhibition of electromagnetic radiation in plane-layered media. I. Plane-wave spectrum approach to modeling classical effects," J. Opt. Soc. Am. B 14, 1149-1159 (1997).
[CrossRef]

R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Holland, W. R.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Houde-Walter, S. N.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Theory of dielectric waveguides," in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, 1988), Chap. 2.

Kruschwitz, B. E.

J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
[CrossRef]

Kuhn, H.

H. Kuhn, "Classical aspects of energy transfer in molecular systems," J. Chem. Phys. 53, 101-108 (1970).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp.1-65.
[CrossRef]

Revelli, J. F.

J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp.1-65.
[CrossRef]

Smith, L. H.

L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

Smith, R. E.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
[CrossRef]

Sullivan, K. G.

Tutt, L. W.

J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
[CrossRef]

Wasey, J. A. E.

L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission form planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

Weber, W. H.

Appl. Phys. Lett.

D. K. Gifford and D. G. Hall, "Emission through one of two metal electrodes of an organic light-emitting diode via surface-plasmon cross coupling," Appl. Phys. Lett. 81, 4315-4317 (2002).
[CrossRef]

L. H., Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

IEEE J. Quantum Electron.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguide using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526 (1992).
[CrossRef]

J. Appl. Opt.

J. F. Revelli, L. W. Tutt, and B. E. Kruschwitz, "Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings," J. Appl. Opt. 44, 3224-3237 (2005).
[CrossRef]

J. Chem. Phys.

H. Kuhn, "Classical aspects of energy transfer in molecular systems," J. Chem. Phys. 53, 101-108 (1970).
[CrossRef]

J. Mod. Opt.

W. L. Barnes, "Topical review fluorescence near interfaces: the role of the photonic mode density," J. Mod. Opt. 45, 661-699 (1988).
[CrossRef]

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission form planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. Lett.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, "Surface plasmon cross coupling in molecular fluorescence near a corrugated thin metal film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Other

See, for example, C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, 1967), pp. 257-265.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp.1-65.
[CrossRef]

Justification for this assumption is based on computations carried out for a series of OLED structures in which (i) the imaginary part of the index of refraction of the ETL was allowed to be nonzero, and (ii) an additional layer was introduced between the ETL and the HTL. The additional layer was assumed to have an index of refraction equal to that of the real part of the ETL, and the emitting dipoles were assumed to be in the middle of this layer. It was found that as the thickness of the additional layer decreased, a new peak emerged in the power spectrum for large values of u (i.e., u > 10), and the area under this peak increased as d−3 where d is the thickness of the additional layer. This new channel is presumably due to dipole-dipole energy transfer and is known in the literature as the Förster transfer, as has been confirmed by numerically comparing the results obtained to Eq. (2.52a) of Ref. 2. Given that virtually all of the dipole energy goes to Förster transfer energy as d approaches zero, almost no light could be extracted from OLED devices if this channel were a nonradiative loss. Because this is not seen experimentally, it is assumed that the dipole-dipole transfer energy is not lost and that the imaginary part of the medium in which the dipoles are embedded is best treated as being effectively zero.

H. Kogelnik, "Theory of dielectric waveguides," in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, 1988), Chap. 2.

The abruptness of these transitions may be an artifact due to the failure of the root search algorithm to find TM-D1A and TM-D1B modes at wavelengths very close to the degeneracy wavelengths.

See, for example, R. W. Gruhlke, "Optical Emission from Surface Waves Supported in Thin Metal Films," Ph.D. dissertation (University of Rochester, 1987).

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Figures (12)

Fig. 1
Fig. 1

Planar OLED waveguide structure. The x direction is the direction of confinement, and the z direction is the direction of propagation. The dashed line indicates the location of the infinitesimally thin dipole emissive layer.

Fig. 2
Fig. 2

Plots of the indices of refraction as functions of wavelength for Alq 3 (solid curve), NPB (dashed–dotted curve), MgAg (dotted curve), and Ag (dashed curve); (a) real part of index of refraction, and (b) logarithm (imaginary part) of index of refraction. These values were used in the computations along with n 5 = 1.70 for the photoresist layer and n 6 = 1.46 for the substrate (glass).

Fig. 3
Fig. 3

Mode dispersion curves for TM modes: (a) OLED1, (b) OLED4, (c) OLED2, and (d) OLED3. The open circles indicate modes for which no peaks could be found, and the solid curves indicate modes for which peaks could be found in the computed TM power spectra. Symbols indicate the observed peaks in the computed TM power spectra and identify the associated modal dispersion curve: open triangle, C and C - D 2 ; open diamond, D 2 - C ; open square, D 1 A ; solid square, D 1 B ; open pentagram, E; and open hexagram, F.

Fig. 4
Fig. 4

Mode dispersion curves for TE modes: (a) OLED1, (b) OLED4, (c) OLED2, and (d) OLED3. The open circles indicate modes for which no peaks could be found, and the solid curves indicate modes for which peaks could be found in the computed TE power spectra. Symbols indicate the observed peaks in the computed TE power spectra and identify the associated modal dispersion curve: open diamond for D 2 and open square for D 1 .

Fig. 5
Fig. 5

TM power spectra as functions of n 2 u for OLED2 at four selected wavelengths: (a) λ = 0.44 μm , (b) λ = 0.55 μm , (c) λ = 0.65 μm , and (d) λ = 0.73 μm . The solid curves indicate the TM power spectra computed from Eq. (2), and the dashed curves indicate the best-fit Lorentzian-sum approximations obtained from Eq. (12).

Fig. 6
Fig. 6

TE power spectra as functions of n 2 u for OLED2 at four selected wavelengths: (a) λ = 0.44 μm , (b) λ = 0.55 μm , (c) λ = 0.65 μm , and (d) λ = 0.73 μm . The solid curves indicate the TE power spectra computed from Eq. (3). Curves obtained from Eq. (12), the best-fit Lorentzian-sum approximations, are indistinguishable from the computed power spectra (solid curves).

Fig. 7
Fig. 7

TM power spectra as functions of n 2 u for OLED1 at λ = 0.49 μm . The solid curve indicates the TM power spectra computed from Eq. (2), the dashed curve indicates the best-fit Lorentzian-sum approximation obtained from Eq. (12), and the dashed–dotted curves indicate the contributions from the Lorentzians of the individual modes.

Fig. 8
Fig. 8

Comparison of power spectra as functions of n 2 u for three different layered structures: (a) TM power spectra, and (b) TE power spectra. The solid curves represent the power spectra for OLED4 at λ = 0.73 μm , the dashed–dotted curves represent the power spectrum of a dipole embedded in an infinite dielectric medium of index n 2 , and the dotted curves represent power spectra for a dipole in a semi-infinite dielectric medium of index n 2 such that the dipole is 0.04 μm away from the dielectric–air interface.

Fig. 9
Fig. 9

Plots of ε, the relative error, computed from Eq. (13) as a function of wavelength for (a) OLED1, (b) OLED4, (c) OLED2, and (d) OLED3. Solid curves represent ε for the TM power spectra and the dashed–dotted curves represent ε for the TE power spectra.

Fig. 10
Fig. 10

Plots of excitation probabilities, P m , computed for the TM modes according to Eq. (6) as functions of wavelength for (a) OLED1, (b) OLED4, (c) OLED2, and (d) OLED3. Symbols identify the mode associated with each curve: open triangle for C and C - D 2 , open diamond for D 2 - C , open square for D 1 A , solid square for D 1 B , open pentagram for E, and open hexagram for F. The excitation probability for mode C is dashed–dotted to emphasize the uncertainty associated with this curve.

Fig. 11
Fig. 11

Plots of excitation probabilities, P m , computed for the TE modes according to Eq. (6) as functions of wavelength for (a) OLED1, (b) OLED4, (c) OLED2, and (d) OLED3. Symbols identify the mode associated with each curve: open diamond for D 2 and open square for D 1 .

Fig. 12
Fig. 12

Plots of relative power flux at the z = 0 plane for modes found in OLED2 at a wavelength of 0.60 μm : (a) excited modes and (b) unexcited modes. The solid and dashed curves in (a) refer to modes TM - D 1 A and TM-F, respectively, and the dashed–dotted curve refers to mode TE - D 1 . The solid and dashed curves in (b) refer to modes TM-C and TM-E, respectively, and the dashed–dotted curve refers to mode TE - D 2 . The distributions in both figures are normalized with respect to the peak value of the power flux that lies within the range of the plot. Vertical dotted lines in these figures show the locations of boundaries between layers and a vertical solid line identifies the ETL–HTL boundary where the dipole sources are located.

Tables (2)

Tables Icon

Table 1 Layer Thicknesses for the Four OLED Devices a

Tables Icon

Table 2 Characteristics of Excited and Nonexcited Modes of OLED2 at λ = 0.60 μm

Equations (271)

Equations on this page are rendered with MathJax. Learn more.

u k ρ k
n eff
n eff
n eff
D 1 A
D 1 B
λ 0.54 μm
λ 0.66 μm
D 2
0.465 μm
C - D 2
D 2 - C
D 2
0.115 μm
0.160 μm
0.190 μm
0.2375 μm
D 2
n 2
n 3
x S
x D
ρ = y y ^ + z z ^
k 2 = k ρ 2 + k x 2
k ( n 2 c ) ω o
k x
k ρ
u k ρ k
b b o = [ 2 3 ( b b o ) HED + 1 3 ( b b o ) VED ] ,
( b b o ) TM = 1 3 [ 1 + 3 2 Re ( 0 d u u 3 1 - u 2 { [ F R ( e ) ] TM - 1 } ) ] + 2 3 [ 1 + 3 4 Re ( 0 d u u ( 1 - u 2 ) 1 - u 2 × { [ F R ( o ) ] TM - 1 } ) ]
= 1 2 Re ( 0 d u 1 - u 2 { u 3 [ F R ( e ) ] TM + u ( 1 - u 2 ) × [ F R ( o ) ] TM } ) 0 p TM ( u ) d u .
( b b o ) TE = 1 2 Re { 0 d u u 1 - u 2 [ F R ( e ) ] TE } 0 p TE ( u ) d u ,
[ F R ( e ) ] TM
[ F R ( o ) ] TM
[ F R ( e ) ] TE
[ F R ( e ) ] TM [ 1 + ρ S TM exp ( 2 ik x x S ) ] [ 1 + ρ D TM exp ( 2 ik x x D ) ] 1 - ρ S TM ρ D TM exp [ 2 ik x ( x S + x D ) ] ,
[ F R ( o ) ] TM [ 1 - ρ S TM exp ( 2 ik x x S ) ] [ 1 - ρ D TM exp ( 2 ik x x D ) ] 1 - ρ S TM ρ D TM exp [ 2 ik x ( x S + x D ) ] ,
[ F R ( e ) ] TE [ 1 + ρ S TE exp ( 2 ik x x S ) ] [ 1 + ρ D TE exp ( 2 ik x x D ) ] 1 - ρ S TE ρ D TE exp [ 2 ik x ( x S + x D ) ] ,
ρ S TM
ρ S TE
ρ D TM
ρ D TE
Φ = d Φ d u d u b b o ,
d u
P m = u m 1 u m 2 p m ( u ) d u 0 [ p TM ( u ) + p TE ( u ) ] d u A - 1 u m 1 u m 2 p m ( u ) d u ,
A = A TM + A TE 0 [ p TM ( u ) + p TE ( u ) ] d u = b b o
p TM ( u )
p TE ( u )
u m 1
u m 2
A > 1
A < 1
S ( λ )
P m ( λ ) = b o ( λ ) S ( λ ) u m 1 ( λ ) u m 2 ( λ ) p m ( u , λ ) d u 0 b o ( λ ) S ( λ ) A ( λ ) .
S ( λ )
b o
n 2 u
0.73 μm
x S
w 2 = 0.04 μm
x D
p SP ( u ) σ SP ( u - u SP ) 2 + α SP 2 .
z = u + iv
z = u SP + SP
1 - ρ S ρ D exp [ 2 ik x ( x S + x D ) ] = 0.
p ( z ) Re [ f N ( z ) k = 1 k = M ( z - z k ) ] = Re [ f N ( z ) ( k = 1 M η k z - z k ) ] ,
z k
f N ( z )
z k = ( n eff k + k ) n 2
p ( u ) Re { f N ( u ) [ k = 1 M n 2 η k ( n 2 u - n eff k + k ) ( n 2 u - n eff k ) 2 + α k 2 ] } k = 1 M σ k ( u ) ( n 2 u - n eff k ) 2 + α k 2 k = 1 M L k ( u ) ,
σ k ( u )
σ k
0.49 μm
p TM ( u )
p TE ( u )
n eff k
p TM ( u )
p TE ( u )
n eff k
n eff k
n eff k
n eff k
α k
σ k
0.73 μm
n 2
n 2
0.04 μm
n 2 u < 1
x S λ
x S 0.02 μm
0.585 μm
x S
0.04 μm
λ 0.5 μm
n 2 u
n 2 u
n eff
( 0.73 μm )
ε 1 ( N - 1 ) H ̄ { j = 1 N [ p ( u j ) - p = 1 P τ ˜ p ( n 2 u j - ξ ˜ p ) 2 + θ ˜ p 2 ] 2 } 1 2 .
H ̄ ( 1 P ) p = 1 P p ( u p )
p ( u p )
u p
τ ˜ p
ξ ˜ p
θ ˜ p
0.55 μm
P m
0.01 μm
λ = 0.44 μm
λ = 0.73 μm
± 0.03
P m
0 P m < 0.05
D 1 A
D 1 B
D 2
D 2
D 1
TM - D 1 A
TM - D 1 B
TE - D 1
TE - D 2
TM - D 1 A
TM - D 1 B
TE - D 1
TE - D 2
D 1 A
D 1 B
λ = 0.54
0.73 μm
TM - D 1 A
TM - D 1 B
TM - D 2
λ 0.46 μm
C - D 2
D 2 - C
| S k ( x , z ) | z = 0 = 1 2 { | Re [ E k ( x ) × H k * ( x ) ] | }
z = 0
0.60 μm
| S k ( x , 0 ) |
P m
TE - D 2
TE - D 2
TE - D 2
n eff
δ λ ( 4 π α )
e - 1
0.03 μm
v = c n eff
T = λ c
TE - D 2
δ ( vT ) = n eff ( 4 πα ) 0.003
TE - D 2
TE - D 1
TE - D 2
TE - D 1
n eff
TE - D 2
TE - D 1
n eff ( 4 πα ) 5
TE - D 1
TM - D 1
TE - D 1
TE - D 1
TE - D 2
TE - D 1
TE - D 2
TE - D 1
TE - D 2
0.60 μm
0.60 μm
TM - D 1 A
TM - D 1 A
n eff
TM - D 1 B
TM - D 2
TE - D 1
TE - D 2
TM - D 1 B
TE - D 1
λ 0.57 μm
TM - D 1 B
TE - D 1
1 > n eff 0.5
n eff 0.5
n eff
n eff
n eff
TM - D 1 B
TE - D 1
n eff
TM - D 2
TM - D 1 A
TM - D 1 B
TM - D 2
C - D 2
D 2 - C
TM - D 2
TM - D 2
TM - D 1 A
TM - D 1 B
0.01 μm
λ = 0.44 μm
λ = 0.73 μm
TM - D 1 A
TM - D 1 B
TM - D 1 A
TM - D 1 B
TM - D 1 A
TM - D 1 B
n eff
TM - D 1 A
TM - D 1 B
TM - D 1 A
TM - D 2
C - D 2
D 2 - C
TM - D 1 A
TM - D 1 B
TE - D 1
TE - D 2
TE - D 1
TE - D 2
TE - D 1
1 > n eff 0.3
TM - D 1 A
TM - D 1 B
n eff 1
TE - D 1
n eff = 1
n eff
Alq 3
n 5 = 1.70
n 6 = 1.46
C - D 2
D 2 - C
D 1 A
D 1 B
D 2
D 1
n 2 u
λ = 0.44 μm
λ = 0.55 μm
λ = 0.65 μm
λ = 0.73 μm
n 2 u
λ = 0.44 μm
λ = 0.55 μm
λ = 0.65 μm
λ = 0.73 μm
n 2 u
λ = 0.49 μm
n 2 u
λ = 0.73 μm
n 2
n 2
0.04 μm
P m
C - D 2
D 2 - C
D 1 A
D 1 B
P m
D 2
D 1
z = 0
0.60 μm
TM - D 1 A
TE - D 1
TE - D 2

Metrics