## Dipole radiation within one-dimensional anisotropic microcavities: a simulation method |

Optics Express, Vol. 19, Issue 19, pp. 18558-18576 (2011)

http://dx.doi.org/10.1364/OE.19.018558

Acrobat PDF (1841 KB)

### Abstract

We present a simulation method for light emitted in uniaxially anisotropic light-emitting thin film devices. The simulation is based on the radiation of dipole antennas inside a one-dimensional microcavity. Any layer in the microcaviy can be uniaxially anisotropic with an arbitrary orientation of the optical axis. A plane wave expansion for the field of an elementary dipole inside an anisotropic medium is derived from Maxwell’s equations. We employ the scattering matrix method to calculate the emission by dipoles inside an anisotropic microcavity. The simulation method is applied to calculate the emission of dipole antennas in a number of cases: a dipole antenna in an infinite medium, emission into anisotropic slab waveguides and waveguides in liquid crystals. The dependency of the intensity and the polarization on the direction of emission is illustrated for a number of anisotropic microcavities.

© 2011 OSA

## 1. Introduction

2. H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics **4**(10), 676–685 (2010). [CrossRef]

3. C. L. Mulder, P. D. Reusswig, A. M. Velázquez, H. Kim, C. Rotschild, and M. A. Baldo, “Dye alignment in luminescent solar concentrators: I. Vertical alignment for improved waveguide coupling,” Opt. Express **18**(S1), A79–A90 (2010). [CrossRef] [PubMed]

4. W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett. **34**(13), 2054–2056 (2009). [CrossRef] [PubMed]

5. K. Driesen, D. Moors, J. Beeckman, K. Neyts, C. Gorller-Walrand, and K. Binnemans, “Near-infrared luminescence emitted by an electrically switched liquid crystal cell,” J. Lumin. **127**(2), 611–615 (2007). [CrossRef]

6. M. O'Neill and S. M. Kelly, “Liquid crystals for charge transport, luminescence, and photonics,” Adv. Mater. (Deerfield Beach Fla.) **15**(14), 1135–1146 (2003). [CrossRef]

7. S. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. Lüssem, and K. Leo, “White organic light-emitting diodes with fluorescent tube efficiency,” Nature **459**(7244), 234–238 (2009). [CrossRef] [PubMed]

8. T. Suzuki, “Flat panel displays for ubiquitous product applications and related impurity doping technologies,” J. Appl. Phys. **99**(11), 111101 (2006). [CrossRef]

9. W. M. V. Wan, R. H. Friend, and N. C. Greenham, “Modelling of interference effects in anisotropic conjugated polymer devices,” Thin Solid Films **363**(1-2), 310–313 (2000). [CrossRef]

10. D. Yokoyama, A. Sakaguchi, M. Suzuki, and C. Adachi, “Horizontal orientation of linear-shaped organic molecules having bulky substituents in neat and doped vacuum-deposited amorphous films,” Org. Electron. **10**(1), 127–137 (2009). [CrossRef]

11. M. P. Aldred, A. E. A. Contoret, S. R. Farrar, S. M. Kelly, D. Mathieson, M. O'Neill, W. C. Tsoi, and P. Vlachos, “A full-color electroluminescent device and patterned photoalignment using light-emitting liquid crystals,” Adv. Mater. (Deerfield Beach Fla.) **17**(11), 1368–1372 (2005). [CrossRef]

12. W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin-layers,” Phys. Rev. B **22**(6), 3030–3038 (1980). [CrossRef]

13. K. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A **15**(4), 962–971 (1998). [CrossRef]

14. J. A. E. Wasey, A. Safonov, I. D. W. Samuel, and W. L. Barnes, “Effects of dipole orientation and birefringence on the optical emission from thin films,” Opt. Commun. **183**(1-4), 109–121 (2000). [CrossRef]

14. J. A. E. Wasey, A. Safonov, I. D. W. Samuel, and W. L. Barnes, “Effects of dipole orientation and birefringence on the optical emission from thin films,” Opt. Commun. **183**(1-4), 109–121 (2000). [CrossRef]

15. P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B **73**(16), 165125 (2006). [CrossRef]

16. P. Bienstman, P. Vandersteegen, and R. Baets, “Modelling gratings on either side of the substrate for light extraction in light-emitting diodes,” Opt. Quantum Electron. **39**(10-11), 797–804 (2007). [CrossRef]

## 2. Calculation method

### 2.1. Physical background & notations

17. W. Lukosz, “Light-emission by multipole sources in thin-layers. 1. Radiation-patterns of electric and magnetic dipoles,” J. Opt. Soc. Am. **71**(6), 744–754 (1981). [CrossRef]

*x*- and

*y*-axis are parallel to the layer stack and the

*z*-axis is normal to the stack. The orientation of the dipole moment

**p**is defined by an inclination angle

*ν*(with respect to the

*z-*axis) and an azimuth angle

*ζ*in the

*xy*-plane. We choose the origin of the

*xyz*-system to coincide with the location of the dipole. Each uniaxial medium

*i*inside the layer stack is characterized by the orientation of the optical axis

**c**

_{i}(extra-ordinary polarization) and the two eigenvalues of the dielectric tensor

**c**

_{i}. The orientation of

**c**

_{i}is also determined by an inclination angle

**E**can be written as a superposition of plane and evanescent waves. The electric field of a single plane or evanescent wave is written as:and there is a similar expression for the magnetic field

**H**.

*ω*is the angular frequency of the dipole antenna. Each plane or evanescent wave is characterized by its wave-vector

**k**:

*k*and

_{x}*k*only couple to waves with the same

_{y}*k*and

_{x}*k*in the other media. This transverse part of

_{y}**k**can be grouped to

*k*depends on the medium and the polarization of the plane wave. In uniaxial materials the electric field of the ordinary polarization is perpendicular to

_{z}**c**, the extra-ordinary polarization has an electric field component parallel to

**c**. The wave-vector can also be written as a sum of a part perpendicular

**c**. The amplitude of the wave-vector in medium

*i*is given by

*z*-component can be found with

*λ*is the wavelength of the light in vacuum and

*n*is the refractive index. For uniaxial anisotropic media there is a different refractive index for the ordinary waves

_{i}*n*and extra ordinary waves

_{i,o}*n*. The value of

_{i,e}*n*is the same for every direction in the medium but

_{i,o}*n*depends on the direction of propagation. Throughout this paper the subscripts ∥, ⊥ and

_{i,e}*z*are used to denote components respectively parallel to

**c**, perpendicular to

**c**and parallel to

*z*.

*z*. In non-absorbing media no power is dissipated by evanescent waves. No direction of propagation can be associated with evanescent waves since these only have a non-zero field in a small area. Evanescent waves represent the near-field of the dipole.

### 2.2. Radiation of elementary dipoles in a homogeneous anisotropic medium

18. P. De Visschere, “Electromagnetic source transformations and scalarization in stratified gyrotropic media,” Prog. Electromag. Res. B **18**, 165–183 (2009). [CrossRef]

*Θ*,

*Ψ*,

*Π*and

*Φ*. An uncoupled differential equation is obtained for

*Θ*and

*Ψ*(Eq. (74) and 75 in [18

18. P. De Visschere, “Electromagnetic source transformations and scalarization in stratified gyrotropic media,” Prog. Electromag. Res. B **18**, 165–183 (2009). [CrossRef]

**c**and

**c**. In these equations the following source terms appear:

**J**is the electric current,

**J**along

**c**,

*u*and

*v*are auxiliary functions. In this case the only source is an oscillating elementary dipole

*u*and

*v*are given by:

*Θ*and

*Ψ*can be found by performing a spatial and temporal Fourier transform on Eq. (3) to (7). Using the relations:

*Ψ*and

*Θ*the two remaining scalar Hertz potentials

*Φ*and

*Π*can be found (by performing the Fourier transform of Eq. (76) and 77 in [18

18. P. De Visschere, “Electromagnetic source transformations and scalarization in stratified gyrotropic media,” Prog. Electromag. Res. B **18**, 165–183 (2009). [CrossRef]

**18**, 165–183 (2009). [CrossRef]

**E**in the Fourier domain from the scalar Hertz potentials

*Θ*and

*Ψ*and source term

*u*:

**E(k)**is obtained by inserting Eq. (8) and (9) and the Fourier transform of Eq. (6) into Eq. (12).

*xyz*-coordinates is then found by the inverse Fourier transform of Eq. (13) along

*k*,

_{x}*k*and

_{y}*k*.

_{z}*k*is explicitly calculated to obtain the plane wave decomposition

_{z}**E(**

*k*

_{x},

*k*

_{y}

**)**. The integral of the field in Eq. (13) over

*k*can be split in two terms and separately solved using contour integration. The first term of Eq. (13) has two poles:

_{z}*z>0*this is the lower half of the complex

*k*plane. In case the poles are purely real a small loss term

_{z}*z>0*and purely real poles, the poles inside the contour are:

**E**(for

*z>0*):

*z<0.*This approach has the advantage that the field is decomposed in plane wave eigenmodes which can be readily used in multilayer stack algorithms, as explained in section 2.3. Another approach is to start from the formulas for the radiation of a dipole in vacuum and to anisotropically transform the problem using the method of Clemmow [19

19. P. C. Clemmow, “The theory of electromagnetic waves in a simple anisotropic medium,” Electr. Engin. Proc. Inst. **110**, 101–106 (1963). [CrossRef]

**c**, this is called the ordinary polarization. For the field in (21),

**c**and

**E**

_{e}is called the extra-ordinary polarization. From the expression of

**E**,

**H**can be determined using

*k*depends on the polarization.

_{z}*z*radiated by a dipole is then found by integrating the

*z*-component of the Poynting vector

**S**(unit W/m

^{2}) over that plane:

**E**and

**H**in Eq. (22) are two separate double integrals over d

*k*d

_{x}*k*. When integrating over a plane of constant

_{y}*z*we can bring both

**E**and

**H**under the same double integral. Because of orthogonality an extra factor

^{2}) can be split in an ordinary

*K*and an extra ordinary part

_{o}*K*. K is calculated for the field in a plane with

_{e}*z>0*(

*K*) or a plane with

^{+}*z<0*(

*K*). The total power radiated by a dipole

^{-}*F*(in W) is:

**c**but the extra-ordinary field can. In an anisotropic medium the electric fields of the eigenmodes are no longer perpendicular to each other (unlike in an isotropic medium).

### 2.3. Radiation of dipole inside an anisotropic microcavity

20. P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Phys. Rev. B **69**(3), 035316 (2004). [CrossRef]

#### 2.3.1. A dipole in an isotropic microcavity

12. W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin-layers,” Phys. Rev. B **22**(6), 3030–3038 (1980). [CrossRef]

13. K. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A **15**(4), 962–971 (1998). [CrossRef]

21. T. Setälä, M. Kaivola, and A. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **59**(1), 1200–1206 (1999). [CrossRef]

*+/−*marks waves that respectively have a Poynting vector

**S**with positive or negative

*z*-component . In Eq. (27) and (28) the numerator expresses the effect of wide angle interference, i.e. interference of the upward emitted wave with the reflection of the downward emitted wave (or vice versa). The denominator embodies multiple beam interference: it sums all reflections between the top and bottom parts of the cavity.

13. K. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A **15**(4), 962–971 (1998). [CrossRef]

#### 2.3.2. A dipole in an anisotropic microcavity

*–z*direction is found with the corresponding expression for

*z<0*. The polarization state of the light is determined by the complex amplitudes of the ordinary and extra-ordinary waves and their difference in phase. One must be careful to simulate all changes in polarization that occur during propagation and reflection or transmission in an anisotropic cavity. In anisotropic media e- and o-waves are coupled when reflection or transmission at an interface takes place, therefore the reflection coefficients have to be replaced by reflection matrices. Equation (27) and (28) should be replaced by:

*l*into a reflected wave with polarization

*m*. For isotropic layer stacks o- and e-waves are uncoupled (

#### 2.3.3. The scattering matrix method

22. D. Y. K. Ko and J. R. Sambles, “Scattering matrix-method for propagation of radiation in stratified media - attenuated total reflection studies of liquid-crystals,” J. Opt. Soc. Am. A **5**(11), 1863–1866 (1988). [CrossRef]

23. D. W. Berreman, “Optics in stratified and anisotropic media - 4x4 matrix formulation,” J. Opt. Soc. Am. **62**(4), 502–510 (1972). [CrossRef]

*i*traveling upward

*N*traveling downward

*i*traveling downward

22. D. Y. K. Ko and J. R. Sambles, “Scattering matrix-method for propagation of radiation in stratified media - attenuated total reflection studies of liquid-crystals,” J. Opt. Soc. Am. A **5**(11), 1863–1866 (1988). [CrossRef]

*j + 1/j*interface to the fields above the interface

*j/j-1*.

*j-1/j*interface to the

*j/j + 1*interface, this causes a phase change proportional to the thickness of the layer

*d*, expressed by the matrix

_{j}*j/j+1*all transverse fields have to be constant, this is expressed by the following boundary conditions:

*j + 1*at the

*j/j + 1*interface and the unit fields of the four eigenmodes (given by Eq. (25) and (26)), the field components

*j/j+1*interface can be calculated. The matrix that links the amplitudes of the four eigenmodes in medium

*j+1*with the four field components

*j/j+1*interface is written as

*x-*and

*y*components of Eq. (25) and (26). The corresponding magnetic field (per unit electric field) is found with

*x-*and

*y-*component are the respective matrix elements of the third and fourth row.

*j*at the

*j-1/j*interface to the amplitude of the eigenmodes in medium

*j*at the

*j+1/j*interface,

*j*(or

*j+1*) and

*j-1/j*interface in medium

*j*to the amplitudes of the eigenmodes at the

*j+1/j*interface in medium

*j+1*. The boundary condition at the

*j+1/j*interface can then be expressed as:

## 3. Calculation examples

### 3.1. Emission from a thin isotropic film into an anisotropic medium

*F*radiated by a dipole emitting with a wavelength

*x*,

*y*or

*z*-axis (respectively called

*p*,

_{x}*p*and

_{y}*p*) inside an anisotropic medium (

_{z}*F*by evaluating the integral in Eq. (24). We then also calculate

*F*for a dipole situated in the middle of an isotropic layer (n=1) with thickness

*d*which is bound on top and bottom side by a semi-infinite anisotropic medium with the same properties as described above.

*F*is then calculated as a function of

*d*(a schematic is shown in Fig. 5 ). The dipole moment is chosen so that this dipole radiates a power of 1 Watt in vacuum. In Fig. 6

*F*is shown as a function of the thickness

*d*of the isotropic layer. For a dipole in a homogeneous anisotropic medium an analytical formula for F (Watt) can be found that depends on the refractive indices of the material and the angle

*ρ*between

**p**and

**c**:

*p*,

_{x}*p*and

_{y}*p*. The solid lines represent F calculated with the anisotropic plane wave decomposition. The dashed lines show F for a dipole in an isotropic layer of different thicknesses. The results of the simulation for a dipole in a homogeneous anisotropic medium are the same as the results of the analytical formula (Eq. (45)). The calculation with a dipole in an isotropic layer between anisotropic media agrees with the analytical solution for

_{z}*d*of the layer and of the projections of the wave vector

*k*

_{x}and

*k*

_{y}. The constructive and destructive interferences in the emission pattern, lead, after integration, to an oscillating behavior of the emitted power F. As the layer thickness increases from

*100nm*to the

*µm*range the number of minima and maxima in the integration increases which causes a damping of the oscillation. For very thick isotropic layers, the anisotropic material no longer influences

*F*.

### 3.2. Emission and waveguiding in a thin anisotropic layer

*5nm*,

*1000nm*and

*200nm*for the emitting layer, 5CB and Al respectively. The dipole is situated in the middle of the emitting layer.

*K*is calculated for an ensemble of randomly oriented dipoles by averaging

*K*is

*W.µm*, so that after integration over

^{2}*µm*, see Eq. (24)), we obtain the total power emitted by the dipole. Again we have chosen the dipole so that 1 Watt would be emitted by the dipole in vacuum.

^{−2}*i*. For waveguided modes

*ϕ*.

*ϕ*. Figure 10 and Fig. 11 show

*yz*-plane (

**c**and waveguided modes occur for

*xz*-plane (

**c**and experience a refractive index equal to

*xz*-plane waveguiding only occurs between

### 3.3. Coupling between ordinary and extra-ordinary waves

*1000nm*thick anisotropic layer, a

*5nm*anisotropic emitting layer and another

*1000nm*anisotropic layer, above that there is a thick layer of air. The optical axes of the anisotropic layers are parallel to the

*xy*-plane. The optical axes of the anisotropic layers on the glass and air side have an azimuth angle respectively

*n*and

_{e,5CB}*n*, so that waveguided modes have a non-zero width.

_{o,5CB}*x*-axis. We can distinguish 3 regions in the emission pattern. For

### 3.4. Anisotropic waveguides

24. J. Beeckman, K. Neyts, and M. Haelterman, “Patterned electrode steering of nematicons,” J. Opt. A, Pure Appl. Opt. **8**(2), 214–220 (2006). [CrossRef]

*α*of 5CB is assumed to follow a Gaussian profile around the center (

*z*=0) of the LC layer. The profile of the inclination angle becomes

*σ*(

*100nm*thick layers with the inclination angle of each layer given by the Gaussian distribution for the middle of that layer. The refractive indices of 5CB and wavelength (

*xz*-plane is shown in Fig. 15a ). In the region

## 4. Conclusions

## Acknowledgments

## References and links

1. | J. M. Bennett, “Polarizers,” in |

2. | H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics |

3. | C. L. Mulder, P. D. Reusswig, A. M. Velázquez, H. Kim, C. Rotschild, and M. A. Baldo, “Dye alignment in luminescent solar concentrators: I. Vertical alignment for improved waveguide coupling,” Opt. Express |

4. | W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett. |

5. | K. Driesen, D. Moors, J. Beeckman, K. Neyts, C. Gorller-Walrand, and K. Binnemans, “Near-infrared luminescence emitted by an electrically switched liquid crystal cell,” J. Lumin. |

6. | M. O'Neill and S. M. Kelly, “Liquid crystals for charge transport, luminescence, and photonics,” Adv. Mater. (Deerfield Beach Fla.) |

7. | S. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. Lüssem, and K. Leo, “White organic light-emitting diodes with fluorescent tube efficiency,” Nature |

8. | T. Suzuki, “Flat panel displays for ubiquitous product applications and related impurity doping technologies,” J. Appl. Phys. |

9. | W. M. V. Wan, R. H. Friend, and N. C. Greenham, “Modelling of interference effects in anisotropic conjugated polymer devices,” Thin Solid Films |

10. | D. Yokoyama, A. Sakaguchi, M. Suzuki, and C. Adachi, “Horizontal orientation of linear-shaped organic molecules having bulky substituents in neat and doped vacuum-deposited amorphous films,” Org. Electron. |

11. | M. P. Aldred, A. E. A. Contoret, S. R. Farrar, S. M. Kelly, D. Mathieson, M. O'Neill, W. C. Tsoi, and P. Vlachos, “A full-color electroluminescent device and patterned photoalignment using light-emitting liquid crystals,” Adv. Mater. (Deerfield Beach Fla.) |

12. | W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin-layers,” Phys. Rev. B |

13. | K. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A |

14. | J. A. E. Wasey, A. Safonov, I. D. W. Samuel, and W. L. Barnes, “Effects of dipole orientation and birefringence on the optical emission from thin films,” Opt. Commun. |

15. | P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B |

16. | P. Bienstman, P. Vandersteegen, and R. Baets, “Modelling gratings on either side of the substrate for light extraction in light-emitting diodes,” Opt. Quantum Electron. |

17. | W. Lukosz, “Light-emission by multipole sources in thin-layers. 1. Radiation-patterns of electric and magnetic dipoles,” J. Opt. Soc. Am. |

18. | P. De Visschere, “Electromagnetic source transformations and scalarization in stratified gyrotropic media,” Prog. Electromag. Res. B |

19. | P. C. Clemmow, “The theory of electromagnetic waves in a simple anisotropic medium,” Electr. Engin. Proc. Inst. |

20. | P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Phys. Rev. B |

21. | T. Setälä, M. Kaivola, and A. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

22. | D. Y. K. Ko and J. R. Sambles, “Scattering matrix-method for propagation of radiation in stratified media - attenuated total reflection studies of liquid-crystals,” J. Opt. Soc. Am. A |

23. | D. W. Berreman, “Optics in stratified and anisotropic media - 4x4 matrix formulation,” J. Opt. Soc. Am. |

24. | J. Beeckman, K. Neyts, and M. Haelterman, “Patterned electrode steering of nematicons,” J. Opt. A, Pure Appl. Opt. |

**OCIS Codes**

(230.7390) Optical devices : Waveguides, planar

(260.1440) Physical optics : Birefringence

(260.2110) Physical optics : Electromagnetic optics

(310.0310) Thin films : Thin films

**ToC Category:**

Physical Optics

**History**

Original Manuscript: June 15, 2011

Revised Manuscript: July 22, 2011

Manuscript Accepted: July 22, 2011

Published: September 8, 2011

**Citation**

Lieven Penninck, Patrick De Visschere, Jeroen Beeckman, and Kristiaan Neyts, "Dipole radiation within one-dimensional anisotropic microcavities: a simulation method," Opt. Express **19**, 18558-18576 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18558

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### References

- J. M. Bennett, “Polarizers,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), pp. 3.1–3.70.
- H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics4(10), 676–685 (2010). [CrossRef]
- C. L. Mulder, P. D. Reusswig, A. M. Velázquez, H. Kim, C. Rotschild, and M. A. Baldo, “Dye alignment in luminescent solar concentrators: I. Vertical alignment for improved waveguide coupling,” Opt. Express18(S1), A79–A90 (2010). [CrossRef] [PubMed]
- W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett.34(13), 2054–2056 (2009). [CrossRef] [PubMed]
- K. Driesen, D. Moors, J. Beeckman, K. Neyts, C. Gorller-Walrand, and K. Binnemans, “Near-infrared luminescence emitted by an electrically switched liquid crystal cell,” J. Lumin.127(2), 611–615 (2007). [CrossRef]
- M. O'Neill and S. M. Kelly, “Liquid crystals for charge transport, luminescence, and photonics,” Adv. Mater. (Deerfield Beach Fla.)15(14), 1135–1146 (2003). [CrossRef]
- S. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. Lüssem, and K. Leo, “White organic light-emitting diodes with fluorescent tube efficiency,” Nature459(7244), 234–238 (2009). [CrossRef] [PubMed]
- T. Suzuki, “Flat panel displays for ubiquitous product applications and related impurity doping technologies,” J. Appl. Phys.99(11), 111101 (2006). [CrossRef]
- W. M. V. Wan, R. H. Friend, and N. C. Greenham, “Modelling of interference effects in anisotropic conjugated polymer devices,” Thin Solid Films363(1-2), 310–313 (2000). [CrossRef]
- D. Yokoyama, A. Sakaguchi, M. Suzuki, and C. Adachi, “Horizontal orientation of linear-shaped organic molecules having bulky substituents in neat and doped vacuum-deposited amorphous films,” Org. Electron.10(1), 127–137 (2009). [CrossRef]
- M. P. Aldred, A. E. A. Contoret, S. R. Farrar, S. M. Kelly, D. Mathieson, M. O'Neill, W. C. Tsoi, and P. Vlachos, “A full-color electroluminescent device and patterned photoalignment using light-emitting liquid crystals,” Adv. Mater. (Deerfield Beach Fla.)17(11), 1368–1372 (2005). [CrossRef]
- W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin-layers,” Phys. Rev. B22(6), 3030–3038 (1980). [CrossRef]
- K. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A15(4), 962–971 (1998). [CrossRef]
- J. A. E. Wasey, A. Safonov, I. D. W. Samuel, and W. L. Barnes, “Effects of dipole orientation and birefringence on the optical emission from thin films,” Opt. Commun.183(1-4), 109–121 (2000). [CrossRef]
- P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B73(16), 165125 (2006). [CrossRef]
- P. Bienstman, P. Vandersteegen, and R. Baets, “Modelling gratings on either side of the substrate for light extraction in light-emitting diodes,” Opt. Quantum Electron.39(10-11), 797–804 (2007). [CrossRef]
- W. Lukosz, “Light-emission by multipole sources in thin-layers. 1. Radiation-patterns of electric and magnetic dipoles,” J. Opt. Soc. Am.71(6), 744–754 (1981). [CrossRef]
- P. De Visschere, “Electromagnetic source transformations and scalarization in stratified gyrotropic media,” Prog. Electromag. Res. B18, 165–183 (2009). [CrossRef]
- P. C. Clemmow, “The theory of electromagnetic waves in a simple anisotropic medium,” Electr. Engin. Proc. Inst.110, 101–106 (1963). [CrossRef]
- P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Phys. Rev. B69(3), 035316 (2004). [CrossRef]
- T. Setälä, M. Kaivola, and A. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics59(1), 1200–1206 (1999). [CrossRef]
- D. Y. K. Ko and J. R. Sambles, “Scattering matrix-method for propagation of radiation in stratified media - attenuated total reflection studies of liquid-crystals,” J. Opt. Soc. Am. A5(11), 1863–1866 (1988). [CrossRef]
- D. W. Berreman, “Optics in stratified and anisotropic media - 4x4 matrix formulation,” J. Opt. Soc. Am.62(4), 502–510 (1972). [CrossRef]
- J. Beeckman, K. Neyts, and M. Haelterman, “Patterned electrode steering of nematicons,” J. Opt. A, Pure Appl. Opt.8(2), 214–220 (2006). [CrossRef]

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