Anisotropic OLED Outcoupling

Changing only the emitting-dipole direction or the extraordinary refractive index of the electron-transport layer (ETL) can alter an OLED's outcoupling, decay rate, and far-field angular distribution. Ke et al. separate these variables into controlled monochromatic sweeps at 539 nm, making the paper a useful method benchmark for anisotropic Emission models. Horizontal electric dipoles (HEDs) lie parallel to the layers; vertical electric dipoles (VEDs) point normal to them.

The paper reports HED outcoupling of 37.2% and 26.2% at ETL birefringence $\Delta n=-0.4$ and +0.4. Dreapex TMM's five-point sweep gives 36.76% → 25.64%, with endpoint errors below 0.6 percentage points. The VED far-field peak also moves in the reported direction, although its absolute angle is about 6–7° higher.

Background

An emitting dipole in a planar OLED couples power into air, the glass substrate, guided modes, absorption, and evanescent channels. HEDs and VEDs couple differently near the metal cathode. A uniaxial organic layer also has different in-plane and normal refractive indices, shifting transverse-magnetic (TM) optical modes and the far-field profile. Transverse-electric (TE) and TM denote polarization components whose electric or magnetic field is normal to the plane of incidence.

Ke et al. use the intrinsic radiative quantum efficiency $q$ to connect intrinsic radiation to the cavity-modified total decay rate. This page reports only aggregate mode channels directly supported and actually run in Dreapex TMM; it does not infer the paper's separate ITO and organic waveguide channels from an aggregate result.

Mapping the Paper to the TMM Model

Stack (glass output side → Ag)

Every internal layer uses the constant published at 539 nm; no external commercial material database is called. The paper text and Figure 2 use 30 nm Alq3, which is the value retained here.

Emitter and anisotropy

Here $q$ is the dimensionless intrinsic radiative quantum efficiency on 0–1, and $\Delta n=n_e-n_o$, where $n_e$ is the extraordinary refractive index along the optical axis and $n_o$ is the ordinary refractive index; both indices are dimensionless. The monochromatic calculation needs only a unit source at 539 nm, not a complete photoluminescence (PL) spectrum; a full electroluminescence (EL) spectrum is also outside this case.

Reproduction Target and Acceptance Criteria

The first run must also close the mode fractions to 100% within numerical precision. Dreapex TMM currently reports Waveguide as an aggregate Mode channel; this case does not claim the paper's layer-resolved waveguide partition.

Modeling Path in Dreapex TMM

Structure

Build the eight layers in the tabulated order from the glass output side toward the metal. Use an incoherent 1 mm constant glass layer with n=1.5; use the paper's Table 1 complex constants for every other layer. Mark the EML as emissive and place the emitting sheet at the layer center.

For the birefringent models, change only the ETL index type to Constant Birefringence, keep the ordinary component fixed, and set the extraordinary real part from 1.327 to 2.127, corresponding to $\Delta n=-0.4…+0.4$. The five HED points use a 50 nm ETL; the two VED endpoints use a 145 nm ETL.

• Download the horizontal-dipole isotropic baseline
• Download the horizontal-dipole $\Delta n=-0.4$ model
• Download the horizontal-dipole $\Delta n=+0.4$ model
• Download the vertical-dipole representative model
• Download the vertical-dipole $\Delta n=-0.4$ model
• Download the vertical-dipole $\Delta n=+0.4$ model

Optical settings

Select Mode, Power Dissipation, and Intensity. All three use a single 539 nm wavelength. Set the normalized in-plane-coordinate range to 0–2 with a 0.005 step and the angular range to 0–89° with a 1° step.

Mode provides aggregate channels and normalized decay rate, Power Dissipation resolves TE/TM power over in-plane wave vector, and Intensity provides the angular distribution. For comparison with Figure 8(a), normalize each angular curve to its own peak.

Example Setup

Horizontal-dipole baseline

The downloadable horizontal-dipole isotropic model fixes a 50 nm ETL, horizontal dipoles, and q=1 to check stack direction, boundary treatment, and mode closure.

The Structure page should show the eight-layer stack, incoherent glass, and the centered emissive Alq3 layer. The top-interface arrow in the screenshot marks the primary output direction.

Expanding the EML should reveal the 539 nm monochromatic file, Parallel orientation, relative position 0.5, and delta distribution.

The Propagation 0 and Emission 3 badges on the Optics page confirm that this run selects only the three emission detectors; the single-wavelength input is fixed at 539 nm.

Birefringence endpoints and dipole orientation

The two Structure screenshots below show the HED $\Delta n=-0.4$ endpoint and the VED $\Delta n=+0.4$ endpoint. The VED emitter screenshot separately confirms Perpendicular orientation; wavelength, position, and detector settings remain identical to the baseline.

Simulation Results and Comparison with Figures 5, 8, and 10

The chart is repeated here to keep the paper's numerical anchors adjacent to the real-run evidence.

Aggregate modes and normalized decay rate

Every Mode result closes to 100% within numerical precision. The isotropic HED baseline first establishes the partition with a 50 nm ETL.

Keeping the HED, ETL thickness, and ordinary constant fixed while increasing the ETL extraordinary index by 0.4 directly reveals the mode redistribution caused by birefringence.

The VED representative point uses the 145 nm ETL discussed for Figure 7. It records that representative state; its difference from the 50 nm HED model cannot be assigned entirely to orientation.

Positive ETL birefringence is the strict single-variable comparison: Evanescent rises by 15.93 percentage points, the Purcell factor rises by 21.3%, and Top Outcoupling falls by 5.53 percentage points. The additional decay therefore enters high-in-plane-wave-vector channels rather than increasing visible far-field outcoupling.

HED birefringence sweep against Figure 10(c)

All five points decrease monotonically with $\Delta n$, and both endpoints pass the ±1.0 pp criterion. Dreapex TMM predicts a total decrease of 11.11 pp, versus 11.0 pp in the paper.

In-plane power dissipation

Power Dissipation shows TE, TM, and total power over the same normalized in-plane coordinate from 0–2. The isotropic HED baseline contains separate peak groups in the radiative, high-index, and high-in-plane-wave-vector regions.

With ETL $\Delta n=+0.4$, a strong high-coordinate peak reaches approximately 12.12 near 1.265; the isotropic baseline's maximum above 1.15 is approximately 0.243. This shift independently supports the large Evanescent increase in Mode.

The VED representative point has zero TE contribution. Its total power is TM-only and reaches approximately 26.20 near 1.07, consistent with the controlled vertical-dipole setting coupling only to TM polarization.

Far-field angular distribution

The Intensity results share the 0–89° grid. The isotropic HED reaches its maximum along the surface normal and decreases monotonically with angle.

The HED with a positively birefringent ETL still peaks at 0°. Its radiative-angle curve nearly overlaps the baseline: total intensity changes by less than 0.4% at both 55° and 80°. At this representative point, birefringence mainly alters high-in-plane-wave-vector dissipation and normalized mode fractions rather than the far-field peak position.

The isotropic VED with a 145 nm ETL is zero at 0° and reaches its maximum at 55°, producing a clear off-axis lobe.

VED peak angle against Figure 8(a)

Both the paper and the simulation move the peak toward a higher angle as birefringence rises from −0.4 to +0.4. Dreapex TMM gives a 6° shift, versus 5.6° in the paper; both absolute endpoints pass the preregistered 8° threshold. The common 6–7° offset shows that the shift is more robust than the absolute angle.

Deviation Analysis

1. The paper's Table 1 omits the glass constant and thick-glass treatment. This case uses an incoherent 1 mm glass with n=1.5 and k=0; Substrate and Top Outcoupling are sensitive to that boundary choice.
2. The comparison uses endpoint scalars explicitly reported in the paper, not machine-readable vectors for the complete curves, so it cannot report a normalized root-mean-square error (NRMSE) for curve shape.
3. Every model uses one delta emitting sheet at the EML center. A recombination-zone distribution would smooth the cavity-position dependence.
4. The current Mode result aggregates guided power into one channel. The paper's separate ITO and organic waveguide components cannot be recovered from that aggregate number.
5. A 539 nm monochromatic result does not need PL, but it cannot be extrapolated to broadband EL or color shift.

Further Extensions

1. Build a two-dimensional sweep over the Figure 6–7 ETL-thickness range and $q$ sequence to extend the present monochromatic endpoint comparison.
2. Sweep $\Delta n=-0.4…+0.4$ separately in the HTL to add the layer contrast in Figures 9 and 10(b/d).
3. Digitize the paper curves into reference CSV files before adding NRMSE and curve-shape thresholds.
4. Run a sensitivity envelope for glass n=1.49–1.52 and coherent treatment so that boundary-assumption error remains separate from algorithm error.

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