Theory

Emission Physics

Dipole emission, power dissipation, modes, and outcoupling in layered devices

This chapter presents the emission physics of layered devices in the order of dipole source, efficiency decomposition, microcavity/waveguide/SPP, power dissipation and in-plane wave vector, and optical modes, then maps those quantities to the app's emission outputs.

Chapter Scope

An external plane wave enters the stack from the surrounding medium; by contrast, emission simulation models the exciton as a radiating point dipole inside the stack. The point-dipole multilayer model applies when each layer is a flat thin film and the device lateral area is much larger than the functional-layer thickness (high width-to-height ratio); edge effects of small-area, thick devices are not captured.

Physical object	Model description	Simulation consequence
Emission source	Radiating point dipole inside the stack	Internal source, as opposed to external plane-wave excitation
Spectrum	Intensity vs wavelength (measurable)	Forward emission spectrum
Angular distribution	Intensity vs angle (measurable)	Forward angular intensity
Power dissipation	Dissipated power vs in-plane wave vector (not directly measurable)	Dispersion basis for separating loss channels
Optical mode	Loss-channel share distribution (not measurable)	Outcoupling, waveguide, evanescent, absorption, and nonradiative shares
Purcell factor	Spontaneous-emission property affecting IQE (hard to measure)	Structural modulation of the spontaneous-emission rate

Together these quantities are used to investigate microcavity, Purcell, planar-waveguide, optical-tunneling, and surface-plasmon-polariton (SPP) effects.

Dipole Emission and Orientation

Unoriented emitters radiate isotropically; isotropic emission is the weighted sum of vertical (z) and horizontal (x,y) dipole radiated-power densities,

K_{iso}=\tfrac{1}{3}K_{v}+\tfrac{2}{3}K_{h}

where iso is isotropic, v is vertical (z), and h is horizontal (x,y). A vertical dipole radiates its far field mainly in-plane (no far-field radiation along z); a horizontal dipole radiates mainly along z (out of plane).

Because the emission layer (EML) index exceeds air, light beyond the critical angle is totally internally reflected at the interface and cannot escape, forming the escape cone. Horizontal dipoles place more power inside the escape cone, so they yield substantially higher light extraction efficiency (LEE) than vertical dipoles, whose energy largely becomes loss.

Quantum Efficiency, Purcell, and EQE

The external quantum efficiency (EQE) of an OLED decomposes into the internal quantum efficiency (IQE) times the light extraction efficiency (LEE):

EQE = IQE\times LEE = \gamma\,\chi_{ST}\,q_{eff}\,LEE

where $\gamma$ is the charge-carrier balance factor, $\chi_{ST}$ is the spin formation ratio ( $=1/4$ for purely random singlet/triplet formation), $q_{eff}$ is the effective quantum efficiency, and $LEE$ is the light extraction efficiency. QLED/PeLED have no spin-statistics bottleneck, so $\chi_{ST}$ drops out:

EQE = IQE\times LEE = \gamma\,q_{eff}\,LEE

LEE is defined as the ratio of photons entering the surrounding medium to photons emitted by the EML, also called outcoupling efficiency. For a Lambertian emitter, geometric optics gives the limit

LEE=\frac{1}{2n^{2}}

so higher-index emission layers (such as QLED/PeLED) have lower geometric LEE. This is only an approximation: because device layers are sub-wavelength, microcavity, Purcell, waveguide, and SPP effects coexist, Snell-based geometric optics cannot resolve the loss budget, and a wave-optics (CPS-type) model is required.

Spontaneous emission is not an intrinsic material property; the optical environment (device structure) modifies it, so quantum efficiency can be engineered structurally. The environment-modified radiative decay rate is

b=q_{0}b_{0}F+(1-q_{0})b_{0}

where $b$ is the environment-modified decay rate, $b_0$ the intrinsic decay rate, $q_0$ the intrinsic quantum efficiency, and $F$ the Purcell factor; when $q_0=1$ , $b=b_0F$ . The Purcell factor gives the effective quantum efficiency

q_{eff}=\frac{q_{0}F}{q_{0}F+1-q_{0}}

and the lifetime ratio

\frac{\tau_{0}}{\tau}=\frac{b}{b_{0}}=1-q_{0}+q_{0}F

Different dipole orientations have different $F$ ; enhancing horizontal and suppressing vertical dipoles via the microcavity raises LEE and cuts waveguide/SPP loss. $F$ also varies with wavelength. The Purcell factor can be written as an in-plane-wave-vector integral

F=\int_{0}^{\infty} f(u)\,du,\qquad u=\sin\theta_{e}\ \text{(isotropic)}

where the integrand $f(u)$ is the dissipated-power spectrum; integrating it gives $F$ .

Emission proceeds as "charge injection and exciton formation -> electro-optical conversion -> optical loss and extraction". The first two steps are electrical inputs, not optical: the charge-carrier balance factor $\gamma$ and spin formation ratio $\chi_{ST}$ together form the model's Conversion Efficiency $=\gamma\chi_{ST}$ , which is not affected by the Purcell effect. The intrinsic quantum efficiency $q_0$ feeds the model's Quantum Efficiency input, which the Purcell effect then maps to the effective quantum efficiency $q_{eff}$ ; the intrinsic lifetime $\tau_0$ is likewise affected by the Purcell effect.

Microcavity, Waveguide, and SPP

The OLED layer stack forms a micro-cavity with planar reflective interfaces at the micro/nano scale, producing wavelength-scale interference that splits into wide-angle and multiple-beam types. Wide-angle interference arises between directly emitted and bottom-reflected light, set mainly by the emitter-to-bottom-mirror distance $d_{bottom}$ :

\frac{2\pi}{\lambda}\,2n\,d_{\mathrm{bottom}}\cos\theta-\phi_{\mathrm{bottom}}=m\,2\pi

Multiple-beam interference arises from repeated round trips, set by the total cavity length $d_{top}+d_{bottom}$ :

\frac{2\pi}{\lambda}\,2n\,(d_{\mathrm{bottom}}+d_{\mathrm{top}})\cos\theta-(\phi_{\mathrm{bottom}}+\phi_{\mathrm{top}})=m\,2\pi

A single metal electrode forms a weak microcavity; adding a semitransparent metal electrode (or DBR) forms a strong microcavity with stronger interference. Microcavity tuning is via the emitter-reflector distance and cavity length (HTL/ETL/EML thickness, dipole position).

Totally internally reflected light forms interference-supported waveguide modes that ultimately become thermal loss. Waveguide losses are typically 30%-70% of total losses (device-dependent), so suppressing them is key to LEE. The waveguide (transverse-resonance) condition is

n_{g}\frac{2\pi}{\lambda_{0}}(2d\cos\theta)-\phi_{gt}-\phi_{gb}=m(2\pi),\quad m=0,1,2,\dots

Waveguide formation depends on cavity length $d$ , index $n$ , angle $\theta$ , wavelength $\lambda$ , and polarization; longer cavities admit more integer $m$ (more modes), so thinner devices are easier to control.

Near a metal-dielectric interface, the emitter couples energy into surface plasmon polaritons (SPP) through the near field, producing non-radiative loss and shortening the fluorescence lifetime (toward zero at close range). By the Drude model, the SPP resonance frequency depends on the metal and dielectric indices; for fixed materials, wavelength, dipole-metal distance, and dipole orientation control SPP loss. TM polarization is required to excite SPPs, and vertical-dipole emission is entirely TM-polarized, so vertical dipoles are the dominant SPP source.

Power Dissipation and In-Plane Wave Vector

The in-plane wave vector is the projection of the wave vector onto the interface plane:

k=\sqrt{k_x^2+k_y^2+k_z^2},\qquad k_{in}=\sqrt{k_x^2+k_y^2}

k_{in}=n_i\frac{\omega}{c}\sin\theta_i=n_i\frac{2\pi}{\lambda_0}\sin\theta_i

Introducing $u_{in}$ and $n_{eff}$ :

u_{in}=\sin\theta_e,\qquad n_{eff}=n_i\sin\theta_i

k_{in}=n_i\frac{2\pi}{\lambda_0}\sin\theta_i=n_e\frac{2\pi}{\lambda_0}u_{in}=\frac{2\pi}{\lambda_0}n_{eff}

The relation of $u_{in}$ and $n_{eff}$ to $\theta$ is wavelength-independent, so they divide modes intuitively; at $u_{in}=1$ (or $n_{eff}=n_e$ ), $\theta_e=90°$ , i.e. light propagates parallel to the interface inside the EML. When

k_{in}>n_e\frac{2\pi}{\lambda_0};\quad u_{in}>1;\quad n_{eff}>n_e

then $\sin\theta_e>1$ and $\theta_e$ becomes complex, corresponding to an evanescent wave, the condition for exciting SPPs.

Under microcavity/waveguide effects, the emitted energy is distributed over $k_{in}$ (different power in different directions), unlike isotropic vacuum radiation; constructive interference appears as sharp features (such as waveguide peaks), and SPP excitation appears as a distinct feature at high $k_{in}$ .

Optical Modes

Emitted energy is binned into optical modes by in-plane-wave-vector interval. In the table below, $n_t$ is the top-layer index, $n_b$ the bottom-layer index, $n_s$ the substrate index, and $n_e$ the EML index:

Mode (in app)	Scientific name	$k_{in}$ interval	Common description (not a definition)
TOC	—	$[0,\ n_t\frac{\omega}{c}]$	top-outcoupled
BOC	—	$[0,\ n_b\frac{\omega}{c}]$	bottom-outcoupled
TOC (top layer is Air)	Air Mode	$[0,\ \frac{\omega}{c}]$	light extraction efficiency / outcoupling efficiency
SUB (top layer is Air)	Substrate Mode	$[\frac{\omega}{c},\ n_s\frac{\omega}{c}]$	light confined in the substrate by reflection at the substrate-air interface
ABS (no incoherent layer)	Absorption Mode	$[0,\ \frac{\omega}{c}]$	absorption loss on the TOC path
ABS (with incoherent layer)	Absorption Mode	$[0,\ n_s\frac{\omega}{c}]$	absorption loss on the TOC and SUB paths
WVG (no incoherent layer)	Waveguide Mode	$[\frac{\omega}{c},\ n_e\frac{\omega}{c}]$	waveguide loss from total internal reflection plus interference
WVG (with incoherent layer)	Waveguide Mode	$[n_s\frac{\omega}{c},\ n_e\frac{\omega}{c}]$	waveguide loss from total internal reflection plus interference
EVA	Evanescent Mode	$[n_e\frac{\omega}{c},\ \infty]$	evanescent-wave loss, generally SPP loss
NRA	Nonradiative Mode	$[0,\ \infty]$	non-radiative loss, occurs when quantum efficiency < 100%

Air mode corresponds to EQE; when both Conversion Efficiency and Quantum Efficiency = 1 (default), Air mode corresponds to LEE. Air mode is also called Outcoupled / Leaky mode, and Evanescent mode is also called SPP mode. The nonradiative mode (NRA) appears only when the intrinsic quantum efficiency $q_0<1$ ; due to Purcell enhancement, the NRA fraction is not simply $1-q_0$ .

The current Mode calculation requires the index ordering

n_t\ \text{or}\ n_b\ <\ n_s\ <\ n_e

. This constraint follows from the interval-partition rules of the table above; if the structure does not satisfy this ordering, the mode partition may fail.

Absorption mode is not the sum of all absorption losses. Waveguide and evanescent light are eventually absorbed too, and counting them as absorption would make the WVG and EVA modes vanish. Absorption mode includes only absorption on the TOC and SUB paths.

Mapping to App Outputs

Output / detector	Physical origin	Interpretation focus
`Power Dissipation`	Dissipated power vs $k_{in}$ (or $u_{in}$ , $n_{eff}$ )	Per-channel dispersion, waveguide peaks, and SPP features
`Intensity`	Dipole emission intensity exiting the stack	Forward emission intensity vs angle/wavelength
`Mode`	Loss shares partitioned by $k_{in}$ interval	TOC/SUB/ABS/WVG/EVA/NRA shares and EQE, LEE
`Intensity Color`	Color representation of exit intensity	Intensity color distribution vs wavelength
`Normalized Spectrum`	Intensity vs wavelength (normalized)	Forward emission spectral shape
`Normalized Angular Distribution`	Intensity vs angle (normalized)	Forward angular intensity distribution
`Emission`	Combined output of Purcell factor $F$ , effective quantum efficiency, etc.	Structural modulation of spontaneous emission (including the wavelength dependence of $F$ )

Continue with Emission Overview and Emission Detectors.

Dispersion Theory

Phase, group delay, GDD, and differential group delay from thin-film transfer matrices

Structure Configuration

Structural modeling, layer stacks, and validation