Resonant-Cavity-Enhanced Photodetector (RCE)

1. Theory

Definition: A resonant-cavity-enhanced (RCE) photodetector is a photodiode whose thin absorbing layer is placed inside a Fabry-Perot cavity formed by two mirrors, so that the light crosses the absorber several times at the resonance wavelength.
Structure: A non-absorbing quarter-wave distributed Bragg reflector (DBR) of large-gap material forms the back mirror with $R_{2}$ close to 1, a lower-reflectivity front mirror with $R_{1} < R_{2}$ admits the light, and non-absorbing spacers set the cavity length so that the absorber lies at an antinode of the standing wave.
Device types: The cavity has been used with p-i-n photodiodes, Schottky photodiodes (including internal photoemission devices), and avalanche photodiodes, and also with a heterojunction phototransistor and a photothyristor switch.
Materials: GaAs/AlAs and GaAs/AlGaAs mirrors with GaAs or InGaAs absorbers near 0.85 μm to 1.0 μm, InGaAs/InAlAs/InP for 1.3 μm to 1.55 μm, low-temperature-grown GaAs on GaAs mirrors for 1.55 μm, Si/SiGe, and HgCdTe/CdTe/GaAs for 10.6 μm.
Efficiency and speed: A conventional detector needs a thick absorber for a high efficiency, which lengthens the transit time; the cavity gives a high efficiency with a thin absorber of 100 nm to 500 nm, so that the transit-time limit $f_{t r} \approx 0.44 v / d$ stays high.
Efficiency enhancement: $η$ is a periodic function of the wavelength with peaks at the resonances, and the peak is above the single-pass value by $ξ = η_{ma x} / η_{s p}$ , e.g. a 100 nm absorber with $α d = 0.1$ rises from 10% to above 90% in a simulation with $R_{2} = 1$ and $R_{1} = 0.7$ .
Measured devices: An InGaAs p-i-n diode reached 66% at 1572 nm with a bandwidth of 31 GHz (bandwidth-efficiency product 20 GHz); GaAs Schottky devices are reported with 50% and 50 GHz (semitransparent Au) and 75% and 60 GHz (ITO).
Selectivity and limits: Wavelengths away from the resonance are reflected, which gives wavelength selection but also a narrow acceptance angle (about $\pm 1 5^{\circ}$ in an InGaAs device) and a sensitivity of the resonance wavelength to the layer thickness (4% for a 4% growth error).

2. Working Principle

Resonance: At the wavelengths for which $2 β L + ϕ_{1} + ϕ_{2} = 2 mπ$ the waves reflected between the mirrors add in phase, so the field in the cavity exceeds that of the incident beam and the absorber takes up a much larger share of the light.
Multiple passes: The light that is not absorbed in the first pass is reflected by the back mirror and crosses the absorber again, and the part that reaches the front mirror is mostly returned, so the absorbed fraction is $η_{ma x}$ of the first table row instead of $1 - e^{- α d}$ .
Impedance matching: The reflection of the whole cavity vanishes for $R_{1} = R_{2} e^{- 2 α d}$ , and for $R_{2} = 1$ all the light is then absorbed; a larger $R_{1}$ reflects the light away and a smaller $R_{1}$ lets it leave through the front after the return.
Standing wave: The absorber is placed at an antinode to raise the absorption, and a thickness $d = mλ /2$ suppresses the standing-wave effects in the formula.
Collection: The photogenerated carriers are collected in the reverse-biased p-i-n or Schottky junction as in a conventional detector, but over the short path $d$ , which gives the high transit-time limit $f_{t r}$ and a low operating voltage because the depleted layer is thin.
Tuning of the resonance: The wavelength is set by $λ_{m} = 2 n_{e f f} L_{e f f} / m$ and can be moved after growth by etching away part of the top layers (a recess etch), by 47 nm in the InGaAs example.
Off resonance: The efficiency falls to $ξ_{min}$ between the peaks, and the width of a peak follows from the finesse of the absorbing cavity.
Linearity: The InGaAs device had a linear response up to 6 mW of optical power and gave 5 mA at a reverse bias of 3 V, with the saturation attributed to the screening of the field by the photogenerated carriers.

3. Applications

Wavelength demultiplexing receivers: A monolithic wavelength-demultiplexing receiver was demonstrated on the basis of the wavelength selectivity, but the cavity loss raises the crosstalk, and the width of a peak (tens of nm) is too large for dense channel spacing.
Wavelength-selective switching: An RCE spectral response combined with the bistability of a photothyristor gave a wavelength-selective optoelectronic switch.
Low-temperature-grown GaAs devices: A GaAs-based p-i-n diode with a low-temperature-grown absorber operates at 1.55 μm with a $3 dB$ bandwidth up to 11.2 GHz, on a GaAs substrate and with GaAs/AlAs mirrors.
Mid-infrared detection: HgCdTe devices with a top mirror above 98% were designed for a 92% absorption at 10.6 μm, and photovoltaic RCE structures were studied for the detection of quantum cascade laser emission at 8 μm to 10.6 μm.

Name	Formula	Related Formulae	Variables/Constants
Quantum efficiency of the resonant-cavity-enhanced detector	$η = [\frac{( 1 - R _{1} ) ( 1 + R _{2} e ^{- α d} )}{1 - 2 R _{1} R _{2} e ^{- α d} c o s ( 2 β L + ϕ _{1} + ϕ _{2} ) + R _{1} R _{2} e ^{- 2 α d}}] (1 - e^{- α d}) η_{i}$	$η_{s p} = (1 - R_{1}) (1 - e^{- α d}) η_{i}$ $β = \frac{2 π n _{e f f}}{λ}$	$R_{1}, R_{2} : p o w er r e f l ec t i v i t i es o f t h e f r o n t an d ba c k mi r r or s (R_{1} < R_{2})$ $α : ab sor pt i o n coe f f i c i e n t o f t h e t hin ab sor b er$ $d : ab sor b er t hi c k n ess$ $η_{i} : f r a c t i o n o f t h e ab sor b e d p h o t o n s w h ose c a r r i er s a r e co l l ec t e d$ $L : c a v i t y l e n g t h$ $ϕ_{1}, ϕ_{2} : p ha se s hi f t s f r o m t h e p e n e t r a t i o n o f t h e f i e l d in t o t h e mi r r or s$ $β : p r o p a g a t i o n co n s t an t w i t h t h e e f f ec t i v e in d e x n_{e f f}$ $η_{s p} : s in g l e - p a ss e f f i c i e n cy w i t h t h e s am e f r o n t s u r f a ce$ $(t h e f or w a r d an d ba c k w a r d w a v es a r e t ak e n t o a dd in in t e n s i t y in s i d e t h e ab sor b er, so t h e s t an d in g - w a v e e f f ec t i s n e g l ec t e d, w hi c h h o l d s w h e n d i s a m u l t i pl e o f λ /2 or w h e n α d ≪ 1; t h e cos in e t er m mak es η p er i o d i c in w a v e l e n g t h w i t h ma x ima a t t h e r eso nan ces)$
Resonance condition and free spectral range	$2 β L + ϕ_{1} + ϕ_{2} = 2 mπ, λ_{m} = \frac{2 n _{e f f} L _{e f f}}{m}$	$Δ λ_{F S R} = \frac{λ ^{2}}{2 n _{g} L _{e f f}}$ $\frac{Δ λ _{m}}{λ _{m}} \approx \frac{Δ L _{e f f}}{L _{e f f}}$	$m : in t e g er or d er o f t h e r eso nan ce$ $L_{e f f} : c a v i t y l e n g t h pl u s t h e p e n e t r a t i o n d e pt h s in t o t h e tw o mi r r or s$ $n_{g} : g r o u p in d e x$ $Δ λ_{F S R} : s p a c in g o f t h e e f f i c i e n cy p e ak s (f r ee s p ec t r a l r an g e)$ $Δ L_{e f f} : c han g e o f t h e o pt i c a l c a v i t y l e n g t h, a s b y e t c hin g a w a y p a r t o f t h e t o p l a y er (a s hi f t o f 1605 nm t o 1558 nm, 47 nm, i s 2.9% o f t h e w a v e l e n g t h, co m p u t e d), or b y a g r o w t h er r or (a 4% t hi c k er s t a c k m o v es 1550 nm t o ab o u t 1612 nm, co m p u t e d)$
Peak efficiency and optimum front-mirror reflectivity	$η_{ma x} = \frac{( 1 - R _{1} ) ( 1 + R _{2} e ^{- α d} ) ( 1 - e ^{- α d} )}{( 1 - R _{1} R _{2} e ^{- α d} ) ^{2}} η_{i}$	$R_{1, o pt} = R_{2} e^{- 2 α d}, d_{o pt} = \frac{1}{2 α} ln \frac{R _{2}}{R _{1}}$ $η_{ma x} (R_{1, o pt}) = \frac{( 1 + R _{2} e ^{- α d} ) ( 1 - e ^{- α d} )}{1 - R _{2} e ^{- 2 α d}} η_{i}$	$η_{ma x} : e f f i c i e n cy a t t h e r eso nan ce (cos in e e q u a l t o 1)$ $R_{1, o pt} : f r o n t r e f l ec t i v i t y t ha t mak es t h e r e f l ec t i o n o f t h e w h o l e c a v i t y v ani s h, so t ha t f or R_{2} = 1 t h e e f f i c i e n cy i s η_{i}$ $(f or R_{1} = 0.2, R_{2} = 0.99, α = 1 0^{4} c m^{- 1} t h e o pt im u m t hi c k n ess i s 0.8 μ m an d η_{ma x} = 0.99 f or d f r o m 0.7 μ m t o 0.95 μ m, co m p u t e d; f or R_{2} = 1 t h e e x p r ess i o n e q u a l s o n e min u s t h e s q u a r e d ma g ni t u d e o f t h e r e f l ec t i o n coe f f i c i e n t o f t h e c a v i t y)$
Enhancement factor over a single pass	$ξ = \frac{η _{ma x}}{η _{s p}} = \frac{1 + R _{2} e ^{- α d}}{( 1 - R _{1} R _{2} e ^{- α d} ) ^{2}}$	$ξ_{α d ≪ 1} \to \frac{1 + R _{2}}{( 1 - R _{1} R _{2} ) ^{2}}$ $ξ_{min} = \frac{1 + R _{2} e ^{- α d}}{( 1 + R _{1} R _{2} e ^{- α d} ) ^{2}}$	$ξ : r a t i o o f t h e e f f i c i e n cy a t t h e r eso nan ce t o t ha t o f a s in g l e p a ss t h r o ug h t h e s am e ab sor b er$ $ξ_{min} : v a l u e a t t h e minima b e tw ee n t h e r eso nan ces (cos in e e q u a l t o - 1)$ $(f or R_{1} = 0.3 (a ss u m e d), R_{2} = 0.95, α d = 0.2 t h e e f f i c i e n cy r i ses f r o m 12.7% t o 71.2%, ξ = 5.6; f or a v er y w e ak ab sor b er w i t h R_{1} = 0.3 (a ss u m e d) an d R_{2} = 0.99, ξ = 9.6, co m p u t e d)$
Finesse and spectral width of the response	$F = \frac{π ρ}{1 - ρ}, δ λ = \frac{Δ λ _{F S R}}{F}$	$ρ = R_{1} R_{2} e^{- α d}$ $λ_{m} (θ) \approx λ_{m} (0) 1 - \frac{s i n ^{2} θ}{n ^{2}}$	$F : f in esse o f t h e ab sor bin g c a v i t y (f r o m t h e A i r y f or m o f t h e d e n o mina t or o f η)$ $ρ : am pl i t u d e f a c t or o f o n e r o u n d t r i p$ $δ λ : f u l l w i d t h a t ha l f ma x im u m o f a r eso nan ce$ $θ : an g l e o f in c i d e n ce in ai r$ $n : r e f r a c t i v e in d e x o f t h e c a v i t y (t h e r eso nan ce m o v es t o s h or t er w a v e l e n g t h w i t h an g l e b y 4.5 nm a t 1 5^{\circ} f or n = 3.4, co m p u t e d)$ $(f or R_{1} = 0.3 (a ss u m e d), R_{2} = 0.95, α d = 0.2, L_{e f f} = 1 μ m, n_{g} = 3.4 (a ss u m e d) t h e f in esse i s 3.7, t h e f r ee s p ec t r a l r an g e 353 nm an d t h e w i d t h 96 nm, co m p u t e d)$
Reflectivity of a quarter-wave Bragg mirror	$R_{D B R} = (\frac{1 - x}{1 + x})^{2}, x = \frac{n _{0}}{n _{s}} (\frac{n _{L}}{n _{H}})^{2 N}$	$t_{H, L} = \frac{λ _{0}}{4 n _{H, L}}$ $Δ λ_{s t o p} = \frac{4 λ _{0}}{π} arcsin \frac{n _{H} - n _{L}}{n _{H} + n _{L}}$	$N : n u mb er o f p ai r s$ $n_{H}, n_{L} : in d i ces o f t h e hi g h - an d l o w - in d e x l a y er s$ $n_{0}, n_{s} : in d i ces o f t h e c a v i t y s i d e an d o f t h e s u b s t r a t e$ $t : l a y er t hi c k n ess$ $Δ λ_{s t o p} : w i d t h o f t h e hi g h - r e f l ec t i v i t y ban d$ $λ_{0} : d es i g n w a v e l e n g t h$ $(t h e t r an s f er - ma t r i x r es u l t f or G a A s / A l A s w i t h n_{H} = 3.5 an d n_{L} = 3.0 i s 96% f or 15 p ai r s an d 99% n ee d s 20 p ai r s; f or I n G a A s / I n A l A s w i t h n_{H} = 3.45 an d n_{L} = 3.2 se v e n p ai r s g i v e o n l y 23%, 29 p ai r s 95% an d 40 p ai r s 99%, co m p u t e d)$
Bandwidth-efficiency product	$BWE = η f_{3 d B}, f_{t r} \approx \frac{0.44 v}{d}$	$BWE_{co n v} \approx 0.44 v \frac{1 - e ^{- α d}}{d} \to 0.44 α v$ $BWE_{R C E} \approx 0.44 \frac{v}{d} η_{ma x}$ $\frac{1}{f _{3 d B}^{2}} \approx \frac{1}{f _{t r}^{2}} + \frac{1}{f _{R C}^{2}}$	$B W E : p r o d u c t o f t h e q u an t u m e f f i c i e n cy an d t h e 3 d B ban d w i d t h$ $v : c a r r i er d r i f t v e l oc i t y in t h e ab sor b er$ $f_{t r} : t r an s i t - t im e l imi t$ $f_{R C} : l imi t o f t h e l o a d an d c a p a c i t an ce (a s o n t h e P I N P h o t o d i o d e p a g e)$ $(t h e co n v e n t i o na l l imi t i s in d e p e n d e n t o f d f or a w e ak ab sor b er an d e q u a l s 26 G H z t o 44 G H z f or α = 1 0^{4} c m^{- 1} an d v = 6 \times 1 0^{6} t o 1 0^{7} c m / s, co m p u t e d; t h e c a v i t y e nhan ces t h e e f f i c i e n cy w i t h o u t l e n g t h e nin g t h e t r an s i t p a t h)$ $(t h e p h o t o n l i f e t im e o f t h e c a v i t y, ab o u t 14 f s f or t h e e x am pl e o f t h e f in esse r o w, co m p u t e d, d oes n o t l imi t t h e ban d w i d t h)$

Important Questions

Ques: Why does a thin absorber inside a Fabry-Perot cavity reach a much higher quantum efficiency than the same absorber in a single pass?

At resonance the round-trip phase is a multiple of $2 π$ , so the field reflected between the mirrors adds in phase and the absorber sees a larger field than that of the incident beam, while the back mirror returns the light that was not absorbed on the first pass. The efficiency is then $η_{ma x}$ of the table, which exceeds the single-pass value by the factor $ξ = (1 + R_{2} e^{- α d}) / (1 - R_{1} R_{2} e^{- α d})^{2}$ . For a 100 nm absorber with $α = 1 0^{4} c m^{- 1}$ ( $α d = 0.1$ ), the single pass gives 9.5%, and with $R_{2} = 1$ and $R_{1} = 0.7$ the formula gives 92% (computed), in agreement with the simulation of the Laser Focus World article of about 10% rising to above 90%. Reference: Laser Focus World, Demand for high-speed detectors drives research (1998); Wikipedia, Resonant-cavity-enhanced photo detector (accessed October 2026; equations missing from the fetched text).

Ques: Why does the efficiency have an optimum front-mirror reflectivity, and what thickness does it fix?

The cavity behaves as an absorber with a reflection coefficient, and the reflection vanishes when the front mirror equals the round-trip loss of the other mirror and the absorber, $R_{1} = R_{2} e^{- 2 α d}$ ; for $R_{2} = 1$ the efficiency is then 1. A larger $R_{1}$ reflects the incident light away, and a smaller one lets the stored light leave through the front. Equivalently, $R_{1}$ and $R_{2}$ fix the best thickness $d = ln (R_{2} / R_{1}) /2 α$ . For $R_{1} = 0.2$ , $R_{2} = 0.99$ and $α = 1 0^{4} c m^{- 1}$ this is 0.8 μm with $η = 0.99$ , and $η$ stays at 0.99 for 0.7 μm to 0.95 μm (computed), as quoted by the Wikipedia article. Without mirrors a single pass needs a thickness of about 5 μm for the same efficiency. Reference: Wikipedia, Resonant-cavity-enhanced photo detector (accessed October 2026; equations missing from the fetched text); Laser Focus World, Demand for high-speed detectors drives research (1998).

Ques: Why does the cavity avoid the trade-off between efficiency and speed, and how large is the bandwidth-efficiency product?

In a conventional diode $η \approx 1 - e^{- α d}$ and $f_{t r} \approx 0.44 v / d$ , so for a weak absorber the product is $0.44 α v$ , independent of $d$ , which is 26 GHz to 44 GHz for $α = 1 0^{4} c m^{- 1}$ (computed). In the RCE diode the thickness stays small while the efficiency rises, $BWE \approx 0.44 (v / d) η_{ma x}$ , i.e. larger by $ξ$ in the ideal case. Measured values are 20 GHz (66%, 31 GHz, 300 nm InGaAs), 25 GHz (50%, 50 GHz) and 45 GHz (75%, 60 GHz) for GaAs Schottky devices, which are comparable to the ideal conventional limit and well above the 7 GHz to 14 GHz of the fastest commercial infrared detectors (45 GHz, 0.2 A/W to 0.4 A/W, computed for 1.55 μm). Reference: Ultrafast and highly efficient resonant cavity enhanced photodiodes, SPIE ITCom 2003, DOI 10.1117/12.511202 (abstract); Bilkent University, InGaAs resonant-cavity-enhanced p-i-n photodiode paper (ee.bilkent.edu.tr/~aytur/papers/02ptl1); Laser Focus World, Demand for high-speed detectors drives research (1998).

Ques: Do the RCE bandwidths follow the transit-time estimate: 64 GHz and 120 GHz, or 31 GHz?

The Wikipedia article states 64 GHz for a 0.5 μm absorber and 120 GHz for 0.25 μm, compared with 10 GHz to 30 GHz for conventional detectors. These two values correspond to $0.44 v / d$ with $v \approx 7 \times 1 0^{6} cm/s$ (computed), so they are transit-time limits and ignore the load and the capacitance. The measured $3 dB$ bandwidth of the 300 nm InGaAs diode is 31 GHz after the removal of the 40 GHz bias tee, against a prediction of 55 GHz by the same authors and a transit-time value of about 100 GHz (computed). The measured figure is the more likely value for a real device, and the 64 GHz and 120 GHz figures are best taken as upper limits. Reference: Wikipedia, Resonant-cavity-enhanced photo detector (accessed October 2026; equations missing from the fetched text); Bilkent University, InGaAs resonant-cavity-enhanced p-i-n photodiode paper (ee.bilkent.edu.tr/~aytur/papers/02ptl1).

Ques: Why is an RCE detector wavelength-selective, and how narrow is its response?

Away from the resonance the cosine term of $η$ reduces the field in the cavity, the light is reflected, and the efficiency falls to $ξ_{min}$ between the peaks. The width follows from the finesse $F = π ρ / (1 - ρ)$ with $ρ = R_{1} R_{2} e^{- α d}$ . For $R_{1} = 0.3$ (assumed), $R_{2} = 0.95$ , $α d = 0.2$ , $L_{e f f} = 1 μ m$ and $n_{g} = 3.4$ (assumed), $F = 3.7$ , the free spectral range is 353 nm and the width is 96 nm (computed), in line with the InGaAs diode that stayed above 50% from 1550 nm to 1620 nm. Such a width is far from the 0.8 nm spacing of a 100 GHz channel grid, and the angular acceptance is limited to about $\pm 1 5^{\circ}$ in the InGaAs device. Reference: Bilkent University, InGaAs resonant-cavity-enhanced p-i-n photodiode paper (ee.bilkent.edu.tr/~aytur/papers/02ptl1); Kaniewski, Muszalski, Piotrowski, Optica Applicata 37 (2007) 405 (dlibra.kdm.wcss.pl, optappl_3704p405); Laser Focus World, Demand for high-speed detectors drives research (1998).

Ques: Which tuning range is right for the InGaAs RCE diode, 1605 nm to 1558 nm or 1605 nm to 1538 nm?

The abstract and the SPIE summary give 1605 nm to 1558 nm, while the body of the paper gives 1538 nm to 1605 nm and also a total of 47 nm. Only 1605 nm to 1558 nm equals 47 nm; the other range is 67 nm (computed). The range of 1558 nm to 1605 nm is therefore the more likely, and the peak efficiency of 66% at 1572 nm lies inside it. The tuning works because etching the top p layers shortens the optical cavity, $Δ λ / λ \approx Δ L_{e f f} / L_{e f f}$ , a change of 2.9% for 47 nm. The same sensitivity explains the growth error: layers 4% too thick moved the mirror centre from 1550 nm to 1610 nm. Reference: Bilkent University, InGaAs resonant-cavity-enhanced p-i-n photodiode paper (ee.bilkent.edu.tr/~aytur/papers/02ptl1); Ultrafast and highly efficient resonant cavity enhanced photodiodes, SPIE ITCom 2003, DOI 10.1117/12.511202 (abstract).

Ques: Why does the measured enhancement of the low-temperature-grown GaAs diode differ from the ideal value, and why is its absolute efficiency so low?

For a very weak absorber $ξ \to (1 + R_{2}) / (1 - R_{1} R_{2})^{2}$ , which is 9.6 for $R_{1} = 0.3$ (assumed, air/GaAs) and $R_{2} = 0.99$ (computed), compared with 8.3 theoretical and 7.5 measured at zero bias and 4.9 at 3 V; the reflectivities are approximate and the source gives no cause for the fall with bias. The absolute efficiency is more than two orders of magnitude below the simulation because the carrier lifetime in the absorber is about 150 fs, so that only a collection factor of about 0.35% (0.45% calculated) of the carriers reaches the contacts. The device is therefore useful for speed, up to 11.2 GHz at 2.5 mW, not for efficiency. Reference: B. Butun et al., High-speed 1.55 μm operation of low-temperature-grown GaAs-based resonant-cavity-enhanced p-i-n photodiodes, Appl. Phys. Lett. (2004) (ee.bilkent.edu.tr/~aytur/papers/04apl1).

Ques: Why is the efficiency of the 1.3 μm Schottky RCE diode only 0.1% even though the cavity gives a nine-fold enhancement?

The photon energy at 1.3 μm is below the band gap of GaAs, so the absorption occurs in the 10 nm Au layer and the carriers cross the barrier by internal photoemission, with the yield proportional to $(h ν - ϕ_{B})^{2}$ (the Schottky-Barrier Photodiode page). A thin metal film absorbs a very small fraction per pass, and the cavity multiplies this by about 9, which gives a peak of 0.1%. The GaAs Schottky diodes with efficiencies of 50% and 75% presumably absorb band to band (assumed: the table gives no wavelength and probably refers to the first window near 0.85 μm). Their bandwidths are 50 GHz and 60 GHz, while the 1.3 μm device gave 20 GHz from a 16 ps response limited by the set-up (an estimated 50 GHz); a 16 ps pulse corresponds to 27 GHz (computed), so the 20 GHz is a limit of the measurement. Reference: High-speed GaAs-based resonant-cavity-enhanced 1.3 μm photodetector, Bilkent University (ee.bilkent.edu.tr/~aytur/papers/00apl1); Ultrafast and highly efficient resonant cavity enhanced photodiodes, SPIE ITCom 2003, DOI 10.1117/12.511202 (abstract).

Ques: Why is the back mirror the main difficulty for RCE diodes at 1.55 μm?

The number of pairs for a given reflectivity grows as the index step shrinks, because $x = (n_{L} / n_{H})^{2 N}$ must be small. With GaAs/AlAs ( $n_{H} = 3.5$ , $n_{L} = 3.0$ ) 15 pairs give 96% and 20 pairs 99%, whereas InGaAs/InAlAs ( $n_{H} = 3.45$ , $n_{L} = 3.2$ ) gives 23% with 7 pairs, 95% with 29 pairs and 99% with 40 pairs (computed). The Laser Focus World article notes that none of the systems for 1.55 μm (InP/InGaAs/InAlAs, AlAs/GaAs/Ge, Si/SiGe) matches GaAs/AlGaAs, and the Kaniewski device compensates with a hybrid back mirror of nine SiO $_{2}$ /Si $_{3}$ N $_{4}$ pairs plus Au, $R = 0.995$ . The GaAs-based 1.55 μm diode uses 15 pairs of GaAs (113.6 nm) and AlAs (134.3 nm), with a high-reflectivity band from about 1450 nm to 1650 nm. Reference: Laser Focus World, Demand for high-speed detectors drives research (1998); Kaniewski, Muszalski, Piotrowski, Optica Applicata 37 (2007) 405 (dlibra.kdm.wcss.pl, optappl_3704p405); B. Butun et al., High-speed 1.55 μm operation of low-temperature-grown GaAs-based resonant-cavity-enhanced p-i-n photodiodes, Appl. Phys. Lett. (2004) (ee.bilkent.edu.tr/~aytur/papers/04apl1).

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