Photon-pair Generation in Chalcogenide Glass

Role of Waveguide Linear Absorption

Nuno A. Silva

1,2

and Armando N. Pinto

1,2

Department of Electronics, Telecommunications and Informatics, University of Aveiro, 3810-193 Aveiro, Portugal

Instituto de Telecomunicac¸

oes, 3810-193 Aveiro, Portugal

Keywords:

Quantum Correlated Photon-pairs, Raman Scattering, Spontaneous Four-wave Mixing, Waveguide Absorp-

tion.

Abstract:

We investigate the impact of waveguide loss on the generation rate of quantum correlated photon-pairs through

four-wave mixing in a chalcogenide glass ﬁber. The obtained results are valid even when the photon-pairs are

generated in a medium with non-negligible loss, αL  1. The impact of the loss is quantiﬁed through the

analysis of the true, total and accidental counting rates at waveguide output. We use the coincidence-to-

accidental ratio (CAR) as a ﬁgure of merit of the photon-pair source. Results indicate that, the CAR parameter

tends to decrease with the increase of the waveguide length, until L < 1/α. However, a continuous increase of

the waveguide length tends to lead to an increase on the CAR value. In that non-negligible loss regime, αL  1,

we are able to observe a signiﬁcant decrease on the value of all coincidence counting rates. Nevertheless, that

decrease is even more pronounced on the accidental counting rate. Moreover, for waveguide length L = 10/α

we are able to obtain a CAR of the order of 70, which is higher than the CAR value for the speciﬁc case of

α = 0 with L = 2 cm, i.e. CAR=42. This indicates that the waveguide loss can improve the degree of quantum

correlation between the photon-pairs.

1 INTRODUCTION

Quantum correlated photon-pairs are important re-

sources in the ﬁeld of quantum communica-

tions (Gisin et al., 2002). That correlated photon-

pairs can be used to implement heralded single photon

sources (Castelletto and Scholten, 2008) or entangled

photon sources (Yuan et al., 2010). In both cases, that

kind of sources are important elements in quantum

key distribution applications (Gisin et al., 2002). The

four-wave mixing process (FWM) can provide a so-

lution to obtain quantum correlated photon-pairs al-

ready inside of optical waveguides (Fiorentino et al.,

2002; Lin et al., 2007). Moreover, when implemented

in a chalcogenide glass ﬁber (As

) the FWM pro-

cess appears as a natural solution to implement on-

chip quantum technologies for generation of quantum

states (Ta’eed et al., 2007; Eggleton et al., 2012; He

et al., 2012). This due to the fact that the chalco-

genide glass presents a high value of nonlinear param-

eter (Lamont et al., 2008), that allows efﬁcient gener-

ation of photon-pairs through FWM over very short

distances, and an almost negligible two-photon ab-

sorption process (Lamont et al., 2008). Moreover, that

glass also presents a low Raman-gain window, which

is essential to reduce the generation rate of uncorre-

lated photons (Xiong et al., 2010; Xiong et al., 2011;

Lin et al., 2007), and a high photosensitivity (Eggle-

ton et al., 2012).

Recently, in (Xiong et al., 2010; Xiong et al.,

2011; Clark et al., 2012) authors investigate the gen-

eration of correlated photon-pairs in As

chalco-

genide glass through FWM process. Nevertheless,

those studies were performed in the limit L  1/α,

where L is the waveguide length, and α is the loss

coefﬁcient. In that regime the loss can be neglected.

In this work, we report theoretically the impact of

waveguide loss on the generation of quantum corre-

lated photon-pairs through FWM process, in As

chalcogenide glass ﬁber. We achieve a coincidence-

to-accidental ratio of the 70, for αL = 10 and for

a pump power of 0.5 W, at waveguide input. We

demonstrate that the difference between total coinci-

dences and true coincidences decreases with the in-

crease of αL, which can be very important for future

implementation of on-chip quantum technologies.

This paper contains four sections. Section 2 deals

with the theoretical model that describes the genera-

tion of the photon-pairs inside a chalcogenide glass

ﬁber with non-negligible loss through spontaneous

A. Silva N. and N. Pinto A..

Photon-pair Generation in Chalcogenide Glass - Role of Waveguide Linear Absorption.

DOI: 10.5220/0004651400050010

In Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2014), pages 5-10

ISBN: 978-989-758-008-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Chalcogenide

Glass Fiber

Signal

Idler

Pump

Signal Idler

AWG

TBPF

Det

TIA

Pump

Figure 1: Schematic representation of the spontaneous

FWM process in a chalcogenide glass ﬁber as a source of

correlated photon-pairs. Details of the setup are presented

in the text.

FWM process. Section 3 reports the obtained theo-

retical results. The ﬁnal section summarizes the main

conclusions of this work.

2 THEORY

In the FWM process, two pump photons (ω

) are an-

nihilated and two new are created, one at Stokes fre-

quency ω

(know as idler ﬁeld), and other at anti-

Stokes frequency ω

(known as signal ﬁeld), such that

2ω

= ω

+ ω

. In Fig. 1, we present a schematic

representation of the spontaneous FWM process in a

chalcogenide glass ﬁber as a source of quantum corre-

lated photon-pairs. Inside the waveguide and simulta-

neously with the FWM are also generated noise pho-

tons through the Raman scattering process. In Fig. 1,

an unique pump ﬁeld is sent a chalcogenide glass ﬁber

in order to induce the spontaneous FWM process. At

waveguide output the signal and idler photons gen-

erated through FWM and Raman scattering, plus the

pump ﬁeld passes through an arrayed waveguide grat-

ing (AWG) to separate the optical ﬁelds. The signal

photons are spectrally ﬁltered by a tunable band-pass

ﬁlter (TBPF) centered at

and collected by the pho-

ton counting module, Det

. The idler photons passes

through a TBPF centered at

and collected by the

photon counting module, Det

. The central frequen-

cies of the ﬁlters are chosen such that 2ω

The output signals from the two photon detectors in

Fig. 1 are collected by a time interval analyzer (TIA)

in order to measure the coincidences.

For a ﬁlter bandwidth, ∆ω

, much narrower than

its mid-frequency, ∆ω

 ω

, the ﬂux of signal and

idler photons at chalcogenide waveguide output is

given by (Silva and Pinto, 2012; Silva and Pinto,

2013; Lin et al., 2007)

= h

†

(L,τ)

(L,τ)i ≈ ∆ν

(L), (1)

where

(L,τ) is the ﬁeld annihilation operator, and

∆ν

is given by

∆ν

2π

dω

(ω

−

(2)

with H

(ω

−

) being a ﬁlter function centered at

, with u = s or i representing the signal or idler

ﬁeld. In (1), F

(L) is given by (Silva and Pinto, 2012;

Silva and Pinto, 2013; Lin et al., 2007)

(L) = |ν

(L,0)|

+ α

dz|µ

(L,z)|

+α

+1)

dz|ν

(L,z)|

+(N

+Θ

)|g

(Ω



(z)µ

(L,z)−

∗

(z)ν

(L,z)



, (3)

where L is the waveguide length, α

is the loss coefﬁ-

cient at frequency

with u 6= v = s or i represents the

signal or idler ﬁeld, Θ(−Ω

) is the Heaviside step

function,

exp{~

/(k

T ) − 1}

, (4)

and

exp{~|Ω

|/(k

T ) − 1}

, (5)

where Ω

− ω

, k

is the Boltzmann constant,

T is the waveguide temperature, and ~ = h/(2π) with

h representing the Planck constant. In (3), g

(Ω

) is

the Raman gain coefﬁcient, A

is the pump ﬁeld enve-

lope function, such that P

(L) = |A

(L)|

represents

the pump power at a distance L in the waveguide, and

(L,z) and µ

(L,z) are deﬁned in (Voss et al., 2006;

Silva and Pinto, 2012; Silva and Pinto, 2013).

The cross correlation between the signal and idler

photons is given by (Silva and Pinto, 2012; Silva and

Pinto, 2013; Lin et al., 2007)

(2)

(si)

(τ) = h

†

(L,t)

†

(L,t + τ)

(L,t)i

≈ |φ

(τ)|

(L,

)

+ I

, (6)

where φ

(τ) is the ﬁlters cross correlation function

(τ) =

2π

dωH

(ω −

(

− ω)e

−iωτ

, (7)

and (Silva and Pinto, 2012; Silva and Pinto, 2013; Lin

et al., 2007)

(L,

) = µ

(L,0)ν

(L,0)+

+ 1)

dzµ

(L,z)ν

(L,z)

+ α

dzν

(L,z)µ

(L,z)− (N

+ Θ

)|g

(Ω



(z)µ

(L,z)−

∗

(z)ν

(L,z)





(z)µ

(L,z)−

∗

(z)ν

(L,z)



dz. (8)

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

From (6) we can deﬁne the total coincidence count-

ing rate, R

, the accidental coincidences, R

, and the

true coincidence counting rate, R

, as follows

(2)

(si)

(τ)dτ

≈

|φ

(τ)|

dτ



(L,

)

+ I



(9a)

dτ ≈ (∆ν

∆ν

(L)F

(L) (9b)



(2)

(si)

(τ) − I



dτ

≈

|φ

(τ)|

dτ



(L,

)



, (9c)

where t

is the coincidence time window (Lin et al.,

2007). Moreover, we can deﬁne the coincidence-to-

accidental ratio as (Silva and Pinto, 2012; Silva and

Pinto, 2013; Lin et al., 2007)

CAR =

, (10)

which is a ﬁgure of merit of the source of correlated

photon-pairs (Chen et al., 2006). We admit that the

signal and idler ﬁlters are rectangular shaped, and

they have the same optical bandwidth, ∆ω

= ∆ω. In

that case

(τ) = ∆ω sinc



∆ωτ



−i

, (11)

and

|φ

(τ)|

dτ = 2

cos(∆ωτ) − 1 + (∆ωt

)Si (∆ωt

)

(12)

where

Si(∆ωt

) =

∆ωt

sinc(t)dt, (13)

is the sine integral function. Moreover, ∆ν

in (1) is

given by ∆ω

/(2π).

3 RESULTS

In this section we present the results for the genera-

tion of photon-pairs inside the chalcogenide waveg-

uide through FWM process. We present results for

the signal and idler photon ﬂuxes as a function of the

frequency detuning between pump and signal ﬁelds.

We analyze the impact of the waveguide loss on the

evolution of the CAR with the frequency detuning be-

tween pump and signal ﬁeld, and with the waveguide

0 2 4

8 10 12 14

Ω

/ 2π (THz)

1e+04

1e+05

1e+06

1e+07

1e+08

1e+09

1e+10

Photon flux (Hz)

Idler flux

Signal flux

Only FWM, f

= 0

Low FWM efficiency

window

Figure 2: Signal and Idler photon ﬂuxes for L = 2 cm and

α = 0. When f

= 0, the Raman scattering process is ig-

nored.

0 2 4

8 10 12 14

18 20

Ω

/ 2π (THz)

Raman gain (W

-1

)

Low-Raman

window

Figure 3: Raman gain coefﬁcient for the chalcodenide glass.

length. Moreover, we also present results for the evo-

lution of the coincidence counts with the waveguide

length.

The pump wavelength used in this work is λ

1550 nm. We assume that all ﬁelds have the same loss

coefﬁcient α

= α

= 60 dB/m, and the waveg-

uide nonlinear parameter is γ = 10 W

−1

/m (Lamont

et al., 2008). The chalcogenide glass ﬁber group-

velocity dispersion at 1550 nm is D

= 29 ps/nm/km

(β

= −3.7 × 10

−26

/m) (Lamont et al., 2008). The

Raman response functions were taken from (Xiong

et al., 2009; Lamont et al., 2008), with τ

= 15.5 fs,

= 230.5 fs, and f

= 0.11. The chalcogenide glass

ﬁber is at room temperature, T = 300 K. We con-

sider ideal rectangular signal and idler ﬁlters with

equal bandwidths of ∆ω/(2π)=50 GHz, and a coin-

cidence time window of t

= 16 ps. Finally, we adopt

a pump power at chalcogenide waveguide input of

(0) = 0.5 W.

In Fig. 2 we present the individual signal and idler

photon ﬂuxes given by (1), as a function of pump-

signal frequency detuning. In the ﬁgure when f

= 0,

Photon-pairGenerationinChalcogenideGlass-RoleofWaveguideLinearAbsorption

45 50 55 60 65

Waveguide length (cm)

1e+08

2e+08

3e+08

4e+08

5e+08

Counting rate (Hz)

Accidental coincidences

Total coincidences

True coincidences

50 55 60 65

0e+00

2e+04

4e+04

6e+04

8e+04

1e+05

αL = 1

Figure 4: Coincidence counting rate as a function of waveg-

uide length, for Ω

/2π = 1.5 THz, with f

= 0.11.

the Raman scattering process is ignored. It can be

seen in Fig. 2 that for small values of frequency detun-

ing most of the photons generated inside the waveg-

uide are due to the FWM process. In that scenario, the

photon ﬂuxes for f

= 0.11 and for f

= 0 are almost

equal. Results also show that, when f

= 0 the signal

and idler photon ﬂuxes rapidly decreases with the in-

crease of the frequency detuning. This is due to the

fact that the phase matching condition ∆β ≈ Ω

in (1) starts to deviates from its minimum value, and

consequently the FWM is no longer efﬁcient for high

values of frequency detuning (Agrawal, 2001). How-

ever, when we consider the Raman scattering process,

the signal and idler photon ﬂuxes increase with the

increase of the frequency detuning, until Ω

/2π <

10 THz. That is due to the fact that we are approach-

ing the Raman gain peak for the chalcogenide waveg-

uide. Due to that we deﬁne a low efﬁciency window

for the FWM process for Ω

/2π > 8 THz.

Figure 3 presents the Raman gain coefﬁcient as

a function of frequency detuning for the chalco-

genide glass ﬁber. Since the Raman scattering signif-

icantly degrades the quality of the correlated photon-

pair source (Lin et al., 2007), we identify two ideal

regimes where the Raman gain coefﬁcient assumes a

small value, Ω

/2π < 5 THz, and Ω

/2π > 16 THz.

From Fig. 2 and Fig. 3, we can deﬁne a frequency re-

gion, Ω

/2π < 5 THz, where the FWM is highly ef-

ﬁcient, and the Raman scattering process exhibits low

efﬁciency window.

Figure 4 presents the evolution of the R

, R

and R

parameters given by (9), with the waveguide

length, L. Results show that, all the counting rates

presented in Fig. 4 increases with the increase of L,

until L ≈ 1/α. The increase of R

with the waveg-

uide length (and consequently the increase of R

)

is due to the stimulated FWM and Raman scatter-

ing processes, which generate uncorrelated photons.

0 1 2 3 4

Ω

/ 2π (THz)

CAR

L = 2.0 cm, αL = 0

L = 3.6 cm, αL = 0.5

L = 7.2 cm, αL = 1

L = 36 cm, αL = 5

L = 72 cm, αL = 10

Figure 5: Coincidence-to-Accidental ratio as a function of

frequency detuning, with f

= 0.11.

The increase of R

with L is due to the increase of

the FWM efﬁciency with the waveguide length. Nev-

ertheless, the increase of the accidental coincidences

with the waveguide length is much lower than the in-

crease of the total and true coincidences. It can also

be seen in Fig. 4 that, a continuous increase of L leads

to a rapidly decrease of all counting rates. This is due

to the waveguide loss coefﬁcient that starts to absorb

most of the generated photons inside the waveguide.

Moreover, the loss coefﬁcient also decrease the pump

power that evolves in the waveguide, which avoids

the generation of photons from stimulated FWM pro-

cess and Raman scattering. For αL  1 the effective

waveguide length is much smaller than its length. It

can also be seen in the inset present in Fig. 4 that,

when L  1/α the R

and the R

parameters are

almost equal. Moreover, in that regime the acciden-

tal counting rate is almost negligible when compared

with R

or R

. This mean that, for L  1/α most of

the photons at waveguide output are signal-idler pairs,

which reveals the high purity nature of the photon-

pair source in this non-negligible loss regime.

Figure 5 presents the CAR given by (10) as a

function of frequency detuning, for several values of

waveguide length. In Fig. 5 we also present results

for the speciﬁc case α = 0 and L = 2 cm. Results

show that for all cases the CAR parameter tends to de-

creases with the increase of Ω

/2π. This is due to the

loss of efﬁciency of the FWM process with the evo-

lution of the frequency detuning. Results also show

that for small values of Ω

/2π, the CAR value de-

creases with the increase of αL, until αL = 1. After,

the CAR starts to increase, and for αL = 10, we are

able to obtain CAR=70, which is much more higher

than the CAR for α = 0 and L = 2 cm, CAR=42. This

is due to the fact, increasing the waveguide length the

parameter tends to zero more rapidly than the R

or R

parameters. Moreover, the results present in

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

45 50 55 60 65

Waveguide length (cm)

CAR

αL = 1

Figure 6: Coincidence-to-Accidental ratio as a function of

waveguide length, for Ω

/2π = 1.5 THz, with f

= 0.11.

Fig. 5 are in line with recent reported experimental re-

sults for the CAR parameter in waveguides with non-

negligible loss coefﬁcient (Xiong et al., 2012).

Finally, in Fig. 6 we present the evolution of the

CAR with the waveguide length. Results show that

the CAR decreases with the increase of L, until L ≈

1/α. That decrease of the CAR with L is due to the

increase on the probability of generating signal and

idler photons through stimulated FWM. That evolu-

tion of the CAR parameter is in line with previous

reported experimental results (Harada et al., 2010).

Nevertheless, a continuous increase of L tends to lead

to an increase of the CAR, until L ≤ 10/α. This is due

to the fact that R

decreases more rapidly with L than

, see Fig. 4. When L  1/α, the CAR assumes an

equal or even a higher value than when L ≤ 1/α. In

that non-negligible loss regime the waveguide absorbs

most of the pump photons, decreasing in that case the

probability of generating uncorrelated photons from

stimulated FWM and Raman scattering processes.

4 CONCLUSIONS

In summary, we investigate the impact of linear loss

on the generation of quantum correlated photon-pairs

in a chalcogenide glass ﬁber. We deﬁne a frequency

regime where the FWM is highly efﬁcient and the

Raman gain coefﬁcient assumes a small value. We

show that the CAR value decrease with the increase

of the frequency detuning between pump and signal

ﬁeld, due to the loss of efﬁciency of the FWM pro-

cess. Moreover, the CAR parameter tends to decrease

with the increase of αL, until L . 1/α. That decrease

on the CAR parameter is mainly due to the increase

of the accidental counting rate. The increase of the

accidental counting rate with the waveguide length is

due to the generation of uncorrelated photons through

stimulated FWM and Raman scattering. After that,

αL > 1, the CAR parameter tends to increase with

the continuous increase of the waveguide length, until

αL = 10. In a non-negligible loss regime, αL > 1, the

total and true coincidence counting rates tends to be

equal, which leads to an increase on the CAR value.

In that case, our ﬁndings show that the presence of a

waveguide with non-negligible loss parameter tends

to improve the quality of the source, when compared

with the limit α = 0. More speciﬁcally, for αL = 10

we are able to obtain a CAR value higher than for

αL = 0, with L = 2 cm.

In waveguides with non-negligible loss we ob-

serve a signiﬁcantly decrease on the generation rate

of signal-idler photon pairs, when compared with the

regime αL  1. Nevertheless, in that regime our anal-

ysis shows that the coincidence counting rate can be

higher than 10 kHz, for a CAR value of the order of

70.

ACKNOWLEDGEMENTS

This work was supported in part by the FCT -

Fundac¸

ao para a Ci

encia e a Tecnologia, through the

PhD Grant SFRH/BD/63958/2009, by the FCT and

European Union FEDER - Fundo Europeu de Desen-

volvimento Regional, through project PTDC/EEA-

TEL/103402/2008 (QuantPrivTel), and by the FCT

and the Instituto de Telecomunicac¸

oes, under the

PEst-OE/EEI/LA0008/2011 program, project “P-

Quantum”.

REFERENCES

Agrawal, G. (2001). Nonlinear Fiber Optics. Academic

Press, 3 edition.

Castelletto, S. A. and Scholten, R. E. (2008). Heralded sin-

gle photon sources: a route towards quantum commu-

nication technology and photon standards. The Euro-

pean Physical Journal Applied Physics, 41:181–194.

Chen, J., Lee, K. F., Liang, C., and Kumar, P. (2006). Fiber-

based telecom-band degenerate-frequency source of

entangled photon pairs. Opt. Lett., 31(18):2798–2800.

Clark, A. S., Collins, M. J., Judge, A. C., M

agi, E. C.,

Xiong, C., and Eggleton, B. J. (2012). Raman scat-

tering effects on correlated photon-pair generation in

chalcogenide. Opt. Express, 20:16807–16814.

Eggleton, B., Vo, T., Pant, R., Schr, J., Pelusi, M.,

Yong Choi, D., Madden, S., and Luther-Davies, B.

(2012). Photonic chip based ultrafast optical process-

ing based on high nonlinearity dispersion engineered

chalcogenide waveguides. Laser & Photonics Re-

views, 6:97–114.

Photon-pairGenerationinChalcogenideGlass-RoleofWaveguideLinearAbsorption

Fiorentino, M., Voss, P., Sharping, J., and Kumar, P. (2002).

All-ﬁber photon-pair source for quantum communica-

tions. Photonics Technology Letters, IEEE, 14(7):983

–985.

Gisin, N., Ribordy, G., Tittel, W., and Zbinden, H. (2002).

Quantum cryptography. Rev. Mod. Phys., 74(1):145–

195.

Harada, K., Takesue, H., Fukuda, H., Tsuchizawa, T.,

Watanabe, T., Yamada, K., Tokura, Y., and Itabashi, S.

(2010). Frequency and polarization characteristics of

correlated photon-pair generation using a silicon wire

waveguide. Selected Topics in Quantum Electronics,

IEEE Journal of, 16(1):325–331.

He, J., Xiong, C., Clark, A. S., Collins, M. J., Gai, X., Choi,

D.-Y., Madden, S. J., Luther-Davies, B., and Eggle-

ton, B. J. (2012). Effect of low-raman window posi-

tion on correlated photon-pair generation in a chalco-

genide Ge

11.5

64.5

nanowire. Journal of Ap-

plied Physics, 112:123101.

Lamont, M. R., Luther-Davies, B., Choi, D.-Y., Madden,

S., and Eggleton, B. J. (2008). Supercontinuum gen-

eration in dispersion engineered highly nonlinear(γ =

10 /w/m) As

chalcogenide planar waveguide. Opt.

Express, 16:14938–14944.

Lin, Q., Yaman, F., and Agrawal, G. P. (2007). Photon-pair

generation in optical ﬁbers through four-wave mix-

ing: Role of Raman scattering and pump polarization.

Phys. Rev. A, 75(2):023803.

Silva, N. and Pinto, A. (2013). Effects of losses and non-

linearities on the generation of polarization entangled

photons. Lightwave Technology, Journal of, 31:1309–

1317.

Silva, N. A. and Pinto, A. N. (2012). Role of absorption

on the generation of quantum-correlated photon pairs

through FWM. Quantum Electronics, IEEE Journal

of, 48:1380 –1388.

Ta’eed, V., Baker, N. J., Fu, L., Finsterbusch, K., Lam-

ont, M. R. E., Moss, D. J., Nguyen, H. C., Eggleton,

B. J., Choi, D.-Y., Madden, S., and Luther-Davies, B.

(2007). Ultrafast all-optical chalcogenide glass pho-

tonic circuits. Opt. Express, 15:9205–9221.

Voss, P. L., K

opr

u, K. G., and Kumar, P. (2006). Raman-

noise-induced quantum limits for χ(3) nondegenerate

phase-sensitive ampliﬁcation and quadrature squeez-

ing. J. Opt. Soc. Am. B, 23(4):598–610.

Xiong, C., Helt, L. G., Judge, A. C., Marshall, G. D.,

Steel, M. J., Sipe, J. E., and Eggleton, B. J.

(2010). Quantum-correlated photon pair generation

in chalcogenide As

waveguides. Opt. Express,

18(15):16206–16216.

Xiong, C., Magi, E., Luan, F., Dekker, S., Sanghera, J.,

Shaw, L., Aggarwal, I., and Eggleton, B. (2009). Ra-

man response in chalcogenide As

ﬁber. In Opto-

Electronics and Communications Conference, 2009.

OECC 2009. 14th, pages 1–2.

Xiong, C., Marshall, G. D., Peruzzo, A., Lobino, M., Clark,

A. S., Choi, D.-Y., Madden, S. J., Natarajan, C. M.,

Tanner, M. G., Hadﬁeld, R. H., Dorenbos, S. N., Zi-

jlstra, T., Zwiller, V., Thompson, M. G., Rarity, J. G.,

Steel, M. J., Luther-Davies, B., Eggleton, B. J., and

O’Brien, J. L. (2011). Generation of correlated pho-

ton pairs in a chalcogenide As

waveguide. Applied

Physics Letters, 98(5):051101.

Xiong, C., Monat, C., Collins, M., Tranchant, L., Pe-

titeau, D., Clark, A., Grillet, C., Marshall, G., Steel,

M., Li, J., O’Faolain, L., Krauss, T., and Eggleton,

B. (2012). Characteristics of correlated photon pairs

generated in ultracompact silicon slow-light photonic

crystal waveguides. Selected Topics in Quantum Elec-

tronics, IEEE Journal of, 18(6):1676–1683.

Yuan, Z.-S., Bao, X.-H., Lu, C.-Y., Zhang, J., Peng, C.-Z.,

and Pan, J.-W. (2010). Entangled photons and quan-

tum communication. Physics Reports, 497:1 – 40.

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