Lasers, solid-state; (140.3945) Microcavities; (140.5680) Rare earth and transition metal solid-state lasers.
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1. Introduction
Chalcogenide glasses (ChGs) are distinguished for having chemical durability,
photosensitivity, high refractive index, low phonon energy, low melting temperature, and
broad infrared transparency [1–3]. Such characteristics make this family of glass attractive for
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11952
the development of infrared integrated optical devices [4–6]. Integration of multiple
monolithic components on a single substrate is beneficial for minimization of size and cost by
enabling systems-on-chip applications. A key enabler for such systems is the demonstration of
monolithic light sources emitting in various wavelength regimes.
Rare earth (RE) elements are incorporated as active emission centers in passive crystalline
and amorphous materials. Many RE transitions are generally quenched in hosts such as
phosphate and silica glasses which have high phonon energies that can bridge low energy
gaps and cause large multi-phonon relaxation rates [7,8]. On the other hand, ChGs have
relatively low phonon energies which reduce the possibility of these non-radiative relaxations
and enable emission of long wavelengths.
RE elements have been incorporated into bulk ChGs and thin films to emit near-infrared,
mid-infrared and far-infrared light [9–15]. Moreover, lasing in RE-doped ChGs fibers,
waveguides, and micro-spheres has been reported. In particular, Nd-doped gallium lanthanum
sulfide (GLS) fibers and laser written waveguides in bulk glass at 1080 nm [16–19]; Nd and
Tm-doped tellurite micro-spheres at 1060 nm and 2 µm, respectively [20–22]; and most
recently Nd-doped GLS micro-sphere at 1080 nm [23]. Also, a theoretical study showed the
feasibility of lasing at 4.5 µm in erbium-doped photonic crystal fibers [24]. However, to date,
no monolithic ChG laser has been demonstrated or investigated.
In this paper, we present our simulation results toward developing a monolithic MIR laser
source, utilizing erbium-doped GLS glass. Bulk erbium-doped GLS showed MIR
photoluminescence emission at 4.5 µm through the transition between 4I9/2 and
4I11/2 energy
levels [25]. Compared to other ChG glasses, GLS is capable of hosting relatively high erbium
concentrations (2.8 × 1020
ions/cm3) without being affected by luminescence quenching [25].
Nevertheless, the considered transition is characterized by a small emission cross section of
2.5 × 1021
cm2. This limits the maximum possible gain to less than 4 dB/cm. For lasing to be
possible under this gain limitation, resonators with minimum quality (Q) factors of 3.5 × 104
are required.
Recently, lift-off and thermal reflow process has been used to demonstrate ChG micro-
disks with Q factors in excess of 105 at 1.55 μm [26]. This is a catalyst for fabricating
monolithic laser sources given the aforementioned specification requirements. In the
subsequent text, lasing at 4.5 µm is examined with 800 nm pumping for erbium-doped GLS
micro-disk. The rate equations of erbium, the pump, and signal disk modes were solved, and a
transfer matrix formulation was used to estimate the output lasing power.
2. Simulation model
The developed model considers pump and signal modes that correspond to wavelengths of
800 nm and 4.5 µm, respectively. Separate bus waveguides introduce and collect the pump
and signal light from the disk as illustrated in Fig. 1. Also, the following constants and
assumptions were used: 1) uniform erbium doping concentration of 2.8 × 1020
cm3
; 2) disk
structure of 80 µm diameter and 600 nm thickness; 3) refractive indices of 2.42 and 2.35 at
the pump and signal wavelengths, respectively, were obtained by fitting experimental data to a
Cauchy relation [27]; 4) transverse electric (TE) polarization modes, with dominant electric
component parallel to the disk plane, were included; 5) Purcell cavity enhancement is
neglected since the photon density in the cavity is high and the micro-disk structure has high
order modes with large radiation; and 6) unidirectional mode propagation was considered.
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11953
P1, S1
P2, S2
P4, S4
P3, S3
Pin
Sin = 0 Sout
𝛋𝐏𝟐
𝛋𝐬𝟐
Fig. 1. Laser configuration consists of a micro-disk with input pump waveguide and output
signal waveguide. P is the pump power and S is the signal power at the positions indicated by the subscripts, κ2 is the power coupling coefficient between the bus waveguides and the disk,
and the subscripts P and S stand for the pump and signal, respectively.
We establish some useful considerations, to ease the development of our model. Since the
disk has a relatively large diameter, the free spectral range will be less than the emission and
absorption line-widths of erbium. Hence, resonance can be assumed for the pump and signal
modes. Also, for the continuous wave (CW) case, steady state condition is imposed. With
these assumptions and no input signal, the internal power in the disk can be related to the
power in the pump and signal buses through the following relations [28]:
2
1
22 2
.
1 (1 )
P
inP P
P
Pa
(1)
2
2.out SS S (2)
where 2
Pa is the round trip power absorption for the pump mode, Pi is the pump power and Si
is the signal power at the positions indicated by the subscripts, 2
,P S is the power coupling
coefficient between the bus waveguides and the disk and the subscripts P and S stands for the
pump and signal, respectively. We can also eliminate the inter-effect of the signal and pump
bus waveguides on the disk pump and signal modes, respectively, by recognizing the
following. The signal mode has much longer wavelength than the pump mode. Therefore, it
possesses a greater evanescent tail length. Hence, the signal bus can be placed far from the
pump mode tail which prevents pump out-coupling. In addition, since the pump light has a
short wavelength, the pump bus can be designed with a width smaller than the signal cutoff.
Hence, the pump bus will also have no coupling with the signal mode. Then, P3 and S1 will be
equal to P2 and S4, respectively. P4 and S2 are related to P1 and S3 by Beer–Lambert law and
the signal coupling coefficient according to the following relations [28,29]:
4
1
4 1 . .
l
M
P
l
P PExp l dl
(3)
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11954
2
1
4
3
2 1
1 4 3
( ). ,
( ). .
l
M M
S S
l
l
M M
S S
l
S S Exp l g l dl
S S S Exp l g l dl
(4)
2
3 2 (1 ).SS S (5)
where l is the azimuthal coordinate along the disk circumference, / ( )M
P S l and ( )M
Sg l are the
absorption and gain coefficients of the pump (P) and signal (S) modes at l. From Eq. (4) and
Eq. (5):
4 2
3 1
2( ). ( ). ln(1 ).
l l
M M M M
S S S S S
l l
l g l dl l g l dl (6)
this equation defines the condition that should be satisfied for the steady state (CW) lasing
case. The out coupled signal power should be exactly recovered by the round trip gain. For
smaller gain, lasing is not possible, while higher gain values do not satisfy the steady state
condition.
The energy evolution of erbium is described using the five-level model as elaborated in
Fig. 2 [30,31]. The ion-ion and ion-photon interactions with the pump and signal light are
calculated according to the subsequent rate equations:
2 21
22 2 14 1 4 33 3 16 1 5 24 2 4
5
1 1 2 2
2
2 22
22 2 14 1 4 16 1 5 44 4
3
24 2 4 2 21 2 3 3 2 2
5
523
33 3 3 4 3
4
( ) ,
2 2
,
2
e a P
P P i i
iP
i i
i
a eS S
S S i i
iS S
dNC N C N N C N C N N C N N
dt
IN a N W N
dNC N C N N C N N C N
dt
C N N a N a N W N W N
dN I IC N N N a N a
dt
2
3 3 4 4 3 3
1
2 24
22 2 14 1 4 16 1 5 44 4 24 2 4 3 4
3
1 4 54 5 4 4 5 5 4 4
1
42 25
33 3 16 1 5 44 4 24 2 4 5 5 5 5
1
5
1
,
- - 2 - ( - )
( - ) - ,
,
.
i
i
a e S
S S
S
a e P
P P i
iP
i
i
i Total
i
N W N W N
IdNC N C N N C N N C N C N N N N
dt
IN N a N a N W N W N
dNC N C N N C N C N N a N W N
dt
N N
(7)
where Ni is the ion concentration at energy level i, IS/P is the signal or pump beam intensity,
ħωS/P is the photon energy, Cij are the energy transfer coupling coefficients that quantify the
ion-ion interactions, /
/
e a
S P is the emission (e) or absorption (a) cross section, aij is the
spontaneous emission rate from level i to level j, Wi is the multi-phonon decay rate from level
i to the next lower energy level, and NTotal is the total erbium doping concentration. The values
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11955
of the energy transfer constants are obtained experimentally [30]. The energy gap law is used
to evaluate the multi-phonon decay rates [32]. The spontaneous emission rate is obtained
using Judd-Ofelt theorem [33]. Finally, McCumber and Füchtbauer-Ladenburg relations are
used to calculate the emission and absorption cross sections at the pump and signal
wavelengths [34,35]. The values of these parameters are provided in the appendix (Table 2).
4I15/2
4I13/2
4I11/2
4I9/2
4F9/2, 4S3/2,
4H11/2, 4F7/2
4F9/2
5
4
3
2
1
6,451
cm-1
10,204
12,400
15,150
Signal
Pu
mp
C22 C14
C33
C16
C44
C24
Fig. 2. Erbium energy levels and ion-ion interaction parameters (Cij). 800 nm pump source excites the ions from the ground state to 4I9/2. The excited ions decay to 4I11/2 to emit 4.5 µm
signal light.
Rosenbrock iterative method was used to find the steady state population distribution of
the ions. The signal gain coefficient (gS), and the pump absorption coefficient due to erbium
(αP,Er), are functions of the pump and signal intensities. These coefficients are given, per unit
area, by the following equations [29]:
4 3
e a
S S Sg N N (8)
, 1 4
a e
P Er P PN N (9)
The cavity modes were calculated for the disk cross section in Fig. 3. A CaF2 substrate
was assumed for its low absorption in the MIR regime. As moisture can be trapped in CaF2, a
GLS thin film to coat the entire substrate was taken into account. To reduce the signal
radiation losses, a large diameter of 80 microns was assumed. Reducing the thickness of the
disk minimizes scattering from the side walls while it increases the signal radiation losses.
Signal radiation was found to be insignificant for a disk thickness of 0.6 µm and a substrate
coating layer of 0.1 µm thickness. A full-vectorial finite difference mode solver on
FIMMWAVE was used to calculate the disk mode profiles at the signal and pump
wavelengths [36]. Having azimuthal symmetry, the two-dimensional solution was calculated
for the disk cross section along the radial and planar directions.
Disk
Coating layer
Substrate
0.6 µm
0.1 µm
80µm
Fig. 3. The micro-disk material cross section showing a CaF2 substrate, and erbium-doped GLS
coating layer and disk. A CaF2 substrate was considered for its low absorption in the MIR regime. As moisture can be trapped in CaF2, a GLS coating layer was sandwiched between the
disk and the substrate (dimensions not drawn to scale for clarity).
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11956
For optical cavities, the Q factor (Q) is used to quantify the power loss relative to the
stored internal energy. An equivalent absorption coefficient (αeq) is obtained using the
following equation [37]:
2
.g
eq
n
Q
(10)
where ng is the group velocity of the mode, and λ is the free space wavelength. Volume
current formulation was used to estimate the mode scattering losses [38]. The Q factors were
evaluated based on preliminary experimental roughness parameters (10 nm roughness
amplitude and 150 nm correlation length) of the demonstrated high Q (due to thermal reflow)
ChG micro-disk [26]. Future fabrication and characterization studies will fine tune these
parameters. The radiation losses were quantified using a perfectly matched layer. The bulk
absorption coefficient of GLS (0.035 cm1
at 800 nm, and 0.006 cm1
at 4.5 µm [39]) was
multiplied by the mode confinement factor to arrive at the mode absorption losses. The signal
mode gain coefficient and pump mode absorption coefficient can be obtained using:
( , ), ( , ) ( , ). .M
S S S P S
DiskArea
g g I x y I x y f x y dxdy (11)
, , ( , ), ( , ) ( , ). .M
P Er P Er S P P
DiskArea
I x y I x y f x y dxdy (12)
where (x,y) is a coordinate point on the disk cross section, fS/P is the signal or pump mode
power profile normalized to 1 W. This detailed model was used to simulate the micro-disk
laser system under consideration. The simulation results are given in the next section.
3. Simulation results
Including the initial transient evolution of the mode powers and ion populations would require
large simulation time. For this reason, we developed a route which utilizes the previously
explained model to find a self consistent steady state solution. Initially, the signal gain was
calculated as a function of the signal and pump intensities using Eq. (7) and Eq. (8) (Fig. 4).
Linear interpolation was used later to find the gain for the intermediate points. The data range
was chosen to cover the saturation limits. This range was discretized such that the maximum
interpolation error is less than 0.2%. Erbium absorption of the pump light was also calculated
in the same way using Eq. (9).
Signal Intensity (W/m2)Pump Intensity (W/m2)
101
103
105107
109102
104106
108
0.4
0.8
1.2
0Sig
nal g
ain
(dB
/cm
)
Fig. 4. Steady state signal gain as a function of the pump and signal intensity for erbium doped
GLS with concentration of 2.8 × 1020 cm3.
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11957
The solutions of the fundamental signal mode and the first eight pump radial modes were
calculated, as shown in Fig. 5. For the different pump modes, there are several competing
factors affecting the obtained signal mode gain. First, the signal mode gain can be maximized
by using the pump mode for which the maximum signal intensity overlaps the area having the
maximum gain, i.e. highest pump intensity. However, as shown, the gain can decrease
drastically as the signal intensity increases. In addition, concentrating most of the pump power
at the signal intensity peak is of no benefit in the saturation region. Using the residual power
to pump larger area of the signal mode would result in higher signal mode gain. Since it is not
straightforward to identify the pump mode that results in the highest signal gain, the signal
gain values assoscieated with the considered pump modes should be identified and compared.
PTE11
35 36 37 38 39 400
0.7
PTE13
Heig
ht
from
the s
ubstr
ate
surf
ace (m
)
35 36 37 38 39 400
0.7
PTE15
35 36 37 38 39 400
0.7
PTE17
35 36 37 38 39 400
0.7
STE11
35 36 37 38 39 400
0.7
1.0
2.0
3.0
1.0
2.0
3.0
0.2
0.5
Radial length from the disk center (m)
W / m2
Fig. 5. Intensity distribution of the signal (S) and pump (P) modes with the total mode power
normalized to 1W. Polarization indicated by the subscripts. The first number is the planar index while the second is the radial index.
The signal mode gain was calculated as a function of the internal pump (Pi) and signal (Si)
power using Eq. (11). The mode intensity profiles were discretized into 50 segments per
micron which results in negligible error in estimating the intensity at each grid point. The gain
was interpolated at each grid point using the data obtained in Fig. 4. A comparison between
the obtained signal gain by exciting several pump modes is shown in Fig. 6. It is clear that
pumping the first order mode does not result in the highest possible gain. Higher values can be
achieved by pumping higher order modes. However, going beyond the 8th order mode (not
shown) minimizes the pump signal overlap (Fig. 5) and hence minimizes the signal mode
gain.
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11958
020
4060100
7550
250
0.2
0.4
0.6
Ga
in (
dB
/cm
)
Fig. 6. Signal mode gain obtained by exciting several pump modes with different radial orders. The gain is computed as a function of the internal signal (Si) and pump (Pi) modes powers.
The passive cavity Q factors and the equivalent absorption coefficients (Eq. (10)) of the
TE11 pump and signal modes are summarized in Table 1. As listed, the losses for both cases
are dominated by scattering. This loss is much greater for the pump mode due to its relatively
small wavelength. As explained in [38], the scattering losses are directly related to the mode
power amplitude within the scattering volume. For the considered pump modes, the difference
in this value was found very small (less than 1%). The pump modes also have ignorable
absorption and radiation losses similar to TE11. Consequently, these modes have close to
equal Q factors. For this reason and because the 7th order mode gives the highest possible
gain, it was chosen to pump the disk. Erbium absorption for the pump mode light was
quantified using Eq. (12) and found to be small at operational pumping power levels.
Table 1. Q factors and Equivalent Absorption Coefficients for the Fundamental Pump
and Signal Modes
Loss type Q Factor Equivalent absorption coefficient (dB/cm)
Pump Signal Pump Signal
Absorption 4.85 × 106 6.10 × 106 0.1607 0.0217
Radiation 1.79 × 108 3.00 × 107 0.0043 0.0043
Scattering 1.50 × 104 2.20 × 106 52.115 0.0565
Total 1.48 × 104 1.53 × 106 52.289 0.0825
The signal power in the disk was calculated as a function of the internal pump power and
the signal coupling coefficient. Due to high internal pump losses, the pump power, and hence
the signal gain, would show high variations along the disk circumference. Therefore, the disk
was discretized azimuthally into 1µm length segments at the disk circumference. The modes
were propagated through these segments, starting from P1 and S1 in Fig. 1 and using Eqs. (3)–
(5). The bisectional method was used to search for the signal power (S1) that satisfies the
steady state lasing conditions given by Eq. (6). The condition was tested for a maximum
tolerance of 0.1%. With the calculated Q factors and the maximum achievable signal gain, the
error in estimating the calculated power is not significant and therefore can be ignored.
The round trip pump power absorption, caused by erbium and the passive cavity losses,
was found to be ~75%. Based on Eq. (1), a pump coupling coefficient of 0.25 would
maximize the pump power accumulation in the disk (P1/Pin) and minimize the needed input
pump power (Fig. 7(a)). This coupling value was used in Eq. (1) to find the input pump power
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11959
(Pin) that corresponds to P1. Due to the high scattering losses, the maximum power
accumulation is limited to 4. This could be elevated by two orders of magnitude if the
scattering losses in the disk were eliminated as shown in Fig. 7(b).
10-3
10-2
10-1
100
10-2
10-1
100
101
102
103
Power coupling coefficient P
2
Po
we
r a
cc
um
ula
tio
n f
ac
tor
P1/P
in
(a) With scattering
(b) No scattering
Fig. 7. Pump power accumulation as a function of the power coupling coefficient: (a) the continuous line shows the basic case with the scattering losses included (Pump Q = 1.48 × 104)
(b) the dashed line shows the case with no scattering losses taken into account (Pump Q = 4.85 × 106).
Equation (2) was used to find the signal power out-coupled from the disk to the signal bus.
As mentioned previously, the laser performance is tightly related to the signal coupling
coefficient. Figure 8(a) shows the signal output power of the disk for the cavity with the
scattering losses taken into account. The threshold power varies directly with the signal
coupling. For coupling coefficient higher than 2 × 103
, lasing is not possible since the signal
gain is not sufficient to recover the internal and external disk losses. For low signal coupling,
the lasing threshold shows saturation at a minimum of 0.2 mW. However, the slope efficiency
decreases drastically by decreasing the coupling to that level.
The output power peaks at a signal coupling of 4 × 104
. This value of signal coupling
gives an optimized performance for the micro-disk device as it maximizes the slope efficiency
(1.26 × 104
) with a lasing threshold of 0.5 mW. Higher coupling values result in small signal
accumulation. On the other hand, decreasing coupling below that level will increase the
accumulation but only a small fraction of the internal signal power couples to the output bus.
Simulated efficiency of erbium-doped ChG fiber, can achieve ~15% [24]. However, fiber
lasers require long lengths (tens of centimeters) and do not offer suitable solution for on-chip
applications. In contrast, the predicted slope efficiency of the micro-disk is very small but it
offers a compact platform for on-chip applications. The low slope efficiency for the micro-
disk case is caused by the high pump scattering from the sidewall roughness. This results in a
small pump accumulation in addition to a relatively high lasing threshold. Progress is taking
place to reduce these losses [26], for which there is a vast untapped opportunity to enhance
lasing characteristics by two orders of magnitude (Fig. 8(b)).
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11960
10-6 10-5 10-4 10-3 10-2
101
100
10-1
Sig
na
l po
we
r (μ
W)
1
2
3
10-6 10-5 10-4 10-3 10-2
10-1
10-2
2
6
4
Sig
na
l po
we
r (μ
W)
𝜿𝑺𝟐
𝜿𝑺𝟐
Fig. 8. Output signal power as a function of the pump power and the signal coupling
coefficient. Lasing is only possible with signal coupling smaller than 2 × 103. The peak output
power is obtained at signal coupling of 4 × 104. (a) For the case of including scattering losses,
pump Q = 1.48 × 104, signal Q = 1.53 × 106 and pump coupling coefficient = 0.25, a maximum
slope efficiency of 1.26 × 104 with threshold of 0.5 mW is obtained. (b) For the case of excluding scattering losses, pump Q = 4.8 × 106, signal Q = 6 × 106 and pump coupling
coefficient = 0.0025, a maximum efficiency of 0.025 with 0.02mW threshold can be achieved.
4. Conclusion
We developed a model to simulate MIR lasing for erbium-doped GLS micro-disk. The
optimal coupling coefficients for the signal and pump waveguides were identified. Lasing at
4.5 µm signal using 800 nm pump was shown to be possible with the recently reported
chalcogenide micro-disk quality factor characteristics [26]. With 80 µm disk diameter, 0.6 µm
thickness and erbium concentration of 2.8 × 1020
cm3
, lasing is possible with a maximum
slope efficiency of 1.26 × 104
and threshold of 0.5 mW for pump and signal coupling
coefficients of 0.25 and 2 × 103
, respectively. The efficiency could be improved to ~0.025 if
scattering losses are eliminated.
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11961
Appendix
Table 2. Rate Equations Parameters of Erbium-Doped GLS System
Emission and absorption cross sections Multi-phonon decay rate
(parameters are found in [40])
e
S
2.5 × 1021 cm2 [25] W2 0
a
P
3 × 1021 cm2 [25] W3 0
a
S
2.5 × 1021 cm2 (Mc-Cumber) W4 800
e
P
0.3 × 1021 cm2 (Mc-Cumber) W5 25
Spontaneous emission rate obtained by Judd-Ofelt (s1) [41] Energy transfer parameters
(cm3/s) [30,31]
a21 546.4 C33 22.5 × 1018
a31 559 C14 5 × 1018
a32 96 C16 5 × 1018
a41 744.3 C44 2 × 1018
a42 174.2 C22 35 × 1018
a43 8 C24 2 × 1018
a51 7076.1 a52 332.3 a53 268 a54 29
Acknowledgments
The authors gratefully acknowledge contributions of Michiel Vanhoutte, from the department
of materials science and engineering at Massachusetts Institute of Technology. This study was
supported by a grant from Masdar Institute of Science and Technology (Abu Dhabi, UAE),
project number 400200.
#144017 - $15.00 USD Received 14 Mar 2011; revised 13 May 2011; accepted 13 May 2011; published 6 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 11962
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