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Notice that the LPG’s cross-coupling operation mode
can be practically implemented based on either inte-
grated- waveguide technology (by simply inducing the
coupling between two physically separated waveguides
[10]) or a fiber-optic approach [4]. Figure 1(b) shows a
schematic of a previously demonstrated all-fiber ap-
proach for implementation of the cross-coupling opera-
tion mode in LPGs [4], i.e. to ensure that both the input
and output signals are carried by the fiber core mode. A
core-mode blocker and a short broadband uniform LPG
can be used for undistorted transference of the desired
output signal from the cladding mode into the core mode.
designations.
3. Numerical Comparison between
BG-Based and LPG-Based Pulse Coders
Let us assume a fiber BG working in reflection and a
fiber LPG working in the cross-coupling operation mode,
both made in standard single-mode fiber (Corning SMF28),
see Figure 4. The grating period for the LPG is assumed
to be Λ = 430 μm, which corresponds to coupling of the
fundamental core mode into the LP06 cladding mode at a
central wavelength of 1550 nm. The BG has a period of
528 nm, corresponding to a Bragg wavelength of
1550nm. The average effective refractive index of the
propagating mode in the BG is neff = 1.4684 and for the
LPG: neff1 = 1.4684 and neff2 = 1.4648 [11-13]. Table 1
shows the estimated space-to-time mapping speeds for
these two examples. Let us further assume that the two
considered BG and LPG devices have the same length of
10cm and they are both identically spatially-apodized for
a target optical OOK bit stream pattern generation, as
shown in Figure 4.
()kz
10zcm
1000
11
()ht
100 011
BG
LPG
(ps)t
0.20.4 0.6
Sp eed=5Tbit/s
()ht
100 011
(ps)t
163326 489 652 815 978
Speed=6.1Gbi t / s
0.81.0 1.2
Figure 4. Comparison of the two OOK pulse-coding ap-
proaches based on space-to-time mapping in BGs and LPGs.
Table 1. The estimated space-to-time mapping speed for the
considered BG and LPG made in S MF28 fib er.
Space-to-time mapping speed
BG V
= c / (2 neff) = 1.022 × 108 (m/s)
LPG V
= c / (neff1- neff2) = 833.3 × 108 (m/s)
In both cases, the amount of peak coupling coefficient
is assumed to be low enough to satisfy weak-coupling
conditions. Based on the space-to-time mapping theory,
by launching an ultra-short optical pulse into the consid-
ered optical filters, the target bit stream patterns (i.e. h(t)
in Figure 4) will be generated at the filters’ output port.
As expected from the different space-to-time mapping
speeds, the bit rate of the generated bit stream pattern by
the LPG device should be nearly 1,000 faster than that
generated by the BG filter.
4. Numerical Simulations
Using coupled-mode theory combined with a transfer-
matrix method [13], we have numerically simulated two
different LPG designs for generation of two 8-symbol
optical QPSK and 16-QAM signals, each with a speed of
4TBaud (4TBaud), from an input ultra-short optical
Gaussian pulse with a (full width at 10% of the peak am-
plitude) duration of 100 fs. Figure 5 shows the results of
these numerical simulations. The LPG design parameters
are those defined above and the input optical pulse is
assumed to be centered at the LPG resonance wavelength
of 1550 nm. In the numerical simulations, the following
wavelength dependence has been assumed for the effec-
tive refractive indices of the two interacting (coupled)
modes [12]: neff1(λ) = 1.4884 - 0.031547λ + 0.012023λ2
for the core-mode and neff2(λ) = 1.4806 - 0.025396λ +
0.009802λ2 for the LP06 cladding-mode, where 1.2 < λ <
1.7 is the wavelength variable in μm.
Figsures 5(a) and (b) show the designed amplitude
and phase grating-apodization profiles for the target
QPSK and QAM coding operations, respectively. The
grating designs are relatively straightforward and simple,
just being spatial-domain mapped versions of the respec-
tive targeted complex time-domain optical data streams.
In particular, Figrues 5(g) and (h) show the amplitude
and phase profiles of the time-domain waveforms at the
outputs of the simulated LPG designs, demonstrating
accurate generation of the targeted 4TBaud data streams,
as per the coding formats defined in Figures 5(c) and (d),
respectively, in excellent agreement with the inscribed
grating-apodization profiles.
Notice that considering the superluminal space-to-time
mapping scaling value in the designed LPG (~833.3
108 m/s), each symbol time period of 250 fs corresponds
to a fairly large spatial period of ~2.07 cm. As antici-
pated, time resolutions in the femtosecond regime (e.g.
for the inter-symbol amplitude transitions and discrete
phase jumps) can be achieved based on readily feasible
millimeter grating spatial resolutions. The spectral re-
sponses of the two designed LPG filters are shown in
Figures 5(e) and (f), respectively. It is worth noting the
intrinsic complexity of these responses (also for the
phase, not shown here), which would make it very chal-
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