Noise tolerance in wavelength-selective switching of optical differential quadrature-phase-shift-keying pulse train by collinear acousto-optic devices Nobuo Goto1,* and Yasumitsu Miyazaki2 1
2
Department of Optical Science and Technology, Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan
Department of Media Informatics, Aichi University of Technology, Gamagori, Aichi 443-0047, Japan *Corresponding author: goto.nobuo@tokushima‐u.ac.jp Received 26 February 2014; revised 3 April 2014; accepted 17 April 2014; posted 23 April 2014 (Doc. ID 207229); published 22 May 2014
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols∕s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method. © 2014 Optical Society of America OCIS codes: (230.1040) Acousto-optical devices; (070.1060) Acousto-optical signal processing; (060.6719) Switching, packet. http://dx.doi.org/10.1364/AO.53.003379
1. Introduction
Wavelength-selective switching and signal processing of wavelength-division-multiplexed (WDM) optical packets are required in photonic networks [1–3]. In present optical networks, various modulation formats such as on–off keying, binary phase-shift keying, and quadrature phase-shift keying (QPSK) are employed as optical packets. The packet bit rate is 40 Gbits∕s in backbone networks. Higher bit rates exceeding 100 Tbits∕s have been experimentally demonstrated with WDM using more advanced modulation formats such as quadrature amplitude modulation and orthogonal frequency-division multiplexing. In optical processing at network nodes, therefore, preservation of the modulation format of 1559-128X/14/163379-09$15.00/0 © 2014 Optical Society of America
optical high-bit-rate packets will be an important issue. Acousto-optic (AO) devices using interaction between optical guided waves and surface acoustic waves (SAWs) have been studied for filtering and switching of WDM signals [4–15]. Recently, in lowpower-consuming WDM networks, reconfigurable optical add/drop multiplexers (ROADMs) have been regarded as key devices and various configurations using collinear AO devices [14,16], microelectromechanical systems (MEMS) [17,18], and liquidcrystal-on-silicon (LCOS) switches [17,19] have been investigated. Although the devices based on MEMS and LCOS have an advantage in flexible and adaptive wavelength selectivity, the devices require freespace propagation. On the other hand, collinear AO devices can be formed with optical channel waveguides as an integrated-optic circuit and are applicable to WDM ROADMs and signal processing in 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3379
WDM network nodes. The wavelength selectivity in collinear AO devices has been improved by employing weighted AO coupling. The authors have studied weighted AO switches and their application to optical packet routing and optical label recognition of high-bit-rate packets [16,20–24]. In this paper, we clarify noise tolerance in the switching of optical differential QPSK (DQPSK) pulse trains. We consider 40 and 100 Gsymbol∕s DQPSK pulse trains having 75 and 150 GHz bandwidth, respectively. As the symbol rate increases, AO switching induces distortion in pulse shape and phase [25], which results in an increase in the bit error rate (BER). Since the BER can be regarded as the most important measure in optical packet transmission and processing, the results obtained will be useful in designing wavelength-selective processing systems for photonic networks. We consider a weighted AO switch consisting of an asymmetric optical directional coupler and a SAW tapered waveguide [26] and a Butterworth-type weighted AO switch consisting of a lossy SAW directional coupler proposed by Song [27,28]. The former device was aimed to suppress sidelobes in filtering characteristics. The latter was proposed to provide flattop passband characteristics. Most of the weighted AO devices reported so far are designed to suppress sidelobes in the filtering response and have similar wavelength-selective switching characteristics to that in the tapered SAW waveguide device [29]. On the other hand, the Butterworth-type AO device is different in its design principle from these sidelobe-suppressed devices and is designed for achieving flattop passband by employing a complicated weighting technique. Since AO devices with improved wavelength selectivity are basically classified into these two types, we compare the switching characteristics in the above two types of device structure. This paper clarifies the difference in switching characteristics for high-bit-rate pulses between these two devices. The BER of the switched DQPSK pulse trains with these two kinds of AO switches is numerically analyzed by the Monte Carlo method. 2. Weighted Collinear AO Devices
A collinear AO device with a tapered SAW waveguide is shown in Fig. 1(a) [26]. The tapered SAW waveguide is employed to realize weighted AO coupling along an interaction region of length lSW . Alternatives for achieving weighted AO interaction include employment of a tilted SAW waveguide [30], a focused SAW [11], and a SAW directional coupler [12]. The peak intensity of the guided SAW excited by a unidirectional interdigital transducer (IDT) is adjustable by controlling the confinement of the guided mode in the waveguide. Usually, the cross section of the optical waveguide in the coupling region is much smaller than that of the SAW waveguide, since the optical guided wavelength is usually less than onetenth of the SAW wavelength. Therefore, only the peak intensity of the SAW at the center of the SAW 3380
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
Unswitched output Optical waveguide (Two modes are supported)
Switched output
Tapered SAW waveguide x
y
z
Acoustic absorber
lSW
Unidirectional IDT DQPSK input pulse train
Unswitched output Optical waveguide (Two modes are supported) Lossy SAW directional coupler
Switched output
y
l3
x
z
l2 lSW
Acoustic absorber
l1
Unidirectional IDT DQPSK input pulse train
Fig. 1. Pulse train processing along a weighted collinear AO device (a) with a tapered SAW waveguide and (b) with a lossy SAW directional coupler (Butterworth type).
waveguide is effective in the AO interaction. Thus a weighted coupling can be realized by varying the SAW field distribution with respect to the z direction. The AO coupling coefficient gz for the tapered SAW waveguide is assumed to be given by 2πz gz g0 1 − α cos ; lSW
(1)
where α is a parameter indicating the weighting strength. A conventional AO coupling without weighting is given by α 0. The coupling coefficient gz has a maximum value at the center of the interaction region, z lSW ∕2, since the SAW field has a peak value there when the waveguide width is reduced. It is noted that the thickness of the SAW waveguide has to be designed to vary along the interaction region to keep the guided SAW velocity constant [21]. For complete switching, g0 has to be set to be g0 lSW π∕2. We assume α 0.5 for a weighted coupling [21]. Figure 2 shows the distribution of gz required for complete switching as a function of the normalized propagation length z∕lSW along the interaction region. The sidelobe is decreased to −22 dB for α 0.5 from −9.3 dB for α 0 [21]. An AO filter with Butterworth filtering characteristics was reported to be realized either by employing a SAW directional coupler and a SAW absorption film or by employing a lossy SAW directional coupler, as
+
150 100
+ +
50
+
0
-100
0
0.2
0.4
0.6 z / lSW
0.8
gz g0 sin κ ∞
p z π z− e−βim z ; zt erf zt 2
Nπ
lSW −
: p π lSW z erf t zt 2
AO
Butterworth, |fAO|2 Butterworth,lsw=42.72mm, lSW=42.72mm, |fAO|2
0.4
Butterworth, |fAOres|2 Butterworth,lsw=42.72mm, lSW=42.72mm, |fAOres|2
0.2
0
100 200 300 400 Optical Frequency Shift (GHz)
500
SW
(2)
where κ∞
AO
SW
Tapered SAW Tapered SAW(a=0.5), (α=0.5),lsw=20mm l =20mm
shown in Fig. 1(b) [27,28]. The optimized AO coupling coefficient gz for this device is given by
SW
Taper lsw=20mm, |fAOres|2 TaperSAW SAW(a=0.5), (α=0.5), l =20mm, |f res|2
1
Fig. 2. Distribution of AO coupling coefficient gz along the interaction region required for complete switching in a conventional device (α 0, lSW 20 mm), tapered SAW waveguide device (α 0.5, lSW 20 mm), and Butterworth-type device (lSW 42.72 mm).
Taper lsw=20mm, |fAO|2 TaperSAW SAW(a=0.5), (α=0.5), l =20mm, |f |2
0.6
0
-
-50
0.8
Phase of Switched Output (rad.)
200
1
Filtering Response
AO Coupling Coefficient for Complete Switching
Butterworth, lsw=42.72mm Butterworth, lSW=42.72mm Tapered SAW (a=0.5), lsw=20mm Tapered SAW (α=0.5), lSW=20mm Conventional (α=0), lSW=20mm Conventional (a=0), lsw=20mm
2
Butterworth,lsw=42.72mm lSW=42.72mm Butterworth,
1.5 1 0.5 0 -0.5 -1 -1.5 -2 0
100 200 300 400 Optical Frequency Shift (GHz)
500
Fig. 3. Filtering response in tapered SAW waveguide switch and Butterworth-type switch: (a) intensity of switched and unswitched outputs and (b) phase of switched output.
(3)
N is the number of sections with alternating polarities, and zt is the entrance taper length of AO coupling. Note that the SAW field coupled to the other SAW waveguide is shifted by π∕2 in phase. Therefore, the phases of the SAW fields in sections l1, l2 , and l3 are different from each other by π, resulting in alternating polarities, as shown in Fig. 2. The alternating polarities in gz are required in addition to decaying along z to achieve Butterworth filtering characteristics. We set the above parameters as N 3, g0 26.228∕lSW , and zt 0.19lSW [27]. The filtering response in wavelength-selective switching with these devices is shown as a function of the optical frequency shift from the Bragg condi2 tion in Fig. 3(a), where jf AO j2 and jf res AO j denote output intensities at the switched output port and the unswitched port, respectively. At the optical frequency at which the optical frequency shift is zero, complete switching is performed due to maximum mode conversion. As the optical frequency shift increases, switching becomes incomplete, because the AO interaction does not satisfy the Bragg condition. The filtering response was obtained by numerically solving the coupled mode equation using the Runge–Kutta method as described in Appendix A. When the optical frequency shifts from the Bragg condition for the interacting SAW frequency, the mode conversion ratio decreases, which limits the bandwidth of the switched optical signal. We assume the interaction length lSW as 20 and 42.72 mm for the tapered SAW waveguide device and for the
Butterworth-type device, respectively. The halfbandwidth of the main lobe in the passband for the tapered SAW waveguide device and the Butterworth-type device is around 230 GHz with these interaction lengths. Although a filtering bandwidth can usually be defined by −3 dB bandwidth in the filtering response, we consider half of the bandwidth of the full mainlobe, that is, around 230 GHz, as a bandwidth in this paper, since the shape of the mainlobe is different between these two types of devices. It is found that the filtering response is almost flat below 100 GHz and decreases in 100–230 GHz in the Butterworth-type device, whereas the response decreases monotonously in 0–230 GHz in the tapered SAW waveguide device. Therefore, the Butterworthtype device has better filter response from the viewpoint of the filtered intensity jf AO j2 than the tapered SAW waveguide device. However, as shown in Fig. 3(b), the phase of the switched output signal has nonlinearity as a function of the optical frequency shift in the Butterworth-type device. The phase in the tapered SAW waveguide device has a discontinuity at around 230 GHz, which is caused by the fact that the switched output is too small to calculate the phase precisely. Except for this discontinuity, the phase relation in the tapered SAW waveguide device is almost linear. It is noted that the linearity in the phase relation is important for maintaining the pulse shape in switching. 3. Switching Characteristics of QPSK Pulse Trains
We consider QPSK optical pulse trains at 40 and 100 Gsymbols∕s. Examples of simulated optical 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3381
1.4 100G Symbol/s QPSK 40G Symbol/s QPSK
Switched
Unswitched
1.2
-40
Optical Intensity
Optical Power Spectrum (dBm)
-20
-60
1 0.8 0.6 0.4 0.2
-80 0
0
100 200 300 400 500 Optical Frequency From Center (GHz)
Fig. 4. Examples of optical power spectrums for 40 and 100 Gsymbol∕s QPSK pulse trains, where a laser source at 193.1 THz with 1 mW is modulated by QPSK data sequences.
0
50
4
100 Time (ps)
Switched
150
200
Unswitched
3
1 0 -1 -2 -3 -4
0
50
100 Time (ps)
150
200
Fig. 6. Switched and unswitched outputs with the tapered SAW waveguide AO device at 40 Gsymbols∕s: (a) intensity and (b) phase.
Similar characteristics for the switched pulse train at 40 Gsymbols∕s with the Butterworth-type AO device are shown in Fig. 8. The rising and falling base
Switched
Unswitched
0.8 Optical Intensity
power spectra for these two pulse trains are shown in Fig. 4, where an optical laser source at 193.1 THz with 1 mW is modulated by QPSK data sequences. The half-bandwidths to decrease by 10 dB are around 75 and 150 GHz for 40 and 100 Gsymbols∕s, respectively. To conserve high-symbol-rate pulse trains through AO processing, the filtering bandwidth has to be wide enough to transmit all the frequency components in the spectrum. We consider a specific QPSK pulse train at 40 Gsymbols∕s, as shown in Fig. 5. The phases of the pulses are assumed to be “0, π∕2, 3π∕2, π, 0, 3π∕2, π∕2” in this example. The output pulse train switched with the tapered SAW waveguide AO device at 40 Gsymbols∕s is shown in Fig. 6. No much degradation in the pulse shape and phase shown in Figs. 6(a) and 6(b), respectively, is found at this symbol rate. The unswitched component of about 5% remains as shown in the dashed red curve in Fig. 6(a). The phase is almost kept constant over the main part of the pulse. The switching characteristics for a 100 Gsymbols∕s pulse train are shown in Fig. 7, where the incident pulse train has similar pulse shapes modulated at the same coded phases as that at 40 Gsymbols∕s shown in Fig. 5. At this symbol rate, the pulse shape is affected by the neighbor pulses, depending on the phases. About 20% of the incident signal remains unswitched, and the switched pulse is broadened. This is caused by the wavelength dependence of the mainlobe shown in Fig. 3(a).
Phase (rad)
2
0.6 0.4 0.2 0
0
20
40 60 Time (ps)
Switched
80
Unswitched
4 3
Phase
4 3 2
1
1
0.8
0 0.6
-1
0.4
-2
0.2 0
Phase (rad)
Optical Intensity
1.2
1 0 -1 -2 -3 -4
0
20
40 60 Time (ps)
80
-3 0
0
π/2
50
3π/2
π
0
100 Time (ps)
3π/2
150
π/2
200
-4
Fig. 5. Incident QPSK pulse train at 40 Gsymbols∕s. 3382
Phase (rad)
2 Intensity
1.4
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
Fig. 7. Switched and unswitched outputs with the tapered SAW waveguide AO device at 100 Gsymbols∕s: (a) intensity and (b) phase.
Switched
1.4
Unswitched
1.2
Unswitched
0.8
1
Optical Intensity
Optical intensity
Switched
1
0.8 0.6 0.4
0.6 0.4 0.2
0.2 0
0 0
50
100 Time (ps)
200
4
3
3
2
2
1 0 -1 -2
40 60 Time (ps)
80
Unswitched
1 0 -1 -3
0
50
100
150
-4
200
Time (ps)
parts of the pulse seem to be a little larger. The unswitched portion, however, is very small thanks to the flattop characteristics. The pulse intensity profile at 100 Gsymbols∕s is also calculated and is found to be more severely distorted, depending on the neighbor pulse phases, as shown in Fig. 9. Although the unswitched intensity is smaller in the Butterworthtype AO device, the pulse intensity profile and the phase profile are very distorted due to the wider pulse widths of the switched pulses in comparison to those in the tapered SAW waveguide device.
40
60
80
Fig. 9. Switched and unswitched outputs with the Butterworthtype AO device at 100 Gsymbols∕s: (a) intensity and (b) phase.
as shown in Fig. 10(b). The modulated phases by I k and Qk are ϕIk and ϕQk , respectively. The optical electric field at the sampling time tk from the DQPSK modulator is given by Input data u I Precoder Q v
Output data DQPSK modulator
Bandwidth filter
AO switch
+
; 4
where ⊕ means logical exclusive OR operation. These precoded sequences I k and Qk are fed to phase modulators placed in a Mach–Zehnder interferometer,
DQPSK decoder
Ir Is
Noise
I
(t)
(t)
To evaluate the effect of AO switching in the transmission system on detection of QPSK codes, we consider a DQPSK transmission model, shown in Fig. 10(a). Original binary bit sequence bk is interleaved to odd- and even-numbered bit sequences uk b2k−1 and vk b2k , respectively, where k is an integer. These two sequences uk and vk are differentially encoded to I k and Qk using previous values of I k−1 and Qk−1 , as given by
Qk uk ⊕ vk vk ⊕ Qk−1 uk ⊕ vk uk ⊕ I k−1
20
Phase modulator
4. Noise Tolerance
I k uk ⊕vk uk ⊕ I k−1 uk ⊕ vk vk ⊕ Qk−1
0
Time (ps)
Fig. 8. Switched and unswitched outputs with the Butterworthtype AO device at 40 Gsymbols∕s: (a) intensity and (b) phase.
(
20
-2
-3 -4
0
Switched
Unswitched
4
Phase (rad)
Phase (rad)
Switched
150
Phase modulator Q
∆t
3dB coupler π/4
fout1
fout2 ∆t
-π/4
fout3
fout4
PD LPF
LPF
+ +
Ir
+ + -
Is
LPF
LPF
Fig. 10. Optical system to evaluate bit-error-rate performance, where the red and blue lines indicate optical and electric signals, respectively. (a) Model of DQPSK transmission system with an AO switch consisting of (b) a DQPSK modulator and (c) a DQPSK demodulator. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3383
1 f mod tk p f 0 0ejϕIk π∕2 ejϕQk 2 p ϕIk − ϕQk π jϕI ϕQ ∕2π∕4 k e k ; 2f 0 0 cos 2 4 (5) where f 0 t represents the pulse envelope of a single pulse. Equation (5) can be rewritten as f mod tk f 0 0ejϕk ;
(6)
where ϕk takes values of π∕4, 3π∕4, 5π∕4, and 7π∕4. The degraded pulse train f 0mod t due to additive noise and AO switching is received at the receiver and demodulated to retrieve the originally transmitted bit sequence. Optical fields at the four output ports of the optical circuit are written as j f out1 t − p f 0mod t − Δt f 0mod tejπ∕4 ; 2 2 1 f out2 t p −f 0mod t − Δt f 0mod tejπ∕4 ; 2 2 1 f out3 t p f 0mod t − Δt − f 0mod te−jπ∕4 ; 2 2 j f out4 t − p f 0mod t − Δt f 0mod te−jπ∕4 ; 2 2
(7)
respectively, for Δϕk ϕk − ϕk−1 0;π∕2;−π∕2;π;−π. The I r;k and I s;k are found to be equal to 2uk − 1A0 and 2vk − 1A0 , respectively. In the demodulator, Bessel LPFs of order four were employed just after the PDs. The cutoff frequency was set at 75% of the symbol rate. The transmitted pulse train is assumed to be a periodic repetition of a de Bruijn sequence [31]. In general, a k-ary de Bruijn sequence Bk; n of order n is a shortest cyclic sequence of length 2n . We employed a sequence of B2; 3, that is, 01011100. In its cyclic sequence, every possible subsequence of length n appears once. This sequence enables us to account for inter-symbol interference caused by one bit on either side of the desired bit or the preceding two bits. In the simulation, we also used a reversed-order sequence, 00111010, in addition to the original sequence. Eight cyclic sequences for each of these two sequences are used as the bit sequences of uk and vk , where the circulation in vk is assumed to be in the reversed direction. Figure 11 shows an eye diagram of the output current I r and I s for 16 bit sequences at 40 Gsymbols∕s with the tapered SAW waveguide AO device without additive noise. At the instances of pulse peaks, the outputs take two different values of around 0.4 or −0.4 depending on the incident codes. At 100 Gsymbols∕s, the output signals are distorted,
where Δt is the pulse period. We consider an ideal case as given by (8)
Then, the fields of Eq. (7) at t tk can be rewritten as j f out1 tk − p f 0 0ejϕk−1 ejϕk ejπ∕4 2 2 1 f out2 tk p f 0 0−ejϕk−1 ejϕk ejπ∕4 2 2 1 f out3 tk p f 0 0ejϕk−1 − ejϕk e−jπ∕4 2 2 j f out4 tk − p f 0 0ejϕk−1 ejϕk e−jπ∕4 : 2 2
I r;k I s;k
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
0.1 0 -0.1 -0.2
-0.4 -0.5 70
80
90
100
110
120
130
110
120
130
Time (ps)
(a) 0.5
(9)
0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4
(10)
where A is the p conversion coefficient. By taking A0 Af 20 0∕4 2, I r;k and I s;k take values I r;k −A0 ; A0 ; −A0 ; A0 ; A0 and I s;k −A0 ; −A0 ; A0 ; A0 ; A0 , 3384
0.2
-0.3
Differentially detected currents at the two paired photodiodes (PDs) with low-pass filters (LPFs) are derived at the sampling point t tk to be A − f 20 0 cosϕk−1 − ϕk − π∕4; 4 A 2 − f 0 0 cosϕk−1 − ϕk π∕4; 4
0.3 Output Current Ir
ϕ0 t ϕt:
0.4
Output Current Is
f 00 t f 0 t;
0.5
-0.5 70
80
90
100 Time (ps)
(b) Fig. 11. Pulse patterns of 40 Gsymbol∕s output currents with the tapered SAW waveguide AO device: (a) Ir and (b) Is .
0.4
relation in the Butterworth device, which causes the larger distortion in pulse shape and phase. It is also found that around a 6 dB larger SNR is required for the 100 Gsymbols∕s rate.
0.3
Output Current Ir
0.2 0.1 0
5. Conclusions
-0.1 -0.2 -0.3 -0.4 34
39
44
49
54
49
54
Time (ps)
(a) 0.4 0.3
Output Current Is
0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 34
39
44 Time (ps)
(b) Fig. 12. Pulse patterns of 100 Gsymbols∕s output currents with the tapered SAW waveguide AO device: (a) Ir and (b) Is .
as shown in Fig. 12, which is caused by the insufficient filtering bandwidth of the AO device. The BER performance was simulated by the Monte Carlo method. Gaussian noise was added before the AO switching. The SNR at the entrance of the AO switch was evaluated as SNR f 20 tk ∕2σ 2n , where σ 2n is the variance of the Gaussian noise. The simulated BER as a function of SNR is shown in Fig. 13. Although the two AO devices were designed to have almost the same bandwidth as the main lobe, about 2 and 0.2 dB larger SNR values are required for the Butterworth-type AO device at 100 and 40 Gsymbols∕s, respectively. The main reason for the difference is considered to be the nonlinear phase -1
Taper SAW, 100Gsymbol/s Taper SAW 40Gsymbol/s Butterworth, 100Gsymbol/s Butterworth, 40Gsymbol/s
-2
Log(BER)
-3 -4
Noise tolerance in switching for high-bit-rate QPSK pulse trains with collinear AO devices was theoretically discussed. As an important measure, BER rate analysis for QPSK pulse processing was investigated. A QPSK pulse train was degraded in shape and phase by AO switching due to wavelength selectivity. The degradation due to switching in the tapered SAW waveguide AO and Butterworth-type AO devices was clarified by computer simulation. The Butterworth AO device showed flattop filtering, resulting in a small unswitched component. However, due to the phase linearity in the tapered SAW AO device, pulse distortion was smaller and better BER was obtained. Wavelength-selective processing with integrated AO devices for use in photonic routers will be investigated in the future. We will also investigate the designing of an optimum AO device for high-bit-rate pulses. We will also consider experimental verification of the degradation of pulse shape and BER for future work. Appendix A: Coupled Mode Equations for AO Interaction
Optical switching can be achieved by AO mode conversion between two optical guided modes along the AO interaction region and by mode splitting at the input and output Y-branches. It is noted that the optical directionally coupled waveguides consist of two asymmetric waveguides [29]. The mode conversion along the interaction region ~ inis analyzed by considering a SAW strain field S; cident optical fields E1 and E2 , and converted optical fields E01 and E02 . We assume that the propagation constant k1 of the mode of E1 is larger than k2 of the mode of E2. These fields are represented by ~ y; z; t As u~ s x; y; z expjKz − Ωt; Sx;
E1 x; y; z; t A1 zu1 x; y expjk1 z − ωt; E01 x; y; z; t A01 zu1 x; y expfjk1 z − ω Ωtg; A2
E2 x; y; z; t A2 zu2 x; y expjk2 z − ωt; E02 x; y; z; t A02 zu2 x; y expfjk2 z − ω − Ωtg; A3
-5 -6 -7
(A1)
-4
-2
0
2 S/N (dB)
4
6
8
Fig. 13. BER as a function of SNR for 40 and 100 Gsymbols∕s pulse trains.
where As , Ai z, A0i z, i 1; 2 are amplitude factors, u~ s x; y; z is the tensor of the SAW strain field distribution, ui x; y, i 1; 2 are vectors of the electric field distribution, and Ω and ω are angular frequencies of the SAW and the incident optical wave, respectively. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3385
Now we consider the coupled mode equations between two optical guided modes. When the two optical modes are incident on the interaction region, the mode conversion is described by two pairs of coupled mode equations as follows [4]:
d 0 dz A1 z −jg21 zA2 z exp−jΔKz; d 0 dz A2 z −jg12 zA1 z expjΔKz;
A4
d 0 dz A2 z −jg12 zA1 z expjΔKz; d 0 dz A1 z −jg21 zA2 z exp−jΔKz;
A5
where ΔK is the shift from the Bragg condition, as given by ΔK k1 − k2 − K:
(A6)
The mode conversion coefficients g12 z and g21 z are given by ZZ
u2 x; y · ε~ x; y · ~px; y∶u~ s x; y; z ZZ Y 2 x; ydxdy; · ε~ x; y · u1 x; ydxdy∕4 ZZ u1 x; y · ε~ x; y · ~px; y∶u~ s x; y; z g21 z ωε0 As ZZ Y 1 x; ydxdy; (A7) · ε~ x; y · u2 x; ydxdy∕4
g12 z
ωε0 As
where p~ x; y is the photoelastic tensor, ε~ x; y is the relative dielectric tensor, and ε0 is the dielectric constant in free space. Y 1 x; y and Y 2 x; y are defined as Y i x; y
ReEi x; y; z; t × H i x; y; z; tz ; Ai zAi z
i 1; 2 (A8)
where the subscript z represents the component in the z direction. Filtering responses with weighted coupling given by Eqs. (1) and (2) are calculated from Eq. (A4) by the Runge–Kutta method as shown in Fig. 3, where gz g21 z g12 z is assumed for simplicity. This work was supported in part by JSPS KAKENHI (24360150). References 1. R. S. Tucker, “Scalability and energy consumption of optical and electronic packet switching,” J. Lightwave Technol. 29, 2410–2421 (2011). 2. K. Sato and H. Hasegawa, “Optical networking technologies that will create future bandwidth-abundant networks,” J. Opt. Commun. Netw. 1, A81–A93 (2009). 3. D. J. Geisler, N. K. Fontaine, R. P. Scott, and S. J. B. Yoo, “Demonstration of a flexible bandwidth optical transmitter/receiver system scalable to terahertz bandwidths,” IEEE Photon. J. 3, 1013–1022 (2011). 3386
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
4. T. Kondo, Y. Miyazaki, and Y. Akao, “Optical tunable switched directional couplers consisting of two thin-film waveguides using surface acoustic waves,” Jpn. J. Appl. Phys. 17, 1231–1243 (1978). 5. K. Yamanouchi, K. Higuchi, and K. Shibayama, “TE-TM mode conversion by interaction between elastic surface waves and a laser beam on a metal-diffused optical waveguide,” Appl. Phys. Lett. 28, 75–77 (1976). 6. K.-W. Cheung, “Acoustooptic tunable filters in narrowband WDM networks: system issues and network applications,” IEEE J. Sel. Areas Commun. 8, 1015–1025 (1990). 7. D. A. Smith, J. E. Baran, J. J. Johnson, and K.-W. Cheung, “Integrated-optic acoustically-tunable filters for WDM networks,” IEEE J. Sel. Areas Commun. 8, 1151–1159 (1990). 8. M. Fukutoku, K. Oda, and H. Toba, “Wavelength-divisionmultiplexing add/drop multiplexer employing a novel polarization independent acousto-optic tunable filter,” Electron. Lett. 29, 905–907 (1993). 9. A. d’Alessandro, D. A. Smith, and J. E. Baran, “Multichannel operation of an integrated acousto-optic wavelength routing switch for WDM systems,” IEEE Photon. Technol. Lett. 6, 390–393 (1994). 10. J. L. Jackel, M. S. Goodmann, J. E. Baran, W. J. Tomlinson, G.-K. Chang, M. Z. Iqbal, G.-H. Song, K. Bala, C. A. Brackett, D. A. Smith, R. S. Chakravarthy, R. H. Hobbs, D. J. Fritz, R. W. Ade, and K. M. Kissa, “Acousto-optic tunable filters (AOTFs) for multiwavelength optical cross-connects: crosstalk considerations,” J. Lightwave Technol. 14, 1056–1066 (1996). 11. A. Kar-Roy and C. S. Tsai, “Integrated acoustooptic tunable filters using weighted coupling,” IEEE J. Quantum Electron. 30, 1574–1586 (1994). 12. D. A. Smith and J. J. Johnson, “Sidelobe suppression in an acousto-optic filter with a raised-cosine interaction strength,” Appl. Phys. Lett. 61, 1025–1027 (1992). 13. J. Frangen, H. Herrmann, R. Ricken, H. Seibert, W. Sohler, and E. Strake, “Integrated optical, acoustically tunable wavelength filter,” Electron. Lett. 25, 1583–1584 (1989). 14. H. Onaka, H. Miyata, Y. Kai, S. Yoshida, K. Sone, Y. Takita, Y. Tsunoda, H. Miyata, and G. Nakagawa, “Compact photonic gateway for dynamic path control using acousto-optic tunable filter,” Opt. Switch. Netw. 5, 75–84 (2008). 15. S. Kakio, S. Shinkai, and Y. Nakagawa, “Simple simultaneous modulation for red, green, and blue laser lights using surfaceacoustic-wave-driven acoustooptic modulator,” Jpn. J. Appl. Phys. 49, 07HD18 (2010). 16. N. Goto and Y. Miyazaki, “Integrated optical multi-/ demultiplexer using acoustooptic effect for multiwavelength optical communications,” IEEE J. Sel. Areas Commun. 8, 1160–1168 (1990). 17. T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150–1157 (2010). 18. M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol. 24, 4433– 4454 (2006). 19. B. Robertson, H. Yang, M. M. Redmond, N. Collings, J. R. Moore, J. Liu, A. M. Jeziorska-Chapman, M. Pivnenko, S. Lee, A. Wonfor, I. H. White, W. A. Crossland, and D. P. Chu, “Demonstration of multi-casting in a 1×9 LCOS wavelength selective switch,” J. Lightwave Technol. 32, 402–410 (2014). 20. N. Goto and Y. Miyazaki, “Label recognition with wavelengthselective collinear acoustooptic switches for photonic label routers,” Jpn. J. Appl. Phys. 44, 4449–4454 (2005). 21. N. Goto and Y. Miyazaki, “Design of tapered SAW waveguide for wavelength-selective optical switches using weighted acoustooptic interaction,” Electron. Eng. Jpn. 154, 36–46 (2006). 22. N. Goto and Y. Miyazaki, “Recognition of wavelength-divisionmultiplexed time-series optical coded labels using collinear acoustooptic devices without time gating for photonic routing,” Jpn. J. Appl. Phys. 46, 4602–4607 (2007). 23. N. Goto and Y. Miyazaki, “Recognition of optical layered binary phase shift keying labels using coherent acoustooptic processor for hierarchical photonic routing,” Jpn. J. Appl. Phys. 49, 07HB14 (2010).
24. N. Goto and Y. Miyazaki, “Wavelength-selective routing of optical short pulses with weighted collinear acoustooptic devices,” Jpn. J. Appl. Phys. 50, 072503 (2011). 25. N. Goto and Y. Miyazaki, “Theoretical study of the switching characteristics of 40 and 100 G bps pulse trains by weighted collinear acoustooptic switches,” Jpn. J. Appl. Phys. 51, 07GA06 (2012). 26. Y. Kanayama, N. Goto, and Y. Miyazaki, “Integrated optical switches for wavelength-division-multiplex communication using collinear acousto-optic guided devices,” International Topical Meeting on Photonic Switching (PS’90), Kobe, April, 1990, paper 13C-23. 27. G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel’fand-Levitan-Marchenko inversescattering method,” J. Opt. Soc. Am. A 2, 1905–1915 (1985).
28. G.-H. Song, “Proposal for acousto-optic tunable filters with near-ideal bandpass characteristics,” Appl. Opt. 33, 7458– 7460 (1994). 29. N. Goto and Y. Miyazaki, “Finite-difference time-domain analysis of wavelength-selective characteristics in weighted acoustooptic switches for wavelength-division-multiplexed photonic routing,” Jpn. J. Appl. Phys. 43, 2958–2964 (2004). 30. N. Goto and Y. Miyazaki, “Sidelobe suppression in integratedoptic collinear acousto-optic matrix switches by using a tilted SAW waveguide,” 4th Optoelectronics Conference (OEC’92), Chiba, July, 1992, paper 16B4-4. 31. J. Wang and J. M. Kahn, “Impact of Chromatic and polarization-mode dispersions on DPSK systems using interferometric demodulation and direct detection,” J. Lightwave Technol. 22, 362–371 (2004).
1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3387
2
Department of Optical Science and Technology, Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan
Department of Media Informatics, Aichi University of Technology, Gamagori, Aichi 443-0047, Japan *Corresponding author: goto.nobuo@tokushima‐u.ac.jp Received 26 February 2014; revised 3 April 2014; accepted 17 April 2014; posted 23 April 2014 (Doc. ID 207229); published 22 May 2014
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols∕s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method. © 2014 Optical Society of America OCIS codes: (230.1040) Acousto-optical devices; (070.1060) Acousto-optical signal processing; (060.6719) Switching, packet. http://dx.doi.org/10.1364/AO.53.003379
1. Introduction
Wavelength-selective switching and signal processing of wavelength-division-multiplexed (WDM) optical packets are required in photonic networks [1–3]. In present optical networks, various modulation formats such as on–off keying, binary phase-shift keying, and quadrature phase-shift keying (QPSK) are employed as optical packets. The packet bit rate is 40 Gbits∕s in backbone networks. Higher bit rates exceeding 100 Tbits∕s have been experimentally demonstrated with WDM using more advanced modulation formats such as quadrature amplitude modulation and orthogonal frequency-division multiplexing. In optical processing at network nodes, therefore, preservation of the modulation format of 1559-128X/14/163379-09$15.00/0 © 2014 Optical Society of America
optical high-bit-rate packets will be an important issue. Acousto-optic (AO) devices using interaction between optical guided waves and surface acoustic waves (SAWs) have been studied for filtering and switching of WDM signals [4–15]. Recently, in lowpower-consuming WDM networks, reconfigurable optical add/drop multiplexers (ROADMs) have been regarded as key devices and various configurations using collinear AO devices [14,16], microelectromechanical systems (MEMS) [17,18], and liquidcrystal-on-silicon (LCOS) switches [17,19] have been investigated. Although the devices based on MEMS and LCOS have an advantage in flexible and adaptive wavelength selectivity, the devices require freespace propagation. On the other hand, collinear AO devices can be formed with optical channel waveguides as an integrated-optic circuit and are applicable to WDM ROADMs and signal processing in 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3379
WDM network nodes. The wavelength selectivity in collinear AO devices has been improved by employing weighted AO coupling. The authors have studied weighted AO switches and their application to optical packet routing and optical label recognition of high-bit-rate packets [16,20–24]. In this paper, we clarify noise tolerance in the switching of optical differential QPSK (DQPSK) pulse trains. We consider 40 and 100 Gsymbol∕s DQPSK pulse trains having 75 and 150 GHz bandwidth, respectively. As the symbol rate increases, AO switching induces distortion in pulse shape and phase [25], which results in an increase in the bit error rate (BER). Since the BER can be regarded as the most important measure in optical packet transmission and processing, the results obtained will be useful in designing wavelength-selective processing systems for photonic networks. We consider a weighted AO switch consisting of an asymmetric optical directional coupler and a SAW tapered waveguide [26] and a Butterworth-type weighted AO switch consisting of a lossy SAW directional coupler proposed by Song [27,28]. The former device was aimed to suppress sidelobes in filtering characteristics. The latter was proposed to provide flattop passband characteristics. Most of the weighted AO devices reported so far are designed to suppress sidelobes in the filtering response and have similar wavelength-selective switching characteristics to that in the tapered SAW waveguide device [29]. On the other hand, the Butterworth-type AO device is different in its design principle from these sidelobe-suppressed devices and is designed for achieving flattop passband by employing a complicated weighting technique. Since AO devices with improved wavelength selectivity are basically classified into these two types, we compare the switching characteristics in the above two types of device structure. This paper clarifies the difference in switching characteristics for high-bit-rate pulses between these two devices. The BER of the switched DQPSK pulse trains with these two kinds of AO switches is numerically analyzed by the Monte Carlo method. 2. Weighted Collinear AO Devices
A collinear AO device with a tapered SAW waveguide is shown in Fig. 1(a) [26]. The tapered SAW waveguide is employed to realize weighted AO coupling along an interaction region of length lSW . Alternatives for achieving weighted AO interaction include employment of a tilted SAW waveguide [30], a focused SAW [11], and a SAW directional coupler [12]. The peak intensity of the guided SAW excited by a unidirectional interdigital transducer (IDT) is adjustable by controlling the confinement of the guided mode in the waveguide. Usually, the cross section of the optical waveguide in the coupling region is much smaller than that of the SAW waveguide, since the optical guided wavelength is usually less than onetenth of the SAW wavelength. Therefore, only the peak intensity of the SAW at the center of the SAW 3380
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
Unswitched output Optical waveguide (Two modes are supported)
Switched output
Tapered SAW waveguide x
y
z
Acoustic absorber
lSW
Unidirectional IDT DQPSK input pulse train
Unswitched output Optical waveguide (Two modes are supported) Lossy SAW directional coupler
Switched output
y
l3
x
z
l2 lSW
Acoustic absorber
l1
Unidirectional IDT DQPSK input pulse train
Fig. 1. Pulse train processing along a weighted collinear AO device (a) with a tapered SAW waveguide and (b) with a lossy SAW directional coupler (Butterworth type).
waveguide is effective in the AO interaction. Thus a weighted coupling can be realized by varying the SAW field distribution with respect to the z direction. The AO coupling coefficient gz for the tapered SAW waveguide is assumed to be given by 2πz gz g0 1 − α cos ; lSW
(1)
where α is a parameter indicating the weighting strength. A conventional AO coupling without weighting is given by α 0. The coupling coefficient gz has a maximum value at the center of the interaction region, z lSW ∕2, since the SAW field has a peak value there when the waveguide width is reduced. It is noted that the thickness of the SAW waveguide has to be designed to vary along the interaction region to keep the guided SAW velocity constant [21]. For complete switching, g0 has to be set to be g0 lSW π∕2. We assume α 0.5 for a weighted coupling [21]. Figure 2 shows the distribution of gz required for complete switching as a function of the normalized propagation length z∕lSW along the interaction region. The sidelobe is decreased to −22 dB for α 0.5 from −9.3 dB for α 0 [21]. An AO filter with Butterworth filtering characteristics was reported to be realized either by employing a SAW directional coupler and a SAW absorption film or by employing a lossy SAW directional coupler, as
+
150 100
+ +
50
+
0
-100
0
0.2
0.4
0.6 z / lSW
0.8
gz g0 sin κ ∞
p z π z− e−βim z ; zt erf zt 2
Nπ
lSW −
: p π lSW z erf t zt 2
AO
Butterworth, |fAO|2 Butterworth,lsw=42.72mm, lSW=42.72mm, |fAO|2
0.4
Butterworth, |fAOres|2 Butterworth,lsw=42.72mm, lSW=42.72mm, |fAOres|2
0.2
0
100 200 300 400 Optical Frequency Shift (GHz)
500
SW
(2)
where κ∞
AO
SW
Tapered SAW Tapered SAW(a=0.5), (α=0.5),lsw=20mm l =20mm
shown in Fig. 1(b) [27,28]. The optimized AO coupling coefficient gz for this device is given by
SW
Taper lsw=20mm, |fAOres|2 TaperSAW SAW(a=0.5), (α=0.5), l =20mm, |f res|2
1
Fig. 2. Distribution of AO coupling coefficient gz along the interaction region required for complete switching in a conventional device (α 0, lSW 20 mm), tapered SAW waveguide device (α 0.5, lSW 20 mm), and Butterworth-type device (lSW 42.72 mm).
Taper lsw=20mm, |fAO|2 TaperSAW SAW(a=0.5), (α=0.5), l =20mm, |f |2
0.6
0
-
-50
0.8
Phase of Switched Output (rad.)
200
1
Filtering Response
AO Coupling Coefficient for Complete Switching
Butterworth, lsw=42.72mm Butterworth, lSW=42.72mm Tapered SAW (a=0.5), lsw=20mm Tapered SAW (α=0.5), lSW=20mm Conventional (α=0), lSW=20mm Conventional (a=0), lsw=20mm
2
Butterworth,lsw=42.72mm lSW=42.72mm Butterworth,
1.5 1 0.5 0 -0.5 -1 -1.5 -2 0
100 200 300 400 Optical Frequency Shift (GHz)
500
Fig. 3. Filtering response in tapered SAW waveguide switch and Butterworth-type switch: (a) intensity of switched and unswitched outputs and (b) phase of switched output.
(3)
N is the number of sections with alternating polarities, and zt is the entrance taper length of AO coupling. Note that the SAW field coupled to the other SAW waveguide is shifted by π∕2 in phase. Therefore, the phases of the SAW fields in sections l1, l2 , and l3 are different from each other by π, resulting in alternating polarities, as shown in Fig. 2. The alternating polarities in gz are required in addition to decaying along z to achieve Butterworth filtering characteristics. We set the above parameters as N 3, g0 26.228∕lSW , and zt 0.19lSW [27]. The filtering response in wavelength-selective switching with these devices is shown as a function of the optical frequency shift from the Bragg condi2 tion in Fig. 3(a), where jf AO j2 and jf res AO j denote output intensities at the switched output port and the unswitched port, respectively. At the optical frequency at which the optical frequency shift is zero, complete switching is performed due to maximum mode conversion. As the optical frequency shift increases, switching becomes incomplete, because the AO interaction does not satisfy the Bragg condition. The filtering response was obtained by numerically solving the coupled mode equation using the Runge–Kutta method as described in Appendix A. When the optical frequency shifts from the Bragg condition for the interacting SAW frequency, the mode conversion ratio decreases, which limits the bandwidth of the switched optical signal. We assume the interaction length lSW as 20 and 42.72 mm for the tapered SAW waveguide device and for the
Butterworth-type device, respectively. The halfbandwidth of the main lobe in the passband for the tapered SAW waveguide device and the Butterworth-type device is around 230 GHz with these interaction lengths. Although a filtering bandwidth can usually be defined by −3 dB bandwidth in the filtering response, we consider half of the bandwidth of the full mainlobe, that is, around 230 GHz, as a bandwidth in this paper, since the shape of the mainlobe is different between these two types of devices. It is found that the filtering response is almost flat below 100 GHz and decreases in 100–230 GHz in the Butterworth-type device, whereas the response decreases monotonously in 0–230 GHz in the tapered SAW waveguide device. Therefore, the Butterworthtype device has better filter response from the viewpoint of the filtered intensity jf AO j2 than the tapered SAW waveguide device. However, as shown in Fig. 3(b), the phase of the switched output signal has nonlinearity as a function of the optical frequency shift in the Butterworth-type device. The phase in the tapered SAW waveguide device has a discontinuity at around 230 GHz, which is caused by the fact that the switched output is too small to calculate the phase precisely. Except for this discontinuity, the phase relation in the tapered SAW waveguide device is almost linear. It is noted that the linearity in the phase relation is important for maintaining the pulse shape in switching. 3. Switching Characteristics of QPSK Pulse Trains
We consider QPSK optical pulse trains at 40 and 100 Gsymbols∕s. Examples of simulated optical 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3381
1.4 100G Symbol/s QPSK 40G Symbol/s QPSK
Switched
Unswitched
1.2
-40
Optical Intensity
Optical Power Spectrum (dBm)
-20
-60
1 0.8 0.6 0.4 0.2
-80 0
0
100 200 300 400 500 Optical Frequency From Center (GHz)
Fig. 4. Examples of optical power spectrums for 40 and 100 Gsymbol∕s QPSK pulse trains, where a laser source at 193.1 THz with 1 mW is modulated by QPSK data sequences.
0
50
4
100 Time (ps)
Switched
150
200
Unswitched
3
1 0 -1 -2 -3 -4
0
50
100 Time (ps)
150
200
Fig. 6. Switched and unswitched outputs with the tapered SAW waveguide AO device at 40 Gsymbols∕s: (a) intensity and (b) phase.
Similar characteristics for the switched pulse train at 40 Gsymbols∕s with the Butterworth-type AO device are shown in Fig. 8. The rising and falling base
Switched
Unswitched
0.8 Optical Intensity
power spectra for these two pulse trains are shown in Fig. 4, where an optical laser source at 193.1 THz with 1 mW is modulated by QPSK data sequences. The half-bandwidths to decrease by 10 dB are around 75 and 150 GHz for 40 and 100 Gsymbols∕s, respectively. To conserve high-symbol-rate pulse trains through AO processing, the filtering bandwidth has to be wide enough to transmit all the frequency components in the spectrum. We consider a specific QPSK pulse train at 40 Gsymbols∕s, as shown in Fig. 5. The phases of the pulses are assumed to be “0, π∕2, 3π∕2, π, 0, 3π∕2, π∕2” in this example. The output pulse train switched with the tapered SAW waveguide AO device at 40 Gsymbols∕s is shown in Fig. 6. No much degradation in the pulse shape and phase shown in Figs. 6(a) and 6(b), respectively, is found at this symbol rate. The unswitched component of about 5% remains as shown in the dashed red curve in Fig. 6(a). The phase is almost kept constant over the main part of the pulse. The switching characteristics for a 100 Gsymbols∕s pulse train are shown in Fig. 7, where the incident pulse train has similar pulse shapes modulated at the same coded phases as that at 40 Gsymbols∕s shown in Fig. 5. At this symbol rate, the pulse shape is affected by the neighbor pulses, depending on the phases. About 20% of the incident signal remains unswitched, and the switched pulse is broadened. This is caused by the wavelength dependence of the mainlobe shown in Fig. 3(a).
Phase (rad)
2
0.6 0.4 0.2 0
0
20
40 60 Time (ps)
Switched
80
Unswitched
4 3
Phase
4 3 2
1
1
0.8
0 0.6
-1
0.4
-2
0.2 0
Phase (rad)
Optical Intensity
1.2
1 0 -1 -2 -3 -4
0
20
40 60 Time (ps)
80
-3 0
0
π/2
50
3π/2
π
0
100 Time (ps)
3π/2
150
π/2
200
-4
Fig. 5. Incident QPSK pulse train at 40 Gsymbols∕s. 3382
Phase (rad)
2 Intensity
1.4
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
Fig. 7. Switched and unswitched outputs with the tapered SAW waveguide AO device at 100 Gsymbols∕s: (a) intensity and (b) phase.
Switched
1.4
Unswitched
1.2
Unswitched
0.8
1
Optical Intensity
Optical intensity
Switched
1
0.8 0.6 0.4
0.6 0.4 0.2
0.2 0
0 0
50
100 Time (ps)
200
4
3
3
2
2
1 0 -1 -2
40 60 Time (ps)
80
Unswitched
1 0 -1 -3
0
50
100
150
-4
200
Time (ps)
parts of the pulse seem to be a little larger. The unswitched portion, however, is very small thanks to the flattop characteristics. The pulse intensity profile at 100 Gsymbols∕s is also calculated and is found to be more severely distorted, depending on the neighbor pulse phases, as shown in Fig. 9. Although the unswitched intensity is smaller in the Butterworthtype AO device, the pulse intensity profile and the phase profile are very distorted due to the wider pulse widths of the switched pulses in comparison to those in the tapered SAW waveguide device.
40
60
80
Fig. 9. Switched and unswitched outputs with the Butterworthtype AO device at 100 Gsymbols∕s: (a) intensity and (b) phase.
as shown in Fig. 10(b). The modulated phases by I k and Qk are ϕIk and ϕQk , respectively. The optical electric field at the sampling time tk from the DQPSK modulator is given by Input data u I Precoder Q v
Output data DQPSK modulator
Bandwidth filter
AO switch
+
; 4
where ⊕ means logical exclusive OR operation. These precoded sequences I k and Qk are fed to phase modulators placed in a Mach–Zehnder interferometer,
DQPSK decoder
Ir Is
Noise
I
(t)
(t)
To evaluate the effect of AO switching in the transmission system on detection of QPSK codes, we consider a DQPSK transmission model, shown in Fig. 10(a). Original binary bit sequence bk is interleaved to odd- and even-numbered bit sequences uk b2k−1 and vk b2k , respectively, where k is an integer. These two sequences uk and vk are differentially encoded to I k and Qk using previous values of I k−1 and Qk−1 , as given by
Qk uk ⊕ vk vk ⊕ Qk−1 uk ⊕ vk uk ⊕ I k−1
20
Phase modulator
4. Noise Tolerance
I k uk ⊕vk uk ⊕ I k−1 uk ⊕ vk vk ⊕ Qk−1
0
Time (ps)
Fig. 8. Switched and unswitched outputs with the Butterworthtype AO device at 40 Gsymbols∕s: (a) intensity and (b) phase.
(
20
-2
-3 -4
0
Switched
Unswitched
4
Phase (rad)
Phase (rad)
Switched
150
Phase modulator Q
∆t
3dB coupler π/4
fout1
fout2 ∆t
-π/4
fout3
fout4
PD LPF
LPF
+ +
Ir
+ + -
Is
LPF
LPF
Fig. 10. Optical system to evaluate bit-error-rate performance, where the red and blue lines indicate optical and electric signals, respectively. (a) Model of DQPSK transmission system with an AO switch consisting of (b) a DQPSK modulator and (c) a DQPSK demodulator. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3383
1 f mod tk p f 0 0ejϕIk π∕2 ejϕQk 2 p ϕIk − ϕQk π jϕI ϕQ ∕2π∕4 k e k ; 2f 0 0 cos 2 4 (5) where f 0 t represents the pulse envelope of a single pulse. Equation (5) can be rewritten as f mod tk f 0 0ejϕk ;
(6)
where ϕk takes values of π∕4, 3π∕4, 5π∕4, and 7π∕4. The degraded pulse train f 0mod t due to additive noise and AO switching is received at the receiver and demodulated to retrieve the originally transmitted bit sequence. Optical fields at the four output ports of the optical circuit are written as j f out1 t − p f 0mod t − Δt f 0mod tejπ∕4 ; 2 2 1 f out2 t p −f 0mod t − Δt f 0mod tejπ∕4 ; 2 2 1 f out3 t p f 0mod t − Δt − f 0mod te−jπ∕4 ; 2 2 j f out4 t − p f 0mod t − Δt f 0mod te−jπ∕4 ; 2 2
(7)
respectively, for Δϕk ϕk − ϕk−1 0;π∕2;−π∕2;π;−π. The I r;k and I s;k are found to be equal to 2uk − 1A0 and 2vk − 1A0 , respectively. In the demodulator, Bessel LPFs of order four were employed just after the PDs. The cutoff frequency was set at 75% of the symbol rate. The transmitted pulse train is assumed to be a periodic repetition of a de Bruijn sequence [31]. In general, a k-ary de Bruijn sequence Bk; n of order n is a shortest cyclic sequence of length 2n . We employed a sequence of B2; 3, that is, 01011100. In its cyclic sequence, every possible subsequence of length n appears once. This sequence enables us to account for inter-symbol interference caused by one bit on either side of the desired bit or the preceding two bits. In the simulation, we also used a reversed-order sequence, 00111010, in addition to the original sequence. Eight cyclic sequences for each of these two sequences are used as the bit sequences of uk and vk , where the circulation in vk is assumed to be in the reversed direction. Figure 11 shows an eye diagram of the output current I r and I s for 16 bit sequences at 40 Gsymbols∕s with the tapered SAW waveguide AO device without additive noise. At the instances of pulse peaks, the outputs take two different values of around 0.4 or −0.4 depending on the incident codes. At 100 Gsymbols∕s, the output signals are distorted,
where Δt is the pulse period. We consider an ideal case as given by (8)
Then, the fields of Eq. (7) at t tk can be rewritten as j f out1 tk − p f 0 0ejϕk−1 ejϕk ejπ∕4 2 2 1 f out2 tk p f 0 0−ejϕk−1 ejϕk ejπ∕4 2 2 1 f out3 tk p f 0 0ejϕk−1 − ejϕk e−jπ∕4 2 2 j f out4 tk − p f 0 0ejϕk−1 ejϕk e−jπ∕4 : 2 2
I r;k I s;k
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
0.1 0 -0.1 -0.2
-0.4 -0.5 70
80
90
100
110
120
130
110
120
130
Time (ps)
(a) 0.5
(9)
0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4
(10)
where A is the p conversion coefficient. By taking A0 Af 20 0∕4 2, I r;k and I s;k take values I r;k −A0 ; A0 ; −A0 ; A0 ; A0 and I s;k −A0 ; −A0 ; A0 ; A0 ; A0 , 3384
0.2
-0.3
Differentially detected currents at the two paired photodiodes (PDs) with low-pass filters (LPFs) are derived at the sampling point t tk to be A − f 20 0 cosϕk−1 − ϕk − π∕4; 4 A 2 − f 0 0 cosϕk−1 − ϕk π∕4; 4
0.3 Output Current Ir
ϕ0 t ϕt:
0.4
Output Current Is
f 00 t f 0 t;
0.5
-0.5 70
80
90
100 Time (ps)
(b) Fig. 11. Pulse patterns of 40 Gsymbol∕s output currents with the tapered SAW waveguide AO device: (a) Ir and (b) Is .
0.4
relation in the Butterworth device, which causes the larger distortion in pulse shape and phase. It is also found that around a 6 dB larger SNR is required for the 100 Gsymbols∕s rate.
0.3
Output Current Ir
0.2 0.1 0
5. Conclusions
-0.1 -0.2 -0.3 -0.4 34
39
44
49
54
49
54
Time (ps)
(a) 0.4 0.3
Output Current Is
0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 34
39
44 Time (ps)
(b) Fig. 12. Pulse patterns of 100 Gsymbols∕s output currents with the tapered SAW waveguide AO device: (a) Ir and (b) Is .
as shown in Fig. 12, which is caused by the insufficient filtering bandwidth of the AO device. The BER performance was simulated by the Monte Carlo method. Gaussian noise was added before the AO switching. The SNR at the entrance of the AO switch was evaluated as SNR f 20 tk ∕2σ 2n , where σ 2n is the variance of the Gaussian noise. The simulated BER as a function of SNR is shown in Fig. 13. Although the two AO devices were designed to have almost the same bandwidth as the main lobe, about 2 and 0.2 dB larger SNR values are required for the Butterworth-type AO device at 100 and 40 Gsymbols∕s, respectively. The main reason for the difference is considered to be the nonlinear phase -1
Taper SAW, 100Gsymbol/s Taper SAW 40Gsymbol/s Butterworth, 100Gsymbol/s Butterworth, 40Gsymbol/s
-2
Log(BER)
-3 -4
Noise tolerance in switching for high-bit-rate QPSK pulse trains with collinear AO devices was theoretically discussed. As an important measure, BER rate analysis for QPSK pulse processing was investigated. A QPSK pulse train was degraded in shape and phase by AO switching due to wavelength selectivity. The degradation due to switching in the tapered SAW waveguide AO and Butterworth-type AO devices was clarified by computer simulation. The Butterworth AO device showed flattop filtering, resulting in a small unswitched component. However, due to the phase linearity in the tapered SAW AO device, pulse distortion was smaller and better BER was obtained. Wavelength-selective processing with integrated AO devices for use in photonic routers will be investigated in the future. We will also investigate the designing of an optimum AO device for high-bit-rate pulses. We will also consider experimental verification of the degradation of pulse shape and BER for future work. Appendix A: Coupled Mode Equations for AO Interaction
Optical switching can be achieved by AO mode conversion between two optical guided modes along the AO interaction region and by mode splitting at the input and output Y-branches. It is noted that the optical directionally coupled waveguides consist of two asymmetric waveguides [29]. The mode conversion along the interaction region ~ inis analyzed by considering a SAW strain field S; cident optical fields E1 and E2 , and converted optical fields E01 and E02 . We assume that the propagation constant k1 of the mode of E1 is larger than k2 of the mode of E2. These fields are represented by ~ y; z; t As u~ s x; y; z expjKz − Ωt; Sx;
E1 x; y; z; t A1 zu1 x; y expjk1 z − ωt; E01 x; y; z; t A01 zu1 x; y expfjk1 z − ω Ωtg; A2
E2 x; y; z; t A2 zu2 x; y expjk2 z − ωt; E02 x; y; z; t A02 zu2 x; y expfjk2 z − ω − Ωtg; A3
-5 -6 -7
(A1)
-4
-2
0
2 S/N (dB)
4
6
8
Fig. 13. BER as a function of SNR for 40 and 100 Gsymbols∕s pulse trains.
where As , Ai z, A0i z, i 1; 2 are amplitude factors, u~ s x; y; z is the tensor of the SAW strain field distribution, ui x; y, i 1; 2 are vectors of the electric field distribution, and Ω and ω are angular frequencies of the SAW and the incident optical wave, respectively. 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3385
Now we consider the coupled mode equations between two optical guided modes. When the two optical modes are incident on the interaction region, the mode conversion is described by two pairs of coupled mode equations as follows [4]:
d 0 dz A1 z −jg21 zA2 z exp−jΔKz; d 0 dz A2 z −jg12 zA1 z expjΔKz;
A4
d 0 dz A2 z −jg12 zA1 z expjΔKz; d 0 dz A1 z −jg21 zA2 z exp−jΔKz;
A5
where ΔK is the shift from the Bragg condition, as given by ΔK k1 − k2 − K:
(A6)
The mode conversion coefficients g12 z and g21 z are given by ZZ
u2 x; y · ε~ x; y · ~px; y∶u~ s x; y; z ZZ Y 2 x; ydxdy; · ε~ x; y · u1 x; ydxdy∕4 ZZ u1 x; y · ε~ x; y · ~px; y∶u~ s x; y; z g21 z ωε0 As ZZ Y 1 x; ydxdy; (A7) · ε~ x; y · u2 x; ydxdy∕4
g12 z
ωε0 As
where p~ x; y is the photoelastic tensor, ε~ x; y is the relative dielectric tensor, and ε0 is the dielectric constant in free space. Y 1 x; y and Y 2 x; y are defined as Y i x; y
ReEi x; y; z; t × H i x; y; z; tz ; Ai zAi z
i 1; 2 (A8)
where the subscript z represents the component in the z direction. Filtering responses with weighted coupling given by Eqs. (1) and (2) are calculated from Eq. (A4) by the Runge–Kutta method as shown in Fig. 3, where gz g21 z g12 z is assumed for simplicity. This work was supported in part by JSPS KAKENHI (24360150). References 1. R. S. Tucker, “Scalability and energy consumption of optical and electronic packet switching,” J. Lightwave Technol. 29, 2410–2421 (2011). 2. K. Sato and H. Hasegawa, “Optical networking technologies that will create future bandwidth-abundant networks,” J. Opt. Commun. Netw. 1, A81–A93 (2009). 3. D. J. Geisler, N. K. Fontaine, R. P. Scott, and S. J. B. Yoo, “Demonstration of a flexible bandwidth optical transmitter/receiver system scalable to terahertz bandwidths,” IEEE Photon. J. 3, 1013–1022 (2011). 3386
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
4. T. Kondo, Y. Miyazaki, and Y. Akao, “Optical tunable switched directional couplers consisting of two thin-film waveguides using surface acoustic waves,” Jpn. J. Appl. Phys. 17, 1231–1243 (1978). 5. K. Yamanouchi, K. Higuchi, and K. Shibayama, “TE-TM mode conversion by interaction between elastic surface waves and a laser beam on a metal-diffused optical waveguide,” Appl. Phys. Lett. 28, 75–77 (1976). 6. K.-W. Cheung, “Acoustooptic tunable filters in narrowband WDM networks: system issues and network applications,” IEEE J. Sel. Areas Commun. 8, 1015–1025 (1990). 7. D. A. Smith, J. E. Baran, J. J. Johnson, and K.-W. Cheung, “Integrated-optic acoustically-tunable filters for WDM networks,” IEEE J. Sel. Areas Commun. 8, 1151–1159 (1990). 8. M. Fukutoku, K. Oda, and H. Toba, “Wavelength-divisionmultiplexing add/drop multiplexer employing a novel polarization independent acousto-optic tunable filter,” Electron. Lett. 29, 905–907 (1993). 9. A. d’Alessandro, D. A. Smith, and J. E. Baran, “Multichannel operation of an integrated acousto-optic wavelength routing switch for WDM systems,” IEEE Photon. Technol. Lett. 6, 390–393 (1994). 10. J. L. Jackel, M. S. Goodmann, J. E. Baran, W. J. Tomlinson, G.-K. Chang, M. Z. Iqbal, G.-H. Song, K. Bala, C. A. Brackett, D. A. Smith, R. S. Chakravarthy, R. H. Hobbs, D. J. Fritz, R. W. Ade, and K. M. Kissa, “Acousto-optic tunable filters (AOTFs) for multiwavelength optical cross-connects: crosstalk considerations,” J. Lightwave Technol. 14, 1056–1066 (1996). 11. A. Kar-Roy and C. S. Tsai, “Integrated acoustooptic tunable filters using weighted coupling,” IEEE J. Quantum Electron. 30, 1574–1586 (1994). 12. D. A. Smith and J. J. Johnson, “Sidelobe suppression in an acousto-optic filter with a raised-cosine interaction strength,” Appl. Phys. Lett. 61, 1025–1027 (1992). 13. J. Frangen, H. Herrmann, R. Ricken, H. Seibert, W. Sohler, and E. Strake, “Integrated optical, acoustically tunable wavelength filter,” Electron. Lett. 25, 1583–1584 (1989). 14. H. Onaka, H. Miyata, Y. Kai, S. Yoshida, K. Sone, Y. Takita, Y. Tsunoda, H. Miyata, and G. Nakagawa, “Compact photonic gateway for dynamic path control using acousto-optic tunable filter,” Opt. Switch. Netw. 5, 75–84 (2008). 15. S. Kakio, S. Shinkai, and Y. Nakagawa, “Simple simultaneous modulation for red, green, and blue laser lights using surfaceacoustic-wave-driven acoustooptic modulator,” Jpn. J. Appl. Phys. 49, 07HD18 (2010). 16. N. Goto and Y. Miyazaki, “Integrated optical multi-/ demultiplexer using acoustooptic effect for multiwavelength optical communications,” IEEE J. Sel. Areas Commun. 8, 1160–1168 (1990). 17. T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150–1157 (2010). 18. M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol. 24, 4433– 4454 (2006). 19. B. Robertson, H. Yang, M. M. Redmond, N. Collings, J. R. Moore, J. Liu, A. M. Jeziorska-Chapman, M. Pivnenko, S. Lee, A. Wonfor, I. H. White, W. A. Crossland, and D. P. Chu, “Demonstration of multi-casting in a 1×9 LCOS wavelength selective switch,” J. Lightwave Technol. 32, 402–410 (2014). 20. N. Goto and Y. Miyazaki, “Label recognition with wavelengthselective collinear acoustooptic switches for photonic label routers,” Jpn. J. Appl. Phys. 44, 4449–4454 (2005). 21. N. Goto and Y. Miyazaki, “Design of tapered SAW waveguide for wavelength-selective optical switches using weighted acoustooptic interaction,” Electron. Eng. Jpn. 154, 36–46 (2006). 22. N. Goto and Y. Miyazaki, “Recognition of wavelength-divisionmultiplexed time-series optical coded labels using collinear acoustooptic devices without time gating for photonic routing,” Jpn. J. Appl. Phys. 46, 4602–4607 (2007). 23. N. Goto and Y. Miyazaki, “Recognition of optical layered binary phase shift keying labels using coherent acoustooptic processor for hierarchical photonic routing,” Jpn. J. Appl. Phys. 49, 07HB14 (2010).
24. N. Goto and Y. Miyazaki, “Wavelength-selective routing of optical short pulses with weighted collinear acoustooptic devices,” Jpn. J. Appl. Phys. 50, 072503 (2011). 25. N. Goto and Y. Miyazaki, “Theoretical study of the switching characteristics of 40 and 100 G bps pulse trains by weighted collinear acoustooptic switches,” Jpn. J. Appl. Phys. 51, 07GA06 (2012). 26. Y. Kanayama, N. Goto, and Y. Miyazaki, “Integrated optical switches for wavelength-division-multiplex communication using collinear acousto-optic guided devices,” International Topical Meeting on Photonic Switching (PS’90), Kobe, April, 1990, paper 13C-23. 27. G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel’fand-Levitan-Marchenko inversescattering method,” J. Opt. Soc. Am. A 2, 1905–1915 (1985).
28. G.-H. Song, “Proposal for acousto-optic tunable filters with near-ideal bandpass characteristics,” Appl. Opt. 33, 7458– 7460 (1994). 29. N. Goto and Y. Miyazaki, “Finite-difference time-domain analysis of wavelength-selective characteristics in weighted acoustooptic switches for wavelength-division-multiplexed photonic routing,” Jpn. J. Appl. Phys. 43, 2958–2964 (2004). 30. N. Goto and Y. Miyazaki, “Sidelobe suppression in integratedoptic collinear acousto-optic matrix switches by using a tilted SAW waveguide,” 4th Optoelectronics Conference (OEC’92), Chiba, July, 1992, paper 16B4-4. 31. J. Wang and J. M. Kahn, “Impact of Chromatic and polarization-mode dispersions on DPSK systems using interferometric demodulation and direct detection,” J. Lightwave Technol. 22, 362–371 (2004).
1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3387
