Polarization independent 4-stage OTDM
multiplexer using plated GRIN lens

doi:10.1364/OE.16.012544

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Polarization independent 4-stage OTDM multiplexer using plated GRIN lens

Libo Cai, Min Zhang, Peida Ye, and Tangjun Li »View Author Affiliations

Optics Express, Vol. 16, Issue 17, pp. 12544-12549 (2008)
http://dx.doi.org/10.1364/OE.16.012544

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▸ Article Outline
– Abstract
1. Introduction
2. Structure and principle
3. Experimental demonstration
4. Conclusions
– References and links

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Abstract

In this paper, a 4-stage optical time domain multiplexing (OTDM) multiplexer based on plated graded index (GRIN) lens is proposed and experimentally demonstrated. A 10Gbit/s return-to-zero (RZ) signal is upgraded to 160Gbit/s. The time-domain accuracy of the multiplexer is evaluated by analyzing the multiplexed 160Gbit/s signal. Experimental results validate the stability of the optical multiplexing behavior and the polarization insensitivity of the proposed multiplexer. The results also show the advantages of our OTDM multiplexer such as the flexible output signal speeds at the output of different stages, the low insertion loss and the temperature and wavelength stability.

1. Introduction

Optical time domain multiplexing (OTDM) multiplexers are very useful passive devices in optical networks. Particularly, the OTDM multiplexer is often used for upgrading the bitrate at single channel and thus it is convenient to generate ultrafast signals with only low speed optical sources. Nowadays, OTDM technique also plays an important role in all-optical information processing and conflict resolution [1

A. Chen, C.-T. Lea, and A. K.-S. Wong, “A new optical TDM Ring Architecture,” IEEE Trans. Commun. 55, 2134–2141 (2007). [CrossRef]

K. M. Feng, C. Y. Wu, D. H. Hsueh, C. S. Ku, C. P. Chang, H. Y. Lin, J. Cheng, and J. Chen, “Demonstration of an optical FIFO multiplexer,” in Optical Fiber Communication Conference and Exposition and National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OMN5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OMN5

]. Novel high speed OTDM schemes and multiplexers have been studied during recent years [3–6

B. Zhang, L. Zhang, L. S. Yan, I. Fazal, J. Y. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express 15, 8317–8322 (2007). [CrossRef] [PubMed]

Conventional OTDM multiplexer is based on fused fiber coupler and its performance is usually degraded due to polarization fluctuation of the input signal, which will rapidly change the distribution of output power among adjacent multiplexed pulses [7–10

K. Morishita and K. Takashina, “Polarization properties of fused fiber couplers and polarizing beamsplitters,” J. Lightwave Technol. 9, 1503–1507 (1991). [CrossRef]

]. The polarization sensitivity can be weakened by controlling the cross section of fused coupler precisely [11

S. G. Farwell, M. N. Zervas, and R. I. Laming, “2×2 fused fiber null couplers with asymmetric waist cross sections for polarization independent (<0.01dB) switching,” J. Lightwave Technol. 16, 1671–1680 (2006). [CrossRef]

] or employing the half-wave plate in the directional coupler [12

C. R. Doerr, L. L. Buhl, and W. Lin, “Simple method for mitigation of polarization crosstalk in silica planar lightwave circuit directional couplers,” IEEE Photon. Technol. Lett. 18, 1816–1818 (2006). [CrossRef]

]. Besides, the perturbations of the optical wavelength, the operating temperature, and the fiber stress will also reduce the accuracy of conventional OTDM multiplexer.

Recently reported OTDM multiplexers can provide qualified and stable OTDM signals but is not widely used in practice because of their high cost. In addition, most of these OTDM multiplexers exhibit polarization dependence. Therefore, polarization-maintaining configuration [6

T. Ohara, H. Takara, I. Shake, T. Yamada, M. Ishii, I. Ogawa, M. Okamoto, and S. Kawanishi, “Highly stable 160-Gb/s OTDM technologies based on integrated MUX/DEMUX and drift-free PLL-type clock recovery,” IEEE J. Quantum Electron. 13, 40–48 (2007). [CrossRef]

] or integrated polarization controllers [13

Andreas Umbach, “4-stage OTDM multiplexer,” http://www.u2t.de/fileadmin/redakteure/Products/Datasheets/DS_OMUX-4_5v0.pdf.

] are used to stabilize the output power in different channels of the multiplexer.

In this paper, we propose and demonstrate a novel 4-stage polarization-independent OTDM multiplexer based on plated GRIN lens. We illustrate the structure of cascaded GRIN lenses which work as one stage of multiplexer. Then we set up an experimental OTDM signal generating system to multiplex a 10Gbit/s RZ signal up to 160Gbit/s. By evaluating the time-domain information of the multiplexed 160Gbit/s signal, we complete the manufacture of the 4-stage multiplexer. A polarization scrambler is employed to vary the polarization state of the input signal and the polarization characteristic of our proposed OTDM multiplexer is researched. The results show that, because of the plated GRIN lenses structure the multiplexer possesses an excellent performance even in the presence of polarization fluctuation. The OTDM multiplexer also has the advantages such as the flexible output signal speeds at the output of different stages, the low insertion loss and cost, and the outstanding temperature and wavelength stability.

2. Structure and principle

The fundamental element of the proposed OTDM multiplexer is plated GRIN lens, which consists of two reverse-connected GRIN lenses coupled with three fiber pigtails and performs the same function as fused fiber coupler. A very thin Half-Reflection-Half-Transmittance (HRHT) mirror is plated between two lenses. The input optical signal at Port 1 will be divided at the HRHT mirror into two equal parts, destined for Ports 2 and 3, respectively.

Fig. 1. Structure of the plated GRIN lens and the inner optical paths.

The refractive index profile of the GRIN lens is

n = n_{0} (1 - \frac{1}{2} A r^{2})

(1)

where n ₀ is the refractive indexes at optical axis, r is the radius of the GRIN lens. Based on the paraxial approximation, the transfer matrix of two reverse-connected GRIN lenses is expressed as [14

C. Kehua, “Propagation analysis of light rays in combinative optical system of SaFoc lens,” Acta Photonica Sin. 21, 323–329 (1992).

]

[\begin{matrix} x_{2} \\ θ_{2} \end{matrix}] = [\begin{matrix} \cos (\sqrt{A_{2}} L_{2}) & \frac{n_{01}}{n_{02} \sqrt{A_{2}}} \sin (\sqrt{A_{2}} L_{2}) \\ - n_{02} \sqrt{A_{2}} \sin (\sqrt{A_{2}} L_{2}) & n_{01} \cos (\sqrt{A_{2}} L_{2}) \end{matrix}] • [\begin{matrix} \cos (\sqrt{A_{1}} L_{1}) & \frac{1}{n_{01} \sqrt{A_{1}}} \sin (\sqrt{A_{1}} L_{1}) \\ - \sqrt{A_{1}} \sin (\sqrt{A_{1}} L_{1}) & \frac{1}{n_{01}} \cos (\sqrt{A_{1}} L_{1}) \end{matrix}] [\begin{matrix} x_{0} \\ θ_{0} \end{matrix}],

(2)

where L ₁, L ₂ are the lengths of the two GRIN lenses, θ ₀ is the incident angle at Port 1 and θ ₂ is refraction angle at Port 3, x ₀ and x ₂ are vertical coordinates of the incident and refractive points, A ₁ and A ₂ are the distributed constants of the refractive index, n ₀₁ and n ₀₂ are the refractive indexes at optical axis in the two lenses.

The GRIN lenses here are of the same parameters, namely A ₁=A ₂, n ₀₁=n ₀₂ and L ₁=L ₂=p/4, where p is the characteristic pitch of the lens. The light ray propagates one pitch during one cycle of the sinusoidal wave and p=2πA ^-1/2. Then we get

[\begin{matrix} x_{2} \\ θ_{2} \end{matrix}] = [\begin{matrix} 0 & \frac{n_{01}}{n_{02} \sqrt{A_{2}}} \\ - n_{02} \sqrt{A_{2}} & 0 \end{matrix}] [\begin{matrix} 0 & \frac{1}{n_{01} \sqrt{A_{1}}} \\ - \sqrt{A_{1}} & 0 \end{matrix}] [\begin{matrix} x_{0} \\ θ_{0} \end{matrix}]

(3)

{\begin{matrix} x_{2} = - \frac{n_{01}}{n_{02}} x_{0} = - x_{0} \\ θ_{2} = - \frac{n_{02}}{n_{01}} θ_{0} = - θ_{0} \end{matrix}

(4)

Equation (4) proves that the optical paths between Ports 1 and 3 are point symmetric. Because of the axis symmetry between Port 1 and 2, the optical paths between Ports 2 and 3 are also axis symmetric. Then the output signals at Ports 2 and 3 will be the same. According to the reversibility of optical path, the two input optical signals at Ports 2 and 3 will be coupled and outputted at Port 1.

Optical interference occurs at the coupling point of the OTDM multiplexer and the influence of the input polarization fluctuation is equivalent to that of the interference effect [15

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

]. Due to the incident angle of the input light at the surface of the lens, in fact there is not only one optical path as shown in Fig. 1. The input light will radiate and then focus at the HRHT mirror in different optical paths. When reaching at the HRHT mirror, the input optical signal can be treated as many point light sources. The influence of polarization fluctuation is weakened by the interactions of these point light sources. So our proposed OTDM multiplexer based on GRIN lens exhibits much lower polarization dependence.

Two plated GRIN lenses aforementioned are needed to compose one stage of our proposed OTDM multiplexer, as illustrated in Fig. 2. Ports 3 and 3′ are coupled directly and a fiber delay line is added between Ports 2 and 2′. Then the signal at Port 1 is doubled and outputted at Port 1′. Our 4-stage multiplexer consists of 4 pairs of such cascaded lenses. The delay times in each stage are 50ps, 25ps, 12.5ps and 6.25ps, respectively. The insertion loss of each stage is about 4dB and thus the total insertion loss of the 4-stage multiplexer is about 16dB.

Fig. 2. One stage of OTDM multiplexer.

3. Experimental demonstration

Figure 3 shows the experimental setup of the 160Gbit/s (10Gibt/s×16) OTDM signal generating system. The laser generates a 10GHz pulse train at 1546nm. The power of the pulse train is -2.40dBm and the pulse width is 1.807ps. Then the pulse train is modulated by a 10Gbit/s return-to-zero (RZ) 2³¹-1 pseudo-random binary sequence (PRBS). The multiplexed 80Gbit/s signal at the third stage of the multiplexer is observed by an oscilloscope as shown in Fig. 4. Because of the limitation of the oscilloscope’s bandwidth, an autocorrelator is used to observe the 160Gbit/s signal at the fourth stage of the multiplexer and the results is shown in Fig. 5. The powers of the signal at the input and output of the 4-stage OTDM multiplexer are 15.6dBm and -0.4dBm, respectively.

Fig. 3. Experimental 160Gbit/s OTDM signal generating system.

Fig. 4. Back-to-back results on the oscilloscope: (a) Waveform of 80GHz pulse train (12.5ps/div), (b) Eye diagram of 80Gbit/s RZ signal (10ps/div).

Fig. 5. Back-to-back results on the autocorrelator: (a) 160GHz pulse train (The autocorrelation window is 200ps, so there are 32 continuous pulses in the window), (b) 160Gbit/s RZ signal.

However, we can still use the oscilloscope to measure the time-domain accuracy at the fourth stage of the multiplexer. We add a large attenuation to two arms (2–2′ and 3–3′) of the fourth stage respectively and use the markers of the oscilloscope to locate two adjacent pulses of the 160GHz pulse train. In other words, we can analyze the waveform of the 160GHz pulse train by measuring two 80GHz pulse trains in the two arms of the fourth stage respectively. According to Fig. 6, the time interval between the two adjacent pulses is 6.243ps. Compared to the ideal value 6.25ps, the absolute error is 0.007ps.

Fig. 6. Time-domain accuracy at the fourth stage of the multiplexer (5ps/div).

The polarization insensitivity of our proposed OTDM multiplexer is also demonstrated in the experimental OTDM signal generating system. First, our proposed multiplexer is replaced by a conventional OTDM multiplexer based on the fused optical coupler and a polarization scrambler is employed before the multiplexer to vary the polarization state of the input 10GHz pulse train. When the polarization scrambler is working, the output multiplexed pulse train is degraded badly as shown in Fig. 7. Then, the conventional multiplexer is removed and our proposed OTDM multiplexer is employed after the polarization scrambler. The eye diagram of the output 80Gbit/s signal is shown in Fig. 8. The polarization fluctuation is minimized by the cascaded GRIN lenses. So there is not obvious influence on the output 80Gbit/s signal of our proposed multiplexer when the polarization scrambler is working. The variation of the signal amplitude is because of the insertion loss of the polarization scrambler.

Fig. 7. Output of the conventional multiplexer without (a) and with (b) polarization scrambler (10ps/div).

Fig. 8. Back-to-back 80Gbit/s RZ signal without (a) and with (b) polarization scrambler (5ps/div).

4. Conclusions

We proposed and experimentally demonstrated a 4-stage OTDM multiplexer based on plated GRIN lens. A 160Gbit/s (10Gbit/s×16) OTDM signal generating experiment was conducted. We also employed a polarization scrambler to vary the polarization state of the input 10Gbit/s signal. The result showed that the multiplexer still had an excellent performance in the presence of polarization fluctuation. The OTDM multiplexer also had the advantages such as the flexible output signal speeds at the output of different stages, the low insertion loss and cost, and the outstanding temperature and wavelength stability.

Acknowledgments

This study is supported by National Natural Science Foundation project (No.60507007), Program for New Century Excellent Talents in University (NCET-06-0094), ‘863’ High Technology Research and Development Program (No.2007AA01Z243), Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT, No.IRT0609) and the 111 Project (No. B07005).

References and links

1.	A. Chen, C.-T. Lea, and A. K.-S. Wong, “A new optical TDM Ring Architecture,” IEEE Trans. Commun. 55, 2134–2141 (2007). [CrossRef]
2.	K. M. Feng, C. Y. Wu, D. H. Hsueh, C. S. Ku, C. P. Chang, H. Y. Lin, J. Cheng, and J. Chen, “Demonstration of an optical FIFO multiplexer,” in Optical Fiber Communication Conference and Exposition and National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OMN5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OMN5
3.	B. Zhang, L. Zhang, L. S. Yan, I. Fazal, J. Y. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express 15, 8317–8322 (2007). [CrossRef] [PubMed]
4.	N. Deng, C. K. Chan, and L. K. Chen, “A Hybrid OTDM Scheme with enhanced demultiplexing performance,” IEEE Photon. Technol. Lett. 19, 1454–1456 (2007). [CrossRef]
5.	H. Murai, M. Kagawa, H. Tsuji, and K. Fujii, “EA-modulator-based optical time division multiplexing/demultiplexing techniques for 160-Gb/s optical signal transmission,” IEEE J. Quantum Electron. 13, 70–78 (2007). [CrossRef]
6.	T. Ohara, H. Takara, I. Shake, T. Yamada, M. Ishii, I. Ogawa, M. Okamoto, and S. Kawanishi, “Highly stable 160-Gb/s OTDM technologies based on integrated MUX/DEMUX and drift-free PLL-type clock recovery,” IEEE J. Quantum Electron. 13, 40–48 (2007). [CrossRef]
7.	K. Morishita and K. Takashina, “Polarization properties of fused fiber couplers and polarizing beamsplitters,” J. Lightwave Technol. 9, 1503–1507 (1991). [CrossRef]
8.	Z. Jing, L. Cai, and T. Li, “Experimental demonstration on 4×10Gb/s optical time domain multiplexing signal,” J. Photon Technol. 8, 18–21 (2005).
9.	Z. Jing, L. Cai, and T. Li, “Experimental investigation in polarization sensitivity of a novel 40-Gbit/s OTDM system,” Proc. SPIE 6019, 1–7 (2005).
10.	L. Cai, Z. Jing, and T. Li, “Function of polarization scrambler in 4×10Gb/s optical time division multiplexing signal generating system,” J. Opt. Commun. Technol. 29, 32–33 (2005).
11.	S. G. Farwell, M. N. Zervas, and R. I. Laming, “2×2 fused fiber null couplers with asymmetric waist cross sections for polarization independent (<0.01dB) switching,” J. Lightwave Technol. 16, 1671–1680 (2006). [CrossRef]
12.	C. R. Doerr, L. L. Buhl, and W. Lin, “Simple method for mitigation of polarization crosstalk in silica planar lightwave circuit directional couplers,” IEEE Photon. Technol. Lett. 18, 1816–1818 (2006). [CrossRef]
13.	Andreas Umbach, “4-stage OTDM multiplexer,” http://www.u2t.de/fileadmin/redakteure/Products/Datasheets/DS_OMUX-4_5v0.pdf.
14.	C. Kehua, “Propagation analysis of light rays in combinative optical system of SaFoc lens,” Acta Photonica Sin. 21, 323–329 (1992).
15.	M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 3, 2008
Revised Manuscript: July 27, 2008
Manuscript Accepted: July 28, 2008
Published: August 5, 2008

Citation
Libo Cai, Min Zhang, Peida Ye, and Tangjun Li, "Polarization independent 4-stage OTDM multiplexer using plated GRIN lens," Opt. Express 16, 12544-12549 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-12544

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References

A. Chen, C.-T. Lea, and A. K.-S. Wong, "A new optical TDM Ring Architecture," IEEE Trans. Commun. 55, 2134-2141 (2007). [CrossRef]
K. M. Feng, C. Y. Wu, D. H. Hsueh, C. S. Ku, C. P. Chang, H. Y. Lin, J. Cheng, and J. Chen, "Demonstration of an optical FIFO multiplexer," in Optical Fiber Communication Conference and Exposition and National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OMN5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OMN5
B. Zhang, L. Zhang, L. S. Yan, I. Fazal, J. Y. Yang, and A. E. Willner, "Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line," Opt. Express 15, 8317-8322 (2007). [CrossRef] [PubMed]
N. Deng, C. K. Chan, and L. K. Chen, "A Hybrid OTDM Scheme with enhanced demultiplexing performance," IEEE Photon. Technol. Lett. 19, 1454-1456 (2007). [CrossRef]
H. Murai, M. Kagawa, H. Tsuji, and K. Fujii, "EA-modulator-based optical time division multiplexing/demultiplexing techniques for 160-Gb/s optical signal transmission," IEEE J. Quantum Electron. 13, 70-78 (2007). [CrossRef]
T. Ohara, H. Takara, I. Shake, T. Yamada, M. Ishii, I. Ogawa, M. Okamoto, and S. Kawanishi, "Highly stable 160-Gb/s OTDM technologies based on integrated MUX/DEMUX and drift-free PLL-type clock recovery," IEEE J. Quantum Electron. 13, 40-48 (2007). [CrossRef]
K. Morishita and K. Takashina, "Polarization properties of fused fiber couplers and polarizing beamsplitters," J. Lightwave Technol. 9, 1503-1507 (1991). [CrossRef]
Z. Jing, L. Cai and T. Li, "Experimental demonstration on 4�?10Gb/s optical time domain multiplexing signal," J. Photon Technol. 8, 18-21 (2005).
Z. Jing, L. Cai and T. Li, "Experimental investigation in polarization sensitivity of a novel 40-Gbit/s OTDM system," Proc. SPIE 6019, 1-7 (2005).
L. Cai, Z. Jing and T. Li, "Function of polarization scrambler in 4�?10Gb/s optical time division multiplexing signal generating system," J. Opt. Commun. Technol. 29, 32-33 (2005).
S. G. Farwell, M. N. Zervas, and R. I. Laming, "2�?2 fused fiber null couplers with asymmetric waist cross sections for polarization independent (<0.01dB) switching," J. Lightwave Technol. 16, 1671-1680 (2006). [CrossRef]
C. R. Doerr, L. L. Buhl, and W. Lin, "Simple method for mitigation of polarization crosstalk in silica planar lightwave circuit directional couplers," IEEE Photon. Technol. Lett. 18, 1816-1818 (2006). [CrossRef]
Andreas Umbach, "4-stage OTDM multiplexer,"http://www.u2t.de/fileadmin/redakteure/Products/Datasheets/DS_OMUX-4_5v0.pdf.
C. Kehua, "Propagation analysis of light rays in combinative optical system of SaFoc lens," Acta Photonica Sin. 21, 323-329 (1992).
M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

Acta Photonica Sin.

C. Kehua, "Propagation analysis of light rays in combinative optical system of SaFoc lens," Acta Photonica Sin. 21, 323-329 (1992).

IEEE J. Quantum Electron.

H. Murai, M. Kagawa, H. Tsuji, and K. Fujii, "EA-modulator-based optical time division multiplexing/demultiplexing techniques for 160-Gb/s optical signal transmission," IEEE J. Quantum Electron. 13, 70-78 (2007). [CrossRef]
T. Ohara, H. Takara, I. Shake, T. Yamada, M. Ishii, I. Ogawa, M. Okamoto, and S. Kawanishi, "Highly stable 160-Gb/s OTDM technologies based on integrated MUX/DEMUX and drift-free PLL-type clock recovery," IEEE J. Quantum Electron. 13, 40-48 (2007). [CrossRef]

IEEE Photon. Technol. Lett.

N. Deng, C. K. Chan, and L. K. Chen, "A Hybrid OTDM Scheme with enhanced demultiplexing performance," IEEE Photon. Technol. Lett. 19, 1454-1456 (2007). [CrossRef]
C. R. Doerr, L. L. Buhl, and W. Lin, "Simple method for mitigation of polarization crosstalk in silica planar lightwave circuit directional couplers," IEEE Photon. Technol. Lett. 18, 1816-1818 (2006). [CrossRef]

IEEE Trans. Commun.

A. Chen, C.-T. Lea, and A. K.-S. Wong, "A new optical TDM Ring Architecture," IEEE Trans. Commun. 55, 2134-2141 (2007). [CrossRef]

J. Lightwave Technol.

K. Morishita and K. Takashina, "Polarization properties of fused fiber couplers and polarizing beamsplitters," J. Lightwave Technol. 9, 1503-1507 (1991). [CrossRef]
S. G. Farwell, M. N. Zervas, and R. I. Laming, "2�?2 fused fiber null couplers with asymmetric waist cross sections for polarization independent (<0.01dB) switching," J. Lightwave Technol. 16, 1671-1680 (2006). [CrossRef]

J. Opt. Commun. Technol.

L. Cai, Z. Jing and T. Li, "Function of polarization scrambler in 4�?10Gb/s optical time division multiplexing signal generating system," J. Opt. Commun. Technol. 29, 32-33 (2005).

J. Photon Technol.

Z. Jing, L. Cai and T. Li, "Experimental demonstration on 4�?10Gb/s optical time domain multiplexing signal," J. Photon Technol. 8, 18-21 (2005).

Opt. Express

B. Zhang, L. Zhang, L. S. Yan, I. Fazal, J. Y. Yang, and A. E. Willner, "Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line," Opt. Express 15, 8317-8322 (2007). [CrossRef] [PubMed]

Proc. SPIE

Z. Jing, L. Cai and T. Li, "Experimental investigation in polarization sensitivity of a novel 40-Gbit/s OTDM system," Proc. SPIE 6019, 1-7 (2005).

Other

K. M. Feng, C. Y. Wu, D. H. Hsueh, C. S. Ku, C. P. Chang, H. Y. Lin, J. Cheng, and J. Chen, "Demonstration of an optical FIFO multiplexer," in Optical Fiber Communication Conference and Exposition and National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OMN5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OMN5
Andreas Umbach, "4-stage OTDM multiplexer,"http://www.u2t.de/fileadmin/redakteure/Products/Datasheets/DS_OMUX-4_5v0.pdf.
M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

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