November 15, 2013 / Vol. 38, No. 22 / OPTICS LETTERS

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Compact wavelength-selective optical switch based on digital optical phase conjugation Zhiyang Li1,* and Havyarimana Claver1,2 1

College of Physical Science and Technology, Central China Normal University, Wuhan 430079, China 2 Department of Physics, University of Burundi, Bujumbura 2700, Burundi *Corresponding author: [email protected] Received August 27, 2013; revised October 9, 2013; accepted October 9, 2013; posted October 10, 2013 (Doc. ID 196475); published November 13, 2013

In this Letter, we show that digital optical phase conjugation might be utilized to construct a new kind of wavelength-selective switches. When incorporated with a multimode interferometer, these switches have wide bandwidth, high tolerance for fabrication error, and low polarization dependency. They might help to build large-scale multiwavelength nonblocking switching systems, or even to fabricate an optical cross-connecting or routing system on a chip. © 2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (130.0130) Integrated optics; (230.0230) Optical devices. http://dx.doi.org/10.1364/OL.38.004789

To construct an optical routing or optical cross connecting (OXC) system for a dense wavelength division multiplexing (DWDM) optical communication network, a large number of optical switches with quantities of in/out ports are needed. People used to cascade many 1 × 2 or 2 × 2 switches based on a Mach–Zehnder interferometer or directional coupler to form large-scale switching networks [1–4]. These cascaded switching networks often encounter blocking problems. They are also large in size due to slow bends employed to connect adjacent switches. Also, demultiplexing before switching and multiplexing after switching are necessary, since these switches are not wavelength selective. Switching based on a resonant ring is wavelength selective [5]. However it is sensitive to fabrication error. Moreover, each wavelength needs a resonant ring, which makes large-scale integration very complicated, not to mention those optical switches based on gratings, microelectromechanical systems, or liquid crystal optical switches that need careful alignment in space [6,7]. In this Letter, we show that digital optical phase conjugation (DOPC) might be utilized to construct a new kind of wavelength-selective switches, which might help to build large-scale nonblocking switching systems with much reduced size and very simplified structure. Optical phase conjugation is usually realized via some nonlinear optical effects [8]. Recently, DOPC using a spatial light modulator (SLM) attracted the interest of many researchers [9–12]. The author showed a little earlier that DOPC might be performed with the aid of an adiabatic waveguide structure (AWS) that decomposes an input optical field into the fundamental eigenmodes of a number of single-mode waveguides [12]. When a bundle of single-mode optical fibers are employed for decomposition, the conjugate field within each single-mode fiber could be reconstructed using SLMs. To fabricate integrated optical switches, we may use planar AWS for decomposition, as illustrated in Fig. 1. In this case the optical phase conjugate reflection within each single-mode waveguide might be carried out using a distributed Bragg grating (DBG) plus the proper phase adjustment under the control of a digitally generated voltage via the electro-optical 0146-9592/13/224789-04$15.00/0

effect. Due to reciprocity, the reflected optical phase conjugate field within each single-mode waveguide would go back, combine, and restore the original input light field. This ability to reconstruct the desired light field at the desired place might be employed for optical switching. Figure 1 illustrates a generalized structure of an optical switch based on DOPC. It has M isolated single-mode waveguides on the left side and N isolated single-mode waveguides on the right side. Between them there is an AWS for decomposition. On each single-mode waveguide on the right side there are sections marked as Pm and CPm for phase modulation and DBGm for selectively reflecting back wavelength λm . Since only guided modes are involved within the device and reflection is negligible in the AWS, the light fields propagating rightward on both the left and right sides could be expressed by column vectors Eleft  a1 ; a2 ; …aM T and Eright  b1 ; b2 ; …; bN T , where ai and bj are the complex amplitudes of the fundamental eigenmodes within each isolated single-mode waveguide on the left side and right side, respectively. In the frame of the mode-matching method, the field on the right side Eright could be related to the field on the left side Eleft by [12,13] Eright  TEleft ;

(1)

where T is an N × M transmission matrix of the AWS for a light field propagating from the left side to the right side,

Fig. 1. General structure of an optical switch based on DOPC. AWS, adiabatic waveguide structure; Pm , phase modulation section; CPm , complementary phase modulation section for wavelength λm . © 2013 Optical Society of America

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φ1;1 B φ2;1 B T@  φN;1

φ1;2 φ2;2  φN;2

  φi;j 

1 φ1;M φ2;M C C:  A φN;M

(2)

E¯ jright  E¯ iright  ΔΨTi;j ;

The element φi;j on the right-hand side of Eq. (2) stands for the complex amplitude of the fundamental eigenmode within the ith single-mode waveguide on the right side, which is caused by a unit fundamental eigenmode field incident from the jth single-mode waveguide on the left side. Similarly, the field on the left side Eleft could be related to the field on the right side Eright by Eleft  T0 Eright ;

(3)

where the prime by the T stands for transposition. If we transform the field Eright on the right side to its conjugation with the help of phase modulation section Pm and reflection of DBGm as illustrated in Fig. 1, using Eq. (3), the reflected light field at left side would be 0¯ Ere left  T Eright :

(4)

If we substitute Eq. (1) into Eq. (4), we get 0 Ere left  T TEleft :

(5)

0

The author has shown that T T is a unit matrix if reflection is negligible and no radiation eigenmodes are generated within the adiabatic structure [12]. In this ¯ situation Ere left  Eleft , which implies that the reflected conjugate light field E¯ right would return to the same waveguide on the left side due to reciprocity and restore the original input light field in its conjugate form. Based on the above theorem, we can perform switching based on DOPC. If a fundamental eigenmode light field with unit intensity incidents from the jth single-mode waveguide on the left side, we have Eleft−j  a1  0; a2  0; …; aj  1; …; aM  0T . Using Eq. (1) we can get the decomposed light field on the right side. If we transform the decomposed light field to its conjugation with the help of Pm and DBGm , we get E¯ jright  φ¯ 1;j ; φ¯ 2;j ; …; φ¯ N;j T :

(6)

The reflected conjugate light field would return to the jth waveguide on the left side due to reciprocity. Similarly, if a fundamental eigenmode light field with unit intensity incidents from the ith single-mode waveguide on the left side, that is, Eleft−i  a1  0; a2  0; …; ai  1; …; aM  0T , we can recover the original input light field at the ith single-mode waveguide on the left side by transforming the decomposed light field on the right side to its conjugation, E¯ iright  φ¯ 1;i ; φ¯ 2;i ; …; φ¯ N;i T :

simply add some modulation to E¯ iright in Eq. (7) to make it equal E¯ jright in Eq. (6),

(7)

Now if we want to switch the light field incidents from the ith single-mode waveguide to the jth single-mode waveguide on the left side, based on DOPC, we can

(8)

where, ΔΨi;j  φ¯ 1;j − φ¯ 1;i ; φ¯ 2;j − φ¯ 2;i ; …; φ¯ N;j − φ¯ N;i . To build a switch based on DOPC as illustrated in Fig. 1, we can chose a multimode interferometer (MMI) [14,15] as the AWS for decomposition, because it has many advantages. First, it has a relatively large tolerance for fabrication error. Second, it has a relatively wide bandwidth. Third, for a properly designed MMI, an input from one waveguide on the left side will be divided equally between all the waveguides on the the right side. This is very desirable in our application, because now the elements of ΔΨi;j have equal amplitudes. So, only phase modulations are needed during switching according to Eq. (8). As illustrated in Fig. 1, to perform phase modulation for wavelength λm , we introduced a phase modulation section Pm on each waveguide on the right side, which is made with electro-optical material covering a length of L. Under the control of digitally generated voltage, the refraction index of the electro-optical material on each waveguide on the right side could be accurately changed by an amount of Δnk so that Eq. (8) is satisfied, that is, 2π Δnk 2L  φ¯ k;j − φ¯ k;i λm

k  1; 2; …; N:

(9)

In the case of N × N MMI, the element φk;i could be calculated using the relation [14]  φk;i 

π 4N i − k2N − i  k  π π 4N i  k − 12N − i − k  1

if i  k  even ; if i  k  odd (10)

where i  1; 2; …N is the index of the waveguides on the left side counted bottom-up and k  1; 2; …; N is the index of the waveguides on the right side counted top-down. Figure 2 shows our finite difference time domain (FDTD) simulation results of a switch based on DOPC employing a 4 × 4 MMI. The MMI is assumed to be fabricated on an indium phosphate (GaAs/InP) wafer. It has a length of 286.6435 μm and width of 12 μm. The refraction indices for core and cladding are 3.3737 and 3, respectively. The length of phase modulation section Pm is set as 80 μm to keep the refraction index change Δnk needed to produce 2π phase modulation at the order of 10−3 . For convenience of simulation, the DBG1 adopted a periodic structure with a total length of 60 μm. Each period consists of two slices with the same width of 0.1172 μm and refraction indices of 3.3737 and 3.3037, respectively. The propagation directions were indicated by the arrows drawn on the left edge. Figures 2(a)–2(c) illustrate how the input field from the first waveguide was switched to the third and fourth waveguides counted bottom-up on the left side. When there is only one working wavelength, the cross talk might be defined as

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result, every time wavelength λm was switched, the unselected wavelengths that pass through DBGm would all be affected. However, when CPm are added, we can cause each CPm to produce a complementary phase modulation Δcnk so that 2π Δnk  Δcnk 2L  Constant: λm

(12)

Now all the wavelengths that pass through DBGm experience first a phase shift controlled by Δnk and then by a phase shift controlled by Δcnk . When Eq. (12) is satisfied, the total phase shift will be the same. In other words, all the wavelengths that pass through DBGm would behave as if they traveled an extended but identical length on every waveguide on the right side. Therefore, the switching of wavelength λm has little influence on the other wavelengths. Briefly, independent multiwavelength switching becomes possible with the help of complementary phase modulation sections. Figure 3 shows our FDTD simulation results of the simultaneous switching of two wavelengths using the same 4 × 4 MMI as in Fig. 2. In Fig. 3(a) a unit field with wavelength λ1  1543 nm was input from the first waveguide counted bottom-up, which was switched to the second

Fig. 2. Switching of a single wavelength λ  1555 nm. On the right are 2D field distributions, and on the left, 1D field distributions along the X direction at the positions indicated by the white dotted lines at (a) Z  1.05, (b) 1.05, and (c) 10.57 μm.

    I jE undesired j2 C cross  10 log undesired  10 log ; (11) I desired jE desired j2 where jE undesired j and jE desired j are field amplitudes in undesired and desired waveguides, respectively. From the field distributions in Fig. 2 we found that the maximum amplitudes of light fields in undesired waveguides are less than 0.15 and the amplitudes of light fields in desired waveguides are larger than 0.85. So the cross talk is below −15 dB. To check the polarization sensitivity, the input light field in Fig. 2(a) was set in TM mode, while the input light field in Fig. 2(b) was set in TE mode. The slight difference in field amplitudes in the fourth waveguide on the left side indicates that the device has a low polarization dependency. For multiwavelength switching, as illustrated in Fig. 1, on each waveguide on the right side we introduced a complementary phase modulation section CPm with the same length of Pm for wavelength λm . Without CPm the switching of one wavelength λm will change the phases of all the unselected wavelengths that pass through DBGm , because they will also experience the phase modulation as described by Eq. (9), which is different for different waveguides k on the right side. As a

Fig. 3. Simultaneous switching of the two wavelengths λ1  1543 nm and λ2  1588 nm. On the right are 2D field distributions, and on the left, 1D field distributions along the X direction at the positions indicated by the white dotted lines at (a) Z  10.64, (b) 18.27, and (c) 7.35 μm.

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waveguide. In Fig. 3(b) a unit field with wavelength λ2  1588 nm was input from the first waveguide but switched to the fourth waveguide. In Fig. 3(c) both λ1  1543 nm and λ2  1588 nm were input at the same time from the first waveguide and were switched to the second and fourth waveguides, respectively, exerting no influence on each other due to the compensation of CP1 . In the above simulation, to check the bandwidth of the device, one wavelength was set at the lowest possible wavelength of λ1  1543 nm. Another wavelength was set at the largest possible wavelength of λ2  1588 nm. Now the maximum cross talk increased to about −13 dB. Out of this band unwanted leakage and reflection would appear in the MMI, resulting in cross talk higher than −13 dB. Therefore, the device exhibited a bandwidth of 45 nm. With a bandwidth of 45 nm, one switch based on DOPC can handle about 56 wavelengths with a gap of 0.8 nm for DWDM application. As explained above, for the switching of one wavelength λm , a phase modulation section Pm , a DBGm , and a complementary phase modulation section CPm are needed, which are all arranged on the straight waveguides on the right side. This serial arrangement brings two advantages. First, the switch is nonblocking; that is, any wavelength from any input waveguide could be switched to any output waveguide if the output waveguide is not busy for the wavelength. Second, avoiding slow bends results in a compact size. In Fig. 3 the DBG1 for λ1  1543 nm adopted a periodical structure with a total length of 60 μm. Each period consists of two slices with an equal width of 0.1166 μm and refraction indices of 3.3737 and 3.3037, respectively. It has a bandwidth of 4 nm. The DBG2 for λ2  1588 nm has a total length of 70 μm. Each period consists of two slices with an equal width of 0.12 μm and refraction indices of 3.3737 and 3.3037, respectively. So the total length of P1 , DBG1 , and CP1 is 220 μm, and the total length of P2 , DBG2 , and CP2 is 230 μm. Even when the length of each DBGm was increased to obtain a bandwidth of 0.8 nm, the addition of one wavelength might bring a device length increment of less than one millimeter. In Figs. 2 and 3

the 12 μm wide MMI supported four input/output waveguides. To support 65 input/output waveguides, the width of a 65 × 65 MMI might increase to 204 μm. Then, on a 16 mm × 64 mm chip we might fabricate 64 MMI, each MMI connecting an input fiber and acting as a 1 to 64 optical switch. These 64 optical switches together are enough to construct a 56wavelengths × 64inputfibers × 64outputfibers OXC system. In conclusion, based on DOPC we can construct compact wavelength-selective optical switches, which might help to build large-scale nonblocking multiwavelength switching systems for DWDM applications, or even to fabricate an OXC or routing system on a chip. References 1. Q. Tao, F. Luo, D. Cai, Q. Liang, Z. Wan, X. Song, and X. Liu, Opt. Appl. XLI, 669 (2011). 2. R. Schiek, R. Iwanow, G. Stegeman, T. Pertsch, F. Lederer, Y. H. Min, and W. Sohler, Appl. Phys. Lett. 87, 011109 (2005). 3. Z. Jin, C. J. Kaalund, and G. Peng, IEEE J. Quantum Electron. 41, 1548 (2005). 4. T. Goh, Proc. SPIE 4582, 49 (2001). 5. G. N. Nielson, D. Seneviratne, F. Lopez-Royo, P. T. Rakich, Y. Avrahami, M. R. Watts, H. A. Haus, H. L. Tuller, and G. Barbastathis, IEEE Photon. Technol. Lett. 17, 1190 (2005). 6. J. Tsai, S. Huang, D. Hah, H. Toshiyoshi, and M. C. Wu, IEEE Photon. Technol. Lett. 16, 1041 (2004). 7. H. Kishikawa, K. Kimiya, N. Goto, and S.-I. Yanagiya, J. Lightwave Technol. 28, 172 (2010). 8. G. S. He, Prog. Quantum Electron. 26, 131 (2002). 9. S. Ke, F. Reto, and C. Meng, Nat. Photonics 6, 657 (2012). 10. T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. K. Park, and Z. Yaqoob, Science Rep. 3, 1909 (2013). 11. L. Zhiyang, Opt. Commun. 293, 10 (2013). 12. L. Zhiyang, Opt. Commun. 283, 3646 (2010). 13. P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001). 14. M. Bachmann, P. A. Besse, and H. Melchior, Appl. Opt. 33, 3905 (1994). 15. L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).

Compact wavelength-selective optical switch based on digital optical phase conjugation.

In this Letter, we show that digital optical phase conjugation might be utilized to construct a new kind of wavelength-selective switches. When incorp...
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