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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 1 — Jan. 7, 2008
  • pp: 248–257
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New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer

Yaw-Dong Wu, Tien-Tsorng Shih, and Mao-Hsiung Chen  »View Author Affiliations


Optics Express, Vol. 16, Issue 1, pp. 248-257 (2008)
http://dx.doi.org/10.1364/OE.16.000248


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Abstract

We propose new all-optical logic gates containing a local nonlinear Mach-Zehnder interferometer waveguide structure. The light-induced index changes in the Mach-Zehnder waveguide structure make the output signal beam propagate through different nonlinear output waveguides. Based on the output signal beam propagating property, various all-optical logic gates by using the local nonlinear Mach-Zehnder waveguide interferometer structure with two straight control waveguides have been proposed to perform XOR/NXOR, AND/NAND, and OR/NOR logic functions.

© 2008 Optical Society of America

1. Introduction

All-optical ultrafast photonic devices using nonlinear optical effect for applications to optical communications and optical signal processing systems have been interested popularly. There has been great interest in the possibility of using nonlinear optical waveguide devices as ultrafast all-optical switching and logic devices for optical signal processing and optical communication systems. Several all-optical switching and logic devices using optical nonlinearity have ever been proposed and implemented [1–8

1. Y. D. Wu, M. H. Chen, and C. H. Chu, “All-Optical Logic Device Using Bent Nonlinear Taperred Y-Junction Waveguide Structure,” Fiber and Integrated Optics. 20, 517–524 (2001).

]. Most of the conventional all-optical devices are based on uniformly nonlinear structure. Therefore, the whole of the waveguide has optical nonlinearity uniformly. In optical waveguide structure of uniform nonlinearity, several interesting optical properties have been shown, however, there are still more attractive propagation characteristics in waveguide structures combined a nonlinear material with a linear one. Some theoretical studies about the optical waveguide structures made from linear and nonlinear materials have been proposed, for example, a waveguide structure composed of linear films bounded by one or two nonlinear media [9–14

9. C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE J. Quantum Electron. 21, 774–783 (1985). [CrossRef]

] or a nonlinear film sandwitched between linear media [15–18

15. A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. 22, 319–324 (1986). [CrossRef]

] or arbitrary layers with nonlinear media [19

19. C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, “Analyzing multilayer optical waveguide with all nonlinear layers,” Optics Express 15, 2499–2516 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2499 [CrossRef] [PubMed]

].

Recently, there has been great interesting in the Mach-Zehnder waveguide interferometer device [20–23

20. X. F. Liu, M.L. Ke, B.C. Qiu, A.C. Bryce, and J.H. Marsh, “Fabrication of monolithically integrated Mach-Zehnder asymmetric interferometer switch,” Indium Phosphide and Related Materials, 2000. Conference Proceedings. 2000 International Conference on. 412–414 (2000).

]. The Mach-Zehnder waveguide interferometer device has been developed for the use of modulating, switching and logic gates, etc. Most of them are operated by the principles of electric-optic effect where the change of refractive index in the arms of Mach-Zehnder interferometer is produced by applying the external electric field. The all-optical Mach-Zehnder waveguide interferometer device has been presented previously [24–25

24. A. M. Kan’an and P. Likam wa, “Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer,” J. Opt. Soc. Am. B. 14, 3217–3223 (1997). [CrossRef]

]. In this paper, based on the principle of optical couplers, a local nonlinear Mach-Zehnder waveguide interferometer structure will be proposed. The nonlinear Mach-Zehnder interferometer with two straight control waveguides will be used to design various all-optical logic gates with XOR/NXOR, AND/NAND, and OR/NOR functions. The light-induced index changes in the Mach-Zehnder waveguide break the symmetry of structure and make the output signal beam propagate through different nonlinear output waveguides. These characteristics are investigated by using the beam propagation method (BPM) [26

26. Y. Chung and N. Dagli, “As assessment of finite difference beam propagation method,” IEEE Journal of Quantum Electronics. 26, 1335–1339 (1994). [CrossRef]

]. By properly fixing the input signal power and launching the control beams, the numerical results show that the proposed waveguide structure could function as all-optical XOR/NXOR, AND/NAND, and OR/NOR logic gates.

2. Analysis

The proposed waveguide structures of all-optical logic gates are composed of the local nonlinear Mach-Zehnder waveguide interferometer with two straight control waveguides and two output waveguides as shown in Fig. 1 (a)–(c). The scheme employs angular deflection of spatial solitons controlled by the phase modulation created in the local nonlinear MZI which functions like a phase shifter. The presence of the evanescent tail of the optical beam in the straight control waveguide will introduce the phase difference between the two arms of the local nonlinear MZI. Here we consider three cases of the different local nonlinear distribution in two arms of the nonlinear Mach-Zehnder interferometer. For the first case, the local nonlinear waveguides are located on two arms of the nonlinear Mach-Zehnder interferometer, as shown in Fig. 1(a). For the second case, the local nonlinear waveguide is only located on the left arm of the nonlinear Mach-Zehnder interferometer, as shown in Fig. 1(b). For the third case, the local nonlinear waveguide is only located on the right arm of the nonlinear Mach-Zehnder interferometer, as shown in Fig. 1(c). The nonlinear Mach-Zehnder interferometer with two local nonlinear waveguides functions like a phase shifter and is used to propagate the signal beam. Since the control beams are useless in the following process, a lossy medium at the end of two straight control waveguides is used to attenuate it. For the nonlinear Mach-Zehnder interferometer, the branching angle is θ1, w1 the width of control waveguide, w2 the width of Mach-Zehnder waveguide, L1 the length of Mach-Zehnder waveguide, L2 the length of nonlinear output waveguides, and L3 the length of local nonlinear waveguides. The distance between the local control waveguide and the nearest signal waveguide is l and the branching angle between the output guides is θ2.

For simplicity, we consider the transverse electric polarized waves propagating along the z direction. The wave equation can be reduced to

2Eyi=ni2c22Eyit2,  i=1,2,,m
(1)

with solutions of the form

Eyi(x,z,t)=εi(x)exp[j(ωtβk0z)]
(2)

where ω is the angular frequency, k 0 is the wave number in the free space, and β is the effective refractive index. For a Kerr-type nonlinear medium, the square of the refractive index of the guiding film can be expressed as[27–28

27. C. T. Seaton, X. Mai, G. I. Stegeman, and N. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

]:

ni2=n0i2+αiεi(x)2,i=2,4,,m1
(3)

where n 0i and αi are the linear refractive index and the nonlinear coefficient of the i-th layer nonlinear guiding film, respectively. The transverse electric field in each layer can be

Fig. 1. The proposed waveguide structures of all-optical logic gates (a) XOR/NXOR gate, (b) AND/NAND gate, (c) OR/NOR gate.
Fig. 2. The structure of multilayer optical waveguides with nonlinear guiding films.

expressed as:

ε1(x)=Esexp(p1x)inthesubstrate
(4)
εi(x)=EI(i2)exp{pi[x(i12)d(i32)w]}+EI(i1){exppi[x(i12)d(i12)w]}
i=3,5,,m2intheinteractionlayers
(5)
εi(x)=bicn{Ai[x(i21)(d+w)+x0i]li}
i=2,4,,m1intheguidingfilm,forβ<ni
(6)
εi(x)=bicn{Ai[x(i21)(d+w)+x0i]li}
i=2,4,,m1intheguidingfilm,forβ>ni
(7)
εm(x)=Ecexp{pm[x(m12)d(m32)w]}inthecladding
(8)

where cn is a Jacobian elliptic function, and the constants d and w are the widths of the guiding film and the interaction layer, respectively.

The constants pi, bi, Ai, li, bi, Ai, and li can be expressed as

pi=k0β2ni2,bi2=qi4+2αik02Kiqi2αik02,
Ai=[(ai2+bi2)(αik022)]12,li=bi2(ai2+bi2),
bi2=Qi4+2αik02Ki+Qi2αik02,Ai=[(ai2+bi2)(αik022)]12,
li=bi2(ai2+bi2),

where the constants ai, ai, qi, Qi, Ki, x 0i, and x0i are all constants which can be determined by a numerical method on a computer.

3. Numerical Results

In this paper, the wave Eq. (1) was solved numerically by using the BPM with 4096 transverse sampling points and a longitudinal step length Δz=0.05µm. The numerical data have been calculated with the value: the total propagation distance z=12500µm, θ1=0.5°, θ2=0.25°, l=3.5µm, w1=1µm, w2=2µm, L1=10000µm, L2=2500µm, L3=4100µm, α=6.3786µm2/V2, nf0=1.55, nc0=1.545, the free space wavelength λ=1.55 µm. We first examine the XOR/NXOR logic functions, as shown in Fig. 3(a)–(d). Figure 3 shows the typical evolutions of the input light waves propagating along the structure with the input control power Pc=23.7 W/m and the input signal power Ps=79 W/m. When there is no control straight through the central output guide C, as shown in Fig. 3(a). When only the right control guide B is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 3(b). When only the left control guide A is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 3(c). When both of the control guides A and B are excited simultaneously, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 3(d). As the results shown above, the output port C functions as an NXOR Gate and the output port D functions as an XOR gate. All logic states of the XOR and NXOR gates are shown in Table 1.

Fig. 3. The XOR/NXOR logic functions with Pc=23.7 W/m and Ps=79 W/m (a) A=0, B=0, (b) A=0, B=1, (c) A=1, B=0, (d) A=1, B=1.

Table 1. The logic states of the XOR and NXOR gates.

table-icon
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| View All Tables

Finally, we examine the OR/NOR logic functions, as shown in Fig. 5(a)–(d). Figure 5 shows the typical evolutions of the input light waves propagating along the structure with the input control power Pc=31.2 W/m and the input signal power Ps=78 W/m. When there is no control beam, the output signal beam will propagate through the right output guide D, as shown in Fig. 5(a). When only the right control guide B is excited, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(b). When only the left control guide A is excited, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(c). When both of the control guides A and B are excited simultaneously, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(d). As the results shown above, the output port C functions as an OR gate and the output port D functions as a XOR gate. All logic states of the OR and NOR gates are shown in Table3.

For the results shown above, we confirm that the proposed waveguide structure could really function as all-optical XOR/NXOR, AND/NAND, and OR/NOR logic gates.

Fig. 4. The AND/NAND logic functions with Pc=30 W/m and Ps=60 W/m (a) A=0, B=0, (b) A=0, B=1, (c) A=1, B=0, (d) A=1, B=1.

Table 2. The logic states of AND and NAND gates.

table-icon
View This Table
| View All Tables
Fig. 5. The OR/NOR logic functions with Pc=31.2 W/m and Ps=78 W/m (a) A=0, B=0, (b) A=0, B=1, (c) A=1, B=0, (d) A=1, B=1.

Table 3. The logic states of OR and NOR gates.

table-icon
View This Table
| View All Tables

4. Conclusions

In conclusion, new all-optical logic devices have been proposed by using the property of repulsion and attraction between optical light waves of two arms in the nonlinear Mach-Zehnder interferometer. When the control beam is on or off, the output signal beam will propagate through different output waveguides. The numerical results show that the proposed devices could really function as all-optical XOR/NXOR, AND/NAND, OR/NOR logic gates. It could be a potential key component in the application of optical signal processing and optical computing. In principle, the logic elements can be implemented by combining the nonlinear material with the planar lightwave circuit fabrication technique. Moreover, several new approaches have been proposed and demonstrated which can realize this device farther.

Acknowledgement

The authors would like to thank M. L. Whang and R. Z. Tasy for their help. This work was partly supported by National Science Council of Taiwan under Grants NSC 96-2221-E-151-025 and NSC 96-2221-E-151-024-MY3 and Ministry of Education of Taiwan under Grants 95C9031, 95TSFC9031, and 95A6077.

References and links

1.

Y. D. Wu, M. H. Chen, and C. H. Chu, “All-Optical Logic Device Using Bent Nonlinear Taperred Y-Junction Waveguide Structure,” Fiber and Integrated Optics. 20, 517–524 (2001).

2.

Y. D. Wu, M. H. Chen, and R. Z. Tasy, “A new all-optical Switching Device by using the nonlinear Mach-Zehnder interferometer with a control waveguides,” Proceedings CLEO/Pacific Rim Conference on Laser and Electro-Optics. I, 292 (2003).

3.

Y. D. Wu, M. H. Chen, and H. J. Tasi, “Novel All-optical Switching Device with Localized Nonlinearity,” Optical Society of America, Optics in Computing Devices.297–299 (2002).

4.

Y. D. Wu, “Nonlinear All-Optical Switching Device by Using the Spatial Soliton Collision,” Fiber and Integrated Optics. 23, 387–404 (2004). [CrossRef]

5.

F. Garzia and M. Bertolotti, “All-optical security coded key,” Optical Quantum Electronics. 33, 527–540 (2001). [CrossRef]

6.

Y. H. Pramono and Endarko, “Nonlinear Waveguides for Optical Logic and Computation,” Journal of Nonlinear Optical Physics & Materials. 10, 209–222 (2001). [CrossRef]

7.

Y. H. Pramono, M. Geshiro, T. Kitamura, and S. Sawa, “Optical Logic OR-AND-NOT and NOR Gates in Waveguides Consisting of Nonlinear Material,” IEICE Trans. Electron. E83-C, 1755–1762 (2000).

8.

Y. D. Wu, M. L. Whang, M. H. Chen, and R. Z. Tasy, “All-optical Switch Based on the Local Nonlinear Mach-Zehnder Interferometer,” Optics Express 15, 9883–9892 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-16-9883 [CrossRef] [PubMed]

9.

C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE J. Quantum Electron. 21, 774–783 (1985). [CrossRef]

10.

L. Leine, C. Wacher, U. Langbein, and F. Lederer, “Evolution of nonlinear guided optical fields down a dielectric film with nonlinear cladding,” J. Opt. Soc. Amer. B. 5, 547–558 (1988). [CrossRef]

11.

S. She and S. Zhang, “Analysis of nonlinear TE waves in a periodic refractive index waveguide with nonlinear cladding,” Opt. Comm. 161, 141–148 (1999). [CrossRef]

12.

Y. D. Wu, M. H. Chen, and H. J. Tasi, “A General Method for Analyzing the Multilayer Optical Waveguide with Nonlinear Cladding and Substrate”, SPIE Design, Fabrication, and Characterization of Photonic Device II. 4594, 323–331 (2001).

13.

Y. D. Wu and M. H. Chen, “Analyzing multiplayer optical waveguides with nonlinear cladding and substrates,” J. Opt. Soc. Am. B. 19, 1737–1745 (2002). [CrossRef]

14.

Y. D. Wu and M. H. Chen, “The fundamental theory of the symmetric three layer nonlinear optical waveguide structures and the numerical simulation,” J. Nat. Kao. Uni. of App. Sci. 32, 7982–7996 (2002).

15.

A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. 22, 319–324 (1986). [CrossRef]

16.

H. Murata, M. Izutsu, and T. Sueta, “Optical bistability and all-optical switching in novel waveguide functions with localized optical nonlinearity,” J. Lightwave Technol. 16, 833–840 (1998). [CrossRef]

17.

Y. D. Wu and Y. C. Jang, “Analyzing and Numerical study of Seven-Layer Optical Waveguide with Localized Nonlinear Central guiding Film,” Proceedings Electrical and Information Engineering Symposium.24–28 (2003).

18.

Y. D. Wu, “Analyzing Multilayer Optical Waveguides with a Localized Arbitrary Nonlinear Guiding Film,” IEEE J. Quantum. Electron. 40, 529–540 (2004). [CrossRef]

19.

C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, “Analyzing multilayer optical waveguide with all nonlinear layers,” Optics Express 15, 2499–2516 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2499 [CrossRef] [PubMed]

20.

X. F. Liu, M.L. Ke, B.C. Qiu, A.C. Bryce, and J.H. Marsh, “Fabrication of monolithically integrated Mach-Zehnder asymmetric interferometer switch,” Indium Phosphide and Related Materials, 2000. Conference Proceedings. 2000 International Conference on. 412–414 (2000).

21.

H. Ehlers, M. Schlak, and U.H.P. Fischer, “Multi-fiber-chip-coupling modules for monolithically integrated Mach-Zehnder interferometers for TDM/WDM communication systems,” Optical Fiber Communication Conference and Exhibit. 3, WDD66-1~66–3 (2001).

22.

L. Pavelescu, “Simplified design relationships for silicon integrated optical pressure sensors based on Mach-Zehnder interferometry with antiresonant reflecting optical waveguides,” Semiconductor Conference, 2001. CAS 2001 Proceedings. International. 1, 201–204 (2001). [CrossRef]

23.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, “All-optical logic gates containing a two-mode nonlinear waveguide,” IEEE Journal of Quantum Electronics. 38, 37–46 (2002). [CrossRef]

24.

A. M. Kan’an and P. Likam wa, “Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer,” J. Opt. Soc. Am. B. 14, 3217–3223 (1997). [CrossRef]

25.

Y. H. Pramono and Endarko, “Nonlinear waveguides for optical logic and computation,” Journal of Nonlinear Optical Physics & Materials. 10, 209–222 (2001). [CrossRef]

26.

Y. Chung and N. Dagli, “As assessment of finite difference beam propagation method,” IEEE Journal of Quantum Electronics. 26, 1335–1339 (1994). [CrossRef]

27.

C. T. Seaton, X. Mai, G. I. Stegeman, and N. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. 24, 593–599 (1985).

28.

H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, “Experimental observation of nonlinear guided waves,” Opt. Lett. 9, 238–240 (1984). [CrossRef] [PubMed]

OCIS Codes
(130.3750) Integrated optics : Optical logic devices
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.1150) Optical devices : All-optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 8, 2007
Revised Manuscript: December 14, 2007
Manuscript Accepted: December 18, 2007
Published: January 3, 2008

Citation
Yaw-Dong Wu, Tien-Tsorng Shih, and Mao-Hsiung Chen, "New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer," Opt. Express 16, 248-257 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-248


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References

  1. Y. D. Wu, M. H. Chen, and C. H. Chu, "All-optical logic device using bent nonlinear tapered Y-junction waveguide structure," Fiber Integr. Opt. 20, 517-524 (2001).
  2. Y. D. Wu, M. H. Chen, and R. Z. Tasy, "A new all-optical switching device by using the nonlinear Mach-Zehnder interferometer with a control waveguides," Proceedings CLEO/Pacific Rim Conference on Laser and Electro-Optics. I, 292 (2003).
  3. Y. D. Wu, M. H. Chen, and H. J. Tasi, "Novel all-optical switching device with localized nonlinearity," Optical Society of America, Optics in Computing Devices, 297-299 (2002).
  4. Y. D. Wu, "Nonlinear all-optical switching device by using the Spatial Soliton Collision," Fiber Integr Opt. 23, 387-404 (2004). [CrossRef]
  5. F. Garzia and M. Bertolotti, "All-optical security coded key," Opt. Quantum Electron. 33, 527-540 (2001). [CrossRef]
  6. Y. H. Pramono and Endarko, "Nonlinear waveguides for optical logic and computation," J. Nonlinear Opt. Phys. Mater. 10, 209-222 (2001). [CrossRef]
  7. Y. H. Pramono, M. Geshiro, T. Kitamura, and S. Sawa, "Optical logic OR-AND-NOT and NOR gates in waveguides consisting of nonlinear material," IEICE Trans. Electron. E 83-C, 1755-1762 (2000).
  8. Y. D. Wu, M. L. Whang, M. H. Chen, and R. Z. Tasy, "All-optical switch based on the local Nonlinear Mach-Zehnder Interferometer," Opt. Express 15, 9883-9892 (2007). [CrossRef] [PubMed]
  9. C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783 (1985). [CrossRef]
  10. L. Leine, C. Wacher, U. Langbein, and F. Lederer, "Evolution of nonlinear guided optical fields down a dielectric film with nonlinear cladding," J. Opt. Soc. Am B. 5, 547-558 (1988). [CrossRef]
  11. S. She and S. Zhang, "Analysis of nonlinear TE waves in a periodic refractive index waveguide with nonlinear cladding," Opt. Commun. 161, 141-148 (1999). [CrossRef]
  12. Y. D. Wu, M. H. Chen, and H. J. Tasi, "A General Method for Analyzing the Multilayer Optical Waveguide with Nonlinear Cladding and Substrate," SPIE Design, Fabrication, and Characterization of Photonic Device II 4594, 323-331 (2001).
  13. Y. D. Wu and M. H. Chen, "Analyzing multiplayer optical waveguides with nonlinear cladding and substrates," J. Opt. Soc. Am. B. 19, 1737-1745 (2002). [CrossRef]
  14. Y. D. Wu and M. H. Chen, "The fundamental theory of the symmetric three layer nonlinear optical waveguide structures and the numerical simulation," J. Nat. Kao. Uni. App. Sci. 32, 7982-7996 (2002).
  15. A. D. Boardman and P. Egan, "Optically nonlinear waves in thin films," IEEE J. Quantum Electron. 22, 319-324 (1986). [CrossRef]
  16. H. Murata, M. Izutsu, and T. Sueta, "Optical bistability and all-optical switching in novel waveguide functions with localized optical nonlinearity," J. Lightwave Technol. 16, 833-840 (1998). [CrossRef]
  17. Y. D. Wu and Y. C. Jang, "Analyzing and numerical study of seven-layer optical waveguide with localized nonlinear central guiding film," Proceedings Electrical and Information Engineering Symposium 24-28 (2003).
  18. Y. D. Wu, "Analyzing multilayer optical waveguides with a localized arbitrary nonlinear guiding film," IEEE J. Quantum. Electron. 40, 529-540 (2004). [CrossRef]
  19. C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, "Analyzing multilayer optical waveguide with all nonlinear layers," Opt. Express 15, 2499-2516 (2007). [CrossRef] [PubMed]
  20. X. F. Liu, M. L. Ke, B. C. Qiu, A. C. Bryce, and J. H. Marsh, "Fabrication of monolithically integrated Mach-Zehnder asymmetric interferometer switch," Indium Phosphide and Related Materials, 2000. Conference Proceedings 2000 International Conference 412-414 (2000).
  21. H. Ehlers, M. Schlak, and U. H. P. Fischer, "Multi-fiber-chip-coupling modules for monolithically integrated Mach-Zehnder interferometers for TDM/WDM communication systems," Optical Fiber Communication Conference and Exhibit. 3, WDD66-1~66-3 (2001).
  22. L. Pavelescu, "Simplified design relationships for silicon integrated optical pressure sensors based on Mach-Zehnder interferometry with antiresonant reflecting optical waveguides," Semiconductor Conference, 2001. CAS 2001 Proceedings. International 1, 201-204 (2001). [CrossRef]
  23. T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron 38, 37-46 (2002). [CrossRef]
  24. A. M. Kan’an and P. Likamwa, "Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer," J. Opt. Soc. Am. B. 14, 3217-3223 (1997). [CrossRef]
  25. Y. H. Pramono and Endarko, "Nonlinear waveguides for optical logic and computation," J. Nonlinear Opt. Phys. Mater. 10, 209-222 (2001). [CrossRef]
  26. Y. Chung and N. Dagli, "As assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1994). [CrossRef]
  27. C. T. Seaton, X. Mai, G. I. Stegeman, and N. G. Winful, "Nonlinear guided wave applications," Opt. Eng. 24, 593-599 (1985).
  28. H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, "Experimental observation of nonlinear guided waves," Opt. Lett. 9, 238-240 (1984). [CrossRef] [PubMed]

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