Abstract

We have analyzed the multi-mode interference effect depending on the wavelength and the polarization states of input beam in a multi-mode Ti:LiNbO3 waveguide at about 1300 nm region. The transmitted optical signal of a Ti:LiNbO3 waveguide shows the periodic oscillation as a function of input wavelength. The measured average periodicity of the oscillation in TM and TE polarization beams were about 18 nm and 48 nm, respectively. Actually, the periodicity is determined by the refractive index difference between the two modes (fundamental and first modes). Therefore, we have explained the experimental results with the theoretical calculations which are derived from a quasi-analytical technique based on the effective-refractive-index method and the equation of coupling length determined by the mode phase factor in the multi-mode waveguide.

© 2009 Optical Society of America

1. Introduction

A Ti:LiNbO3 waveguide can provide various good optical properties such as a low propagation loss, electro-optic, thermo-optic, acousto-optic, and nonlinear optic effects. Therefore, a Ti:LiNbO3 waveguide has been well utilized in various optical devices such as electro-optic modulator [1], optical switch [2,3], polarization mode dispersion compensator [4], wavelength converter [5], optical logic gate [6], Solc-type wavelength filter [7], and compact laser sources [8]. In basic, an integrated optic device based on a waveguide can give various functionalities by using not only integration elements (metal electrodes, acoustical absorber, photorefractive grating, periodically reversed microdomains, etc.) but also waveguide mode conditions. However, most of the Ti:LiNbO3 waveguide devices have been exploited based on a single-mode waveguide. Indeed, graded index waveguide such as a multi-mode Ti:LiNbO3 waveguide can make a multi-mode interference (MMI) effect [9] which reproduce an input optical field profile along the waveguide in single or multiple images with certain periodic intervals. A MMI effect is mainly adapted in a functional photonic integrated circuits based on semiconductor [10,11] and fiber devices [12,13] for optical switches [10,14], sensors [11-13], wavelength division multiplexer [15,16] and so on. However, up to now, no research has been reported on a MMI effect in a Ti:LiNbO3 waveguide except the application device for temperature insensitive comb filter [17]. In this paper, we have observed and analyzed the MMI effect depend on the wavelength and the polarization states of input beam in a Ti:LiNbO3 waveguide which has multi-mode guiding condition at about 1300 nm region. We have also compared the experimental results and the theoretical calculations which are derived from the refractive indices (fundamental and first modes) of a Ti:LiNbO3 waveguide [18] and the beat length determined by the mode phase factor in the multi-mode waveguide [19].

2. Ti:LiNbO3 waveguide fabrication and experimental setup

A 33-mm long Ti:LiNbO3 channel waveguide of with a 7-µm width was fabricated by diffusing 980-nm thick Ti stripes upon the −Z face of 0.5-mm thick Z-cut LiNbO3 substrate along the X axis of crystal line. The diffusion time of Ti stripes was 9 h which is 1.5 h more than that of a usual single-mode Ti:LiNbO3 waveguide (@ 1550 nm) fabrication process [20]. Such a long diffusion time allows a multi-mode guiding at 1300 nm wavelength region. The multi-mode guiding condition (TEM00, TEM10) at about 1300 nm was confirmed by using a broadband light source and an infrared camera. The full width at half-maximum (FWHM) of the horizontal and vertical direction were measured to be 5.5 and 2.8 µm, respectively. The propagation losses for TM and TE modes of waveguide were determined by the Fabry-Perot method to be 0.11 dB/cm and 0.05 dB/cm, respectively (@ 1550 nm) [21].

 

Fig. 1. Experimental setup to observe the MMI effect in a Ti:LiNbO3 waveguide depending on the wavelength and the polarization states of input beam; WSFL : wavelength swept fiber laser, and OSA : optical spectrum analyzer, PC : polarization controller, PBS : polarization beam splitter, BS : beam splitter, IR Camera : infrared camera.

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The experimental setup to analyze the MMI effect in a Ti:LiNbO3 waveguide is shown in Fig. 1. An optical signal from a home-made wavelength swept fiber laser (WSFL) which has 10 mW average power and 15 kHz repetition ratio was collimated and end-fire coupled into the Ti:LiNbO3 waveguide by a ×10 objective lens. The polarization direction of input beam was adjusted 45° against optical axis of the Ti:LiNbO3 waveguide and the output signal from the waveguide was separated by polarization beam splitter into a TM- and a TE- polarized beams. These two orthogonal polarized beams were monitored by an optical spectrum analyzer. A 1% of the transmitted TM-polarized beam was reflected by a beam splitter and monitored by an infrared camera. During the experiment, the temperature of the Ti:LiNbO3 waveguide was kept at 25°C by Peltier device.

3. MMI effect in a Ti:LiNbO3 waveguide

Figure 2 shows the mode profiles of output beam (TM polarization) from the Ti:LiNbO3 waveguide which were measured at the IR camera in a Fig. 1. As shown in Fig. 2, the input beam profile was reproduced according to the wavelength of WSFL in single or multiple images (see the movie file Media 1). Such kind of a self-imaging effect can be explained by the MMI in a multi-mode graded index waveguide [9]. In other words, the interference between TEM00-and TEM10-modes leads to the periodic oscillation in waveguide images. To measure the optical spectrum of a 99% of the TM-polarized beam, the transmitted beam was coupled into a single-mode fiber which is connected to the optical spectrum analyzer (OSA) by ×10 objective lens.

 

Fig. 2. Output beam mode profiles as a function of wavelength. The wavelength of WSFL was swept from 1277.5 nm to 1318.5 nm (Media 1).

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The measured optical spectrum of transmitted TM-polarized beam is shown in Fig. 3. The black scatter-line indicates the optical spectrum which was measured at position A (after Lens3 in Fig. 1) through the iris diaphragm. As the same way, the other spectrum (blue scatter-line) in Fig.3 was measured at position B. The measured optical spectra of the direct and the mirror images [17] show a periodic oscillation as a function of wavelength of input beam. The measured periodicity of both spectra were about 18.1 nm and phase difference between two fringe spectra was about 180°, which means that this waveguide can be used for not only a wavelength filter [17] but also functional devices such as MMI coupler [22], multimode splitter [23], optical switch [10], wavelength division multiplexer [15] and so on.

 

Fig. 3. Transmitted optical signal of TM polarized beam as a function of wavelength. The black scatter-line and blue scatter-line indicate the optical spectra which are measured at position A and B, respectively.

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The period and the number of oscillation in a certain sample (Ti:LiNbO3) length L, can be calculated by the following equation;

Ni=L2Lc=ni,0ni,1λ0L,

where n0 and n1 are the effective refractive indices of the fundamental and first-order modes, i indicates polarization direction (ordinary or extraordinary) of input beam and the coupling length Lc is defined by

Lc=πβi,0βi,1=λ02(ni,0ni,1),

where β0 and β1 are the propagation constants of the fundamental and first-order modes and λ0 is the wavelength of input beam. The values of the effective refractive indices in a Ti:LiNbO3 waveguide are given following equation;

n(x,y)=nsub+δn(x,y),

where nsub and δn(x,y) are the refractive index of bulk LiNbO3 and refractive index change by Ti diffusion, respectively. x and y indicate ordinary and extraordinary directions. The value of δn(x,y) used in theoretical calculation was induced by a quasi-analytical technique based on the effective-refractive-index method [18].

 

Fig. 4. (a) The calculated effective refractive indices of the fundamental and first-order modes in a TM polarized beam. (b) The number of oscillation in a 33-mm Ti:LiNbO3 waveguide as a function of input wavelength. The black and red lines indicate theoretical and experimental data, respectively. The filled (oe-17-13-10718-i001.jpg) and open (oe-17-13-10718-i002.jpg) circles indicate maximum constructive position and destructive position, respectively.

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Figure 4(a) and (b) show the calculated effective refractive indices of extraordinary wave and the number of oscillation in a 33-mm Ti:LiNbO3 waveguide as a function of input wavelength at room temperature. Actually, when light propagate through a Ti:LiNbO3 waveguide, the input beam profile is reproduced according to not only the wavelength of input beam (see. Fig. 2) but also the position of waveguide. Therefore, longer length of waveguide can provides larger number of periodic oscillation (Eq. (1)). In our case, the number of oscillation was calculated more than 50 at about 1300 nm region as you can see in Fig. 4(b). The values of both refractive indices (fundamental and first-order modes) decreased when wavelength increased. However, the refractive index difference between two modes was almost constant to the wavelength and it was about 2.1×10-3. Therefore, the periodicity of the oscillation showed a slight decrease as a function of the wavelength and the calculated average value was about 18.1 nm which is almost same value of the measured periodicity in Fig. 3.

In the case of TE polarization, the calculated refractive index difference between two modes (fundamental and first modes) was about 1.38×10-3 which is smaller than that of TM polarization case (see Fig. 6(a)). Therefore, the periodicity of the oscillation was longer than that of TM polarization case. Fig. 5 shows the optical spectra as a function of wavelength at position A and B (after Lens4 in Fig. 1). The periodicity of both spectra were rapidly reduced as increased of input beam wavelength and the periodicity varied from 55 nm to 42 nm at 1300 nm wavelength region. Such kind of long period and rapid decrease of the periodicity are due to the small index difference between two modes (fundamental and first-order modes).

 

Fig. 5. Transmitted optical signal of TE polarized beam as a function of wavelength. The black scatter-line and blue scatter-line indicate the optical spectra which are measured at position A and B, respectively.

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The theoretical calculation results on effective refractive indices of ordinary wave are shown in Fig. 6(a). As shown in Fig. 6(b), the number of oscillation was less than that of TM polarization case (Fig. 4(b)). The calculated periodicity was about 41.1 nm which is a little bit shorter than that of the measured value in Fig. 5.

 

Fig. 6. (a) The calculated effective refractive indices of the fundamental and first-order modes in a TE polarized beam. (b) The number of oscillation in a 33 mm Ti:LiNbO3 waveguide as a function of input wavelength. The black and red lines indicate theoretical and experimental data, respectively. The filled (oe-17-13-10718-i003.jpg) and vacant (oe-17-13-10718-i004.jpg) circles indicate maximum constructive position and destructive position, respectively.

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4. Conclusion

The MMI effect in a multi-mode Ti:LiNbO3 waveguide have been analyzed depending on the wavelength and the polarization states of input beam at 1300 nm region. The periodicity of the oscillation which is induced by a MMI effect in a Ti:LiNbO3 waveguide is decided by the refractive index difference between two modes (fundamental and first modes) and the length of a waveguide. The measured average periodicity of the oscillation in TM- and TE- polarized beams were about 18 nm and 48 nm, respectively. The difference of the periodicity depending on the polarization of input beam was explained by a quasi-analytical technique based on the effective-refractive-index method and the equation of coupling length determined by the mode phase factor in the multi-mode waveguide. The theoretical calculation shows good agreement with the experimental results. We believe that such kind of a MMI Ti:LiNbO3 waveguide device which is integrated with electrodes, acoustical absorber, photorefractive grating, periodically reversed microdomains and so on, can be used for a future multi-functional integrated devices.

Acknowledgments

This work was supported by the Korea Science and Engineering Foundation (KOSEF) NCRC grant funded by the Korea government (MEST) (No. R15-2008-006-02001-0) and Asian Laser Center Program through a grant provided by the Gwangju Institute of Science & Technology in 2009..

References and links

1. R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE -17, 946–959 (1981). [CrossRef]  

2. T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001). [CrossRef]  

3. Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-4-701. [CrossRef]   [PubMed]  

4. R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999). [CrossRef]  

5. Y. L. Lee, C. Jung, Y. Noh, M. Park, C. Byeon, D. Ko, and J. Lee, “Channel-selective wavelength conversion and tuning in periodically poled Ti:LiNbO3 waveguides,” Opt. Express 12, 2649–2655 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-12-2649. [CrossRef]   [PubMed]  

6. Y. L. Lee, B. Yu, T. J. Eom, W. Shin, C. Jung, Y. Noh, J. Lee, D. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO3 waveguide,” Opt. Express 14, 2776–2782 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2776. [CrossRef]   [PubMed]  

7. Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007). [CrossRef]  

8. M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003). [CrossRef]  

9. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13, 615–627 (1995). [CrossRef]  

10. C.-H. Bae and F. Koyama, “Design and Fabrication of Multi-Mode Interference Hollow Waveguide Optical Switch with Variable Air Core,” Jpn. J. Appl. Phys. 45, 6648–6653 (2006). [CrossRef]  

11. A. Irace and G. Breglio, “All-silicon optical temperature sensor based on Multi-Mode Interference,” Opt. Express 11, 2807–2812 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2807. [CrossRef]   [PubMed]  

12. M. R. Layton and J. A. Bucaro, “Optical fiber acoustic sensor utilizing mode-mode interference,” Appl. Opt. 18, 666–670 (1979). [CrossRef]   [PubMed]  

13. A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003). [CrossRef]  

14. M. P. Earnshaw and D. W. E. Allsopp, “Semiconductor Space Switches Based on Multimode Interference Couplers,” J. Lightwave Technol. 20, 1–8 (2002). [CrossRef]  

15. Y. L. Sam and Y. H. Won, “1×3 Wavelength demultiplexer based on multimode interference with an index-modulation region,’” Microwave Opt. Technol. Lett. 43, 400–403 (2004). [CrossRef]  

16. L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995). [CrossRef]  

17. Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009). [CrossRef]  

18. E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988). [CrossRef]  

19. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994). [CrossRef]   [PubMed]  

20. G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

21. R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985). [CrossRef]  

22. V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004). [CrossRef]  

23. D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008). [CrossRef]  

References

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  1. R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE- 17, 946–959 (1981).
    [Crossref]
  2. T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001).
    [Crossref]
  3. Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-4-701.
    [Crossref] [PubMed]
  4. R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
    [Crossref]
  5. Y. L. Lee, C. Jung, Y. Noh, M. Park, C. Byeon, D. Ko, and J. Lee, “Channel-selective wavelength conversion and tuning in periodically poled Ti:LiNbO3 waveguides,” Opt. Express 12, 2649–2655 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-12-2649.
    [Crossref] [PubMed]
  6. Y. L. Lee, B. Yu, T. J. Eom, W. Shin, C. Jung, Y. Noh, J. Lee, D. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO3 waveguide,” Opt. Express 14, 2776–2782 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2776.
    [Crossref] [PubMed]
  7. Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
    [Crossref]
  8. M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
    [Crossref]
  9. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13, 615–627 (1995).
    [Crossref]
  10. C.-H. Bae and F. Koyama, “Design and Fabrication of Multi-Mode Interference Hollow Waveguide Optical Switch with Variable Air Core,” Jpn. J. Appl. Phys. 45, 6648–6653 (2006).
    [Crossref]
  11. A. Irace and G. Breglio, “All-silicon optical temperature sensor based on Multi-Mode Interference,” Opt. Express 11, 2807–2812 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2807.
    [Crossref] [PubMed]
  12. M. R. Layton and J. A. Bucaro, “Optical fiber acoustic sensor utilizing mode-mode interference,” Appl. Opt. 18, 666–670 (1979).
    [Crossref] [PubMed]
  13. A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
    [Crossref]
  14. M. P. Earnshaw and D. W. E. Allsopp, “Semiconductor Space Switches Based on Multimode Interference Couplers,” J. Lightwave Technol. 20, 1–8 (2002).
    [Crossref]
  15. Y. L. Sam and Y. H. Won, “1×3 Wavelength demultiplexer based on multimode interference with an index-modulation region,’” Microwave Opt. Technol. Lett. 43, 400–403 (2004).
    [Crossref]
  16. L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995).
    [Crossref]
  17. Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
    [Crossref]
  18. E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
    [Crossref]
  19. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994).
    [Crossref] [PubMed]
  20. G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).
  21. R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
    [Crossref]
  22. V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
    [Crossref]
  23. D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
    [Crossref]

2009 (1)

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

2008 (1)

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

2006 (2)

2004 (4)

2003 (3)

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
[Crossref]

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

A. Irace and G. Breglio, “All-silicon optical temperature sensor based on Multi-Mode Interference,” Opt. Express 11, 2807–2812 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2807.
[Crossref] [PubMed]

2002 (1)

2001 (2)

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001).
[Crossref]

1999 (1)

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

1995 (2)

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995).
[Crossref]

1994 (1)

1988 (1)

E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[Crossref]

1985 (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[Crossref]

1981 (1)

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE- 17, 946–959 (1981).
[Crossref]

1979 (1)

Alferness, R. C.

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE- 17, 946–959 (1981).
[Crossref]

Allsopp, D. W. E.

Bachmann, M.

Bae, C.-H.

C.-H. Bae and F. Koyama, “Design and Fabrication of Multi-Mode Interference Hollow Waveguide Optical Switch with Variable Air Core,” Jpn. J. Appl. Phys. 45, 6648–6653 (2006).
[Crossref]

Bava, G. P.

E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[Crossref]

Besse, P. A.

Breglio, G.

Bucaro, J. A.

Byeon, C.

Choi, I. W.

Choi, Y.-W.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Dou, Y.-P.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Earnshaw, M. P.

Eom, T. J.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Y. L. Lee, B. Yu, T. J. Eom, W. Shin, C. Jung, Y. Noh, J. Lee, D. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO3 waveguide,” Opt. Express 14, 2776–2782 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2776.
[Crossref] [PubMed]

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Faerbert, A.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Feise, G.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Fischer, G.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Gaylord, T. K.

V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
[Crossref]

Glingener, C.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Gong, Q.-H.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Grundkoetter, W.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

Guo, H.-C.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Herrmann, H.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Hinz, S

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Imaeda, M.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Irace, A.

Ishizuki, H.

T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001).
[Crossref]

Iwai, M.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Johnson, E. G.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
[Crossref]

Jung, C.

Jung, H. S.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Kee, C.-S.

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Kim, W.-K.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Ko, D.

Ko, D.-K.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-4-701.
[Crossref] [PubMed]

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Koyama, F.

C.-H. Bae and F. Koyama, “Design and Fabrication of Multi-Mode Interference Hollow Waveguide Optical Switch with Variable Air Core,” Jpn. J. Appl. Phys. 45, 6648–6653 (2006).
[Crossref]

Layton, M. R.

Lee, H. Y.

Lee, H.-M.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Lee, H.-Y.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Lee, J.

Lee, Y. L.

Lee, Y. L.|

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Li, Y.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Lierstuen, L. O.

L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995).
[Crossref]

Liu, D.-Y.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Mehta, A.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
[Crossref]

Meindl, J. D.

V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
[Crossref]

Melchior, H.

Mirvoda, V.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Mohammed, W.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
[Crossref]

Montrosset, I.

E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[Crossref]

Mule’, V.

V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
[Crossref]

Noe, R.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Noh, Y.

Noh, Y.-C.

Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-4-701.
[Crossref] [PubMed]

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Oh, K.

Park, M.

Pavel, N.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

Quiring, V.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

Regener, R.

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[Crossref]

Ricken, R.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

Sam, Y. L.

Y. L. Sam and Y. H. Won, “1×3 Wavelength demultiplexer based on multimode interference with an index-modulation region,’” Microwave Opt. Technol. Lett. 43, 400–403 (2004).
[Crossref]

Sandel, D.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Schoepflin, A.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Schreiber, G.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

Shin, W.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Y. L. Lee, B. Yu, T. J. Eom, W. Shin, C. Jung, Y. Noh, J. Lee, D. Ko, and K. Oh, “All-optical AND and NAND gates based on cascaded second-order nonlinear processes in a Ti-diffused periodically poled LiNbO3 waveguide,” Opt. Express 14, 2776–2782 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2776.
[Crossref] [PubMed]

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Shoji, I.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Sohler, W.

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[Crossref]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

Strake, E.

E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[Crossref]

Suche, H.

Y. L. Lee, C. Jung, Y.-C. Noh, I. W. Choi, D.-K. Ko, J. Lee, H. Y. Lee, and H. Suche, “Wavelength selective single and dual-channel dropping in a periodically poled Ti:LiNbO3 waveguide,” Opt. Express 12, 701–707 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-4-701.
[Crossref] [PubMed]

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

Sudbo, A.

L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995).
[Crossref]

Suhara, T.

T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001).
[Crossref]

Taira, T.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Villalaz, R.

V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
[Crossref]

Won, Y. H.

Y. L. Sam and Y. H. Won, “1×3 Wavelength demultiplexer based on multimode interference with an index-modulation region,’” Microwave Opt. Technol. Lett. 43, 400–403 (2004).
[Crossref]

Yamaguchi, S.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Yang, H.

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Yang, W.-S.

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

Yoshida-Dierolf, M.

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

Yoshino, T.

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Yu, B.

Yu, B.-A.

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Yu, N. E.

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (2)

G. Schreiber, H. Suche, Y. L. Lee, W. Grundkoetter, V. Quiring, R. Ricken, and W. Sohler, “Efficient cascaded difference frequency conversion in periodicall poled Ti:LiNbO3 waveguides using pulsed and cw pumping,” Appl. Phys. B 73, 501–504 (2001).

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[Crossref]

Appl. Phys. Lett. (1)

M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, “High-power blue generation from a periodically poled,” Appl. Phys. Lett. 83, 3659–3661 (2003).
[Crossref]

Chin. Phys. Lett. (1)

D.-Y. Liu, Y. Li, Y.-P. Dou, H.-C. Guo, H. Yang, and Q.-H. Gong, “Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses,” Chin. Phys. Lett. 25, 2500–2005 (2008).
[Crossref]

Electron. Lett. (1)

R. Noe, D. Sandel, S Hinz, M. Yoshida-Dierolf, V. Mirvoda, G. Feise, H. Herrmann, C. Glingener, A. Schoepflin, A. Faerbert, and G. Fischer, “Integrated optical LiNbO3 distributed polarization mode dispersion compensator in 20 Gbit/s transmission system,” Electron. Lett. 35, pp. 652–654 (1999).
[Crossref]

IEEE J. Quantum Electron. QE (1)

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE- 17, 946–959 (1981).
[Crossref]

IEEE Photon. Technol. Lett. (5)

T. Suhara and H. Ishizuki“Integrated QPM Sum-Frequency Generation Interferometer Device for Ultrafast Optical Switching,” IEEE Photon. Technol. Lett. 13, 1203–1205 (2001).
[Crossref]

L. O. Lierstuen and A. Sudbo, “8-Channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. 7, 1034–1036 (1995).
[Crossref]

Y. L. Lee, Y.-W. Choi, H. S. Jung, T. J. Eom, W. Shin, D.-K. Ko, W.-S. Yang, H.-M. Lee, W.-K. Kim, and H.-Y. Lee, “Temperature insensitive dual comb filter based on multi-mode interference Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 21, 507–509 (2009).
[Crossref]

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15, 1129–1131 (2003).
[Crossref]

V. Mule’, R. Villalaz, T. K. Gaylord, and J. D. Meindl, “Photopolymer-Based Diffractive and MMI Waveguide Couplers,” IEEE Photon. Technol. Lett. 16, 2490–2492 (2004).
[Crossref]

J. Lightwave Technol. (3)

M. P. Earnshaw and D. W. E. Allsopp, “Semiconductor Space Switches Based on Multimode Interference Couplers,” J. Lightwave Technol. 20, 1–8 (2002).
[Crossref]

E. Strake, G. P. Bava, and I. Montrosset, “Guided Modes of Ti:LiNbO3 Channel Waveguides: A Novel Quasi-Analytical Technique in Comparision with the Scalar Finite-Element Method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[Crossref]

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Jpn. J. Appl. Phys. (1)

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[Crossref]

Microwave Opt. Technol. Lett. (1)

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[Crossref]

Opt. Express (4)

Other (1)

Y. L.| Lee, N. E. Yu, C.-S. Kee, D.-K. Ko, Y.-C. Noh, B.-A. Yu, W. Shin, T. J. Eom, and J. Lee “Waveguide-type wavelength-tunable Solc filter in a periodically poled Ti:LiNbO3 waveguide,” IEEE Photon. Technol. Lett.19, 1505–1507 (2007).
[Crossref]

Supplementary Material (1)

» Media 1: MOV (947 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup to observe the MMI effect in a Ti:LiNbO3 waveguide depending on the wavelength and the polarization states of input beam; WSFL : wavelength swept fiber laser, and OSA : optical spectrum analyzer, PC : polarization controller, PBS : polarization beam splitter, BS : beam splitter, IR Camera : infrared camera.

Fig. 2.
Fig. 2.

Output beam mode profiles as a function of wavelength. The wavelength of WSFL was swept from 1277.5 nm to 1318.5 nm (Media 1).

Fig. 3.
Fig. 3.

Transmitted optical signal of TM polarized beam as a function of wavelength. The black scatter-line and blue scatter-line indicate the optical spectra which are measured at position A and B, respectively.

Fig. 4.
Fig. 4.

(a) The calculated effective refractive indices of the fundamental and first-order modes in a TM polarized beam. (b) The number of oscillation in a 33-mm Ti:LiNbO3 waveguide as a function of input wavelength. The black and red lines indicate theoretical and experimental data, respectively. The filled (oe-17-13-10718-i001.jpg) and open (oe-17-13-10718-i002.jpg) circles indicate maximum constructive position and destructive position, respectively.

Fig. 5.
Fig. 5.

Transmitted optical signal of TE polarized beam as a function of wavelength. The black scatter-line and blue scatter-line indicate the optical spectra which are measured at position A and B, respectively.

Fig. 6.
Fig. 6.

(a) The calculated effective refractive indices of the fundamental and first-order modes in a TE polarized beam. (b) The number of oscillation in a 33 mm Ti:LiNbO3 waveguide as a function of input wavelength. The black and red lines indicate theoretical and experimental data, respectively. The filled (oe-17-13-10718-i003.jpg) and vacant (oe-17-13-10718-i004.jpg) circles indicate maximum constructive position and destructive position, respectively.

Equations (3)

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N i = L 2 L c = n i , 0 n i , 1 λ 0 L ,
L c = π β i , 0 β i , 1 = λ 0 2 ( n i , 0 n i , 1 ) ,
n ( x , y ) = n sub + δ n ( x , y ) ,

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