Abstract

In this work, we report the development of an external-cavity wavelength-swept amplified spontaneous emission (ASE) source with high output power and high tuning speed based on an efficient electro-optic effect of beam deflection. The wavelength-swept ASE source is capable of delivering stable output power with averaged intensity of 100 mW in a wide spectrum tuning range of over 80 nm around the wavelength of 1550 nm. The light source will have important applications in optical communications, biomedical imaging, spectral analysis and sensing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
  35. S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
    [Crossref]
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    [Crossref]

2017 (4)

2016 (4)

B. Johnson, W. Atia, D. C. Flanders, M. Kuznetsov, B. D. Goldberg, N. Kemp, and P. Whitney, “SNR of swept SLEDs and swept lasers for OCT,” Opt. Express 24(10), 11174–11186 (2016).
[Crossref] [PubMed]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

2014 (3)

2013 (4)

Y. C. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express 21(15), 17760–17768 (2013).
[Crossref] [PubMed]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

2012 (2)

2011 (1)

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

2010 (1)

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5(1), 39–42 (2010).
[Crossref]

2009 (2)

2008 (2)

2007 (2)

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

A. Q. Liu and X. M. Zhang, “A review of MEMS external-cavity tunable lasers,” J. Micromech. Microeng. 17(1), R1–R13 (2007).
[Crossref]

2006 (2)

2005 (1)

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

2004 (1)

2003 (1)

A. Lohmann and R. R. A. Syms, “External cavity laser with a vertically etched silicon blazed grating,” IEEE Photonics Technol. Lett. 15(1), 120–122 (2003).
[Crossref]

2001 (2)

B. Pezeshki, “New approaches to laser tuning,” Opt. Photonics News 12(5), 34–38 (2001).
[Crossref]

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

1997 (1)

1991 (1)

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

1990 (1)

A. T. Schremer and C. L. Tang, “External-cavity semiconductor laser with 1000 GHz continuous piezoelectric tuning range,” IEEE Photonics Technol. Lett. 2(1), 3–5 (1990).
[Crossref]

Adler, D. C.

Agranat, A. J.

An, D.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Aoki, M.

Arimoto, H.

Atia, W.

Baofeng, D.

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

Biedermann, B. R.

Chang, Y. C.

Chang, Y.-C.

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

Chao, J. H.

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Chen, C. J.

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Chen, R. T.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Chinn, S. R.

Cole, R. H.

Coles, H. J.

Conti, C.

Dalton, L. R.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

DelRe, E.

Di Mei, F.

Duan, B.

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

Eigenwillig, C. M.

Findeisen-Tandel, S.

Flanders, D. C.

Foshee, J.

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

Fujimoto, J. G.

Fujimoto, M.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

Fujiura, K.

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Goldberg, B. D.

Guenther, K. H.

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

Hands, P. J. W.

Hendon, C. P.

Himel, M. D.

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

Hoffman, R. C.

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Y. C. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express 21(15), 17760–17768 (2013).
[Crossref] [PubMed]

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

Hu, X. Q.

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

Huber, R.

Imai, T.

T. Imai, M. Ueno, Y. Sasaki, and T. Sakamoto, “Analyses of optical rays in KTN optical beam deflectors for device design,” Appl. Opt. 56(25), 7277–7285 (2017).
[Crossref] [PubMed]

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

T. Imai, J. Miyazu, and J. Kobayashi, “Charge distributions in KTa1-xNbxO3 optical beam deflectors formed by voltage application,” Opt. Express 22(12), 14114–14126 (2014).
[Crossref] [PubMed]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Jang, C.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Johnson, B.

Kato, K.

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Kemp, N.

Kim, J.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Kitatani, T.

Kobayashi, J.

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

T. Imai, J. Miyazu, and J. Kobayashi, “Charge distributions in KTa1-xNbxO3 optical beam deflectors formed by voltage application,” Opt. Express 22(12), 14114–14126 (2014).
[Crossref] [PubMed]

S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
[Crossref]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

T. Sakamoto, S. Toyoda, M. Ueno, and J. Kobayashi, “High-speed optical beam scanning using KTN crystal,” IEEE CPMT Symposium Japan (ICSJ), 173–176 (2014).
[Crossref]

Kosterev, A. A.

Kuznetsov, M.

Lee, K. K. C.

Leung, M. K. K.

Ling, Y.

Liu, A. Q.

A. Q. Liu and X. M. Zhang, “A review of MEMS external-cavity tunable lasers,” J. Micromech. Microeng. 17(1), R1–R13 (2007).
[Crossref]

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

Liu, H.

Lohmann, A.

A. Lohmann and R. R. A. Syms, “External cavity laser with a vertically etched silicon blazed grating,” IEEE Photonics Technol. Lett. 15(1), 120–122 (2003).
[Crossref]

Lu, C.

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

Lu, X.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Maki, J. J.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Mariampillai, A.

McDonald, D.

Miyazu, J.

T. Imai, J. Miyazu, and J. Kobayashi, “Charge distributions in KTa1-xNbxO3 optical beam deflectors formed by voltage application,” Opt. Express 22(12), 14114–14126 (2014).
[Crossref] [PubMed]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Moharam, M. G.

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

Morris, S. M.

Mott, A. G.

Y. C. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express 21(15), 17760–17768 (2013).
[Crossref] [PubMed]

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

Munce, N. R.

Naganuma, K.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

Okabe, Y.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

Parravicini, G. B.

Parravicini, J.

Pezeshki, B.

B. Pezeshki, “New approaches to laser tuning,” Opt. Photonics News 12(5), 34–38 (2001).
[Crossref]

Pierangeli, D.

Ryan, N.

Sakamoto, T.

T. Imai, M. Ueno, Y. Sasaki, and T. Sakamoto, “Analyses of optical rays in KTN optical beam deflectors for device design,” Appl. Opt. 56(25), 7277–7285 (2017).
[Crossref] [PubMed]

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
[Crossref]

T. Sakamoto, S. Toyoda, M. Ueno, and J. Kobayashi, “High-speed optical beam scanning using KTN crystal,” IEEE CPMT Symposium Japan (ICSJ), 173–176 (2014).
[Crossref]

Sasaki, Y.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

T. Imai, M. Ueno, Y. Sasaki, and T. Sakamoto, “Analyses of optical rays in KTN optical beam deflectors for device design,” Appl. Opt. 56(25), 7277–7285 (2017).
[Crossref] [PubMed]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Sasaura, M.

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Schremer, A. T.

A. T. Schremer and C. L. Tang, “External-cavity semiconductor laser with 1000 GHz continuous piezoelectric tuning range,” IEEE Photonics Technol. Lett. 2(1), 3–5 (1990).
[Crossref]

Shi, X.

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

Shinoda, K.

Spinozzi, E.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5(1), 39–42 (2010).
[Crossref]

Standish, B. A.

Steier, W. H.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Sugai, E.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Sun, L.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Swanson, E. A.

Syms, R. R. A.

A. Lohmann and R. R. A. Syms, “External cavity laser with a vertically etched silicon blazed grating,” IEEE Photonics Technol. Lett. 15(1), 120–122 (2003).
[Crossref]

Taboada, J. M.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Takei, A.

Tang, C. L.

A. T. Schremer and C. L. Tang, “External-cavity semiconductor laser with 1000 GHz continuous piezoelectric tuning range,” IEEE Photonics Technol. Lett. 2(1), 3–5 (1990).
[Crossref]

Tang, D. Y.

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

Tang, S.

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Tang, Y.

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

Tatsumi, S.

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

Tittel, F. K.

Toyoda, S.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
[Crossref]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

T. Sakamoto, S. Toyoda, M. Ueno, and J. Kobayashi, “High-speed optical beam scanning using KTN crystal,” IEEE CPMT Symposium Japan (ICSJ), 173–176 (2014).
[Crossref]

Tsuchiya, T.

Tsuji, S.

Uchiyama, H.

Ueno, M.

T. Imai, M. Ueno, Y. Sasaki, and T. Sakamoto, “Analyses of optical rays in KTN optical beam deflectors for device design,” Appl. Opt. 56(25), 7277–7285 (2017).
[Crossref] [PubMed]

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
[Crossref]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

T. Sakamoto, S. Toyoda, M. Ueno, and J. Kobayashi, “High-speed optical beam scanning using KTN crystal,” IEEE CPMT Symposium Japan (ICSJ), 173–176 (2014).
[Crossref]

Vitkin, I. A.

Wang, C.

Wang, J.

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

Wang, X.

X. Zhang, H. Liu, Z. Zhao, X. Wang, and P. Wu, “Electric-field control of the ferro-paraelectric phase transition in Cu:KTN crystals,” Opt. Express 25(23), 28776–28782 (2017).
[Crossref]

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

Weidmann, D.

Whitney, P.

Wieser, W.

Wilkinson, T. D.

Wu, P.

Yagi, S.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Yamada, M.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

Yamagishi, S.

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

Yamaguchi, J.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Yamamoto, K.

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

Yang, V. X. D.

Yao, X.

Yin, S.

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Y. C. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express 21(15), 17760–17768 (2013).
[Crossref] [PubMed]

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

Zhang, C. H.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Zhang, H.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Zhang, X.

Zhang, X. M.

A. Q. Liu and X. M. Zhang, “A review of MEMS external-cavity tunable lasers,” J. Micromech. Microeng. 17(1), R1–R13 (2007).
[Crossref]

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

Zhao, Z.

Zhou, Q.

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Zhu, W.

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Express (3)

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, and K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[Crossref]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, and K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[Crossref]

S. Toyoda, M. Ueno, S. Yagi, and J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[Crossref]

Biomed. Opt. Express (1)

Electron. Lett. (1)

S. Toyoda, M. Ueno, T. Sakamoto, and J. Kobayashi, “350 kHz large-angle scanning of laser light using KTa1−xNbxO3 optical deflector,” Electron. Lett. 50(25), 1965–1966 (2014).
[Crossref]

IECE Trans. Electron. (1)

Y. Sasaki, T. Sakamoto, M. Ueno, S. Toyoda, J. Kobayashi, T. Sakamoto, M. Fujimoto, S. Yamagishi, M. Yamada, and S. Yagi, “Electro-optic deflector based on KTN crystal for phase-stable swept light source for OCT,” IECE Trans. Electron. E99(C), 250–256 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

X. M. Zhang, A. Q. Liu, C. Lu, and D. Y. Tang, “Continuous wavelength tuning in micromachined Littrow external-cavity lasers,” IEEE J. Quantum Electron. 41(2), 187–197 (2005).
[Crossref]

IEEE Photonics Technol. Lett. (3)

M. D. Himel, X. Shi, X. Q. Hu, M. G. Moharam, and K. H. Guenther, “Electrooptic beam deflection using the leaky mode of a planar waveguide,” IEEE Photonics Technol. Lett. 3(10), 921–923 (1991).
[Crossref]

A. Lohmann and R. R. A. Syms, “External cavity laser with a vertically etched silicon blazed grating,” IEEE Photonics Technol. Lett. 15(1), 120–122 (2003).
[Crossref]

A. T. Schremer and C. L. Tang, “External-cavity semiconductor laser with 1000 GHz continuous piezoelectric tuning range,” IEEE Photonics Technol. Lett. 2(1), 3–5 (1990).
[Crossref]

J. Lightwave Technol. (1)

J. Micromech. Microeng. (1)

A. Q. Liu and X. M. Zhang, “A review of MEMS external-cavity tunable lasers,” J. Micromech. Microeng. 17(1), R1–R13 (2007).
[Crossref]

Nat. Photonics (1)

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5(1), 39–42 (2010).
[Crossref]

Opt. Eng. (1)

L. Sun, J. Kim, C. Jang, D. An, X. Lu, Q. Zhou, J. M. Taboada, R. T. Chen, J. J. Maki, S. Tang, H. Zhang, W. H. Steier, C. H. Zhang, and L. R. Dalton, “Polymeric waveguide prism-based electro-optic beam deflector,” Opt. Eng. 40(7), 1217–1222 (2001).
[Crossref]

Opt. Express (7)

Opt. Lett. (6)

Opt. Photonics News (1)

B. Pezeshki, “New approaches to laser tuning,” Opt. Photonics News 12(5), 34–38 (2001).
[Crossref]

Proc. SPIE (5)

Y.-C. Chang, S. Yin, R. C. Hoffman, and A. G. Mott, “Broadband large field of view electro-optic modulators using potassium tantalate niobate (KTN) crystals,” Proc. SPIE 8847, 88470L (2013).
[Crossref]

Y. Sasaki, S. Toyoda, T. Sakamoto, J. Yamaguchi, M. Ueno, T. Imai, T. Sakamoto, M. Fujimoto, M. Yamada, K. Yamamoto, E. Sugai, and S. Yagi, “Electro-optic KTN deflector stabilized with 405-nm light irradiation for wavelength-swept light source,” Proc. SPIE 10100, 101000H (2017).
[Crossref]

S. Tatsumi, Y. Sasaki, S. Toyoda, T. Imai, J. Kobayashi, and T. Sakamoto, “700-kHz beam scanning using electro-optic KTN planar optical deflector,” Proc. SPIE 9744, 97440L (2016).
[Crossref]

Y. Tang, J. Wang, X. Wang, D. Baofeng, S. Tang, and J. Foshee, “KTN-based electro-optic beam scanner,” Proc. SPIE 7135, 713538 (2008).
[Crossref]

J. Foshee, S. Tang, Y. Tang, X. Wang, and B. Duan, “A novel high-speed electro-optic beam scanner based on KTN crystals,” Proc. SPIE 6709, 670908 (2007).
[Crossref]

Sci. Rep. (1)

W. Zhu, J. H. Chao, C. J. Chen, S. Yin, and R. C. Hoffman, “Three order increase in scanning speed of space charge-controlled KTN deflector by eliminating electric field induced phase transition in nanodisordered KTN,” Sci. Rep. 6(1), 33143 (2016).
[Crossref] [PubMed]

Other (1)

T. Sakamoto, S. Toyoda, M. Ueno, and J. Kobayashi, “High-speed optical beam scanning using KTN crystal,” IEEE CPMT Symposium Japan (ICSJ), 173–176 (2014).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic of the high-power wavelength-swept ASE source design. A: Littrow configuration with a reflection-type grating; B: three-prism beam expender; C: cylindrical concave lens; D: KTN crystal placed on a thermoelectric controller (TEC); E: polarizer; F: polarization-maintaining single-mode fiber with GRIN lens; G: a semiconductor optical amplifier; H: optical detector (or optical spectrum analyzer).
Fig. 2
Fig. 2 Wavelength tuning as a function of bias voltage. Multiple measurements were taken to verify the repeatability and stability of the light source system.
Fig. 3
Fig. 3 Characterization of the beam output under different operation current of the BOA. Beam output power without (a) or with three-prism beam expender (b). Linewidth without (c) or with three-prism beam expender (d).
Fig. 4
Fig. 4 EO wavelength tuning of beam output under 500 mA amplifier current.
Fig. 5
Fig. 5 Dependence of swept-wavelength range on applied voltage with Squared-wave and Sawtooth-wave electric fields.

Equations (4)

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λ=asin(Δθ+ θ 0 ) ,
β(x)= n 0 3 g 11 e 2 N 2 L(x d 2 + εV eNd ) ,
β( d 2 )= n 0 3 g 11 eNLε V d ,
λ(V)=c n 0 3 g 11 eNLε V V 0 d + λ 0 ,

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