## Ultra-wideband design of waveguide magneto-optical isolator operating in 1.31μm and 1.55μm band

Optics Express, Vol. 15, Issue 2, pp. 639-645 (2007)

http://dx.doi.org/10.1364/OE.15.000639

Acrobat PDF (99 KB)

### Abstract

The design of an ultra-wideband waveguide magneto-optical isolator is described. The isolator is based on a Mach-Zehnder interferometer employing nonreciprocal phase shift. The ultra-wideband design is realized by adjusting the wavelength dependence of reciprocal phase difference to compensate for that of nonreciprocal phase difference in the backward direction. We obtained the ultra-wideband design that provides isolation > 35dB from 1.25μm to >1.65μm. This is the proposal of magneto-optical isolator that operates both in 1.31μm band and 1.55μm band.

© 2007 Optical Society of America

## 1. Introduction

1. F. Auracher and H. H. Witte, “A new design for an integrated optical isolator,” Opt. Commun. **13**,435–438 (1975). [CrossRef]

6. Y. Shoji and T. Mizumoto, “Wideband design of nonreciprocal phase shift magneto-optical isolators using phase adjustment in Mach-Zehnder interferometer,” Appl. Opt. **45**,7144–7150 (2006). [CrossRef] [PubMed]

## 2. Principle of wideband design

*θ*) and the reciprocal phase difference (

_{N}*θ*) decrease as wavelength becomes longer. Here, the sign of the nonreciprocal phase difference is important for the wideband design. In the conventional design, the nonreciprocal phase difference is set to be +π/2 for backward propagation. The reciprocal phase difference is set to be +π/2 for satisfying the anti-phase condition in the backward propagation. Therefore, the deviations of nonreciprocal and reciprocal phase difference from respective designed values are added to each other in the backward propagation. In the wideband design, the nonreciprocal phase difference is set to be -π/2 in the backward propagation. Reciprocal phase difference of 3π/2 is installed so as to satisfy the anti-phase condition for the backward propagation. In this design, the deviations of nonreciprocal and reciprocal phase difference from their designed values are canceled and the wavelength dependence of total phase difference is reduced dramatically in the backward propagation. Hence, large backward loss is obtainable in a wide wavelength range.

_{R}*L*and

_{1}*L*are the lengths of sections that are added to adjust a reciprocal phase difference.

_{2}*W*and

_{1}*W*are the waveguide widths of respective sections, which determine the longitudinal propagation constants

_{2}*β*and

_{1}*β*. The reciprocal phase difference

_{2}*θ*is given by

_{R}*β*-

_{2}L_{2}*β*and set to 3π/2 at the designed wavelength. Rather wideband design was achieved in our previous work [6

_{1}L_{1}6. Y. Shoji and T. Mizumoto, “Wideband design of nonreciprocal phase shift magneto-optical isolators using phase adjustment in Mach-Zehnder interferometer,” Appl. Opt. **45**,7144–7150 (2006). [CrossRef] [PubMed]

## 3. Numerical approach for ultra-wideband design

*θ*and

_{N}*θ*are not linear functions of wavelength in our previous design. That is, in the wavelength concerned,

_{R}*θ*shows a convex change against the wavelength, while

_{N}*θ*is concave as shown in Fig. 3(a). The total phase difference for backward propagation becomes concave as shown in Fig. 3(b). This curve determines the backward loss. The wavelength dependence of

_{R}*θ*should be convex to minimize the wavelength dependence of total phase difference in backward propagation.

_{R}*β*and

_{1}*β*becomes large at shorter wavelength as shown in Fig. 4(b). When the section lengths

_{2}*L*and

_{1}*L*are equal, the phase difference between two sections exhibits the wavelength dependence as is indicated by a solid curve in Fig. 4(c). When the section length

_{2}*L*is reduced keeping

_{1}*L*as well as

_{2}*W*and

_{1}*W*are constant, the wavelength dependence of the phase difference changes as shown in Fig. 4(c). Based on such a behavior, we can change the wavelength dependence of the reciprocal phase difference, from convex to concave dependence, by controlling the section length difference

_{2}*L*-

_{1}*L*. Also, by controlling section widths

_{2}*W*and

_{1}*W*, we can adjust the gradient of wavelength dependence of reciprocal phase difference.

_{2}*θ*=3π/2 at a designed wavelength. Then, the deviation of total phase difference from π is minimized in the backward propagation, and large backward loss is obtainable in a wider wavelength range. The forward loss is slightly deteriorated in the wideband design compared with the case of conventional one, since the wavelength dependences of nonreciprocal and reciprocal phase difference add up to each other. The center wavelength where the forward loss becomes minimum is to be chosen properly to minimize the forward loss at band edges and to provide sufficient backward loss in a desired wavelength range. In the following design that covers both 1.31μm and 1.55μm.wavelength bands, we set the center wavelength at 1.43μm.

_{R}## 4. Calculation results

_{2}Fe

_{5}O

_{12}(Ce:YIG) is assumed as a magneto-optic garnet guiding layer, which is grown on a (111)-oriented (Ca, Mg, Zr) doped GGG substrate. SiO

_{2}is deposited as an upper cladding layer. A rib waveguide formed on the guiding layer is assumed in this paper. The slab and rib heights are 0.40 μm and 0.08 μm, respectively. The waveguide width is set at the range from 2.0 μm to 3.0 μm. Since such flat waveguide can be approximated as four layered structure by an effective index method, the wavelength dependences of a nonreciprocal and a reciprocal phase shifter are calculated directly by solving the eigenvalue equation with the refractive indices of constituent layers and the Faraday rotation coefficient of Ce:YIG. Details of the calculation are given in Ref. [6

6. Y. Shoji and T. Mizumoto, “Wideband design of nonreciprocal phase shift magneto-optical isolators using phase adjustment in Mach-Zehnder interferometer,” Appl. Opt. **45**,7144–7150 (2006). [CrossRef] [PubMed]

*θ*is convex and that of reciprocal phase difference

_{N}*θ*is concave as shown in Fig. 3(a). To make the curve associated with

_{R}*θ*convex, both waveguide widths and lengths of the reciprocal phase shifter are tailored keeping

_{R}*β*

_{2}*L*-

_{2}*β*

_{1}*L*=3π/2 at a wavelength of 1.43μm. In the following design, we set the width of arm1 to be

_{1}*W*=2.0μm, which is the waveguide width of whole device.

_{1}*θ*calculated for some different waveguide widths, where

_{R}*L*is set to be 1000μm and

_{1}*L*is slightly adjusted around 1000μm so as to realize

_{2}*θ*=3π/2 at a wavelength of 1.43μm. As

_{R}*W*becomes large, the variation of

_{2}*θ*vs wavelength becomes more convex. When the path length

_{R}*L*is varied, the wavelength dependence of

_{1}*θ*changes as is shown in Fig. 5(b). Here,

_{R}*W*is fixed at 2.4μm, and

_{2}*L*is adjusted around

_{2}*L*so as to realize

_{1}*θ*=3π/2 at a wavelength of 1.43μm. As

_{R}*L*becomes longer, the variation of

_{1}*θ*vs wavelength becomes more convex.

_{R}*θ*can be adjusted to have similar wavelength dependence to

_{R}*θ*. Table 1 shows examples of optimized parameters for some waveguide widths. Here, we set the waveguide width

_{N}*W*=2.0μm and change

_{1}*W*from 2.4μm to 3.0μm. The lengths

_{2}*L*and

_{1}*L*are chosen to achieve similar wavelength dependence to

_{2}*θ*. Figure 6 shows calculated wavelength dependences of the phase differences for

_{N}*W*=2.0μm,

_{1}*W*=3.0μm,

_{2}*L*=930μm and

_{1}*L*=930.28μm. As is observed in this figure,

_{2}*θ*has very similar wavelength dependence to

_{R}*θ*.

_{N}## 5. Conclusion

## References and links

1. | F. Auracher and H. H. Witte, “A new design for an integrated optical isolator,” Opt. Commun. |

2. | T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, “Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd |

3. | J. Fujita, M. Levy, R. M. Osgood, Jr. L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. |

4. | H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, “Application of magneto-optical waveguides in integrated optics: review,” J. Opt. Soc. Am. B |

5. | H. Yokoi, T. Mizumoto, N. Shinjo, N. Futakuchi, and Y. Nakano, “Demonstration of an optical isolator, with a semiconductor guiding layer that was obtained by use of a nonreciprocal phase shift,” Appl. Opt. |

6. | Y. Shoji and T. Mizumoto, “Wideband design of nonreciprocal phase shift magneto-optical isolators using phase adjustment in Mach-Zehnder interferometer,” Appl. Opt. |

**OCIS Codes**

(230.3120) Optical devices : Integrated optics devices

(230.3240) Optical devices : Isolators

**ToC Category:**

Optical Devices

**History**

Original Manuscript: November 8, 2006

Revised Manuscript: January 10, 2007

Manuscript Accepted: January 10, 2007

Published: January 22, 2007

**Citation**

Yuya Shoji and Tetsuya Mizumoto, "Ultra-wideband design of waveguide magneto-optical isolator operating in 1.31μm and 1.55μm band," Opt. Express **15**, 639-645 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-639

Sort: Year | Journal | Reset

### References

- F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13,435-438 (1975). [CrossRef]
- T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4,347-352 (1986). [CrossRef]
- J. Fujita, M. Levy, R. M. Osgood, Jr. L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76,2158-2160 (2000). [CrossRef]
- H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22,240-253 (2005). [CrossRef]
- H. Yokoi, T. Mizumoto, N. Shinjo, N. Futakuchi, and Y. Nakano, "Demonstration of an optical isolator, with a semiconductor guiding layer that was obtained by use of a nonreciprocal phase shift," Appl. Opt. 39,6158-6164 (2000). [CrossRef]
- Y. Shoji and T. Mizumoto, "Wideband design of nonreciprocal phase shift magneto-optical isolators using phase adjustment in Mach-Zehnder interferometer," Appl. Opt. 45,7144-7150 (2006). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.