Abstract

We correct the calculation method [Opt. Lett. 35, 1335 (2010)] of enhancement of nonreciprocal phase shift on the magneto-optical material boundary.

© 2013 Optical Society of America

Nonreciprocal phase shift (NPS) [1] in magneto-optical waveguides can be calculated as the following equation [2]:

ΔβTM=2ωε0γExxExdxdyβTMExHydxdy.

The dilemma is as follows: at the material boundary, γ jumps from a limited value to zero, while Ex also jumps simultaneously, which means γ could be zero, while dEx/dx could be infinitely large. A solution was proposed in my previous paper to solve the dilemma by using the linear transition zone [3]. It seems reasonable but is actually wrong. In fact, the electric displacement is always continuous. So Eq. (1) can be rewritten as

ΔβTM=2ωε0γεExxDxdxdyβTMExHydxdy.

In this way, the enhancement resulting from the previously proposed transition zone [1] does not exist anymore. With Eq. (2), we recalculate the nanoscale air gap structure. The results are shown in Fig. 1. From Fig. 1, it is not difficult to find that NPS drops significantly when the gap is filled with low index material. However, when the index exceeds 5.5, an NPS larger than intimate contact (gap height=0) appears and increases as the index increases. This enhancement can be explained by the fact that more energy is dragged toward the materials boundaries.

 

Fig. 1. NPS versus gap height with different bonding material indices.

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This work is supported by the Nature Basic Research Program of China (No. 2013CB632105).

References

1. H. Yokoi, Opt. Commun. 31, 189 (2008).

2. N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999). [CrossRef]  

3. R. Chen, G. Jiang, Y. Hao, J. Yang, M. Wang, and X. Jiang, Opt. Lett. 35, 1335 (2010). [CrossRef]  

References

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  1. H. Yokoi, Opt. Commun. 31, 189 (2008).
  2. N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
    [CrossRef]
  3. R. Chen, G. Jiang, Y. Hao, J. Yang, M. Wang, and X. Jiang, Opt. Lett. 35, 1335 (2010).
    [CrossRef]

2010

2008

H. Yokoi, Opt. Commun. 31, 189 (2008).

1999

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Bahlmann, N.

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Chen, R.

Dotsch, H.

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Hao, Y.

Hertel, P.

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Jiang, G.

Jiang, X.

Lohmeyer, M.

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Wang, M.

Yang, J.

Yokoi, H.

H. Yokoi, Opt. Commun. 31, 189 (2008).

IEEE J. Quantum Electron.

N. Bahlmann, M. Lohmeyer, H. Dotsch, and P. Hertel, IEEE J. Quantum Electron. 35, 250 (1999).
[CrossRef]

Opt. Commun.

H. Yokoi, Opt. Commun. 31, 189 (2008).

Opt. Lett.

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Figures (1)

Fig. 1.
Fig. 1.

NPS versus gap height with different bonding material indices.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

Δ β TM = 2 ω ε 0 γ E x x E x d x d y β TM E x H y d x d y .
Δ β TM = 2 ω ε 0 γ ε E x x D x d x d y β TM E x H y d x d y .

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