Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Lotspeich, Appl. Opt. 14, 327 (1975).
  2. M. K. Barnoski, Introduction to Integrated Optics (Plenum, New York, 1973), pp. 56–66.
  3. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Chap. 11.
  4. A. W. Snyder, R. de la Rue, IEEE Trans. Microwave Theory Tech. MTT-18, 650 (1970).
  5. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), Chap. 2.

1975 (1)

1970 (1)

A. W. Snyder, R. de la Rue, IEEE Trans. Microwave Theory Tech. MTT-18, 650 (1970).

Barnoski, M. K.

M. K. Barnoski, Introduction to Integrated Optics (Plenum, New York, 1973), pp. 56–66.

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Chap. 11.

de la Rue, R.

A. W. Snyder, R. de la Rue, IEEE Trans. Microwave Theory Tech. MTT-18, 650 (1970).

Lotspeich, J. F.

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), Chap. 2.

Snyder, A. W.

A. W. Snyder, R. de la Rue, IEEE Trans. Microwave Theory Tech. MTT-18, 650 (1970).

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, R. de la Rue, IEEE Trans. Microwave Theory Tech. MTT-18, 650 (1970).

Other (3)

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), Chap. 2.

M. K. Barnoski, Introduction to Integrated Optics (Plenum, New York, 1973), pp. 56–66.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Chap. 11.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Illustrating the behavior of f1(ξ) for TE modes (Ks = Kc = 1)

Tables (2)

Tables Icon

Table I Limitations of the Proposed Method

Tables Icon

Table II Numerical Results of kf1/2 Obtained from the Proposed Method, Compared with Exact Values and Formula Values given by Ref. 1a

Equations (32)

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

k f l = tan 1 ( K s k s k f ) + tan 1 ( K c k c k f ) + m π , ( m = 0 , 1 , 2 ) ,
K s = K c = 1 ,
K s = ( n f n s ) 2 , K c = ( n f n c ) 2 .
( k f l ) 2 + ( k s l ) 2 = ( k 0 l ) 2 ( n f 2 n s 2 ) = R s 2 ,
( k f l ) 2 + ( k c l ) 2 = ( k 0 l ) 2 ( n f 2 n c 2 ) = R c 2 ,
a ξ m = f 1 ( ξ ) ,
f 1 ( ξ ) = 1 π tan 1 ( K s 1 ξ 2 1 ) + 1 π tan 1 ( K c 1 ξ 2 1 ) ,
a = R s / π = ( 2 l / λ 0 ) n f 2 n s 2 , and
ξ = k f l / R s .
K = ( R c / R s ) 2 = ( n f 2 n c 2 ) / ( n f 2 n s 2 ) , ( K 1 ) .
0 ξ 1 .
b f 1 ( ξ ) 1 ,
b = 1 π tan 1 ( K c K 1 ) , 0.5 > b 0 .
f 2 ( ξ , ) = ( 1 b ) 1 ξ + ( 1 ξ ) + b ,
f 1 ( 0 ) = f 2 ( 0 , ) = 1 ,
f 1 ( 1 ) = f 2 ( 1 , ) = b .
f 1 ( ξ ) < 0 , f 2 ( ξ , ) < 0 .
f 1 ( ξ ) < 0 , f 2 ( ξ , ) < 0 .
= ( ξ ) = b + ( 1 b ) 1 ξ f 1 ( ξ ) 1 ξ ( 1 ξ ) .
1 ( 0 ) = lim ξ 0 = 1 + b + 2 π ( 1 K s + 1 K c K ) .
2 ( 0 ) = lim ξ 1 = { 1 2 2 π K s , ( K = 1 ) ; 1 b 2 π K s , ( K > 1 ) .
( ξ ) < 0
f 2 [ ξ , 2 ( 0 ) ] > f 1 ( ξ ) > f 2 [ ξ , 1 ( 0 ) ] .
( a + ) ( 1 ξ ) + ( 1 b ) 1 ξ ( a b m ) = 0 .
ξ = 1 [ ( 1 b ) + ( 1 b ) 2 + 4 ( a + ) ( a b m ) 2 ( a + ) ] 2 .
ξ 2 ( 1 ) > ξ > ξ 1 ( 1 ) .
ξ 2 ( 1 ) > ξ 2 ( 2 ) > ξ > ξ 1 ( 2 ) > ξ 1 ( 1 ) .
ξ i ( j + 1 ) = 1 { [ 1 b i ( j ) ] + [ 1 b i ( j ) ] 2 + 4 [ a + i ( j ) ] ( a b m ) 2 [ a + i ( j ) ] } 2 , i ( j + 1 ) = b + ( 1 b ) 1 ξ i ( j + 1 ) f 1 [ ξ i ( j + 1 ) ] 1 ξ i ( j + 1 ) [ 1 ξ i ( j + 1 ) ] , i = 1 , 2 ; j = 0 , 1 , 2 , . }
ξ 2 ( 1 ) > ξ 2 ( 2 ) > > ξ 2 ( n + 1 ) > ξ > ξ 1 ( n + 1 ) > > ξ 1 ( 2 ) > ξ 1 ( 1 ) .
ξ ± = ξ 2 ( n + 1 ) + ξ 1 ( n + 1 ) 2 [ 1 ± | δ ( n + 1 ) | ] ,
| δ ( n + 1 ) | ξ 2 ( n + 1 ) ξ 1 ( n + 1 ) ξ 2 ( n + 1 ) + ξ 1 ( n + 1 ) .
= ½ [ 1 ( 0 ) + 2 ( 0 ) ]

Metrics