**> ** **1 ,**

**angles 0^ such that**

**,B.R.**

**£m**

**< ** **1**

**the leaky rays of a fibre are more strongly**
**the scattering centres at the core-cladding**

**(2) ** **The total power radiated from an irregularity in the**

**dielectric waveguide is greater than if the irregularity was**
**in free space with the same incident field.**

**The former result, (1) above, is obvious from a geometric**
**optics approach (see fig. 4a). One can see that the distance that the**
**outer-cladding interface is from the inner-cladding core interface is**
**immaterial in determining the amount of power radiated from the**

**structure. ** **The dominant factor in determining the amount of radiated**
**power is the complement, 0^, of the critical angle of the outer**

**cladding interface, **a 0. **If **a,0 **is large then most of the radiation from**

**c ** **c**

**the irregularity in the core becomes power propagating in the cladding**
**modes of the multiply clad waveguide.**

**Although, from the above argument, the total radiated power**
**from the multiply clad optical fibre will not be affected by the**

**distance between the inner and outer core-cladding interfaces, the rate**
**at which this radiation escapes from the multiply clad fibre will vary.**
**Since the radiation emanating from the inner-cladding boundary at an**
**inclination 0 > tt/2 - a 0 to the axis, where a 0 is, as above, the local**

**z ** **c ** **c**

**critical angle at the outer core-cladding boundary, becomes a tunnelling**
**leaky ray relative to the outer-cladding interface, depending on the**
**radius of the outer-cladding surface, this radiation will escape at a**
**rate consistent with the tunnelling coefficient at the outer boundary. As**
**can be seen from fig. 4b, the skewness angle y 1 which critically affects**
**the tunnelling leaky ray loss, decreases as the radius of the outer**
**cladding interface increases relative to the inner-cladding. ** **As the**
**tunnelling leakage increases, with decreasing skewness of the radiation**

**[19], the rate of loss of the radiation from the multiply clad fibre**
**should increase as the radius of the outer-cladding is increased, i.e.**
**in the limit of an infinite inner-cladding, the singly clad fibre result**
**should apply.**

**This geometric optics argument raises doubt as to the correct**
**ness then of the calculation of Yip **

*et at.*

**, showing that the finitely**

**cladded fibre radiates more from an irregularity than the irregularity**

**would, if it were in free space.**

**Snyder states that these studies on**

**multiply clad waveguides confirm the validity of the Volume Current**

**Irregularity**

______

*****

_____
**Fig. 4: ** **Radiation from a dielectric irregularity in the presence of an**
**outer core-cladding interface. ** **In fig. 4b, we have plotted two**
**radii for the outer core-cladding boundary, p 1,p2 .**

**Method even down to any small outer-cladding radii of the order**

**p / p . ~ 5, where p. is the radius of core of the waveguide and p is the**

**o** **i** **l** **o**

**radius of the inner cladding, as in fig. 4a. However, the author does**
**not agree, since from the above argument, it does not appear that the**
**ratio p /p. plays the dominant role in determining the accuracy of the**

**o ** **1**

**Volume Current Method, except for p / p . ~ 1, i.e. there is no inner-**

**o ** **1**

**cladding. ** **The significant factor in determining the accuracy of the**
**Volume Current Method is the outer-cladding dielectric permittivity**
**relative to that of the inner-cladding. Assuming that the outer-cladding**
**is air, this factor becomes (£2 - e Q), which is no longer very small**
**since for typical waveguides £2 ~ 2.25 e0 [7].**

**In the waveguide with infinite cladding, the core-cladding**
**dielectric difference strongly affects only the power propagating at**
**angles to the axis ** **Thus for diffuse (i.e. wide angle)**

**scattering processes it can be seen that the Volume Current Method**
**should provide valid estimates of the total power radiated. ** **The**
**calculations are in error by including the power flowing in the 2tt0^**

**(<< 1) steradians centred about 0 = 0 that constitutes the power**
**scattered into the bound modes (or rays) of the fibre. ** **However,**
**although all the power scattered into the directions with 0 >0**

**z ** **c**
**eventually escapes from the core of the fibre, the rate at which this**
**power escapes depends on the nature of the ray (i.e. either a leaky**
**tunnelling ray or a refracting ray). ** **This effect introduces additional**
**phase interference between the radiation fields and thus the radiation .**
**pattern of the scattered power will not be accurately determined by the**
**Volume Current Method, as Yip and Martucci have recently shown [8].**

**Let us digress, momentarily, and investigate the efficiency of**
**the isolated point dipoles as an excitation mechanism for a monomode**
**weakly guiding step-index waveguide. ** **This simple study provides**

**valuable insight into the relative accuracy of the above calculations.**

**3.3.1(b) ** **The Efficiency of Dipole Sources in Excitation**
**of the Fundamental Mode of a Step-Index Fibre**

**irregularity behaves as a point dipole radiator. ** **To determine the**
**relative accuracy of the Volume Current calculation, we need to**

**calculate the relative amount of power coupled into the bound modes of**
**the optical fibre in comparison to the total power radiated from the**
**source. ** **This is known as the excitation efficiency of a source. ** **In**
**this short digression, we calculate the efficiency of a point dipole in**
**excitation of the H E ^ mode of a monomode step-index fibre, using the**
**well known excitation formula of waveguide theory [19], viz.**

**P**

**q**

**2**

**J dV ** **,** **(10)**

**th**

**where P ** **is the power coupled into the q ** **mode with electric field E**

**q ** **^<1**

**by a current source, J occupying a volume V ' . ** **The electric field E^ is**
**that of the mode carrying unit power so that**

**E x h • z dA = 1 ,**