and E = ∑ ν$_{M}$ ,m a M ν$_{M}$ $_{,m}$.h (+) ν$_{M}$ ( kr ) . L Y$_{ν}$$_{M}$$_{,m}$ ( θ, φ ) √ ν$_{M}$ ( ν$_{M}$ +1) + i k ∑ ν$_{E}$,m a E ν$_{E}$$_{,m}$. ∇ × ( h (+) ν$_{E}$ ( kr ) . L Y$_{ν}$$_{E}$$_{,m}$ ( θ, φ ) √ ν$_{E}$ ( ν$_{E}$ +1) ) (8) E = ∑ λ a$_{λ}$ · E$_{λ}$ ; H = ∑ λ a$_{λ}$ · H$_{λ}$ (9) $^{a$_{ν,}$}$− m = ( − 1) m +1 · $_{a}$∗ $_{ν,m}$. (10) a$_{λ}$ = k 2 ∫ Ω$_{0}$ r · ( E × H ∗ $_{λ}$) rd Ω . (11) dP d Ω = c 8 πk 2 · ‖ ( − i ) ν$_{E}$ +1 ∑ ν$_{E}$,m a ( E ) ν$_{E}$$_{,m}$. L Y$_{ν}$$_{E}$$_{,m}$ ( θ, φ ) √ ν$_{E}$ ( ν$_{E}$ + 1) × ˆ r + ( − i ) ν$_{M}$ +1 ∑ ν$_{M}$ ,m a ( M ) ν$_{M}$ ,m · L Y$_{ν}$$_{M}$$_{,m}$ ( θ, φ ) √ ν$_{M}$ ( ν$_{M}$ $_{+ 1)}$‖ $^{2}$. (12) P total = c 8 π ∫ Ω$_{0}$ Re (ˆ r · ( E × H ∗$_{))}$$_{r}$ $^{2}$d Ω = c 8 π ∑ λ ‖ a + λ ‖ $^{2}$. (13) where λ refers to TE and TM waves. In addition it can be demonstrated [16] that we have The coefficients a$_{λ}$ are determined by an integration with respect to the solid angle which includes the entire allowed domain Ω$_{0}$ Hence, we can express the angular distribution of radiated power, defined as dP d Ω = c 8 $_{π}$r $^{2}$E × B ∗ , as follows: In addition we can write the total radiated power as: The tapered and metal-coated optical fiber tip used in NSOM[26–28] is characterized by a “funnel” geometry in which an aluminum layer (thickness of ∼ 100 nm) is evaporated onto a glass cone truncated at its apex by a small disk (diameter of 2 a ∼ 60 nm, see Fig. 2). The shape of the tip reveals a partially conical geometry. Therefore, the system is -to first approximation- equivalent to a conical antenna and it can be described by a quasi-multipole IV. THE RADIATION PATTERN OF A COATED TAPERED FIBER TIP 7