The signal pulses will be broadened through the fiber and so we need a very sharp cutoff filters with demultiplexers.  The  in-line fiber filter becomes the appropriate filters.  Most of these demultiplexers used after erbium-doped fiber amplifier (EDFA) which need a sharp wavelength bandpass filter (BPF) to filter out wavelengths other than the signal wavelength Exact  analysis of in-line fiber filter is occurred by derive a polynomial expression for the dopant ratios of GeO₂ and P₂O₅.   The refractive index of silica doped either GeO₂ or P₂O₅ is defined as a function of both the wavelength and the dopant ratio. The calculations of the dopant ratios of the pair materials (GeO₂ and P₂O₅) are done at a specific filter cutoff wavelength (λ_c) for both high pass filter (HPF) and low pass filter (LPF).  Two in-line fiber filters (HPF and LPF) are cascaded to make a sharp bandpass filter (BPF).  The length of in- line fiber filter must be very short to overcome the weak of the propagation constsnt throuh it.  The normalized frequency is discused.  A theoritical 8-channels demultiplexer is done.  The design of demultiplexer becomes very easy.