The MZ modulator represents two optical channels OC1 and OC2 in the form of
two strip optical waveguides connected at the input and the output by the optical
Y-couplers (Fig. 2.1a). The input Y-coupler distributes the laser emission with the
strength of electric component E L of EMF between these two optical channels. In
OC2, emission with the electric component strength E 2L of EMF is modulated due to
the linear electro-optical effect in the optical phase by the microwave voltage
u ¼ u g (t) from the output of the RF filter. In the optical channel OC1, emission of
this component is not modulated. The group delay time at the output of the optical
channel OC2 with respect to the MZ input depends on the instantaneous value of the
control voltage: T 2M ¼ T 2M [u(t)]. At the output of OC1, the delay time T 1M keeps
constant. Optical emission from outputs of OC1 and OC2 with electric components
strengths E 1L and E 2L of EMF are combined (summed) in the output X-coupler and
pass to the input of the single optical fiber, in which they are delayed by the group time
and, having passed through it, act on the light-sensitive area of the photodetector.
In the general case, output emission with electric component strengths E 1L and
E 2L of EMF of the OC1 and OC2 channels of the MZ modulator may pass to the
photodetector input not through the single mutual light guider, but each emission
(from these two) through the own separate light guider. In this case, the delay
difference will be:
ΔT M ¼ T 2M À T 1M þ T 2FOS À T 1FOS :
ð2:4Þ
In the case when the fiber-optical system is formed by the single optical fiber
(from 100 m and to 1 km and more), ΔT M ¼ T 2M À T 1M . In the general case, optical
fibers included into RF FODL are dispersive optical delay lines, i.e., the delay time
in them is a function of the optical frequency. In the vicinity of the average laser
generation frequency ν 0 , a dependence of delay T FOS versus the optical frequency ν
is approximately the linear function:
T FOS ν
ð Þ ¼ T FOS ν 0
ð Þ þ T FOS ν 0
ð Þ Á ν À ν 0
ð
ÞÁτ D
ð2:5Þ
where τ D is the delay slope and determines by the polarization, mode, material and
waveguide dispersion of the fiber system in the time domain and by the spatial
dispersion of the fiber-optical system and is at average the value of τ D ¼ 2–15 ps/
(nm km) (or 10
À7 s/GHz) for modern single-mode optical fibers. Thus, in the general
case, OEO represents the oscillating system with dissipation, in which structure the
dispersive delay line is included. But, taking into consideration that narrowband
lasers with the spectral line width of 1 kHz to 1 MHz are used for operation in
low-noise OEO, we neglect the optical fiber dispersion during the analysis of OEO.
An influence of the optical fiber dispersion, when using the high-dispersive optical
fibers in OEO, will be considered in Chap. 7 of the present book.
The control of the generation frequency ω in OEO with RF FODL under
consideration is explained starting from the phase balance equations of the steadystate auto-modulated oscillations [10]:
φ ω, A, B
ð
Þþφ k ω
ð Þ þ φ e ω
ð Þ ¼ À2πm, m ¼ 1, 2, . . .
ð2:6Þ
26
2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line
two strip optical waveguides connected at the input and the output by the optical
Y-couplers (Fig. 2.1a). The input Y-coupler distributes the laser emission with the
strength of electric component E L of EMF between these two optical channels. In
OC2, emission with the electric component strength E 2L of EMF is modulated due to
the linear electro-optical effect in the optical phase by the microwave voltage
u ¼ u g (t) from the output of the RF filter. In the optical channel OC1, emission of
this component is not modulated. The group delay time at the output of the optical
channel OC2 with respect to the MZ input depends on the instantaneous value of the
control voltage: T 2M ¼ T 2M [u(t)]. At the output of OC1, the delay time T 1M keeps
constant. Optical emission from outputs of OC1 and OC2 with electric components
strengths E 1L and E 2L of EMF are combined (summed) in the output X-coupler and
pass to the input of the single optical fiber, in which they are delayed by the group time
and, having passed through it, act on the light-sensitive area of the photodetector.
In the general case, output emission with electric component strengths E 1L and
E 2L of EMF of the OC1 and OC2 channels of the MZ modulator may pass to the
photodetector input not through the single mutual light guider, but each emission
(from these two) through the own separate light guider. In this case, the delay
difference will be:
ΔT M ¼ T 2M À T 1M þ T 2FOS À T 1FOS :
ð2:4Þ
In the case when the fiber-optical system is formed by the single optical fiber
(from 100 m and to 1 km and more), ΔT M ¼ T 2M À T 1M . In the general case, optical
fibers included into RF FODL are dispersive optical delay lines, i.e., the delay time
in them is a function of the optical frequency. In the vicinity of the average laser
generation frequency ν 0 , a dependence of delay T FOS versus the optical frequency ν
is approximately the linear function:
T FOS ν
ð Þ ¼ T FOS ν 0
ð Þ þ T FOS ν 0
ð Þ Á ν À ν 0
ð
ÞÁτ D
ð2:5Þ
where τ D is the delay slope and determines by the polarization, mode, material and
waveguide dispersion of the fiber system in the time domain and by the spatial
dispersion of the fiber-optical system and is at average the value of τ D ¼ 2–15 ps/
(nm km) (or 10
À7 s/GHz) for modern single-mode optical fibers. Thus, in the general
case, OEO represents the oscillating system with dissipation, in which structure the
dispersive delay line is included. But, taking into consideration that narrowband
lasers with the spectral line width of 1 kHz to 1 MHz are used for operation in
low-noise OEO, we neglect the optical fiber dispersion during the analysis of OEO.
An influence of the optical fiber dispersion, when using the high-dispersive optical
fibers in OEO, will be considered in Chap. 7 of the present book.
The control of the generation frequency ω in OEO with RF FODL under
consideration is explained starting from the phase balance equations of the steadystate auto-modulated oscillations [10]:
φ ω, A, B
ð
Þþφ k ω
ð Þ þ φ e ω
ð Þ ¼ À2πm, m ¼ 1, 2, . . .
ð2:6Þ
26
2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line