Phase Drift in Long Optical Delay Lines

Phase drift in long optical delay lines

A feasibility study

31/07/2011

1. AM modulation in electroptic system

Modulating the intensity of the optical carrier by the MZM (Mach Zehnder Modulator) is a double side modulation.

In the MZM output we get:

Modulating by RF voltage results in AM DSB modulation

Three optical signals with 3 different frequencies are transmitted into the fiber, the original carrier with two side lobes.

In the photodiode, the three signals interfere :

The signals are coherent and the photodiode current is proportional to the optical power which is the square of the sum of the three signals.

Filtering the second harmony we get back the modulation signal. (The photodiode averages the optical frequency)

2. The Dispersion effect in optical fibers

Dispersion in the fiber causes a different group delay between the side lobes and the carrier. Dispersion causes a time delay among the three signals.

D is the dispersion coefficient of the fiber at wavelength λ (nm), measured in psec/nm*km units and L is the fiber length in km.

For SMF – the standard single mode fiber, D=17 psec/nm*km at 1550nm.

At 1550nm, 10GHz equals 0.08nm. The time delay between the sidelobes and the central optical carrier after 10km of fiber is 13.6 picoseconds.

Adding the time delays in the equation of the photodiode current gives:

We used the following trigonometric identities:

and left only components with the RF frequency.

τ is the change in the group delay due to the fiber dispersion between the optical carrier and the RF sidelobe.

The phase of the RF signal after detection by the photodiode is the optical frequency which is 10E15 rad/sec multiplied by the group delay change.

RF output power is reduced by the interference factor of:

For RF frequency of 10GHz, dispersion constant of 17psec/nm*km and fiber length of 4km, τ = 5.44 psec and the added phase is 5440 radians.

3. Phase drift and fluctuations:

Phase fluctuations arise from the change in the dispersion constant in temperature.

10GHz modulation of 1550nm optical carrier sets side lobes at +/-0.08nm.

For delay line of 20 microseconds, 4km of fiber are required.

Standard single mode fiber D=17 psec/nm*km

So group delay is 5.44 psec

RF phase fluctuation rise from change in optical carrier frequency and change in the group delay.

Using a DFB laser source, even a change of 1GHz in the optical frequency shall lead to change of 5 milliradians – 0.28 degrees. Optical frequency is much more stable than 1GHz, Thus, the first term is negligible.

The second term is the dominant source of phase fluctuations. The source of change is environmental effects on the dispersion constant of the fiber. It is affected by temperature, mechanical stresses (air pressure, acoustic waves and vibrations) and other external physical effects.

Only the temperature effect was measured. Other external effects can be reduced by a good isolation of the fiber spool.

Change of dispersion constant D for SMF over temperature was measured and an average value is 1.5E-3 psec/(nm*km*C) which results in

Phase change per centigrade is 0.60 rad which is 34 degrees/C

In order to reduce the temperature sensitivity of the RF phase, we can build the long fiber delay line from two sections of fiber. First section shall be a standard single mode fiber, and the second section shall be a DCF fiber (Dispersion Compensating Fiber) with opposite behavior of its dispersion constant, even with a different value.

Lengths of the two sections shall be chosen to cancel the total temperature sensitivity of the group delay:

Published measurements claim that the temperature dependence sign of the dispersion constant is the same as the slope over wavelength. Also, the temperature dependence is quite linear over wide temperature range. DCF fibers are designed to have dispersion constant with opposite sign and also a slope with opposite sign. We expect our DCF fibers to have a temperature dependence of the dispersion constant with opposite sign compared to the standard single mode fiber.

Temperature gradients on the spool of the fiber can be handled by a sophisticated winding.

4. Conclusions

1. Using a standard single mode fiber for an optical delay line shall lead to phase drift over temperature of 10 degrees per centigrade per km of fiber.
2. Adding a section of DCF fiber can eliminate the phase drift and reduce phase drift and fluctuations to less than 1 degree over the required temperature range.
3. Care must be taken in the winding process to eliminate other effects on the dispersion constant of the fiber.