A Mach-Zehder modulator is not perfectly balanced. Moreover it is subject to drift caused by thermal changes, thermal inhomogeneity, aging, photo refractive effects, static electrical charge accumulation… This drift causes the transfer function to move in the horizontal direction ; the modulation signal is then applied to a changing operating point, that can modify strongly the obtained modulation.

 The bias voltage applied to the DC electrodes aims to :

- selecting the desired operating point of the modulator

- compensating for the possible modulator drift and locking the device operating point so as to keep stable operation conditions

 The bias voltage can be supplied by a simple voltage source and manually adjusted so as the desired operating point is reached. In such conditions, the voltage will have to be re-adjusted manually in case of drift of the modulator. This may be workable in laboratory with low drift modulators and stable environmental conditions

However, for a long term operation and especially in all systems that have to operate over changing temperature conditions, an automatic bias control circuit is necessary so as to permanently supply the right DC voltage and to lock the selected operating point.


An electro-optic effect is a change in the optical properties of a material in response to an electric field that varies slowly compared with the frequency of light. The term encompasses a number of distinct phenomena, which can be subdivided into changes in absorption and changes in refractive index.

As far the changes in refractive index are concerned, there are two main electro-optic effects : The Kerr effect (quadratic) and the Pockells effect (linear). In LiNbO3 modulators, the change in the refractive index linearly proportional to the electric field (Pockells effect) is used.

The extinction ratio (or contrast) is the ratio between the optical power transmitted at the output ofthe interferometer in the ON state (Pmax) and the interferometer in the OFF state (Pmin) 

ER (dB) = 10 log Pmax/Pmin

The extinction rate can be degraded if the two arms of the Mach-Zehnder interferometer are not strictly identical (loss imbalance) or if there is a coupling of evanescent waves between the optical modes going through the two arms of the interferometer. The multimodality of the waveguides is also an important factor in the degradation of the extinction rate. In general, sensitivity to the fabrication process is often at the root of these problems.


Also called , the half wave voltage is the voltage required for inducing a phase change of π for the light going through the modulator.

For intensity modulators, the half wave voltage is the voltage required to turn the modulator output from minimum to maximum transmission (or vice-versa)

For many applications, the half wave voltage is the voltage the modulator must be fed with and it is therefore a main specification of the device.


Ludwig Mach (November 18, 1868 in Prag; † September 1951) was a scientist.

Ludwig Mach was the eldest son of Ernst Mach who gaves his name to the Mach Number representing the ratio of speed of an object moving through a fluidnd the local speed of sound. From 1879 to 1883, Ludwig Mach attended das KK German High School in Prag, then he studied in a private school for 2 years. He also attended the public High School in Arnau in 1886-1887.

From 1887 to 1892, he attended Prag Medicin School and gratuated in 1895. During his studies, he also assisted his father in his physics lectures. At this time also started his cooperation work with his father. He mostly took charge of optic matters and instrument construction.

In 1889 the first joint publication was published. Since the 1890s, he pursued his father’s and Peter Salcher’s photographic attempts. In 1892 he developed, along with his father, the Mach-Zehnder Interferometer. In the same years, Ludwig Zehnder invented also the same interferometer but it appears both physicists conducted their work independently.

He invented in 1894 a new aluminium alloy, containing from 2 to 30 percent of Magnesium. He called it Magnalium and patented it. Thanks to its commercialisation, he was able to receive now and then substential amounts of money.

In early 1896, he began to work for Carl Zeiss in Jena, at the Ernst Abbe Institute, but he quit in september.

An intensity modulator based on a Mach-Zehder interferometer. The intensity modulation is obtained by creating  phase differences between the two arms of the interferometer. Depending on the overall phase difference, the light recombines more or less efficiently, or does not recombine at all, at the output of the interferometer, conducting to a modulation of the output power.

In LiNb03 intensity modulators, the interferometers is made up with waveguides in the material and the phase difference obtained by applying an electric field on both arms.

Go to our Intensity Modulators Page

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Friedrich Carl Alwin Pockels (1865 - 1913) obtained his doctorate from Göttingen University in 1888. From 1900 until 1913, he was a professor of theoretical physics in the Faculty of Sciences and Mathematics at the University of Heidelberg where he carried out extensive studies on electro-optic properties of crystals - the Pockels effect is basis of many practical electro-optic modulators (Courtesy of the Department of Physics and Astronomy, University of Heidelberg, Germany.)

The Pockels effect (after Friedrich Carl Alwin Pockels who studied the effect in 1893), or Pockels electro-optic effect, produces birefringence in an optical medium induced by a constant or varying electric field. In the Pockels effect, also known as the linear electro-optic effect, the birefringence is proportional to the electric field. In the Kerr effect, the refractive index change (birefringence) is proportional to square of the field. The Pockels effect occurs only in crystals that lack inversion symmetry, such as lithium niobate or gallium arsenideand in other noncentrosymmetric media such as electric-field poled polymers or glasses.

Proton exchange is a commonly used technique when making optical waveguides in lithium niobate. It is known as APE (Annealed Exchanged Proton). The process substitutes Li+ lithium ions on the surface of the wafer by H+ protons contained in an acid bath. Defining the geometrical patterns of the waveguides in photosensitive resin by masking and photolithography makes up the first step in fabrication. Once the patterns in resin have become established, the wafer is immersed in a heated acid bath for a fixed length of time. The temperature and length of exchange are determinant factors in obtaining the index profile of the waveguide. In our case the proton exchange is carried out in a bath of benzoic acid. The substitution of L+ ions by H+ ions only takes place on the surface of the wafer and only on zones that are not masked by resin. Locally, the lithium niobate undergoes an increase in the refractive index according to the extraordinary axis and a decrease in refractive index according to the ordinary axes. Annealing then enables the protons concentrated on the surface to be diffused in order to obtain a stable waveguide profile. The length of annealing time again plays a major role. In the end, the waveguide will have undergone a positive variation of the extraordinary refractive index while the ordinary refractive index will be slightly under the ordinary index of the substrate. A direct consequence of this is that APE technology can only guide one single polarization, as according to the ordinary axes, guide conditions are not combined (the exchange index being lower than the substrate index).