Electro optical modulators

1. Integrated-optical waveguides

Integrated-optical waveguides are able to guide light along a determined path analogue to optical fibre. They are fabricated on or in planar substrates and it is the properties of this substrate that determine the waveguide properties such as electrooptical modulation. The waveguide consists of a channel with higher refractive index compared to the surrounding material (Fig. 1.1).

The refractive index transition at the channel walls can be steplike or smoothly like described here. The light is guided by means of total internal reflection at the channel walls. Depending on the wavelength, substrate refractive index, refractive index increase, width and depth of the channel one or more transverse oscillation states (modes) can be excited. The single mode operation is of great interest since it is essential for the function of many integrated-optical elements.

Integrated-optical elements are usually provided with optical fibres particularly in optical communication technology. To achieve a good coupling efficiency to the fibre, single mode waveguides are typically three to nine microns in width and depth, depending on wavelength. Various elements like Y-branches, polarisers, phase- and amplitude modulators, switches or wavelength multiplexers can be implemented using integrated-optical waveguides.

If an electric field is applied to a waveguide using electrodes of the length L, the refractive index changes in the area between the electrodes which is followed by a phase shift of the guided light. Because of the very small waveguide cross section it is not possible to place electrodes to produce a homogeneous electric field. Therefore a coplanar electrode arrangement on the crystal surface is preferred (Fig. 2.1). This generates an inhomogeneous field distribution with an efficiency G lower than 1. In lithium niobate modulators made in x-cut crystals it amounts to approximately 0,65.

The phase shift is linear to the applied voltage (Fig. 2.2). A good approximation of phase shift can be described by:

$$\Delta \phi = \frac {\pi L}{\Lambda}n^3_3 r_{33}\cfrac {V}{g} \Gamma $$

The half of voltage V_π, which causes a phase shift of π, is calculated by:

$$ V_{\pi} = -\frac {\Lambda g}{n^3_3 r_{33} L \Gamma} $$

This typically amounts to a few volts. For longer wavelengths it is higher than for shorter ones at a given electrode geometry. For example it can be expected to be 3 V in the red at 635 nm and 10 V in the telecommunication wavelength range about 1550 nm. Since the maximum applicable voltage is approximately ±30 V, phase shifts between 20 π in the red and 6 π at 1550 nm can be reached. Due to the very fast electrooptic response, together with low control voltages and the use of sophisticated travelling wave electrode geometry, it is possible to achieve modulation at frequencies in the gigahertz range.

A phase modulator is inserted into an integrated Mach-Zehnder interferometer to form an amplitude modulator (Fig. 3.1). It is advantageous to place electrodes in push-pull arrangement at both interferometer arms. Applying a voltage leads to a phase difference in both branches, which causes a change of the output power at the device output by means of interference. So the device transmission can be controlled between a minimum and a maximum value (P_min to P_max). A phase difference of π is needed for switching from on to off state or vice versa.

The needed voltage is called the half wave voltage V_π of the amplitude modulator. Due to the push-pull-operation the half wave voltage of an amplitude modulator is the half of that of a phase modulator with equal electrode length. For example it can be expected to be 1.5 V in the red at 635 nm and 5 V in the telecommunication wavelength range about 1550 nm. The extinction ratio is given by the ratio of maximum to minimum output. It amounts typically to 500:1 in the red and more than 1000:1 in the infrared range.

The output power versus control voltage is periodic (Fig. 3.2) in cosine form:

$$P = P_{min} + (P_{max} - P_{min})\biggl(\cfrac{1}{2} cos \biggl (\frac {\pi (V-V_0)}{V_\pi}\biggr) + \cfrac {1}{2}\biggr)$$

The half wave voltage is required to switch from transmission state into the off-state and vice versa. Using a push-pull electrode arrangement it is the half of that of a phase modulator with identical electrode length. The operation point differs from the theoretical value V₀=0. It must be controlled by special electronics.

Applying a rf signal as modulation voltage to the electrodes this electrical input is translated into an amplitude information (Fig. 3.3). This amplitude output depends on the voltage magnitude and shape, thus related to the position of the modulators operation point. The figure depicts the transmission of a binary pulsed electrical input into a binary optical output signal. If the voltage levels would not be correct, that is that the voltage is too high or the offset is not correct the modulator will react with non correct optical output levels in binary operation or with higher harmonics in analog operation.

1. Wavelength and wavelength range

Various properties of the modulators, in particular the half wave voltage and insertion loss, depend on the operation wavelength. While the half wave voltage decreases at shorter wavelengths, the insertion loss increases, which is mostly due to Rayleigh scattering and a little due to absorption.

The usable wavelength range (spectral or optical bandwidth) of proper modulator operation is limited by the modal behaviour of the waveguide. It depends on the substrate material and the central wavelength. The singlemode operation and definite modulation is guaranteed within this range.

For a given central wavelength for which the modulator was fabricated the modulator can accept laser wavelengths out of a range which is coloured in the figure 4.1. For example at 1060 nm central wavelength the optical bandwidth is ± 40 nm, i.e. the modulator can operate between 1020 nm and 1200 nm. At longer wavelength the insertion loss increases due to waveguide cut-off and at shorter wavelengths the modulation is nondefinite due to interference of higher oscillation modes, respectively, leading to contrast loss in amplitude modulators or residual amplitude modulation in phase modulators. Amplitude modulation is possible with extinction ratio of more than 1000:1 in the near infrared spectral region, in the red the extinction amounts to more than 500:1

2. Technical data

The modulators are available for a variety of wavelengths (in the range from 635nm-1550nm, shorter wavelengths on request). In principle every wavelength can be provided if a laser whose wavelength is near to the desired wavelength is available. The modulator data of some standard wavelengths are depicted in the data sheets.

The modulators are produced with fibre pigtails with the standard length of 1 m. Other lengths are possible on request. At the input port a polarisation maintaining fibre is required. The output fibre is also polarisation maintaining, but standard singlemode (non-PM) fibres are available on request also.

The polarisation in the fibre is aligned to the stress rods in slow axis direction usually. Bow-tie fibres are used as standard. Panda fibres can be provided on request.

The devices can be delivered with bare fibre ends or fibre connectors, preferably FC/PC- or FC/APC-connectors with 8° angled polished surface. The polarisation is aligned to the connector key as depicted in the figure 5.2. Other connectors or other polarisation alignment canbe provided on request.

The best connection between two fibres is the splice. It is very important to align the fibres best. Additional losses may occur if using fibre connectors because of the non-concentricity of the cores and the manufacturing tolerances of the connectors, especially for red light.

1. Standard phase- and amplitude modulator wiring scheme

All phase modulators and the standard amplitude modulators are available without elec­tronics inside the modulator case (Fig. 6.1). Both ends of the hot electrode on the modulator crystal are connected to SMA connectors. The ground electrodes are connected to the modulator case as well as the ground of the SMA connectors. One SMA connector can be used as rf-input, at the second connector a 50 Ω terminator is recommended to avoid reflections of the rf-signal which may disturb the modulation and the control electronics. The input modulator impedance is 50 Ω, the ohmic resistance between both ports between 5 and 10 Ω for the HF version and about 150 Ω for the standard version.The capacity amounts to app. 20 pF. The terminator can be removed for measuring purposes or to connect the modulator with further electronics. The modulator is electrically and optically symmetric. At higher modulation speed (500 MHz or more) the optical transmission direction must be the same as the electrical transmission direction.

The optical rise time is app. 200 ps for the HF version and 1 ns for the standard version if a short rise time electrical input signal is applied. A bias, which is necessary to control the operation point, causes a current through the hot electrode which may heat the electrode and the terminator. This can be prevented using a wiring scheme which is described in the further chapters.

2. Wiring scheme inside the amplitude modulator with separate rf- and bias-inputs

To separate the rf- and the bias-inputs a wiring scheme can be integrated into the modulator case (Fig. 6.2). All modulator electrodes are electrically isolated from the modulator case. The hot electrode is terminated internally, while the ground electrodes are connected to the ground by use of capacitors which cause a rf-connection, but a bias separation. So the bias can be fed by a second connector up to a frequency at which the capacitors become transmittant. This is approximately 10 kHz with 100 nF capacitors and approximately 100 kHz if 10 nF capacitors are used.

The optical rise time is app. 500 ps for the HF version and 1 ns for the standard version if a short rise time electrical input signal is applied. The bias does not cause a current through the hot electrode. The bias caused current is due to the capacitive resistance, thus frequency dependent. At dc the bias caused current is zero.

3. Separation of rf and bias using an amplitude modulator with standard modulator wiring scheme

The described bias scheme can be built up externally if a modulator with standard wiring scheme is used. Here the modulator case must be placed isolated and be connected to the ground using capacitors (Fig. 6.3). It is useful to place the modulator case and the surrounding circuitry in a rf-sealed case. If the lengths of the wires are short enough the electrical and optical properties are identical to the integrated version which was described in the previous chapter. The advantage is that the modulator can be removed from the outer case and be used as a standard one.

The modulator is switched between two voltage levels for which the optical output power is zero (in the figure -0.5 and 3.5 volts). The modulator is switched from the off-state via the on-state to the next off-state (blue line and blue arrows in Fig. 7.1).

It transmits a light pulse during the switching process. The optical pulse length corresponds to the rise time of the input voltage (1 ns in Fig. 7.2).

Switching mode:

The modulator is switched between two voltage levels, for one the optical output is zero and for the other the optical output is maximum (in the figure -0.5 and 1.5 volts). The modulator is switched from the off-state to the next on-state (blue line and blue arrows in Fig. 7.3). It will be switched on or switched off vice versa. The optical rise time corresponds to the rise time of the input voltage.

If a light pulse should be generated its length corresponds to the time between on-switching and off-switching (100 ns in Fig. 7.4).

2. Determination of V₀ and V_π

The parameters Determination of V₀ and V_π of the characteristic curve can be determined as follows:

A laser or laser diode is coupled to the modulator input fibre. The modulator output fibre sends its light into a photodiode. The electrical modulator input is connected to a frequency generator and a high ohmic oscilloscope x-input using coaxial cables. The photodiode is connected to the 50 Ohm oscilloscope y-input. The x-y- plot shows the characteristic curve, where V_π and V₀ can be determined. It is useful to save the curve data using a computer and to do a cosine fit then (Fig. 7.5).

3. DC-behaviour of lithium niobate modulators

Waveguide modulators made of lithium niobate react on dc-voltage with the so-called dc-drift (Fig. 7.6). After applying a dc voltage a charge transport in the crystal takes place. That´s why the electric field which is applied to the electrodes is compensated partially, so that the effective electric field decreases partially with time. This process is related with the number of free charge carriers and with the dark- and photoconductivity of the crystal, respectively. Since the dark conductivity depends on the temperature and the crystal purity, while the photoconductivity depends on the crystal purity, wavelength and optical power density (i.e. the optical power in the waveguide), the duration of the compensation process depends on these values. It takes some minutes to some hours. The duration will become shorter the higher the temperature and optical power density and the shorter the wavelength. The compensation saturates at approx. 75 % of the initial value. The compensation time does not depend on the initial voltage. That means that the amount of the drift per time (i.e. the first derivate of the curve phase against time) becomes faster at higher dc voltages.

This partial compensation process of the electric field which passes the waveguide causes a partial back-drift of the initial optical phase shift which was caused by the applied voltage. At phase modulators it can be measured directly by use of an interferometer. In the case of amplitude modulators the optical phase shift is followed by an amplitude modulation of the optical output due to its cosine characteristic curve. This can be measured as shift of V₀. V_π does not change its value.

The diagram shows an example of the phase drift which was measured at a 1550 nm amplitude modulator with an optical power of some milliwatts at room temperature. The phase is given in % of the initial value and was calculated by use of the cosine characteristic curve of the modulator. The applied voltage (2V) was a little higher than V_π  (1.59 V), that means that the inital phase has been 1,25 π. It is to be seen that the time which is needed for stabilisation is more than one hour if the modulator is used in the infrared at moderate optical power. The drift will be faster if higher optical power or shorter wavelengths are used, but the modulator reacts more on changes of the light and environmental conditions also. 

A stabilisation of the operation point can be done as follows:

3.1. Dynamic mode:

Due to the periodicity of the output signal it is possible to modulate at different parts of the characteristic curve, which are differing by a multiple of 2*V_π . The operation point should jump between two equivalent voltage values with alternating sign, in the sketch (Fig. 7.7) depicted as V_- and V₊ . Then the modulation occurs alternating on both red parts of the characteristic.

To avoid dc-drift the applied voltage V should be measured and integrated for a time which is short enough against the duration of the dc-drift (< 1 second) while the modulator operates at the operation point V_- . The value A_- with: $$A_- = \int_{V_-} V (t) dt $$

After this the operation point has to switch to V₊ where the modulator operates until the value A₊ with $$A_+ = \int_{V_+} V (t) dt $$ is reached, where $$ |A_+| = |A_-| $$ must be fulfilled.

Then the operation point has to switch to V_- again and so on. This causes that the average value of the applied voltage is zero and no dc-drift can occur. It must be taken into account that the modulator passes the periodic characteristic while changing between V_- and V₊ which produces an unwanted optical power modulation.

1. Size AMxxx

The modulators are available in standard cases. Their measures are sketched as follows:

2. Size AMxxxb

Their measures are sketched as follows:

1. Pulse slicing

One essential modulator application is to generate and to shape short pulses using cw laser light. The advantage is that the pulse shape can be controlled independently on the laser type. This is needed in some laser applications, especially in fibre oscillator-amplifier arrangements. For example a short light pulse is generated if an electrical egde with the amplitude 2xV_π or an electrical pulse of the amplitude V_π is applied (Fig. 9.1 and 9.2). An analogue temporal shaping of light pulses can be done in similar manner, like it is depicted using a two-step pulse (Fig. 9.3).

2. Pulse picking

Single pulses or pulse combs can be selected from fast laser pulse chains. Thus the amplitude modulator operates as pulse picker to reduce the repetition rate of the laser. The following example shows the pulse picking from a 1060 nm, 150 fs, 76 MHz pulse chain with picking factors 20 and 40, respectively. In most cases picking by a factor between 100 and 1000 is necessary.

The operation principle acts as follows (Fig. 9.5):

A synchronise signal which is taken from the pulsed laser feeds an electrical delay line. This is used to equalise the runtimes of the pulses in the fibre and wires and the driver operation time. A counter counts the synchronise signal pulses up to a preset number. The counter output pulse feeds a pulse generator which drives the modulator thus opening it for the transmission on one or a number of light pulses.