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1 2 Direct modulation Consider the static optical power-versus-current characteristic of a laser diode; if we bias at point IB and then superimpose modulation, then the optical power will track changes in this. We show it here for sinusoidal modulation: Electrical-to-optical conversion: modulators Stavros Iezekiel PL (mW) Department of Electrical and Computer Engineering University of Cyprus IL PL = P0 (1 + m cos ω mt ) = P0 + p (t ) PL (t ) = s L I L (t ) P0 PL IL (mA) I L = I B [1 + m cos ωmt ] = I B + i (t ) IB • HMY 645 • Lecture 08 • Spring Semester 2015 4 3 Although the method of direct modulation is a useful one, it suffers a number of problems: 1. As well as the intensity of the light, the wavelength is modulated. (This phenomenon is called chirp.) Along with fibre dispersion, this leads to a chirpinduced dispersion limit on transmission distance. Ti-diffused optical waveguide Electrodes CW light 2. The maximum bandwidth we can modulate up to is only a few tens of GHz at the very best. 3. The maximum quantum efficiency (η) in theory is 100%, and this places an upper limit on the slope efficiency (and therefore the “gain”). sL = η hc qλ Lithium niobate substrate Modulated light EXTERNAL MODULATION 6 In addition to direct modulation, we can also modulate the light from a laser with an external component known as a modulator. Hence the terms external modulation and external modulator. External modulation CW Laser External modulator Modulated light output RF input + Bias Optical power This will depend on the CW laser output power as well as drive conditions One advantage of external modulation is that it can be used to implement optical phase modulation, which opens up the possibility of coherent optical communications and therefore increased receiver sensitivity. Laser emits constant optical power. This then passes through an optical modulator (external modulator) – this is a voltage driven device. As we adjust the voltage, the amount of optical power absorbed will vary. In this way, we achieve modulation of the optical power coming out of the modulator. Bias point and modulation depth chosen to give incrementally linear slope Vπ P0 + p (t ) V VB + v(t ) 7 Other advantages of external modulation compared to direct modulation: 8 Material Considerations • Laser diodes suffer from chirp which then introduces dispersion penalty. Not an issue with external modulation. Obviously the key requirement is that some optical property of the material must change in response to a changing electrical parameter. • It is possible to produce formats such as single sideband (SSB) or double-sideband suppressed carrier (DSB-SC) • Electro-optic effect • An applied electric field changes the refractive index • This leads to phase changes • Can also produce intensity modulation when combined with an interferometer • Slope efficiency of laser diodes is limited by fundamental quantum efficiency (100% max), whereas for external modulation the slope efficiency scales with CW laser power. • Laser diodes limited to 30 GHz max (unless optical injection locking is used), whereas up to at least 100 GHz has been reported with modulators. • Many Mach-Zehnder modulators are based on lithium niobate and are difficult to integrate with other components, but electro-absorption modulators lend themselves to monolithic integration with driver electronics. • Recent work by Intel, for example, on silicon modulators paves the way for integration with CMOS electronics. • Acousto-optic effect • A sound wave (resulting from electric field applied to a piezoelectric) changes the refractive index • Electro-absorption effect • Applied electric field changes the absorption 9 10 To date, the dominant type of modulator is the lithium niobate Mach-Zehnder, which is based on the electro-optic effect. Comparison of electro-optic materials Electro-optic effect: A small change in refractive index n results from an electric field E: Pockels effect Only certain crystalline solids show the Pockels effect, as it requires lack of inversion symmetry It is linear with respect to electric field and hence voltage Moodie, CIP 1 1 = + rE + RE 2 + ... n 2 n02 Kerr effect Observed in all optical materials with varying magnitudes, but generally weaker than Pockels effect. Apart from presence of electro-optic effect, other important material properties include optical loss, maximum optical power handling capability and stability (thermal and optical). In general, the Pockels effect is used since it is stronger (Kerr effect is primarily exploited for optical fibre solitons). Modulators can be made from inorganic materials, semiconductors or polymers The Pockels coefficients rij are elements of a 6 x 3 tensor 11 12 However, for the moment lithium niobate (an inorganic material) dominates, not because it excels with respect to loss, stability, maximum optical power or electro-optic sensitivity, but because it offers the best compromise between all four key parameters. Lithium niobate is also relatively cheap since it is also widely used in surface acoustic wave filters. It can be grown using the Czochralski process in wafer sizes large enough to accommodate the relatively long and narrow structures required for Mach-Zehnder modulators. Polymer modulator fabricated using SU-8 based rubber stamp as a potential route to low cost manufacturing. 14 13 Light from a laser can be described by its electric field. To keep things simple we consider a purely monochromatic laser (i.e. a “perfect” laser), for which the emitted field at some fixed distance from the laser is given by: Lucent E (t ) = Eo (t )e j (ωo ( t ) t +φo ( t )) Optical phase Amplitude (complex quantity) Optical frequency (i.e. 100’s of THz) In analogy with electronic communications, we are able to modulate amplitude, frequency or phase. MACH-ZEHNDER MODULATORS Amplitude modulation in optical communications is known as intensity modulation, and this is the most common approach. It can be achieved either through direct or external modulation. Frequency and phase modulation can only be achieved with an external modulator, and can only be detected with a coherent photoreceiver. We will not consider these techniques any further here. 15 The optical intensity is directly proportional to the square of the electric field magnitude. The optical power emitted by the laser is, in turn, directly proportional to the intensity. So we can write: 2 optical power ∝ E (t ) = Eo (t ) 16 External modulators that are based on the interferometer principle are known as Mach-Zehnder modulators (MZM). To understand the basic principle, we need to remember something about superposition (and constructive and destructive interference). 2 So the optical power varies only with variations in the amplitude of the electric field, and this is achieved either through direct modulation or an external modulator. We will now consider the operation of an external modulator based on the principle of an interferometer: Consider some examples: Constructive interference: 1.0 1.0 Electrical input (modulation) = Modulator 1.0 -0.2 1.2 + -0.2i = = 0.8 time "Quadrature phase" ±90° interference: + + 0.2 Unmodulated light from laser Destructive interference: 1-0.2i time time 17 Now consider the optical waveguide structure of a MZM: The two waveguide arms have equal length, so the delay and hence phase shift is equal for both paths. Input light 18 The waveguides are formed from titanium which is diffused onto a layer of lithium niobate, which forms the substrate. Lithium niobate is a material that has a strong electro-optic effect – if we apply a voltage to it, then its refractive index changes. We can show that this is equivalent to introducing a phase shift. Ti-diffused optical waveguide Electrodes CW light Output light Y-junction. The incoming light is split equally into two paths at this point. So the light on each of these paths for an ideal device will be 3 dB less in optical power compared to the input light. Lithium niobate substrate Second Y-junction. Here light from the two arms is combined in phase. However, the optical power of the output will be lower than that of the input due to losses in the waveguides and at the Yjunctions. We refer to this as the insertion loss of the MZM Modulated light In the MZM shown above, a voltage applied to the electrodes will introduce a phase shift into the upper arm. For zero volts there is no phase shift and we have constructive interference, but if we increase the voltage to some value (called Vπ) then there is a π radians relative phase shift leading to total extinction. Values in between will lead to varying levels of absorption. 20 19 Just as we have a light-current characteristic for a laser diode, we have a voltage-light characteristic for a MZM: Po Pi πVm Po T ff = 1 + cos Pi 2 Vπ Po = T ff Pi T ff < 1 1 The transfer characteristic is given by: If we apply a bias voltage of nVπ/2 (where n is odd) and a small-signal modulation component given by vm(t), then linearization of the above equation around the bias point will yield: Reduction due to optical insertion loss of modulator T ff π (VB + vm (t ) ) T ff Po T ff ≈ = 1 + cos Vπ Pi 2 2 π vm (t ) 1 ± Vπ from which the slope efficiency (in W/V) is obtained as: 0 0 1 Vm = Vπ 2 3 4 Vm Vπ dPo T ff π Pi = dvm 2Vπ So by increasing the optical power from the CW laser, we can increase the efficiency of the modulator. 22 21 Choice of the bias point is an important consideration, because the sinusoidal shape of the MZM transfer characteristic means there are no linear parts to the curve, so if we want to have almost linear operation we must choose points on the curve that are good approximations to a straight line. Also, we can show that the best bias points will be those for which the slope of the characteristic is maximised (in order to prove efficiency). So if we use an appropriate bias point (say 3Vπ/2), and then apply modulation, we have the following: Po Pi If we assume constant CW input power, then: Po = T ff Pi πVm 1 + cos 2 Vπ dPo T ff Pi = dVm 2 Bias point and modulation depth chosen to give incrementally linear slope 1 Reduction due to optical insertion loss of modulator T ff Po + p (t ) Pi π πVm − sin V V π π Finding the maxima/minima for this derivative yields the following as suitable bias points: 0 0 Vm 1 3 5 = , , ,..... Vπ 2 2 2 1 VB + v(t ) Vπ 2 3 4 Vm Vπ