Optical data sources.
Optical data sources are devices that are used to generate the signals for optical communications. There are two basic devices of interest here the light emitting diode (LED) and the laser diode. Basically they are current driven devices that produce light as a function of the current input. Typical ideal, linear, characteristics of these are given in the figures Power Vs. Current for an ideal light emitting diode and Power Vs. Current for laser diode.
Internal (direct) optical modulators.
One of the basic requirements of an optical communication system is that it should be capable of conveying messages. These messages may be presented to the optical communication system as an analogue or digital data signal. The optical signal is essentially a high frequency carrier with frequencies at hundreds of terahertz. The message signals are usually of a much lower frequency. To impose the message onto the optical carrier means a method of modulation is needed. Analogue or digital signals may be the modulating signal but in line with modern communications the focus here will be mainly on digital. In terms of an optical communication/network the modulator can be considered one of the main front end components.
Modulation of optical signals.
Optical signals may be intensity, frequency, phase modulated as in electronic systems or polarisation modulated, more appropriate to optical systems.
A typical system is shown in the figure Optical modulator. Here the high frequency optical signal (say hundreds of terahertz) is modulated with a relatively low frequency signal. The receiver circuitry needs to detect the signal but only the low frequency part is needed.
The description usually attributed to amplitude modulation of an electronic signal in that the signal voltage (electric field) is varied in sympathy with the amplitude of the modulating signal. Now if amplitude shift keying was considered this is suggesting that the amplitude of the carrier vary discretely in amplitude with the modulating signal. The simplest technique is ON-OFF keying where the amplitude is on or off (representing a '1' or '0' of a binary modulator. This can be achieved with an optical signal the parameter that is turned on or off is the intensity.
Here the intensity (power) is made to vary with the modulating signal.
Typically in a semiconductor device (LED or laser diode) the bias current is set to a particular value and the high frequency baseband current signal is superimposed onto the bias current.
Direct (internal) LED modulation. Digital power( intensity) modulation.
If the modulation is assumed linear then a representative waveform is as that shown in the figure LED modulated waveforms.
With regard to the power transfer characteristics of the LED or Laser the modulation can be described graphically via figures intensity modulated waveform (LED) for an LED and figure intensity modulated waveform (laser diode) for a laser diode.
Modulation response of LEDs.
Although the description tends to suggest that the modulation produces a good replica of the modulating signal if operated over the linear region in practise the devices do have a bandwidth.
If a sinusoidal signal is used to modulate an LED then the frequency response of the device can be measured by varying the modulation frequency. This gives an indication as to how fast the LED can be modulated in terms of data rates. The frequency response of an LED can be modulated is determined by the recombination time (a parameter of the material of the LED). A simple formula to determine the bandwidth can be written as:
Where Po is the unmodulated optical output power P(w) the optical output power at a frequency w radians/sec (frequency of the power variation) and t the recombination time, which is a parameter of the material. A typical response is shown in the figure Typical modulation response of LED where t = 10 ns.
The usual definition of bandwidth is when the output power response has fallen to half its dc value.
This defines how much, often as a percentage of the maximum, the modulated signal power extends about the bias point.
Non-linear response of a LED.
In practice LEDs may exhibit a non linear response in their transfer characteristics and a typical suggested response uses a polynomial description e.g.
where Ib is the bias (DC) current and ai polynomial coefficients that describe the device.
Direct (internal) laser diode modulation. Digita l power( intensity) modulation.
Digita l power( intensity) modulation.
If the modulation is assumed linear then a representative waveform is as that shown in the figure Intensity modulated waveform (laser diode).
Note in the case of a laser diode a careful choice of bias current Ib is needed to ensure that negative excursions of the modulated waveform do not enter the pre-threshold value causing signal distortion.
Step response of laser diode.
When a laser diode is directly modulated the results are quite different from an LED. The circuitry is relatively simple and only requires serious attention at microwave frequencies. An important feature of this is the possible integration of drive circuitry and laser on the same device. Typically lasers based on the III-V semiconductors allow the construction of electronic circuits in much the same way as silicon does, e.g. a single device containing laser and detector.
The laser diode does exhibit some interesting phenomena when modulated. Consider the case when a step current input is applied, the light output does not settle immediately the current is applied (note this not shown in the figure Intensity modulated waveform (laser diode). A delay is evident between the first instance of input current and the output intensity see figure relaxation oscillation in a laser diode.
This phenomena is called the relaxation oscillation. It results from interplay between the population inversion and the fields within the laser. The oscillation occurs whilst the carriers and photons attempt to reach an equilibrium point.
A turn on delay (not shown in the figure) also occurs with a step input and manifests itself as zero modulated output until the delay time is reached.
Frequency response of modulated diode.
As in the LED the frequency response of a laser is determined by modulation with sinusoidal currents at increasing frequency. Optical data communication systems need devices which are capable of being modulated at high data rates well into the Gigahertz (109 Hz) region. Consequently much attention is focused on using semiconductor devices to do just that.
The frequency characteristics of a laser diode are determined by modulating the device with high frequency sinusoidal signals.
The small signal frequency response (the response relative to zero frequency modulation) is approximated by:
What is immediately recognisable is that it resembles a second order system. wm is the modulation frequency, wo natural system frequency and s a system parameter. A typical response is show in the figure Frequency response of modulated laser diode. The plot shows a movement away from the typical LED response with evidence of a peak at the upper frequency end.
This is followed by a notable fall off of in amplitude with a further increase in frequency. Although increasing bandwidth is achievable with an increase in bias current a significant peak is noticeable.
Before looking at external modulators directional couplers will be described, which are often used for this type of modulation.
Coupling of an optical signal is described by the transfer of signal energy between closely placed waveguides. This occurs in a so called directional couplers and relies on a concept known as the evanescent field for its operation.
The evanescent field in a waveguide.
In a wave guide such as an optical fibre the confinement of the electromagnetic wave is not completely within the guide. A phenomena occurs that introduces the so called evanescent field. The evanescent field is a field that propagates outside of the waveguide, with the wave, in the direction of propagation. The actual field profile as it propagates along the wave guide is typical of that shown in the figure Evanescent field in a waveguide. The bell shaped profile of the field is representative of the amplitude of the wave in a lateral direction.
Note a portion of the field is propagating outside of the confinement area. This does not represent a power loss as the there is no propagation laterally. Effectively the evanescent field can be considered to eventually decay to zero in the lateral direction.
Mode coupling is effected by placing in close proximity a section of the wave guide see the figure Mode coupling.
A number of things can occur with this situation. i). As the signal reaches the end of the coupling section it leaves via the same waveguide, ii). the signal is shared by some ratio between the waveguides iii). the signal leaves via the other fibre. The effect is known as "mode coupling" and can be considered as coupling of the evanescent field into an adjacent waveguide. The analysis is protracted and complicated but a number of parameters of interest arise. The power coupling of the field to the other guide is total if the length of the physical coupling length (L) equals a parameter called the coupling length Lc. In between this the power coupling is zero or partial and is given by the formula;
, where pL/Lc is in radians. This expression is also known as the power coupling ratio.
where L is the actual coupling length of the fibre and Lc the coupling length. This describes the operating principle of a device called the directional coupler.
The basic 3 dB 2´2 coupler) - matrix description.
A coupler can be constructed such that it forms a device that splits the input signal equally, in terms of power, at the output. That is a signal entering at port 1 (see figure 3 dB coupler) splits into two signals at ports 3 and 4. This can be used as a basic building block for higher order couplers.
The coupler can be described by the power/intensity transfer function given by:
where h(m,n) represents the power coupling coefficient between ports m and n, and g the proportion of power lost through the coupler (insertion loss). This equation shows that coupling occurs also with a signal input to port 2. Note signals can be applied to both ports simultaneously.
External optical modulators.
Direct modulation is one way of modulating an optical carrier. Another technique is external modulation and is fundamentally different to direct modulation the basic scheme is shown in figure External modulation.
The concept of external modulation is based on sampling or switching of the continuous input waveform. The switch has a gating function and allows the passage of optical signals determined by the electrical modulating signal. Effectively the current input to the laser is unchanged and the laser is biased to constant output.
The electro-optic effect.
All materials possess a refractive index that determines the phase velocity of an optical signal passing through the signal. Normally the refractive index is constant but can change due to external physical effects. Typical physical effects include e.g. the application of, an electric field, mechanical stress and temperature changes.
Phase modulation using the electro-optic effect.
A typical switch may be based on the Electro-optic effect. In this method an electrical signal imposed on a material affects the refractive index.
E.g. a material may undergo a change in refractive index due to the electro-optic effect equal to Dn, when a voltage is applied, this can be translated into a corresponding phase change by noting that a wavelength is equal to a phase change of 2p.
If the distance the wave travels is L through a refractive index n then the number of wavelengths over this distance is Ln/l.
If the refractive index is now n + dn due to the Electro-optic effect the number of wavelengths over this distance is L(n + Dn)/l.
The number of wavelengths difference is:
L(n + Dn)/l. - Ln/l = LDn/l.
As a wavelength is equal to 2p radians then the radian (phase difference) is:
Df = 2pLDn/l.
The pre (no voltage applied) and post (voltage applied) modulated waves have a relative phase difference of Df.
The electro-optic effect produces this change due to an applied voltage V (see figure phase modulation with electro-optic effect).
Here electrodes are placed on the electro-optic material and a voltage applied. The voltage causes polarisation of the material and this changes the refractive index.
The Electro-optic material has a particular coefficient which is given as r. If the electro-optic material has a refractive index n before the application of a voltage then the refractive index change is written as:
Dn = n3rV/2d.
the accompanying phase change is:
Df = pn3rVL/dl (multiply by 2pL/l)
Df = (pn3rL/dl)V i.e. a linear function of V.
A common way of representing the modulation property is in terms of the voltage required to produce a p phase shift thus:
p = pn3rVL/dl.
then Vp = dl/n3rL
substituting Vp = dl/n3rL into Df = (pn3rL/dl)V gives:
Df = pV/ Vp.
However because of the polarisation dependence of the electro-optic effect then r may only take a particular value for a certain polarisation. Thus to meet the specifications of a phase modulator then it may be necessary to use incident light of a certain polarisation.
Lithium Niobate (LiNbO3) is a popular material used in Electro-optic modulators, it has low loss and a high Electro-optic coefficient. The Electro-optic material typically forms part of a waveguide structure utilised to take advantage of the Electo-optic effect produced. A typical structure is shown in the figure Symmetric electro-optic Mach Zehnder modulator.
A signal with power Pin splits power wise into the two arms to form two waves, one wave (the upper arm) is subject to the electro-optic effect and undergoes a phase shift relative to the lower one. The two fields superpose (add) linearly at the output junction to give a power output signal Pout.
Power transfer function.
If the power input to an electro-optic modulator is Pin then the output-modulated power using the Mach Zehnder configuration is given as: Pout = Pincos2(Df/2)
where Df is the relative phase difference between the two signals.
As Df is a function of V then Pout can be written in terms of Vp: Pout = Pincos2(pV/ Vp2), where V is the applied voltage.
A typical response is shown graphically in the figure. Transmission and phase function of symmetric electo-optic Mach Zehnder modulator.
Shown here is the transmission Pout/Pin against the Vp and against the relative phase shift produced in p radians.
Without biasing the input voltage then the linear region can be made to occur between 0 V and a modulating voltage this achieved by imposing a pi/2 phase shift in one arm (making it longer). The transmission function is now:
Pout = Pincos2((p/2 )((V/ Vp) + 1/2)
This allows linear modulation of a unipolar digital signal.
These devices are based on semiconductor materials and like electro-optic they are used to modulate the intensity of a laser light source. It is based on the Franz–Keldysh effect, whereby an electric field causes the absorption spectrum of a material to change. The spectra shifts towards a lower energy when the voltage is applied, see figure Shift of absorption spectra.
Figure. Shift of absorption spectra.
As can be seen for a particular signal the absorption can be made to increase when the voltage is applied. As attenuation is the main parameter here then a simple transmission function for this device is:
where g(V) is the voltage dependent absorption and L the electro-absorption modulation length. All the signal is assumed to be confined within the device and insertion loss neglected.
1. The following response depicts the "ideal" output of a laser after modulating with a square wave current of amplitude 2.5 mA. Assume the modulation occurs over the linear region of the power current curves and all power generated is output from the laser. Determine the power output per current input over the range of modulation.
2. A laser diode has a linear power current response of 5W/A after threshold has occurred. The threshold value is 1 mA. The diode is biased at 20 mA. Assume zero power is output before threshold has occurred. The laser is modulated with a sinusoidal current with amplitude 5 mA
Determine the modulation index.
3. Calculate the modulation response of an LED if the recombination time is 5 ns and the modulating frequency 55 MHz.
4. The frequency response of an LED resembles what order of system? Use your answer to estimate (qualitatively) the response of an LED to a square wave modulating signal.
5. Identify the undamped natural frequency and the damping factor from the equation:
6. A signal power of 10 mW is input to a Mach Zehnder modulator, determine the power, after it leaves the phase shifter and before it arrives at the output junction, if the relative phase shift produced is pi/100.
7. Calculate the value of phase shift needed to produce an output power that is half the power of the input power in a Mach Zehnder modulator.
8. Describe what problem can occur when modulating a symmetric electro-optic Mach Zehnder modulator with a sinusoidal signal.
9. Do you think the output of a symmetric Mach Zehnder, that uses the electro-optic effect, has a wavelength response? Explain your answer.
10. Calculate the phase shift produced when a signal of wavelength 1.55 mm is passed through an electro-optic material of length 1 mm, electrode separation 1 mm, refractive index 3 and electro-optic coefficient 5.74´10-12 mV-1 when a voltage of 10 V is applied.
11. Give reasons as to why reducing the length of the electrodes and increasing their separation can affect the frequency response.
12. The power transfer function of a symmetric Mach Zehnder modulator is often written as, Pout = Pina cos2(Df/2). If a is always less than or equal one then explain what its purpose may be.
13. What would be the numerical value of the power coupling coefficient when a directional coupler with no insertion loss acts as a 3 dB coupler?
14. Determine the coupling ratio of a DC that has a physical coupling length of Lc/5.