B Chapter 17
`
`Energy per
`photon depends
`on the photon
`wavelength.
`
`Power is an
`instantaneous
`measurement; it
`varies with time.
`
`Electrical power is usually given as the product of the voltage (V ) times the current (/):
`
`P = VI
`or, power (in watts) = volts X amperes. The relationship can take other forms if you use
`Ohm’s law, V = IR (voltage = current X resistance):
`I/2
`r2
`Power = ------= I R
`R
`
`Recall that voltage across a resistance is the strength of the electric field, and you can see
`that electrical power looks like optical power. It’s easy to measure the voltage or current in
`electronics, but it’s not easy to measure the amplitude of the electric field in light waves.
`Thus in electronics you may measure the voltage and current and multiply them to get
`power, but in optics you measure power directly.
`A closer comparison of optical power and electronic power shows more about their
`differences and similarities. The energy carried by an electron depends on the voltage or
`electric field that accelerates it. Earlier, I mentioned the electron volt as a unit of energy.
`One electron volt is the energy an electron carries after it is accelerated through a potential
`of one volt. The total power is thus the number of electrons passing through a point times
`the voltage that accelerated them.
`Each photon has a characteristic energy, which depends on its wavelength or frequency.
`If the light is at a steady level, the amplitude of the light wave measures the number of pho-
`tons per unit time. Thus the total energy delivered by the light is the energy per photon
`times the number of photons (the wave amplitude).
`This makes the two types of power look the same, and that stands to reason. Electrical
`power is the energy per unit time delivered by electrons, where the electron energy depends
`on the voltage that accelerated the electrons. Optical power is the energy per unit time
`delivered by photons, each of which has a fixed energy that depends on its wavelength. The
`total power measures the rate at which these photons are arriving.
`There is a complication to this picture. Normally, a constant voltage accelerates all elec-
`trons to the same energy. However, all photons arriving at a given point do not have the
`same energy unless they all have the same wavelength. Lasers can deliver monochromatic
`light, with all photons having almost the same energy, but optical measurements were
`developed long before lasers, when there was no easy way to account for differences in photon
`energy. Instead of trying to count photons, optical power measurements usually average out
`the differences and give the results in watts.
`Peak and Average Power
`Power is an instantaneous measurement of the flux of energy at a given moment. This
`means that it can vary with time. In general, two types of power are measured in optical
`systems: peak pow er and average power.
`The peak power is the highest power level reached in an optical pulse, as shown in
`Figure 17.2. This power may not be sustained long. In a fiber-optic system, this is the highest
`level reached while a signal is being transmitted.
`
`MASIMO 2014
`PART 7
`Apple v. Masimo
`IPR2020-01526
`
`

`

`Fiber-Optic Measurements
`
`FIGURE 17.2
`Peak and average
`power, and total
`pulse energy.
`
`P u lse E n erg y
`
`Peak P ow er
`
`T im e
`
`Peak power is the
`highest level in an
`optical pulse;
`average power is
`the average over
`an interval.
`
`The ultimate
`limits on
`communications
`come from pulse
`energy.
`
`The average power measures the average power received over a comparatively long
`period, often a second. In a communication system, this is the average over many pulses
`and quiet intervals. For a digital fiber-optic system in which the transmitter is sending “on”
`pulses half the time (a 50% duty cycle), the average power is half the peak power because
`the power is either fully on or fully off. In the example of Figure 17.2, the average power
`is less than half the peak power because the power is lower than the peak during most of
`the pulse, and because no power is delivered between pulses.
`The average power of an ideal digital transmitter also depends on the modulation
`scheme. Some modulation patterns and data streams do not keep the transmitter emitting
`light half the time.
`In practice, fiber-optic measurements average power levels over many pulses to give
`average power rather than peak power. However, transmitter output may be specified as
`peak power, so it pays to check.
`Pulse energy is another measurement that can be valuable. An example is trying to cal-
`culate how many photons arrive per pulse in high-speed systems, because that number
`drops with data rate. Suppose the average power in two signals is 10 (xW. If one signal
`carries 2.5 Gbit/s and the second carries 10 Gbit/s, the pulses in the faster system will
`be only one-fourth the duration, and during that interval they will deliver only
`one-fourth the total energy carried by a pulse lasting four times as long. If you delve deeply
`into communication theory, you will find that the ultimate limits on communications
`often are stated as the minimum pulse energy needed to deliver a bit of information.
`Pulse energy measures the total energy received during a pulse, as shown in the shaded
`area in Figure 17.2. If the power is uniform during the length of the pulse, as in a series of
`square digital pulses, the pulse energy Q is the product of the power P times the time t:
`
`Q = P X t
`
`If the instantaneous power varies over the length of the pulse, you need to integrate power
`over the pulse duration, which is mathematically expressed as:
`
`As long as the power remains level during the pulse, multiplication works fine.
`
`Q =
`
`P {i)dt
`
`

`

`Chapter 17
`
`The definition of
`decibels looks
`different for
`power and
`voltage.
`
`optical power
`can be measured
`in decibels
`relative to 1 mW
`(dBm) or 1 pW
`(dB|x).
`
`Optical Power Measurement Quirks
`Before I go deeper into measuring various forms of optical power, I’ll warn you about a few
`potentially confusing measurement quirks. In electrical measurements, the decibel power
`ratio is often defined in terms of voltage or current. These are in the form
`20 log
`
`Power ratio (dB) = 20 log
`
`where V and / are voltage and current, respectively.
`Fiber-optic measurements usually give a different-looking equation in terms of powers
`P\ and .fl-
`
`Power ratio (dB) = 10
`
`Why the different factor preceding the log of the power ratio? Because electrical power is
`proportional to the square of voltage or current. If you measure the ratio of voltage or cur-
`rent, you have to square it to get the power ratio, which is the same as multiplying the log
`of the ratio by 2. You don’t have to do that if you measure power directly, either optically
`or electrically. Electrical measurements are usually in voltage or current, but optical meas-
`urements are in power, so it may seem that the difference is between optical and electrical.
`However, the real difference is between measuring power directly or indirectly. Both for-
`mulas are correct, but be careful to use the proper one.
`A second potentially confusing point is measurement of optical power in some peculiar-
`seeming units. Normally, power is measured in watts or one of the metric subdivisions of
`the watt— milliwatts, microwatts, or nanowatts. Sometimes, however, it is convenient to
`measure power in decibels to simplify calculations of power level using attenuation mea-
`sured in decibels. The decibel is a dimensionless ratio, so it can’t measure power directly.
`However, power can be measured in decibels relative to a defined power level. In fiber
`optics, the usual choices are decibels relative to 1 mW (dBm) or to 1 |xW (dB(x). Negative
`numbers mean powers below the reference level; positive numbers mean higher powers.
`Thus, + 10 dBm means 10 mW, but —10 dBm means 0.1 mW. Zero means there is no
`difference from the reference level, so 0 dBm is 1 mW.
`Such measurements come in very handy in describing system design. Suppose, for instance,
`that you start with a 1-mW source, lose 3 dB coupling its output into a fiber, lose another
`10 dB in the fiber, and lose 1 dB in each of three connectors. You can calculate that simply
`by converting 1 mW to 0 dBm and subtracting the losses:
`
`Initial power
`Fiber coupling loss
`Fiber loss
`Connector loss
`
`Final Power
`
`0 dBm
`— 3 dB
`—10 dB
`— 3 dB
`
`- 1 6 dB
`
`

`

`Fiber-Optic Measurements
`
`Convert the —16 dBm back to power, and you find that the signal is 0.025 mW; however,
`that often isn’t necessary because many specifications are given in dBm. This ease of calcu-
`lation and comparison is a major virtue of the decibel-based units.
`
`Types of Power Measurement
`As Table 17.1 indicates, optical power measurements may include the distribution of
`power per unit area or angle. The main concern of fiber-optic measurements is with total
`optical power within a fiber, or reaching a detector; but the distribution of optical power
`can be vital for other applications, such as illuminating and imaging. You should under-
`stand the differences because the terminology can be confusing and it’s important to
`understand what you’re measuring.
`
`LIGHT DETECTORS
`Light detectors measure total power incident on their active (light-sensitive) areas— a value
`often given on data sheets. Fortunately, the light-carrying cores of most fibers are smaller
`than the active areas of most detectors. As long as the fiber is close enough to the detector,
`and the detector’s active area is large enough, virtually all the light will reach the active
`region and generate an electrical output signal.
`The response of light detectors depends on wavelength. As you learned in Chapter 11,
`silicon detectors respond strongly at 650 and 850 nm but not at the 1300 to 1700 nm
`wavelengths used in long-distance systems. On the other hand, InGaAs detectors respond
`strongly at 1300 to 1700 nm but not to the shorter wavelengths. In addition, detector
`response is not perfectly uniform across their entire operating region. You have to consider
`the wavelength response of detectors to obtain accurate measurements.
`Recall also that detectors cannot distinguish between different wavelengths within their
`operating regions. If eight W DM channels all reach the same detector, its electrical output
`will measure their total power, not the power of one channel.
`In addition, individual detectors give linear response over only a limited range. Powers
`in fiber-optic systems can range from over 100 mW near powerful transmitters used to
`drive many terminals to below 1 p.W at the receiver ends of other systems. Special detectors
`are needed for accurate measurements at the high end of the power range.
`
`IRRADIANCE AND INTENSITY
`Things are more complicated when measuring the distribution of optical power over a large
`area. For this case, another parameter becomes important, called irradiance (usually
`denoted E in optics), the power density per unit area (e.g., watts per square centimeter).
`Figure 17.3 compares the irradiance on a surface with the total power a detector collects
`from an optical fiber.
`You cannot assume irradiance is evenly distributed over the surface unless the light
`comes from a “point” source (i.e., one that is very distant or looks like a point), and the entire
`surface is at the same angle to the source. A book lying flat on the ground is uniformly
`illuminated by the sun, but the entire earth is not, because its surface is curved. Total power
`
`Light detectors
`measure total
`incident power.
`
`Irradiance (E) is
`power per unit
`area. Intensity (I)
`is power per unit
`solid angle.
`
`

`

`Chapter 17
`
`FIGURE 17.3
`Total power and
`irradiance.
`
`C o re
`
`Total power reaching detector
`through fiber is radiant fiux (watts).
`
`(P) from a light source is the irradiance (E ) collected over the entire illuminated area (A).
`For the simple example of the book in the sun, the total power is
`
`P = E X A
`
`If the surface is not uniformly illuminated, the total power is integrated over the entire
`surface:
`
`P =
`
`EA
`
`The E for irradiance could be confused with the E more widely used for energy.
`Fortunately, irradiance is rarely used in fiber optics, and when the symbol E is used its
`meaning should be clear.
`The term intensity (I) also has a specific meaning in light measurement— the power per
`unit solid angle (steradian), with the light source at the center of the solid angle. This mea-
`sures how rapidly light is spreading out from the source.
`Irradiance and intensity are often confused, and the power per unit area is often called
`intensity. This mistake is understandable because both units measure the distribution of power,
`one over a surface area, the other over a range of angles. The easiest way to tell is to look at the
`units; if someone measures “intensity” in watts per square centimeter, they’re really talking
`about irradiance. There are fewer situations where power is measured per steradian.
`Most fiber-optic measurements concern total power. However, irradiance and intensity
`may be important when measuring the concentration of power inside a fiber core, or when
`beams are directed through free space.
`
`RADIOMETRY AND PHOTOMETRY
`Optical measurements are divided into two broad categories, radiometry and photometry,
`which are sometimes confused. Photometry is limited to measuring light visible to the
`human eye, at wavelengths of 400 to 700 nm; invisible light doesn’t count for photometry.
`
`Radiometry
`measures all
`wavelengths.
`Photometry
`measures only
`visible light.
`
`

`

`Plastic Fiber
`
`Fiber-Optic Measurements
`
`FIGURE 17.4
`Detector response
`at different
`wavelengths.
`
`W ave le n g th (nm )
`
`Radiometry measures the total power of both visible and invisible light in watts, and it’s
`radiometry that is used for fiber-optic measurements.
`Photometry has its own measurement units, lumens, which are used to measure the visible
`light from bulbs. Lumens are not directly convertible to watts because lumens are weighted to
`account for how the eye’s sensitivity varies with wavelength. Light at 550 nm, where the eye is
`most sensitive, counts more on a photometric scale than 450 or 650 nm, where the eye is less
`sensitive. Photometry ignores the infrared wavelengths used in fiber-optic communications.
`You should know what photometry is because many optical power meters are calibrated in
`both radiometric and photometric units, but you should use the radiometric units.
`An ideal radiometer would be sensitive across the entire visible, ultraviolet, and infrared spec-
`trum, but real detectors don’t work that way. As you learned in Chapter 11, each type of
`detector responds to a different range of wavelengths, and is not equally sensitive across its entire
`range. Figure 17.4 shows the variations over the ranges of important detectors compared to the
`windows for fiber transmission. Power meters are calibrated to reflect detector response.
`In practice, fiber-optic power meters are calibrated for measurements at the major fiber
`system windows, 650, 850, 1300, and 1550 nm. They may not be calibrated at interme-
`diate wavelengths, and as you can see in Figure 17.4, at some wavelengths they may not
`even respond. All power meters measure average power. They respond much more slowly
`than signal speeds, so they can’t track instantaneous power fluctuations.
`
`Wavelength and Frequency Measurements
`
`Wavelength-measurement requirements vary widely, depending on the application. Precise
`knowledge of source wavelengths is critical in dense-WDM systems, where the transmission
`channels are closely spaced and must be matched to the transmission of demultiplexing
`components. Knowledge of the spectral response of system components also is vital in
`WDM systems, particularly for filters used in demultiplexing signals. On the other hand,
`wavelength need not be known precisely in systems carrying only one wavelength.
`
`Fiber-optic power
`meters are
`calibrated for
`standard
`transmission
`windows.
`
`Wavelength is
`critically important
`in W DM systems.
`
`

`

`Chapter 17
`
`Wavelength and Frequency Precision
`So far, I have usually described wavelengths in round numbers, such as 1550 nm. That’s
`common in optics; engineers who work with light think in terms of wavelength. However,
`wavelength is not as fundamental a characteristic of a light wave as its frequency. The wave-
`length depends on the refractive index of the medium transmitting the light; the frequency
`is constant. This is why standard channels and spacing for DWDM systems are specified in
`terms of frequency.
`Earlier, you learned that the wavelength in a vacuum equals the speed of light divided
`by frequency, v.
`
`X = -
`v
`
`However, this equation holds only in a vacuum. When the light is passing through a
`medium with refractive index n, the equation becomes
`
`X = —
`nv
`
`Precise
`measurements and
`calculations are
`vital with WDM
`systems.
`
`which means the wavelength decreases by a factor 1 In.
`I have used round numbers in much of this book because they’re usually good enough.
`Why punch 10 digits into your calculator when you can learn the same concept by punch-
`ing only 2 or 3? Those approximations don’t work for dense-WDM systems. You have to
`use exact numbers or you get into trouble. To understand why, run through a set of calcu-
`lations first using the approximation of 300,000 km/s for the speed of light; then use the
`real value. Let’s calculate the vacuum wavelength corresponding to the base of the ITU
`standard for WDM systems, 193.1 THz.
`Using round numbers,
`
`X =
`
`3 X 108
`(193.1 X 1012)
`
`= 1553.60 nm
`
`Using the exact value for c, the wavelength is
`
`X =
`
`2.997925 X 10s
`(193.1 X 1012)
`
`= 1552.52 nm
`
`The difference is less than 0.1%, but that’s enough to shift the wavelength by more than
`one whole 100-GHz frequency slot. In short, the wavelength tolerances in dense-WDM
`systems are too tight to get away with approximations. You have to be precise.
`Because of the importance of precision, frequency units may be used in measurements
`rather than the more familiar wavelength units. You should be ready to convert between
`the two when necessary, always using the precise formulas.
`If you’ve been watching carefully, you will note that the wavelengths given so far are for
`light in a vacuum, where the refractive index is exactly 1. Why don’t we use the wavelengths
`in air, which has a refractive index of 1.000273? It’s primarily a matter of convention and
`simplicity. Physicists have long used vacuum wavelengths, and adjusted them slightly—when
`
`The wavelengths
`assigned to
`optical channels
`are the values in
`vacuum, not in air.
`
`

`

`Fiber-Optic Measurements
`
`Wavelength
`measurements can
`be absolute or
`relative.
`
`necessary— for transmission through air. If you wanted to convert frequency to wavelength
`in air, you would have to add a factor of n to all your equations, which could introduce
`errors. In addition, light often goes through other media, such as the glass in an optical
`fiber, and the refractive index of air varies with pressure and temperature.
`From a physical standpoint, frequency is a more fundamental quantity. A light wave
`with a frequency of 193.1 THz oscillates at the same frequency in a vacuum, air, or glass.
`Yet the wavelengths differ because the refractive index differs among the three media. This
`is a major reason that the standards for DWDM optical channels are stated in frequency
`rather than wavelength.
`
`Ways of Measuring Wavelength
`It is not easy to measure wavelength precisely; it takes sophisticated instruments and care-
`fully controlled conditions. Precise measurements became essential as DW DM systems
`packed channels close together, making it critical to separate and identify optical channels
`precisely. A few basic concepts are critical to understanding these measurements and the
`specific instruments covered in the next chapter.
`Wavelength measurements can be absolute or relative. Absolute measurements tell you the
`precise wavelength (or frequency) of a light source. Relative measurements tell you the dif-
`ference between the wavelengths of two light sources, often in frequency units. In general,
`relative comparisons are easier to make.
`In practice, absolute measurements are made by comparing the wavelength with some
`well-defined standards of length or frequency. One way is to monitor changes in interfer-
`ence in two arms of an interferometer as the length of one is changed; another is to mea-
`sure the difference in frequency between the unknown source and a standard, such as a
`laser with precisely defined wavelength.
`The accuracy of both absolute and relative measurements depends critically on calibration
`of the instruments, accuracy of the standards, and the comparison process. For example, pre-
`cise measurements require accounting for the fact that air has a refractive index of 1.000273
`at room temperature near 1550 nm. Although that number is only slightly higher than the
`refractive index of a vacuum, the small wavelength shift corresponds to a frequency difference
`of about 50 GHz in the 1550 nm window. That’s significant for DWDM systems.
`
`Linewidth Measurements
`In addition to measuring the central wavelength of a laser source, you often need to mea-
`sure the range of wavelengths in the signal, called the linewidth or spectral width. Where
`fiber dispersion is an issue or where a DWDM system carries closely spaced wavelengths,
`the linewidth should be small and often is measured in frequency units— for example,
`150 MHz for a temperature-stabilized DFB laser emitting continuously. On this scale,
`frequency units are more convenient than wavelength; at 1550 nm, 100 GHz is about
`0.8 nm, so 150 MHz is about 0.0012 nm. (External modulation adds to that linewidth.)
`At lower speeds, where dispersion is not a critical concern, such as where a simple diode
`laser is modulated directly, the linewidth is much larger and is generally measured in wave-
`length units. In this case, wavelength units are more convenient.
`
`

`

`m Chapter 17
`
`FIGURE 17.5
`Only a
`narrowband source
`can measure
`transmission o f a
`narrow-line
`demultiplexer.
`
`Narrowband
`Light Source
`(Can Resolve
`Narrow-Line Feature)
`
`Broadband Light Source
`(Cannot Resolve
`Narrow-Line Feature)
`
`10 0 %
`
`T ransm ission
`o f N a rro w -L in e -
`F ib e r G ratin g
`
`Spectral response
`measures how
`systems and
`components
`respond to
`different
`wavelengths.
`
`1550
`
`1555
`
`1560
`
`Spectral Response Measurements
`In addition to knowing the wavelength of the transmitter, you need to know how a fiber-
`optic system and its components respond to different wavelengths. This is called spectral
`response. For most components, the most important response is loss or attenuation as a
`function of wavelength. In the case of filters, multiplexers, and demultiplexers, you need to
`know how light is divided as a function of wavelength. That is, you need to know how
`much light is routed in different directions at various wavelengths. For optical amplifiers,
`the important feature is gain as a function of wavelength.
`Spectral response measurements require a properly calibrated light source that emits a
`suitably narrow range of wavelengths. Figure 17.5 illustrates the problem by comparing
`two light sources with the transmission of a fiber Bragg grating that selectively reflects at
`1555 nm for wavelength-division demultiplexing. A narrow-line source such as a tunable
`laser can accurately measure the response of the fiber grating, but a broadband source can-
`not, because its light contains a range of wavelengths much broader than the range of wave-
`lengths the grating reflects.
`
`Phase measures a
`light wave's
`progress in its
`oscillation cycle.
`
`Phase and Interference Measurements
`
`In Chapter 2 you learned that light waves have a property called phase. Recall that a light
`wave consists of an electric field and a magnetic field, each of which periodically rise and
`fall in amplitude, as shown in Figure 17.6. The amplitude varies in a sine-wave pattern, so
`the position in that cycle is measured as an angle, in degrees or radians. One wavelength is
`a complete cycle of 360° or 2 t t radians. Normally the phase is measured from the point
`where the amplitude begins increasing from zero. Amplitude peaks at 90°, returns to zero
`at 180°, has a negative peak at 270°, then returns to zero at 360°.
`
`

`

`Fiber-Optic Measurements
`
`FIGURE 17.6
`Phase and
`interference o f
`light waves.
`
`P h a se o f W ave D e gre es
`
`The absolute phase of a light wave is difficult to measure, but the relative phase can be
`measured simply by interferometry if the light is coherent. In Chapter 16, you learned that
`the operation of many fiber-optic modulators and switches depends on phase shifts
`between light traveling through two parallel arms. The same principle is used to measure
`phase shift. A laser beam is split, then recombined and the power is measured. If the light
`beams add constructively, the relative phase shift is 0°. If the beams add destructively, the
`phase shift is 180°. Other values can be interpolated.
`In practice, the phase shift usually is measured relatively, as an angle between 0° and
`360° (a whole wave), although the actual shift in phase may be a number of wavelengths
`plus an angle between 0° and 360°. That’s a matter of convenience. Relative phase shift is
`easier to measure, and usually the relative shift is more important for device operation. The
`absolute phase shift between two waves can be measured using devices that count the number
`of interference peaks, but it’s rarely necessary for fiber optics.
`Actual phase measurements are messier than our simple example. Two beams must be equal
`in amplitude and precisely 180° out of phase to cancel each other completely by destruc-
`tive interference. They also must be perfectly coherent, with exactly the same wavelength.
`
`

`

`m Chapter 17
`
`Polarization is the
`alignment of the
`electric field in a
`light wave.
`
`Loss or gain may
`depend on
`polarization.
`
`Those conditions are virtually impossible to obtain, so in practice phase shift measure-
`ments are made by looking for the maximum and minimum.
`
`Polarization Measurements
`
`The polarization direction of a light wave is defined as the orientation of the electric field,
`which automatically sets the direction of the magnetic field that is perpendicular to it.
`Light waves with their electric fields in the same linear plane are linearly polarized. If the
`field direction rotates along the light wave, the light is elliptically or circularly polarized.
`If the fields are not aligned with each other in any way, the light is unpolarized.
`Several polarization characteristics significant in fiber-optic systems may require mea-
`surements. The simplest in concept is the direction of the polarization. This can be measured
`by passing the light through a polarizer and rotating the polarizer to see at what angles the
`transmitted light is brightest and faintest.
`Polarization dependence arises when the loss or gain of a component depends on the
`polarization of the light passing through it. This can create a problem by modulating the
`light signal according to its polarization, which introduces noise into the system.
`Polarization-dependent loss measures the maximum differences in attenuation for light of
`various degrees of polarization. For example, if an optical component has 3-dB attenuation
`when transferring horizontally polarized light and 6 dB for vertically polarized light, it has
`a polarization-dependent loss of 3 dB— if those are the maximum and minimum values for
`attenuation. Polarization-dependent loss can be measured by adding polarization analyzers
`to conventional loss measurement instruments.
`Polarization-dependent gain is a variation in gain for light of different polarizations pass-
`ing through an optical amplifier, the inverse of polarization-dependent loss. It is particu-
`larly important for semiconductor optical amplifiers.
`Polarization-mode dispersion (PMD) is the spreading of pulses arising from the disper-
`sion of light between the two orthogonal polarization modes, as described in Chapter 5.
`The degree of PMD is not constant for a fiber; it varies statistically with time, depending
`on environmental conditions. This means that measurements of PMD have to be made
`over a period of time. Specialized instruments can measure the instantaneous polarization
`direction, the instantaneous PMD, and the differential group delay or pulse spreading
`caused by PMD.
`
`Time and Bandwidth Measurements
`
`Bandwidth and
`time measurements
`indicate
`transmission
`capacity.
`
`As you learned in Chapter 5, system bandwidth is limited by the spreading or dispersion
`of pulses in the fiber, transmitter, and receiver. This means that time and bandwidth mea-
`surements in fiber-optic systems are related. You can think of them as different ways to
`measure the information transmission capacity of the system. Time measurements directly
`measure how fast the system can respond to a pulse. Bandwidth depends on this time
`response, but it also can be measured directly.
`
`

`

`Fiber-Optic Measurements
`
`Pulse Timing
`Figure 17.7 shows the key parameters in measuring pulse timing.
`
`9 Rise time is the time the signal takes to rise from 10% to 90% of the peak power.
`^ Pulse duration normally is the time from when the signal reaches half its
`maximum strength to when it drops below that value at the end of a pulse. This is
`called fu ll width at h a lf maximum, abbreviated FWHM.
`9 Fall time is the interval the signal takes to drop from 90% to 10% of peak power.
`^ Pulse spacing or pulse interval is the interval between the start of one pulse and the
`point where the next should start. If the signal is on for 1 ns and there is a 1-ns delay
`before the next pulse can start, the pulse spacing is 2 ns. The pulse spacing means the
`interval between transmitting one data bit and transmitting the next, whether the bits are
`“Os” or “Is.”
`• Repetition rate is the number of pulses or data bits transmitted per second, which
`in practice is the pulse spacing divided into 1:
`
`Repetition rate
`
`pulse spacing
`
`Thus if the pulse spacing is 1 ns, the repetition rate is 1 Gbit/s.
`• Jitter is the uncertainty in the timing of pulses, typically measured from the point
`at which they should start.
`
`Measurements are made by feeding the optical signal to a detector, which generates
`an electronic output that instruments measure. This means that time response measured
`for the light pulse also includes the time response of the detector and the instrument.
`This effect can be significant at high data rates and must be considered in making fast
`measurements.
`
`P u lse S p a cin g
`
`FIGURE 17.7
`Pulse timing.
`
`T im e
`
`

`

`Repetition rates in even the slowest fiber-optic systems are extremely fast on a human
`scale— a million or more pulses per second— so you cannot see signal-level variations in
`real time. They are recorded on an oscilloscope or other display, which allows you to see
`events that are too fast for your eyes to perceive.
`Bandwidth and Data Rate
`Bandwidth and data rate of communication systems differ in subtle but important ways.
`Bandwidth usually is an analog measurement of the highest signal frequency the system can
`carry. D ata rate or bit rate is a digital measurement of the maximum number of bits per
`second actually transmitted. (Baud strictly speaking refers to the number of signal transi-
`tions per second, which may not equal data rate.) Both bandwidth and data rate deserve a
`bit more explanation.
`The carrier frequency in an analog system is modulated with an analog signal spanning
`a range of frequencies. Typically it cuts off at some low minimum frequency, but the most
`important limit is the upper frequency cutoff, which arises from dispersion effects in fiber-
`optic systems. The attenuation increases with signal frequency, and the bandwidth limit nor-
`mally is defined as the point where signal amplitude is reduced 3 dB, as shown in Figure 17.8.
`As you can see in the figure, higher frequencies suffer more attenuation.
`Note that the signal bandwidth is distinct from the range of wavelengths transmitted by
`the fiber. You should think of the range of wavelengths as the optical bandwidth, distinct
`from the signal bandwidth. Optical attenuation is not the same as signal attenuation. An
`optical amplifier can compensate for optical attenuation by increasing the optical power,
`
`Chapter 17
`
`Signal bandwidth
`measures analog
`transmission
`capacity.
`
`FIGURE 17.8
`Frequency response
`o f an analog fib er-
`optic system.
`
`

`

`Fiber-Optic Measurements
`
`THINGS TO THINK ABOUT
`