R is in the unit of ma/mw or A/W. For semiconductor detectors, the value is approximately, 0.5 ma/mw.

Transcription

1 Light Detection Conventiona methods for the detection of ight can be categorized into photo-synthesis, photographic pate, and photoeectric effect. Photo-synthesis and photographic pate are based on ight-induced chemica reactions. Photoeectric effect is based on the generation of mobie eectrons under the excitation of photons. In the case of photomutipier tubes, photo-eectrons trave in vacuum from cathode to anode through a series of dynodes. The photon energy must be higher than the work function in order to free an eectron from the metaic cathode. The kinetic energy of the free eectron is increased by the appied eectric fied. When it reaches the next dynode, it has sufficient energy to excite more eectrons from the dynode. The impact ionization process mutipies the number of eectrons by few thousand times. The output is a current which fows through an externa oad resistor. The generated votage is proportiona to the optica signa. Semiconductor detectors are based on the excitation of eectrons from the vaance band to the conduction band. For each eectron generated, there is aso a hoe created in the vaance band. In order to form an externa current, eectrons and hoes must be separated immediatey. Eectrons shoud fow to the n-side region and hoes shoud be coected in the p-side. Therefore, a pn junction and an externay appied reverse bias are needed. Since photons are absorbed in a region with a thickness according to the strength of the absorption constant, there usuay is an intrinsic i-region which is thick enough to absorb most of the ight. A pn junction with an intrinsic region in between is named a p-i-n or simpy pin detector. This is the basic structure of a semiconductor detectors. The detection circuit consists of an externa power suppy to provide the reverse bias and a oad resistor. A current fows through the oop when ight iuminates the photodetector. The absorption coefficient of a semiconductor is highy waveength dependent. There is a sharp increase by four orders magnitude when the photon energy increases above the bandgap. The coefficient is of the order of 10 4 cm -1. For GaAs, the transition takes pace at a waveength of 0.9 micron. For Si, it is 1.1 micron and for Ge, 1.6 micron. Si is a superb photodetector for imaging in the visibe region. A camcorders have a Si CCD inside with up to 000x000 pixes. For optica communications, the preferred materia is InGaAs which can absorb ight efficienty in the micron region. Athough Ge can be used, it is noiser than InGaAs. The efficiency of a photodetector is measured by the ratio of the number of eectrons generated and the number of impinging photons. The quantum efficiency, η, is 50-90%. On the onger waveength side it drops off because photons no onger have sufficient energy to excite eectrons above the bandgap. On the shorter waveength side, it aso drops off because photons are absorbed near the surface. They often become trapped by the surface defects rather than forming an externa current. The responsivity is defined as: e R =η h ν

2 R is in the unit of ma/mw or A/W. For semiconductor detectors, the vaue is approximatey, 0.5 ma/mw. Question: If the transmitter coupes 1 mw into a fiber with a oss of 0. db/km. The ink is 100 km ong. What is the photocurrent at the receiver end? In addition to pin photodiode, there are other structures which can aso support an interna fied to coect carriers, for exampe, the Schottky diode and metasemiconductor-meta (MSM) detector. Over the years, there have been many refinement in detector design, e.g., anti-refection coating, interdigitated eectrode, waveguide detector, traveing wave eectrode, etc. The purpose is to increase the sensitivity and the response time. Detectors with bandwidth in the GHz are commerciay avaiabe. There have an interna capacitance in the pc range. The transit time for carriers to trave through the structure is aso in the 10 psec range. Many are fiber pigtaied. There is no need of aignment in the aboratory or in the fied. For high speed appications, the externa oad resistor is 50 Ω. Otherwise, the RC charging time may arbitrariy imited the performance. Photodiodes provide no interna gain. They require eectronic ampifier to increase the eve of the signa. To further increase the sensitivity, avaanche photodetectors (APD) can be considered. APD is the semiconductor equivaent of a photomutipier tube. Photoexcited carriers acceerate in a strong eectric fied. The kinetic energy is used to excite secondary carriers via the avaanche effect. An interna gain of the order of can be reaized. Of course, a arger bias votage is needed. The device must be carefuy biased, otherwise, dark carrent may increase and therma run-away may damage the device. Eectrons acceerating in a semiconductor are subject to coisions with phonons and impurities. They do not acceerate ineary with the appied fied. There is a saturation veocity for traveing in a semiconductor. Different from vacuum photomutipier tubes, the avaanche effect in semiconductor is bipoar. In other words, both eectrons and hoes can create secondary carriers. Eectrons acceerate to the n-side whie hoes acceerate in the backward direction toward the p-side. The avaanche effect takes pace in a compicated tree structure. This causes an excess noise. Ony when the ionization rate of eectron is much arger than that of the hoe can the excess noise be ow. Si has an ionization ratio of 0. However, for many semiconductors, the ratio is ony 3-7. APD offers a gain, M, in sensitivity. However, the noise, i.e., mean square fuctuations of the current is mutipied by: M Noise F( M ) = M + x Noise imits the performance of optica communications systems. For digita systems, noise generates error bits. Usuay, the decision eve is set at the mid-point between the zero and the one state. The noise must be substantia to trip the decision eve in making an error. That is why the digita systems are more immune to noise. By using the eye diagram, the performance of the system can be examined quaitativey. In order to have

3 quantitative measurement, a bit-error-rate measurement system is needed. The signa-tonoise ratio is directy reated to the bit-error rate. Noise affects the anaog system in terms of oss of fideity. The quaity of the system can aso be measured in terms of signa to noise ratio. Since noise represents randomy fuctuating events, we must use statistica distributions to characterize noise. For a randomy varying waveform in time, we can find the probabiity of measuring certain ampitude and pot the probabiity density function as a function of ampitude. If there are many contributing factors to the noise, the Gaussian random variabe is a vaid representation: The front factor is simpy for normaization so that the sum of a probabe events is unity. p p( V ) dv = 1 V 1 σ ( V ) = e πσ With PDF defined, one can cacuate average vaues, i.e., moments. For exampe: V = V p( V ) dv And the mean square fuctuation becomes: V = ( V < V > ) p( V ) dv For Gaussian distribution, ony the second moment is needed. It determines σ. The Gaussian distribution is a continuous distribution. When the photon numbers are sma, a discrete probabiity distribution is needed. Photons foow the Poisson distribution: n p( n) = N N e n! where N-bar is <n>. Question: Can you find <n>, <(n-<n>)^>? There are other distributions, such as the binomia distribution. For optica communications, the Gaussian and the Poisson distributions are the most essentia PDFs. Noise can aso be characterized in the frequency domain. The frequency-domain information is nothing more than the Fourier transform of the time-domain signa.

4 1 iωt 1 V ( ω) = V ( t) e dt T V ( t) e π π The spectra power density is given by: S T 4π VT ( ω) ( ω ) = T Shot noise The quantum nature of photons and eectrons is the cause of the shot noise. Athough the resut is simpe, the derivation requires some effort. We simpy state the resut here. The mean square fuctuation in current is given by: < in >= eidc ν The spectra power density is independent of frequency, therefore, it is a white noise. The tota amount of noise is given by the product of the spectra power density and the bandwidth. There are other types of noises which do have frequency dependence, such as 1/f noise and pink noise. For exampe, the ampitude noise of a semiconductor aser has a resonance peak, therefore, it is a pink noise. The 1/f noise affects the system performance at ow frequency. Since the shot noise is a broadband noise, imiting the bandwidth of the receiver can reduce the amount of shot noise. A ow bandwidth corresponds to a ong averaging time. The shot noise becomes ess important if you accumuate a arge number of photons in a ong window period. Likewise, if the photon energy is ow, for the same power, there are more photons. Therefore, microwave communications systems are not imited by shot noise. They are imited by the therma noise. Cooing can substantiay improve the performance of microwave communications systems. The deep space communications system may have a microwave ampifier running at iquid He temperature. Both the average dc power of the signa and the eakage or dark current of the photodector can contribute to the shot noise. For high speed systems, the detector is sma with a eakage current beow 5 na. The dark current contribution to the shot noise can often be ignored. Therma noise T iωt The fow of eectrons in a conductor is aso affected by the quantum nature of eectrons. As ong as the temperature is above absoute zero, the therma agitation of eectrons generates the therma noise. The resut is aso quite simpe. 4kT < i N >= R ν For signa to noise ratio cacuations, we treat the square of the signa current as the signa and have: dt

5 S ( RP) = N 4kT [e( RP) + ] ν R For intensity moduation and direct detection system, you may easiy prove that the minimum detectabe optica power corresponding to S/N=1 is in the range of -40 dbm. 0dBm is 1 mw, -40 dbm is mw. Question: Try to cacuate the minima detectabe power in an optica communications system running at 1.55 micron and room temperature, with a bandwidth of 1 GHz and a oad resistance of 50 Ohm. The quantum efficiency of the detector is 70%. Coherent Systems To reduce the importance of therma noise, we must increase the signa power. This can be achieved by using Er-doped fiber ampifier (EDFA), APD, and by impementing the coherent communications systems. In fact, radio-frequency and microwave systems are a coherent systems. The coherent system can offer the utimate performance in terms of quantum or shot noise imited sensitivity and number of channes. However, it aso requires stabe yet tunabe asers and poarization maintaining fibers. The cost wi be high. At this time, dense waveength division mutipexing (WDM) is preferred because of ower cost and compatibiity with existing systems. In a coherent system, there is a oca osciator at the receiver end. The incoming weak signa beats with the strong oca osciator to generate a beating signa with is ampifier and used to recover the information. There are three moduation schemes, ampitude moduation (ampitude shift keying), frequency moduation (frequency shift keying) and phase moduation (phase shift keying) for anaog and digita systems. Let's use AM as an exampe. The weak incoming signa is ampitude moduated with a moduation index m. The eectric fied has an ampitude: E s = E0(1 + mcosω t) cosω t The oca osciator generates: E = E cosω t 1 o m o E 1 >>E 0. We assume that the oca osciator osciates at the same optica frequency as the incoming signa. This is caed homodyne detection. If there is a fixed difference in frequency, it is caed heterodyne. Heterodyne shifts the beating signa from dc to a fixed intermediate frequency (IF). It is easier to buid a fiter because the information bandwidth is no more than 10% of the IF frequency. The detector is a square aw detector. It detects the optica power or square of the eectromagnetic fied. By adding signa and oca osciator, squaring the sum, and by averaging over many optica cyces, there are a dc term, a signa term, and the second harmonic term. The second harmonic term is eiminated by a bandpass fiter.

6 1 < ( Es + E ) > E + E0 E1 (1 + mcosωmt ) The one-haf factor comes from time averaging of cosine square. Since the optica power is proportiona to the square of the eetric fied, we can write the detector current as: i = RP + R P P (1 + m cosω t) s m The dc term contributes to the shot noise which becomes ineary proportiona to the power of the oca osciator. Since the oca osciator generates more than 1 mw of optica power. The shot noise dominates the therma noise. The signa to noise ratio becomes: One can easiy prove for the same operating conditions, coherent system can offer 30 db improvement over the non-coherent system. S N P Ps R = erp ν For free space communications, 30 db improvement can transate into a factor of 30 in distance. For fiber, it simpy represents a 150-km gain. This is not as crucia. However, coherent systems offer the utimate sensitivity and the argest number of channes which can by mutipexed into one fiber.