Frank C. De Lucia Vol. 21, No. 7 /July 2004 /J. Opt. Soc. Am. B 1273

Noise, detectors, and submillimeter–terahertzsystem performance in nonambient environments

Frank C. De Lucia

Department of Physics, Ohio State University, Columbus, Ohio 43210

Received June 23, 2003; revised manuscript received February 10, 2004; accepted March 10, 2004

Because many sources of radiation in the submillimeter–terahertz have relatively low power, the developmentof sensitive detectors has been important. Equally important is the selection of detector and source method-ologies appropriate for specific scientific or technological applications. Discussed is the effect of Bose–Einstein statistics, blackbody mode structure, and detector optical and electronic bandwidths to developclosed-form expressions for the contributions from experimental backgrounds to overall system noise. Theresults obtained allay the oft-expressed concerns that many important experiments, especially those conductedat elevated temperatures or in harsh environments such as plasmas, are either difficult or not possible withhigh-resolution cw systems. To the contrary, in the large majority of cases this excess background noise is notobservable. Experimental examples are provided. © 2004 Optical Society of America

OCIS codes: 040.1880, 300.6190, 300.6270, 300.6390.

1. INTRODUCTIONIt has long been know that there are many attractive sci-entific and technological applications for the region of theelectromagnetic spectrum that lies between the micro-wave and the infrared. These include laboratory studiesof gas-phase molecular systems; atmospheric and astro-nomical remote sensing; imaging; communications; andspectroscopic and time-resolved studies of the condensedphase, including semiconductors. It is also well knownthat research in this region is often technology limited,and although many system approaches have been pro-posed and demonstrated, only a few have found broad ap-plication.

This spectral region has variously been referred to asthe millimeter, near millimeter, submillimeter, far infra-red, and terahertz, with rough boundaries of 3 mm (100GHz) and 30 m (10 THz). For the purposes of this paper,I refer to this region as the submillimeter–terahertz(SMM–THz). Because this region includes the point (6THz) where kT 5 hn, phenomena at longer wavelengths(up to ;3 THz, which are the primary focus of this paper)can be rather different than at shorter wavelengths(which often have much in common with the infraredspectral region).

Growing out of its laboratory base,1–6 cw submillimetertechniques have become robust enough to be the basis of anumber of spectacular advances in astrophysics7 and at-mospheric science,8 including major satellite and ground-based facilities. In addition, the characteristics of thisregion make it ideally suited for laboratory investigationsin nonambient and often harsh environments. There isan extensive literature of the spectroscopy at high tem-perature of the vapors of solids, such as NaCl, NaH, andAlF (see Chap. 4 of Ref. 9); active laser plasmas10,11; anddischarges containing free radicals12,13 and ions.14–17

These, as well as other applications, have been discussedin more detail in a recent book.18

In spite of these many successes it has been noted that

0740-3224/2004/071273-07$15.00 ©

the power radiated in the SMM–THz by systems at el-evated temperatures can be large (a 10-mm-square black-body at 300 K radiates 46 mW below 6.25 THz19) in com-parison with the small amounts (often between 1-mW and1-mW cw) of power provided by many of the source tech-nologies and that this power would preclude use of other-wise sensitive cw SMM–THz detectors. In addition, ithas been asserted numerous times that time-domain ap-proaches, which look only at this background radiationwith a small duty cycle, provide the means for overcomingthis apparent problem and provide a superior means forinvestigating hot objects, plasmas, flames, and other non-ambient environments.19–31

In this paper I show that cw submillimeter experi-ments (and to a lesser extent far-infrared Fourier-transform experiments) are actually orders of magnitudemore favorable, and many notable experiments have ap-peared in the literature.18 In fact, it is rare that this en-vironmental noise is even observable. Thus it is the pur-pose of this paper to consider the impact of noise on thedetection problem in this spectral region for systems inharsh or nonambient environments. I review the theo-retical basis, develop useful closed-form expressions inthe context of an example system, and show experimentalexamples.

2. ABSORPTION SPECTROSCOPY IN THESUBMILLIMETER–TERAHERTZFigure 1 shows the elements of a canonical cw absorptionspectroscopy system for the SMM–THz. A widely usedapproach combines harmonic generation from millimeter-wave oscillators and cooled helium temperature detectorsthat view both the emissions of the interaction cell andthe source.3,5,32–34 An alternative development path wasbased on use of backward-wave oscillators (BWOs) andacoustic detectors.4,35 More recently, BWO sources havebeen combined with cryogenic detectors in a variety ofsystem configurations.36–38

2004 Optical Society of America

1274 J. Opt. Soc. Am. B/Vol. 21, No. 7 /July 2004 Frank C. De Lucia

Source brightness (W/Hz) is an important system pa-rameter because only the power contained within thelinewidth of the physical phenomena being probed is use-ful. Doppler-limited lines in the SMM–THz have line-widths of ;1 MHz. The spectral power of these cw elec-tronic sources is contained within this Doppler limit; thusthey can both resolve the Doppler limit and provide alltheir power to the physical system. Integrated over this1 MHz, source powers of 1 mW and 1 mW correspond tobrightness temperatures of 1014 and 1011 K, respectively.

As an example of a result from a simple implementa-tion of Fig. 1, consider Fig. 2, which shows as a series ofblowups a spectrum of nitric acid. With this fast scansubmillimeter spectroscopic technique (FASSST), a free-running BWO is scanned rapidly (.10,000 MHz/s) tofreeze thermal and power supply instabilities.38 The fre-

Fig. 1. Block diagram showing the flow of energy and noisethrough a SMM–THz spectrometer. The solid line in the centerrepresents a single mode that couples the source to the detector.The dashed lines represent the multimode limits of the solidangle a observed by the detector.

Fig. 2. Spectrum of nitric acid (HNO3) between 266 and 308GHz (upper), 292 and 295 GHz (middle), and 293.3 and 293.7GHz (lower). The spectrum shown in the upper trace required;1 s to record, whereas the segment shown in the lower trace re-quired ;0.01 s.

quency calibration is established in software from opticaland spectroscopic references to ,1/10 of the Dopplerwidth. Similar systems have also been developed withharmonic-generation sources. The brightness of thesource in comparison with the noise sources in the systemmakes it possible to use ;1026-s integration times andthis rapid (;1-s) observation of a complex spectrum.

A. Source NoiseLet us first consider the contribution of cw SMM–THzelectronic sources to the overall system noise. Typicalsources include electronic beam devices, such as klystronsand BWOs, or solid-state devices, such as transistors orGunn diodes. Because of the large number of electrons(;1017) and photons (;1018) per second associated withthese sources, with good power supplies they can be veryquiet. Experimentally, the noise characterization ofthese devices, observed with either electronic spectralanalysis techniques or the measurement of narrow spec-troscopic lines, shows that their noise components arepredominately lower in frequency than a few kilohertz.Much of this is technical noise (e.g., microphonics, vibra-tions, 1/f noise in amplifiers), and systems are ordinarilydesigned to have signal recovery frequencies of a few ki-lohertz or higher. Experimental experience confirms thisexpectation of low source noise, with its contribution tosystem noise often unobservable even with cryogenic de-tectors. This is in contrast to the amplitude and fre-quency noise often observed on systems driven by opticallasers.39,40 Because these source noise limits are systemspecific and would reduce only the significance of thenoise from the spectroscopic environment that is the prin-cipal topic of this paper, I do not discuss them furtherhere.

B. Noise from the Spectroscopic EnvironmentIn addition to the thermal noise, which I discuss in detailbelow, there are other potential sources of noise thatmight be associated with probes of nonambient environ-ments. Plasmas represent perhaps the most importantcategory because they are nonequilibrium systems thatare of interest both as spectroscopic sources and in a num-ber of remote sensing applications. Although electrontemperatures can be ;104 K, interactions with SMM–THz radiation are better considered in the context of theplasma frequency, which is given by

fp '1

2pS Ne2

mee0D 1/2

. (1)

For an electron density of N 5 1018 electrons/m3, fp; 10 GHz.41 The plasma frequency marks the transi-tion at which the plasma changes from being reflective totransparent. Because the SMM–THz probe frequency ismuch higher for the applications mentioned above, noiseassociated with the emission from the plasma is not sig-nificant. An example involving the HCN far-infrared dis-charge laser is discussed in Subsection 5.B.

Frank C. De Lucia Vol. 21, No. 7 /July 2004 /J. Opt. Soc. Am. B 1275

C. Detector–Amplifier NoiseAlthough the source technologies for cw systems18 havevaried, since the introduction of the helium-cooled bolom-eter to these systems3 a large majority have used eitherInSb hot-electron bolometers or Si/Ge lattice bolometerscooled by 4He. Important parameters for a detector (andits following preamplifier) include its optical bandwidth b;its responsivity r 5 Vout /P in that relates the voltage out-put of the detector to its signal power input; and the out-put bandwidth B, which is a measure of the system obser-vation time.

For these detectors, b ; 1012 Hz, r 5 1000–5000V/W, and B 5 1 –106 Hz. Characterized in the contextof the amount of signal to produce a signal-to-noise ratioof 1 in a 1-Hz bandwidth—the noise-equivalent power(NEP)—these detectors typically have optical NEPs of;10212 W/Hz1/2, although some have been extended to alower NEP at the expense of speed or by use of lower tem-peratures.

It is necessary to consider not only the noise contribu-tions from the optical flux that changes the resistance ofthe bolometer, but also electrical noise associated with theresistance of the bolometer element itself (and perhapsadditional noise associated with the preamplifier). Thedominance of one over the other is largely determined bythe responsivity of the bolometer element r. If r is small,only small electrical voltage changes result from noise onthe optical signal input, and the noise of the system isdominated by the internal electrical noise of the detector.Conversely, if r is large enough, the noise of the systemcan be dominated by noise associated with the optical in-put.

Below, I show that electrical rather than photon noiseis dominant for the detectors that are ordinarily used.An important consequence of this, a central thesis of thispaper, is that cw spectroscopic systems that use thesecryogenic detectors are insensitive to optical noise thatmight be associated with background thermal emission,even from environments that might be considered harsh.Moreover, although these detectors are often approxi-mately 2 orders of magnitude less sensitive than idealthermal detectors, the brightness and power of the cwsources are so great that sensitive systems result.

3. THEORETICAL BACKGROUND, USEFULRELATIONS, AND PHYSICALINTERPRETATIONA. Fluctuations in the Thermal BackgroundThe limiting source of noise in a SMM–THz system hasits origins in the fluctuation in the number of photons inthe thermal background.42,43 The energy density be-tween n and n 1 dn in a blackbody is given by

r~n! 58phn3

c3 F 1

exp~hn/kT ! 2 1Gdn, (2)

with the average energy per mode

^E& 5hn

exp~hn/kT ! 2 1. (3)

Because it will make only small differences in theSMM–THz and will have no effect on the conclusions ofthis paper, we make the long-wavelength approximationhn ! kT. This makes possible the development ofsimple closed-form expressions and provides intermediateresults with transparent physical interpretations. Inthis limit Eq. (2) becomes

r~n! 58pkTn2

c3 dn, (4)

and Eq. (3) becomes

^E& 5 kT, (5)

with the number of photons per mode

nm 5kT

hn. (6)

Because the photons within each mode are governed byBose–Einstein statistics, the fluctuations are given by

Dnm2 5 nm~nm 1 1 !. (7)

In the long-wavelength limit, nm @ 1 and

Dnrms ; nm . (8)

Thus the noise due to the photons within a given mode iscompletely correlated. On the other hand, the fluctua-tions in the noise between different modes is uncorre-lated, and the fluctuation in the number of photons n in Ndifferent modes is

Dn2 5 NDnm2. (9)

The number of modes N in a volume V in the intervaln → n 1 dn is

N 58pn2

c3 Vdn. (10)

The fluctuation in the number of photons in the volume Vgives rise to an energy fluctuation

eV2 5 ~hn!2Dn2 5

8p~kT !2n2

c3 Vdn. (11)

With the assumption that the detector responds to radia-tion from dc to some maximum frequency nmax , the fluc-tuation of the energy in this interval is

DEV2 5

8p~kT !2nmax3

3c3 V. (12)

However, we are ordinarily interested in the fluctuationsin the power radiated by this blackbody onto a detector ofA, inclined at an angle u. If we consider a time Dt,geometry44 yields

DEA/Dt2 5

2~kT !2nmax3

3c2 Aa cos uDt. (13)

The noise power associated with the observation periodDt 5 1/(2B) is then

PN 5 F4~kT !2nmax3 ABa cos u

3c2 G 1/2

. (14)

1276 J. Opt. Soc. Am. B/Vol. 21, No. 7 /July 2004 Frank C. De Lucia

In comparison the power emitted within dn into this solidangle is given by

Pdn 58pkTn2dn

c3

cA

4

a

2pcos u. (15)

Or below nmax ,

P 52pkTnmax

3 A

3c2

a

2pcos u. (16)

An estimate of the accuracy of these equations thathave been developed in the long-wavelength approxima-tion can be made by comparison with the exactexpression43

PN 5 H 4~kT !5

c2h3 a cos uAB@J4~x1! 2 J4~x2!#J 1/2

, (17)

where

Jn~x ! 5 E0

x xnex

~ex 2 1 !2 dx, (18)

x 5hn

kT, (19)

and x1 and x2 represent the upper and lower limits of theoptical bandwidth of the detector.

For the special case nmax 5 3 THz, a cos u 5 1/5, B5 1 Hz, and A 5 1 cm2, Eq. (17) yields

PN 5 3.64 3 10213 W. (20)

In comparison, Eq. (14) yields

PN 5 3.70 3 10213 W. (21)

If background noise is a potential problem, a is usuallyrestricted to accept a single diffraction-limited mode. Inthis case,

Aa cos u ; ~l/2!2, (22)

and Eq. (14) becomes

PN ; kT~Bnmax!1/2 ; kTnmaxS B

nmaxD 1/2

. (23)

For nmax 5 1 THz, T 5 300 K, and B 5 1 Hz,

PN ; 4 3 10215 W. (24)

For nmax 5 1 THz, T 5 300 K, A 5 1 cm2, and a cos u5 2p, Eq. (16) yields for the total power

P 5 10 3 1026 W. (25)

This differs from Eq. (24) by ;9 orders of magnitude be-cause of the restriction of the detector acceptance to asingle mode and the integrating factor associated with theratio of the optical-to-electronic bandwidth shown as thelast term in approximation (23).

In the other (but unphysical) extreme when the opticalbandwidth nmax equals the output bandwidth B,

PN ; kTB. (26)

Except for the approximation associated with the defini-tion of a diffraction-limited aperture over the entire rangeof frequencies below nmax , which leads to Eq. (22), this is

the familiar result for the noise in a single microwavemode. For these same parameters, but the unphysicaloutput bandwidth (B 5 nmax),

PN 5 4.1 3 1029 W. (27)

B. Responsivity and Electrical NoiseTo determine the effect of the noise associated with radia-tion from high temperature and other nonambient back-grounds, we need to also consider the electrical noise as-sociated with the detector. Typically, two closely relatedfigures of merit are considered. First, the NEP(W/Hz21/2) is the signal power required to produce a 1/1signal-to-noise ratio referenced to a common integrationbandwidth of 1 Hz. The second is the responsivity (r)whose units are volts per watt, which is a measure of theelectrical voltage produced by the incident signal power.

If we assume the electrical noise in the system is pro-duced by the Johnson noise associated with the resistanceR0 of the detector element in a 1-Hz bandwidth

NJ 5 ~4kTR0!1/2, (28)

then

NEP 5 NJ /r. (29)

The responsivity of the detector element is determined bythe details of the physics, which may be complex, but for atypical value at 4 K of r 5 5000 V/W and R ; 104 V,

NEP ; 5 3 10213 V/Hz1/2, (30)

which is a typical NEP for an InSb or Si/Ge bolometer at4 K. Because this is 2 orders of magnitude larger thanthe limit set by the fluctuations in a 300 K blackbody [Eq.(24)], a background temperature of ;30,000 K would berequired for the thermal noise to become significant.

4. REAL SUBMILLIMETER DETECTORSBefore I discuss the experimental results, I discuss thenoise properties of three classes of detectors that arewidely used in cw submillimeter experiments (4 K InSbhot-electron bolometers and Si/Ge lattice bolometers, 0.3K Si bolometers, and 300 K Schottky diodes) in the con-text of the question at hand: Are these detectors im-pacted by thermal noise from a 300 K or higher back-ground, and, if so, how significant is that impact,especially with high temperature or other nonambient(plasmas, etc.) backgrounds?

Cooled InSb bolometers similar to those that we origi-nally used for high-resolution spectroscopy of 300 K orhotter experiments in this spectral region3 are typicallyoperated near 4 K. Although their response falls atshorter wavelengths because of the frequency dependenceof their photon absorption mechanism, typically cooled fil-ters are used to cut off the room-temperature radiation,starting at a few terahertz. Their active elements are;5 mm 3 5 mm, and system NEPs of ;10212 W/Hz1/2 aretypical. This limit is set by the responsivity (V/W) of thedetector and the noise properties of the following preamp-lifier, not the fluctuation in the thermal radiation, which

Frank C. De Lucia Vol. 21, No. 7 /July 2004 /J. Opt. Soc. Am. B 1277

we have seen in the calculation above is approximately 2orders of magnitude lower. Consequently, their opticalsystems (either microwave horns or quasi-optical sys-tems) can be designed to accept more than one diffraction-limited mode without significant contribution from thethermal background to overall system performance.

On the other hand, Si bolometer systems cooled by 3Herefrigerators to ;0.3 K have enough responsivity to ap-proach the NEP of ;4 3 10215 W/Hz set by the blackbodyfluctuations. Consequently, for these systems it is ad-vantageous to restrict the detector view to only the modecontaining the desired signal.5

Room-temperature Schottky diode detectors are typi-cally matched into a waveguide mode with an antennastructure. It is generally difficult to do this efficientlyeven across a full waveguide band. As a result, these de-tectors typically respond to ;100 GHz or less of the ther-mal radiation. Because this is a relatively small portionof the blackbody spectrum, they also show no additionalnoise when looking into hot environments.

Figure 3 shows some of the functions developed abovefor the range nmax 5 0.1 → 3 THz and compares themwith the characteristics of sources and detectors used incw systems. The two horizontal lines at the top of thegraph are the source powers of 1 mW and 1 mW. The twohorizontal lines toward the bottom of the graphs are theNEPs for responsivity-limited 4He and 3He detectors.The most important point comes from a comparison of theresponsivity-limited detector noise to the noise associatedwith environmental noise (which is less) and to the powerof the cw sources (which is much more). Thus the limitsassociated with cw systems in the submillimeter are notdue to the noise power associated with the thermal back-ground (which, as we have seen, can be of the order ofPN , 10214 W, many orders of magnitude less than thethermal power), but that the low-power 1-mW and 1-mWsources are so bright they often drive these detectors orthe systems being probed far into saturation. As a re-sult, the limits imposed on cw systems by noise come not

Fig. 3. Top two horizontal lines represent source power levels of1 mW and 1 mW. The lower two horizontal lines represent NEPstypical of 4He temperature detectors (the higher of the two) and3He temperature detectors. The rest of the lines represent prop-erties of a 300 K blackbody below some maximum frequencynmax .

from fluctuations, but rather by the ratio of saturated out-put voltage of the detector to electrical noise.

If it is possible to make the detectors intrinsically moresensitive so that they become background limited, thiswould not, of course, reduce the sensitivity of the system,but can effect the trade-offs in the optimization of overallsystem performance. For example, at the optical end ofthe terahertz where background-limited photoconductordetectors become possible, the spectrum of noise of laser-based sources (which are typically noisier than the elec-tronic sources used in cw submillimeter systems) needs tobe considered in system trade-offs; and considerably moreelaborate schemes are needed to mitigate this technicalsource noise.40

5. EXPERIMENTAL EXAMPLESThere are a large number of examples in the literature ofuse of cw submillimeter techniques to study systems at el-evated temperatures or in plasmas or flames. None ofthe ones of which I am aware show any observable radi-ated noise from these backgrounds. Here I show two ex-amples to illustrate the results shown above.

A. Gas-Phase Spectroscopy at High TemperatureLet us first consider a direct example, the gas-phase spec-troscopy of SiO at high temperature.45 This is a problemof astrophysical interest because of the discovery someyears ago of SiO masers in the interstellar medium.46

The laboratory experiment was conducted by placing SiOin an oven, heating the oven to ;1650 K, and using a non-linear harmonic generator to produce ;1 mW of power tobe detected by an InSb detector operating at 1.6 K.

Figure 4 shows an absorption of ;0.1% of this power bythe J 5 1 –2, n 5 1 absorption of SiO at 86 GHz as ob-served on an oscilloscope screen. The noise in Fig. 4 isdue to the detector preamplifier of the 4 K InSb detector,and the observed baseline is due to coherent multipath ef-

Fig. 4. Oscilloscope display (60-Hz sweep, ;3 kHz of videobandwidth) of the J 5 1 –2, n 5 1 transition of SiO. This tran-sition corresponds to that observed as a maser in the interstellarmedium.

1278 J. Opt. Soc. Am. B/Vol. 21, No. 7 /July 2004 Frank C. De Lucia

fects. As predicted by the results above, the noise fromthe high-temperature background was unobservable.

Similar results have been obtained in a study of rota-tional transitions of water in excited vibrational states.47

In that study a cell heated to 1400 K was used to observerotational transitions in the 010 (1595 cm21), 100 (3657cm21), 001 (3756 cm21), and 020 (3190 cm21) vibrationalstates without any observable contribution to the overallsystem noise from the thermal background. More re-cently, THz–TDS observations of rotational transitions inthe lowest lying of these states, the 010, have beenreported.26

B. Diagnostics of Laser PlasmasContinuous-wave submillimeter techniques have alsobeen used in a number of experiments to study collisionalenergy transfer in active laser plasma as well as to per-form spectroscopy in these plasmas. Molecular dischargelasers are a complicated but interesting and useful sourceof radiation in this spectral region. The complexitycomes from both the many different temperatures thatexist in molecular plasma as well as the chemistry drivenby them. Figure 5 shows an experiment in which cw sub-millimeter power was transmitted quasi-opticallythrough the plasma of a HCN discharge laser and de-tected with an InSb bolometer at 1.6 K. Figure 6 showsrotational resonances from molecules in 4 of the 12 differ-ent vibrational states that were observed.11,16,48,49

Fig. 5. HCN discharge laser with a submillimeter probe for thestudy of the energy transfer and chemistry that leads to thepopulation inversion and lasing.

Fig. 6. Rotational absorption spectrum of the J 5 2 –3 transi-tions of HCN in the 011, 001, 110, and 100 vibrational states witha laser current of 900 mA.

With this probe it was possible to establish the rota-tional, translational, and vibrational temperatures of theseveral molecular species involved and to build a quanti-tative energy transfer and chemical model of the entiresystem. In contrast, prior to this study it had not beenpossible with other spectroscopic techniques to identifyeven the existence of HCN in this plasma; and, as a re-sult, many complex models involving CN radicals, etc.,had been hypothesized.50

There was, however, an interesting noise source thatmodulated the carrier of the probe radiation. Becausethe index of refraction depends on the electron density inthe plasma, the optical path lengths of the multipathprobe varied as well. The interference among the mul-tiple paths translated these fluctuations in the index ofrefraction into amplitude noise. However, it was shownthat this effect decreased as frequency square, whichcoupled with the frequency-cubed increase in absorptionstrength gave a gain in the signal-to-noise ratio of fre-quency to the fifth power. In practice, this noise sourcebecame undetectable above 200 or 300 GHz.

6. CONCLUSIONFor cw systems that use sensitive cryogenic submillime-ter detectors, the noise power associated with the fluctua-tions in thermal, plasma, flame, and other backgrounds isorders of magnitude less than the thermal power itself.More importantly, it is also typically negligible and ordersof magnitude smaller than other system noise contribu-tions. As a result, the sensitivity and resolution of coher-ent cw submillimeter techniques, which have so success-fully been applied to problems in spectroscopy, chemicalphysics, astronomy, and atmospheric science, can be ap-plied with no degradation to a wide variety of problems innonambient environments.

ACKNOWLEDGMENTThe author acknowledges the U.S. Army Research Officefor the support of this research.

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