We have developed an up-conversion spectrometer for signals at single photon levels near the infrared region based on a tunable up-conversion detector that uses a periodically poled lithium niobate waveguide as the conversion medium. We also experimentally studied its characteristics including sensitivity, dark count rate, spectral scan speed, signal transfer function of the waveguide, and polarization sensitivity. The overall single photon detection efficiency of the up-conversion spectrometer is about 32%. With its ultra high sensitivity the spectrometer can measure spectra for signals at a level as low as -126 dBm. We have demonstrated the spectrometers high sensitivity by measuring the spectrum of a greatly attenuated multimode emission from a laser diode at the 1310 nm band.
©2009 Optical Society of America
An infrared (IR) spectrometer for weak light at single-photon level is an important tool in many areas of research in physics, chemistry and biology, and may have applications in forensics . A traditional optical spectrum analyzer (OSA) usually uses either dispersive elements, such as prisms or diffractive gratings, or a tunable narrow-band filter, to separate or select light at different wavelengths which is then suitably detected. For ultra-violet light, visible light and light with wavelengths shorter than 1 μm, there are many choices for detectors with excellent performance. In this region, the detection efficiency of silicon-based detectors (or arrays) is very high while their intrinsic noise level is very low. For example, silicon avalanche photodiodes (Si-APDs) have a detection efficiency as high as 70% and a dark count rate of less than 100/second. However, the Si-APDs or other silicon-based detectors do not work in the IR region. The current IR detectors either have high noise characteristics (no-cooling InGaAs array detectors), which limits its sensitivity, or need a bulky cryogenic cooling system (e.g. liquid-nitrogen-cooled InGaAs array detectors).
To achieve highly sensitive detection for IR signals, the weak signal beam is coupled into a periodically poled lithium niobate (PPLN) waveguide, together with a strong pump source at a fixed wavelength. The signal photons are up-converted (in terms of frequency) from their IR wavelength to a shorter wavelength by a sum frequency generation (SFG) process. The converted photons can then be efficiently detected by silicon detectors [2–6]. Only those photons, whose momentum and energy conservation requirements satisfy the phase-matching condition in the waveguide, can be converted and then detected. Based on this principle, an up-conversion spectrometer can be constructed when a tunable pump source is used [7–9]. In this case, we can obtain a spectrum of the signal without using dispersive elements or tunable narrow-band filters. Furthermore, by using a pulsed pump, time-resolution spectroscopy can be conveniently realized .
We have developed an up-conversion spectrometer, which uses a tunable pump source around 1550 nm to convert photons from the 1310 nm band into the 710 nm band in a PPLN waveguide. The converted photons are then detected by a Si-APD. In this paper, we experimentally study the performance of the up-conversion spectrometer, reporting its sensitivity, maximum input signal power, scan speed, waveguide transfer function response and polarization sensitivity.
2. System configuration
The configuration of the up-conversion spectrometer is shown in Fig. 1. Similar to the up-conversion detector that we developed previously [5,6], the spectrometer uses a PPLN waveguide (HC Photonics) as a nonlinear medium to implement the SFG. The waveguide is a reverse-proton-exchange PPLN waveguide with magnesium oxide doping. The waveguide is 52.3 mm long (50 mm uniform grating) and both ends have an anti-reflection (AR) coating for 1310 nm, 1550 nm and 710 nm. As opposed to the PPLN waveguide used in ref [5,6], which had both the input and the output fiber coupled, the waveguide used in this spectrometer has only the input end fiber (SMF-28) coupled, and its coupling efficiencies are 64% for 1310 nm and 71% for 1550 nm. The output end of the waveguide is not fiber coupled, but rather is free-space with an AR coating. This configuration not only reduces the coupling loss at output end, but also allows us to use dispersive prisms, instead of narrow band-pass filters, to suppress the noise. This improvement helps us to implement a higher detection efficiency than that reported in ref [5,6]. A tunable CW laser near 1550 nm (New focus: TLB 6321) controlled by a computer via a GPIB port provides the seed light. If needed, the seed light can be modulated into a pulse train for noise reduction or for performing time-resolution measurements. Because the pump wavelength varies during the spectrum measurement, the modulator used here should be wavelength insensitive within that range. The light is then amplified by an erbium-doped fiber amplifier (EDFA) (IPG: EAR-0.5K-C). Two 1310/1550 wavelength division multiplexer (WDM) couplers, each with an extinction ratio of 25 dB, are used to suppress noise around 1310 nm at the output of the EDFA. The amplified pump is then combined with the 1310 nm signal beam being measured in a third WDM coupler. The combined signal and pump are then coupled into the PPLN waveguide. The input polarization state of both the signal and the pump are adjusted by the polarization controllers, PC1 and PC2 respectively, before the coupler. The output light of the PPLN waveguide, including the newly generated photons at 710 nm (SFG), the pump at 1550 nm and its second harmonic generation at 775 nm, are separated by two dispersive prisms. The pump light (1550 nm) is clearly separated after the first prism and blocked by a beam block. Because the 775 nm beam is close to the 710 nm beam being detected, a second dispersive prism is used to further separate them, and we use an adjustable iris to block the 775 nm beam. Because all the light beams are linearly polarized and their polarization is aligned with the p-polarization direction of the prisms, there is almost no intrinsic loss when the incident angle of the 710 nm light is close to the Brewster’s angle. A 20 nm band-pass filter (Omega Optical, Inc.: 3RD700–720) is used to reduce other noise, such as photons leaked from the environment. The 710 nm photons are then detected by a Si-APD (PerkinElmer: SPCM-AQR-14). The output count signal of the Si-APD is then sent back to the computer. The computer controls the 1550 nm tunable laser to scan the pump wavelength and also collects and processes the counts from Si-APD.
The quasi-phase-matching (QPM) condition in the periodically poled structure of the PPLN limits the acceptance bandwidth of the signal for a particular pump wavelength and therefore acts as a filter in the frequency domain. In theory, the longer the QPM structure (waveguide), the narrower the acceptance bandwidth. In our case (a 5 cm PPLN waveguide), the measured acceptance bandwidth is 0.2 nm. Because the line-width of the 1550 nm tunable laser is just 150 kHz, the up-conversion spectrometer resolution is determined by the QPM acceptance bandwidth of the waveguide. According to the QPM condition, one can get the spectrum of the measured signal by scanning the pump wavelength.
3. Performance of up-conversion spectrometer
3.1. Sensitivity of an up-conversion spectrometer
High sensitivity is the main objective of the up-conversion spectrometer. The sensitivity is mainly determined by the detection efficiency and the dark count rate.
The detection efficiency can be estimated by the following formula [2–4]:
where ηo is the overall detection efficiency of the up-conversion detector; ηloss is the total loss in the detector, including the component insertion loss and waveguide coupling loss; ηcon is the internal conversion efficiency in the PPLN, that can be estimated according to Eq. (1); η det is the detection efficiency of Si-APD at the converted wavelength, which is 710 nm in our case. According to the specification of the Si-APD, η det is about 65%. Ppump represents the pump power near 1550 nm, α is a constant, and L is the length of the waveguide. The measured conversion efficiency vs. pump power is shown in Fig. 2 (a). The maximum overall detection efficiency is 32%, which corresponds to 100% of internal conversion efficiency after we exclude the component loss, waveguide coupling loss, and the detection efficiency of the Si-APD. The dependence of the detection efficiency on the pump power satisfies Eq. (1).
The dark count rate has been extensively studied in single-photon frequency up-conversion technology [2–6]. The dark counts are contributed mainly by three parts: the intrinsic dark counts of the Si-APD, dark counts caused by the noise in the pump tail at the signal wavelength, and dark counts caused by the Raman scattering. The intrinsic dark count rate is constant, about 100 counts per second in our case . The dark counts caused by the noise in the pump tail occur as the pump noise at 1310 nm is up-converted to 710 nm and detected by Si-APD. We observed about a 20 kHz dark count rate caused by the noise of the pump at the maximum conversion efficiency. We use two WDM couplers (a 50 dB extinction ratio in total) to greatly suppress this noise. The dark counts caused by the Raman scattering occur as 1310 nm photons are generated by Raman scattering with the strong pump light in the transmission fiber and waveguide, and then up-converted to 710 nm and detected by Si-APD. In this spectrometer, we use a 1550 nm laser as a pump, whose wavelength is longer than that of the signal being measured. Because the anti-Stokes component of the Raman process is much weaker than the Stokes component, a dark count rate of less than 2500 counts per second is achieved when the conversion efficiency is maximized. Furthermore, the dark count noise itself has a spectrum. Figure 2 (b) shows the spectrum of the dark count noise from 1530~1570 nm and the peak is around 1550~1555 nm. From the spectrum, the dark count rate is 100 counts per second (50 counts per 500 ms) when the pump is off, which represents the intrinsic dark count rate of the Si-APD. From Fig. 2 (a) we can see that the dark count rate increases with the pump power. In the experimental set up, when the power and polarization of the pump are kept unchanged, the dark count spectrum is very stable. Therefore, we can subtract the dark counts from the measured spectrum of the signal being measured. In that case, only the deviation of the dark counts affects the measurement result.
The sensitivity is jointly limited by the detection efficiency and the deviation of the dark counts. Our measured maximum overall detection efficiency is 32%. The dark counts have a shot noise behavior, whose deviation is equal to the square root of the average number of counts. The maximum dark count rate in the measurement range is about 2500 counts per second, and the maximum dark count deviation is 50 counts per second. To get a clear spectrum, the signal counts should be one order of magnitude greater than the dark count deviation, or 500 counts per second, which corresponds to 1563 photons/s or -126 dBm of the signal when we take the detection efficiency of 32% into account.
Compared to the work in reference , we use WDM couplers to remove the noise from the pump, and use the PPLN waveguide with an AR-coating to reduce the transmission loss, and therefore improve the conversion efficiency and the dark count rate. Furthermore, we measure the spectrum of the dark count rate and subtract it from the measured result. With this operation, only the shot noise of dark count rate, instead of the dark count rate itself, influences the sensitivity of the spectrometer. With these improvements, the sensitivity of this spectrometer is 16 dB higher than that in reference .
3.2. The detection “dead time” and maximum measurement power
A major limitation to the maximum measurement power is imposed by the Si-APD and is referred to as “dead time”. After the Si-APD receives a photon, the avalanche process generates an electrical output signal. The device then needs a certain amount of time (dead time, tdead) to recover its initial operation state before detection of the next photon. During this period, the bias voltage across the p-n junction of the APD is below the breakdown level and no photon can be detected. This is especially significant when the power of the signal being measured becomes stronger. When the input signal is coherent light and the photon arrival time satisfies a Poisson distribution, the actual count rate can be estimated by :
where tdead is 50 ns for the Si-APD used in the spectrometer. R1 is the detection count rate for the Si-APD assuming tdead is zero, and can be calculated by:
where η is the detection efficiency; Pinput and λinput are the power and wavelength of the signal being measured; ħ is Plancks constant and c is the speed of light. We used attenuated light from a 1310 nm tunable laser (Santec: TSL-210V) to measure the count rate as a function of the input power. The calculated value is given by Eq. (2) and (3) and the measured values are shown in Fig. 3 (a). When the signal power is lower than -90 dBm, the influence of the dead time on the count rate is small and negligible, but when the power further increases, the influence will be significant. Figure 3 (b) shows the calculated ratio of R/R1 as a function of the signal power. When the signal power is lower than -95 dBm, the ratio is larger than 0.96 and we do not need to consider the influence of the dead-time. When the signal power is between -95 dBm to -80 dBm, the influence of the dead time is significant and the measured spectrum should be calibrated using the ratio curve (in Fig. 3 (b)) to recover the actual spectrum. When the signal power is larger than -80 dBm, more than half of the signal photons are lost due to the dead time and, additionally, the Si-APD is saturated and it is not suitable to use the spectrometer to measure the signal directly. Therefore, the most suitable measurement power range of the spectrometer is from -126 dBm to -95 dBm while the signal between -95 dBm to -80 dBm should calibrated to remove the influence of the dead-time. Any signal above -80 dBm should to be attenuated before using the up-conversion spectrometer.
3.3. Waveguide transfer function
While a traditional spectrometer uses wavelength dispersive elements, the up-conversion spectrometer is based on the QPM condition. The transfer function response of a finite-length of uniform QPM grating is a sinc2 function as given in the following equation [12,13]:
where PSFG, Ppump, Psignal are the power of SFG, pump, and signal light, L is the waveguide length, and Δk is the wave-vector-mismatching and can be calculated by the following equation:
where λSFG, λpump and λsignal are SFG, pump, and signal wavelengths; nSFG, n pump, and nsignal are the indices of the nonlinear material for the corresponding wavelength. ∧ is the poling period for the mth order quasi-phase-matched condition of the nonlinear PPLN waveguide.
From Eq. (4) and Eq. (5), for a given signal wavelength (near 1310 nm in our case), the SFG spectrum over pump wavelength is a sinc2 function instead of a single peak. It causes some “fake” side peaks in the spectrum measurement when the spectrometer is used to measure a signal with a narrow linewidth. In theory, the two main side peaks are as large as about 5% of the main peak, while in practice, imperfect poling and period uniformity will cause the side peaks to be larger than theoretically predicted and they can also be asymmetric. Because periodic poling at periods of 10–15 microns in congruent lithium niobate is well developed, we believe the main reason for the imperfect transfer function to be the imperfect period uniformity of the waveguide over its 5 cm length.
The measured spectrum can be seen as the convolution of the waveguide transfer function and the measurement noise. In order to reduce the “fake” side peaks in the spectrum of a signal with a narrow linewidth, a deconvolution of the spectrum can be performed. The relation can be expressed by the following formula:
where Smeasured and Ssignal are the measured spectrum and the actual signal spectrum. F is the transfer function of the waveguide, which can be measured accurately by an optical power meter using strong light from a tunable laser. ε is the total measurement noise, including the dark counts and other measurement noise.
When the measurement noise, ε, is small, we can deconvolve the measured spectrum, Smeasured, to recover the actual signal spectrum, Ssignal . However, the measurement noise is also deconvolved by F and then added into the result in the process. The lower the signal-to-noise ratio of the measurement, the worse the estimation of the deconvolved signal. Therefore, to do the recovery by deconvolution, the measurement result must have a sufficiently high signal-to-noise ratio.
A 1310 nm tunable laser (Santec TSL-210V) with a linewidth of 100 MHz was used as the signal. After been greatly attenuated (about 100 dB), a spectrum of the laser light was measured, shown in Fig. 4 (a), by the up-conversion spectrometer. In the measured spectrum, there are two small side peaks around the main peak due to the transfer function of the waveguide. The measurement result can be deconvolved by the transfer function, and the result is shown in Fig. 4 (b). After deconvolution, we can see a clear peak at 1310 nm, the two side peaks are removed, but the deconvolution of the noise causes some ripples at other wavelengths. The algorithm used to get the result in Fig. 4 (b) is the most simple and straightforward deconvolution calculation using the fast Fourier transform function. Currently, many advanced deconvolution algorithms have been developed to improve the recovered results in a low signal-to-noise ratio situation. For example, if we have some knowledge of the type of noise in the measurement (shot noise or white noise), we may be able to further improve the recovered results by using some advanced algorithms such as the Wiener deconvolution algorithm .
3.4. Spectral resolution and scan speed
Spectral resolution and scan time are other important parameters for a spectrometer. The resolution of the spectrometer is determined by spectral bandwidth and length of each tuning step of the pump laser as well as the QPM acceptance bandwidth of a waveguide. The linewidth of the tunable pump laser is 300 kHz, corresponding to a spectral bandwidth of 2.4 × 10-6 nm. The tuning step of the pump laser used in the experiment is 0.02 nm (FWHM). The acceptance spectral width for the 5 cm long PPLN waveguide is measured to be 0.2 nm, and dominates the resolution of the up-conversion spectrometer because it is much larger than the spectral bandwidth and tuning resolution of the pump laser. According to Eq. (4) and Eq. (5), the bandwidth of QPM crystal is inversely proportional to the waveguide length L. Therefore, a longer waveguide will result in a better spectral resolution. Due to fabrication tolerances, it is hard to get a PPLN waveguide longer than 5 cm, which is used in this experiment. Therefore, the spectral resolution of an up-conversion spectrometer is limited to about 0.2 nm under current technological conditions. A better spectral resolution can be realized when longer QPM structures are available or other experimental arrangements are implemented.
During a measurement by the spectrometer, the tunable pump laser in the up-conversion spectrometer scans at its operating tuning rate between set measurement points, and remains at each measurement point (wavelength) for a set length of time counting detection events. Therefore, the total scan speed of the up-conversion spectrometer is determined by the operating tuning speed of tunable laser, the number of steps per unit wavelength range and the integration time at each measurement point. The total scan speed can be estimated by the following equation:
where vs is the spectrometer scan speed, vt is the tuning speed of pump laser (12 nm/s in our case), n is the number of steps per nanometer and tin is the integration time at each measurement point. n can be selected according to the desired measurement resolution. In the case of our up-conversion spectrometer, a value of n = 10 (each step = 0.1 nm) is chosen for good resolution given the acceptance spectral width of 0.2 nm. tin can be selected by the power of the signal being measured, usually 50~500 ms. In this case, the scan speed of the spectrometer is about 0.2~1 nm/s.
3.5. Polarization sensitivity
Because the PPLN waveguide is based on proton-exchange, it is effective only for guiding the e-polarized light, and the o-polarized light is not transmitted. In effect, the device is therefore polarization sensitive. Figure 5 (a) shows the dependence of the conversion efficiency on the deviation (shifting) angle of the 1310 nm input polarization state. The deviation angle is the angle (in Jones space) between the given input polarization state and the state at which the conversion efficiency is maximized. The conversion efficiency is normalized to its maximum value. As shown in the figure, the polarization extinction ratio of the PPLN waveguide is more than 25 dB. We also compared the measurement results with the polarization sensitivity of an ideal polarizer, in which the transmittance as a function of deviation angle θ equals cos2(θ). The high polarization extinction ratio of the PPLN waveguide provides a unique characteristic for up-conversion spectrometers, acting as a polarizer inserted at the front of a traditional spectrometer. Then, the measurement result is the spectrum of the signal at a certain polarization orientation. When the signal being measured is polarized in a certain direction, an up-conversion spectrometer allows us to measure its spectrum and reduce the noise in other polarization orientations. The up-conversion spectrometer is especially suitable for applications in which a polarization spectrum is of interest.
In many cases, polarization-insensitive spectra are needed. The up-conversion spectrometer also can be implemented by combining two detection units as shown in Fig. 5 (b). A polarizing beam splitter (PBS) is used to split the components of two orthogonal polarization orientations into two up-conversion detection units. The two signals are aligned with the polarization of these respective PPLN waveguides to obtain the maximum counts, and then the counts are combined in a computer. In this configuration, the spectrometer cannot only measure the spectra of arbitrarily polarized IR light, but can also determine the power in each polarization of the orthogonal basis.
4. Experimental result
To demonstrate and verify the functionality of the spectrometer, we used it to measure the longitudinal-mode spectrum of a laser diode. For comparison, an optical spectrum analyzer (OSA, Ando AQ-6315A) was used first to record the strong light spectrum, as shown in Fig. 6 (a). The spectrum shows one main peak with an amplitude of -33 dBm at 1316 nm, two side peaks (-35 dBm) at 1315 nm and 1317 nm, and some smaller peaks (less than -40 dBm) at the 1312 ~1314 nm range. We then used the up-conversion spectrometer to measure the spectrum of the light after we greatly attenuated it by 75 dB. The scanning range of the pump laser is from 1540 nm to 1550 nm with a scanning step of 0.1 nm. The integration time at each measurement point is 500 ms. The measured six peaks are clearly shown in Fig. 6 (b). The power of all six peaks is less than -110 dBm and the power of the smallest peak is as weak as about -120 dBm. The total time used to record this spectrum was about 1 minute. This experiment demonstrates the ultra high sensitivity of the up-conversion spectrometer. The resolution of the up-conversion spectrometer is limited by the QPM condition, which can be improved by increasing the length of the waveguide.
We have developed an up-conversion spectrometer based on a PPLN waveguide. We experimentally studied the up-conversion spectrometer, including its sensitivity, maximum input signal power, scan speed, the waveguide transfer function response and polarization sensitivity. The detection efficiency of the up-conversion spectrometer is about 32% and its sensitivity is -126 dBm. Its working dynamic range is from -126 dBm to -80 dBm. We experimentally demonstrated its ultra high sensitivity by measuring greatly attenuated light from a laser diode near 1310 nm.
The authors would like to thank Dr. Qiang Zhang and Dr. Carsten Langrock from Edward L. Ginzton Laboratory, Stanford University for the technical discussions. This research was supported by the NIST quantum information initiative. 1 The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology.
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