Fourier-transform, integrated-optic spatial ... - OSA Publishing
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OPTICS LETTERS / Vol. 36, No. 16 / August 15, 2011
Fourier-transform, integrated-optic spatial heterodyne spectrometer on a silica-based planar waveguide with 1 GHz resolution Nicolas K. Fontaine,1,* Katsunari Okamoto,2 Tiehui Su,1 and S. J. B. Yoo1 1
Department of Electrical and Computer Engineering, University of California, One Shields Avenue, Davis, California 95616, USA 2
AiDi Corporation, 2-2-4 Takezono, Tsukuba, Ibaraki 305-0032, Japan *Corresponding author: [email protected]
Received May 10, 2011; revised July 1, 2011; accepted July 15, 2011; posted July 20, 2011 (Doc. ID 147315); published August 10, 2011 Spatial heterodyne spectrometers (SHS) can achieve high resolution with excellent optical throughput. We demonstrate a planar waveguide SHS incorporating 64 asymmetric Mach–Zehnder interferometers and show measurements that verify 1 GHz resolution across a 64 GHz measurement range. © 2011 Optical Society of America OCIS codes: 230.7390, 300.6300, 230.3120.
0146-9592/11/163124-03$15.00/0
with greater efficiency than coupling to one single-mode input aperture. In particular, photonic lanterns could aid in coupling light from a multimode fiber into each AMZI with 1–2 dB excess loss [7]. Each component of the DCT of sðf Þ, P k , is obtained by measuring the power output from each AMZI. The kth AMZI has a path length of ðk − 1ÞΔL, produces a cosine-shaped spectral transmission, and provides complementary outputs. Mathematically, the normalized DCT coefficients are Z p − qk 1 f 0 þFSR=2 ¼ sðf Þ cosðβðk − 1ÞΔL þ ϕk Þdf ; Pk ¼ k qk þ pk S f 0 ð1Þ where pk , qk are the power detected on the kth detector pair (upper and lower arm of the AMZI), ϕk is the kth DCT
(a) Input spectrum, s(f )
(b) Measured DCT of s(f ) Amplitude
Input Spectrum, s(f )
Output DCT, Pk
(N-1) ∆L
(c) Silica PLC
Measurement Range Selection Filter Input Apertures
∆L=1610 µm N = 64
2∆L
Dummy Crossing Waveguides
∆L
Input s(f)
pN qN
No delay
p1 q1
(d)
Broad AWG
Narrow AWG
Measurement Range Selection Filter λ1 λ1 Input λ9
Detector Array
Spectral Intensity
Multiple input aperture interferometric spectrometers, in particular SHSs, offer advantages in size, resolution, and optical throughput compared to grating-based imaging spectrometers [1–3]. Unlike conventional grating-based spectrometers, which rely on dispersive imaging, the SHS records the Fourier transform of the spectrum spatially across the output plane rather than the spectral intensity and obtains the spectrum by computing the inverse transform. The important advantages over imaging spectrometers are: increasing the resolution does not require narrowing of the input aperture and, therefore, étendue (light collection ability) is not compromised for resolution, and phase errors are correctable during postprocessing of the data. Recently, the SHS concept was adapted to planar waveguides using an array of N asymmetric Mach–Zehnder interferometers (AMZI), i.e., delay interferometers [4], and demonstrated in silica planar waveguides with 20 GHz resolution [5]. These planar SHSs measure a discrete cosine transform (DCT) [Fig. 1(b)] of a signal’s spectrum, sðf Þ [Fig. 1(a)]. In this Letter, we demonstrate operation of an SHS with 1 GHz resolution across a 64 GHz measurement range fabricated in planar silica using 4:5 μm×4:5 μm waveguides with a 1.5% index contrast [6]. The étendue advantage of the planar waveguide SHS compared to a grating spectrometer for equivalent spectral resolution is a consequence of the multiple input apertures [3,4]. Figure 1(c) describes the implementation of the SHS. The array of N AMZIs provides a set of cosine-shaped spectral transmissions and also N singlemode input apertures. The optical power detected at each AMZI output is one component, P k , of the DCT of sðf Þ. Compared to a planar waveguide grating spectrometer, which requires a single-mode input aperture, the effective width of the input aperture of the multiaperture SHS is N times larger. Therefore, the width of the input aperture can be increased without reducing the spectral resolution. Here, each input aperture (planar waveguide) has a mode area of 24:6 μm2 and a numerical aperture of 0.18. Therefore, the étendue of each waveguide is 2:4 × 10−6 mm2 sr and of the entire system is 1:5 × 10−4 mm2 sr. In practice, light can be collected with a multimode fiber and coupled to the N single-mode AMZI input apertures
(e) Narrow AWG Transmission 64 λ5 9 x 64 Splitter
λ9
FSR Wide AWG Cascaded AWG
1
λ5 Frequency
Fig. 1. (Color online) (a) Sample input spectrum and (b) its discrete cosine transform (DCT). (c) Layout of 64-channel SHS and (d) measurement range selection filter. (e) Illustration of cascaded AWG transmission. © 2011 Optical Society of America
August 15, 2011 / Vol. 36, No. 16 / OPTICS LETTERS 64 GHz Measurement Range
(b)
1
(c)
0 -1 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5 Wavelength (nm) (d)
Wavelength (nm) 1549 .8 15
50
.6
64 GHz
1
Amplitude
Normalized Transmission
Transmission (10 dB/div)
(a)
Phase (1 rad/div)
AMZI phase error, β is the propagation constant, and S is the total power in the measurement range, which is equal to half the device free spectral range (FSR) beginning from the start frequency, f 0 . Specifically, the kth AMZI provides a spectral transmission function with a ðÞ cosine shape, H k ðωÞ ¼ 1=2αk ½1 cosðβðk − 1ÞΔL þ ϕk Þ, where αk is an unknown input coupling coefficient and the corresponds to the upper and lower arm outputs. Transmission through each AMZI multiplies sðf Þ and the ðÞ cosine function, H k ðωÞ, and the slow detectors provide the integration operation by measuring the power. Often, the coupling of the input light to the different AMZIs is not uniform (i.e., an unknown value of αk ). Measuring the complimentary outputs enables normalization of the DCT coefficients, which removes the effect of αk and is similar to field flattening in a traditional SHS [5,8]. Figure 1(c) shows the device schematic. Integrated onto the planar lightwave circuit (PLC) is an arrayedwaveguide grating (AWG) based measurement range filter [Fig. 1(d)], which is coupled to the spectrometer through a 9 × 64 power splitter. Note, for experimental simplicity the PLC contains a single-mode input. The AMZI array is interleaved to reduce its size but forces the waveguides to cross, which introduces 0:05 dB loss per crossing. Dummy crossing waveguides are added to equalize the number of crossings between the upper and lower arms of each AMZI [5]. Additionally, the waveguide loss is below 0:019 dB=cm. The path length increment of 1:6 mm fixes the FSR to 128 GHz and the longest arm’s length is 100:8 mm, which sets the filter resolution to 1 GHz. The measurement range selection filter [Fig. 1(d)] comprises a 32-channel AWG with 10 GHz channel spacing (320 GHz FSR) with its outputs directed to the inputs of a 64-channel AWG with 320 GHz channel spacing (164 nm FSR). The cascaded transmission, illustrated in Fig. 1(e), has a 10 GHz bandwidth and a 164 nm FSR. The nine outputs (λ1 to λ9 ) are spaced at 10 GHz (i.e., 90 GHz total bandwidth) and are coupled to the AMZI array through the 9 × 64 splitter. In a device without phase errors sðf Þ is recovered using an inverse DCT of P, which is a vector containing the P k values. The output is discrete and represented by the vector s with si ¼ sðΔf ði − 1Þ þ f 0 Þ. The frequency step, Δf , or spectral resolution, is equal to c=½2ΔLnðN − 1Þ. To account for phase errors, the retrieval algorithm relates s to P through an N×N matrix, M, by discretizing Eq. (1) across the measurement range. Each element is M i;k ¼ cosðπ=Nði − 1Þðk − 1Þ þ ϕk Þ. The matrix form allows retrieval of sðf Þ in a device with phase errors through s ¼ M −1 P in the data processing stage. For transmission measurements we use a swept frequency interferometer with high-resolution (500 MHz) and a rapid update rate (5 Hz) [9]. To collect light, a single-mode fiber is scanned across the 128 outputs. Figure 2(a) shows the transmission of the k ¼ 35 output, which has the shape of both the selection filter and the cosine shape of the AMZI. Figure 2(b) shows the transmission of the AMZI with the longest path-length difference. Since the selection filter is coupled to the AMZIs through its nine outputs through the power splitter, its shape is slightly different for each arm and contains some spectral dips. However, its 90 GHz bandwidth is still larger than the 64 GHz measurement range. All the AMZIs
3125
-1
(e)
1
10
20
30 40 Arm Number (k+1)
50
60 64
Fig. 2. (Color online) Transmission measurements of AMZI ðþÞ ð−Þ outputs H k ðωÞ (blue) and H k ðωÞ (red) for (a) k ¼ 35 and (b) k ¼ 64. (c) H k ðωÞ (blue) compared to a cosine fit (gray). (d) H k ðωÞ for all AMZI and (e) the measured phase errors.
obtain >15 dB extinction between the nulls and peaks, indicating that the AMZIs are power balanced. The phase errors, ϕk , are extracted by fitting a cosine function to the normalized transmission, H k ðωÞ ¼ ðþÞ ð−Þ ðþÞ ð−Þ ½H k ðωÞ − H k ðωÞ=½H k ðωÞ þ H k ðωÞ. Figure 2(c) shows the cosine fit and H 35 ðωÞ. Figure 2(d) shows the measured normalized transmission for all 64 AMZIs (columns). Fitting cosine functions to all H k ðωÞ enables calculation of the phase errors [Fig. 2(e)]. Since the fits are accurate across the FSR, there are no wavelengthdependent phase errors within the FSR. The accuracy and stability of the phase-error measurement depends on the measurement technique and temperature stability (stabilized to 20 °C) of the device as each transmission is measured (128 outputs). Yet, independent measurements completed on separate days show variations of 0:1 rad. Figure 3 shows spectral measurements of a singlefrequency laser measured in 0:1 nm increments across the entire measurement range between 1549.9 and 1550:4 nm. Separately measuring all 128 channels requires approximately 20 minutes and introduces an unknown coupling error and a time-dependent error to each P k . Figures 3(a) and 3(c) show the raw measurements of the power coupled into the output fiber of all 128 outputs for 1550.35 and 1549:95 nm. The nonuniformity of the output indicates that the input light is spread unevenly across the different input apertures. Figures 3(b) and 3(d) show the normalized coefficient vector, P,
1
(e)
−1 1 (f) 0
1550.35 nm
0
0 1 (g)
1550.25 nm
−0.5 1 10 20 30 40 50 Arm Number
64 0 Power (a.u.)
Power (µW)
(c) 1549.95 nm
1
0
1 (h) 1550.15 nm
0 1 (i) 1550.05 nm
(d) Normalized Coefficients
Power (a.u.)
Pk
0.5 0
−0.5 1 10 20 30 40 50 Arm Number
(b)
1 (a)
0 Frequency (5 GHz/div)
(c) Wavelength (0.1 nm/div)
Frequency (5 GHz/div)
Fig. 4. (Color online) Two-line results with (a) 10 GHz separation and (b) 2 GHz separation. Inset, measurement with OSA.
(b) Normalized Coefficients
0.5 Pk
1550.35 nm No Phase Error Correction
0
1
Power (a.u.)
Power (µW)
(a) 1550.35 nm
Power (a.u.)
OPTICS LETTERS / Vol. 36, No. 16 / August 15, 2011 Power (a.u.)
3126
0 1 (j) 1549.95 nm
64 0 Frequency (5 GHz/div)
Fig. 3. (Color online) Single-frequency spectrum measurements. (a),(c) single-ended coefficients pk (blue) and qk (red). (b),(d) Normalized coefficients. Retrieval of 1550:35 nm line (e) without and (f) with phase-error correction. (g),(h),(i),(j) Additional measurements. In (e),(f) dots are discrete spectral data, and lines are Fourier interpolated.
which includes correction for the uneven input coupling as indicated by Eq. (1). In a device without phase errors, a single-frequency input should produce a set of P k with a perfect sinusoidal shape versus k. To illustrate the effectiveness of an SHS device with significant phase errors, we compare the spectrum of a 1550:35 nm line recovered with and without including phase-error correction [Figs. 3(e) and 3(f)]. The recovered discrete spectra, s, are Fourier interpolated by zero padding in the temporal domain to improve the visual appearance of the curves. Including phase errors enables recovery of a clean single-frequency line at the correct frequency location, whereas neglecting the phase errors results in an incorrect spectrum with energy spread across the entire window. Figures 3(e) and 3(j) present additional measurements of the single-frequency laser as it is tuned across the entire measurement range. The line is strong and located at the correct frequency, which verifies measurement fidelity across the measurement range. Figure 4 shows two-line measurements that include phase-error correction to verify the 1 GHz spectral resolution. A high-extinction Mach–Zehnder modulator
biased at its null point and driven by a sinusoid generates a two-line spectrum with precise and adjustable spacing. Figure 4(a) shows measurement of a 10 GHz spaced twoline spectrum showing two lines with the nearly equal power and the correct frequency spacing. Figure 4(b) shows measurement of a two-line spectrum with 2 GHz spacing. The SHS cleanly resolves the two lines and the null between the lines, and therefore obtains 1 GHz resolution. For comparison, the inset shows an independent measurement using a high-resolution optical spectrum analyzer (OSA) (0:02 nm resolution). In conclusion, we demonstrated a planar SHS spectrometer with 64 GHz measurement range and 1 GHz resolution. Future experimental modifications are expected to greatly improve the performance. For instance, using a detector array to simultaneously measure all outputs will reduce temporal variations across P and coupling errors from the manual fiber scanning, which will improve the normalization of each P k [8]. Use of multimode input collection fiber, interference selection filter rather than an AWG, and possibly a photonic lantern is expected to greatly increase the étendue of the system. This type of integrated high-resolution spectrometer can offer solutions for environmental sensing, space applications, and optical performance monitoring due to its compact size and relatively inexpensive fabrication. References 1. J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, and R. R. Conway, Appl. Opt. 41, 1343 (2002). 2. J. M. Harlander, J. E. Lawler, J. Corliss, F. L. Roesler, and W. M. Harris, Opt. Express 18, 6205 (2010). 3. P. Cheben, I. Powell, S. Janz, and D.-X. Xu, Opt. Lett. 30, 1824 (2005). 4. M. Florjanczyk, P. Cheben, S. Janz, A. Scott, B. Solheim, and D.-X. Xu, Opt. Express 15, 18176 (2007). 5. K. Okamoto, H. Aoyagi, and K. Takada, Opt. Lett. 35, 2103 (2010). 6. N. K. Fontaine, K. Okamoto, T. Su, and S. J. B. Yoo, in Optical Fiber Communications Conference (Optical Society of America, 2011), p. OWM2. 7. D. Noordegraaf, P. M. W. Skovgaard, M. D. Maack, J. BlandHawthorn, R. Haynes, and J. Lægsgaard, Opt. Express 18, 4673 (2010). 8. C. R. Englert and J. M. Harlander, Appl. Opt. 45, 4583 (2006). 9. G. D. VanWiggeren and D. M. Baney, IEEE Photon. Technol. Lett. 15, 1267 (2003).
OPTICS LETTERS / Vol. 36, No. 16 / August 15, 2011
Fourier-transform, integrated-optic spatial heterodyne spectrometer on a silica-based planar waveguide with 1 GHz resolution Nicolas K. Fontaine,1,* Katsunari Okamoto,2 Tiehui Su,1 and S. J. B. Yoo1 1
Department of Electrical and Computer Engineering, University of California, One Shields Avenue, Davis, California 95616, USA 2
AiDi Corporation, 2-2-4 Takezono, Tsukuba, Ibaraki 305-0032, Japan *Corresponding author: [email protected]
Received May 10, 2011; revised July 1, 2011; accepted July 15, 2011; posted July 20, 2011 (Doc. ID 147315); published August 10, 2011 Spatial heterodyne spectrometers (SHS) can achieve high resolution with excellent optical throughput. We demonstrate a planar waveguide SHS incorporating 64 asymmetric Mach–Zehnder interferometers and show measurements that verify 1 GHz resolution across a 64 GHz measurement range. © 2011 Optical Society of America OCIS codes: 230.7390, 300.6300, 230.3120.
0146-9592/11/163124-03$15.00/0
with greater efficiency than coupling to one single-mode input aperture. In particular, photonic lanterns could aid in coupling light from a multimode fiber into each AMZI with 1–2 dB excess loss [7]. Each component of the DCT of sðf Þ, P k , is obtained by measuring the power output from each AMZI. The kth AMZI has a path length of ðk − 1ÞΔL, produces a cosine-shaped spectral transmission, and provides complementary outputs. Mathematically, the normalized DCT coefficients are Z p − qk 1 f 0 þFSR=2 ¼ sðf Þ cosðβðk − 1ÞΔL þ ϕk Þdf ; Pk ¼ k qk þ pk S f 0 ð1Þ where pk , qk are the power detected on the kth detector pair (upper and lower arm of the AMZI), ϕk is the kth DCT
(a) Input spectrum, s(f )
(b) Measured DCT of s(f ) Amplitude
Input Spectrum, s(f )
Output DCT, Pk
(N-1) ∆L
(c) Silica PLC
Measurement Range Selection Filter Input Apertures
∆L=1610 µm N = 64
2∆L
Dummy Crossing Waveguides
∆L
Input s(f)
pN qN
No delay
p1 q1
(d)
Broad AWG
Narrow AWG
Measurement Range Selection Filter λ1 λ1 Input λ9
Detector Array
Spectral Intensity
Multiple input aperture interferometric spectrometers, in particular SHSs, offer advantages in size, resolution, and optical throughput compared to grating-based imaging spectrometers [1–3]. Unlike conventional grating-based spectrometers, which rely on dispersive imaging, the SHS records the Fourier transform of the spectrum spatially across the output plane rather than the spectral intensity and obtains the spectrum by computing the inverse transform. The important advantages over imaging spectrometers are: increasing the resolution does not require narrowing of the input aperture and, therefore, étendue (light collection ability) is not compromised for resolution, and phase errors are correctable during postprocessing of the data. Recently, the SHS concept was adapted to planar waveguides using an array of N asymmetric Mach–Zehnder interferometers (AMZI), i.e., delay interferometers [4], and demonstrated in silica planar waveguides with 20 GHz resolution [5]. These planar SHSs measure a discrete cosine transform (DCT) [Fig. 1(b)] of a signal’s spectrum, sðf Þ [Fig. 1(a)]. In this Letter, we demonstrate operation of an SHS with 1 GHz resolution across a 64 GHz measurement range fabricated in planar silica using 4:5 μm×4:5 μm waveguides with a 1.5% index contrast [6]. The étendue advantage of the planar waveguide SHS compared to a grating spectrometer for equivalent spectral resolution is a consequence of the multiple input apertures [3,4]. Figure 1(c) describes the implementation of the SHS. The array of N AMZIs provides a set of cosine-shaped spectral transmissions and also N singlemode input apertures. The optical power detected at each AMZI output is one component, P k , of the DCT of sðf Þ. Compared to a planar waveguide grating spectrometer, which requires a single-mode input aperture, the effective width of the input aperture of the multiaperture SHS is N times larger. Therefore, the width of the input aperture can be increased without reducing the spectral resolution. Here, each input aperture (planar waveguide) has a mode area of 24:6 μm2 and a numerical aperture of 0.18. Therefore, the étendue of each waveguide is 2:4 × 10−6 mm2 sr and of the entire system is 1:5 × 10−4 mm2 sr. In practice, light can be collected with a multimode fiber and coupled to the N single-mode AMZI input apertures
(e) Narrow AWG Transmission 64 λ5 9 x 64 Splitter
λ9
FSR Wide AWG Cascaded AWG
1
λ5 Frequency
Fig. 1. (Color online) (a) Sample input spectrum and (b) its discrete cosine transform (DCT). (c) Layout of 64-channel SHS and (d) measurement range selection filter. (e) Illustration of cascaded AWG transmission. © 2011 Optical Society of America
August 15, 2011 / Vol. 36, No. 16 / OPTICS LETTERS 64 GHz Measurement Range
(b)
1
(c)
0 -1 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5 Wavelength (nm) (d)
Wavelength (nm) 1549 .8 15
50
.6
64 GHz
1
Amplitude
Normalized Transmission
Transmission (10 dB/div)
(a)
Phase (1 rad/div)
AMZI phase error, β is the propagation constant, and S is the total power in the measurement range, which is equal to half the device free spectral range (FSR) beginning from the start frequency, f 0 . Specifically, the kth AMZI provides a spectral transmission function with a ðÞ cosine shape, H k ðωÞ ¼ 1=2αk ½1 cosðβðk − 1ÞΔL þ ϕk Þ, where αk is an unknown input coupling coefficient and the corresponds to the upper and lower arm outputs. Transmission through each AMZI multiplies sðf Þ and the ðÞ cosine function, H k ðωÞ, and the slow detectors provide the integration operation by measuring the power. Often, the coupling of the input light to the different AMZIs is not uniform (i.e., an unknown value of αk ). Measuring the complimentary outputs enables normalization of the DCT coefficients, which removes the effect of αk and is similar to field flattening in a traditional SHS [5,8]. Figure 1(c) shows the device schematic. Integrated onto the planar lightwave circuit (PLC) is an arrayedwaveguide grating (AWG) based measurement range filter [Fig. 1(d)], which is coupled to the spectrometer through a 9 × 64 power splitter. Note, for experimental simplicity the PLC contains a single-mode input. The AMZI array is interleaved to reduce its size but forces the waveguides to cross, which introduces 0:05 dB loss per crossing. Dummy crossing waveguides are added to equalize the number of crossings between the upper and lower arms of each AMZI [5]. Additionally, the waveguide loss is below 0:019 dB=cm. The path length increment of 1:6 mm fixes the FSR to 128 GHz and the longest arm’s length is 100:8 mm, which sets the filter resolution to 1 GHz. The measurement range selection filter [Fig. 1(d)] comprises a 32-channel AWG with 10 GHz channel spacing (320 GHz FSR) with its outputs directed to the inputs of a 64-channel AWG with 320 GHz channel spacing (164 nm FSR). The cascaded transmission, illustrated in Fig. 1(e), has a 10 GHz bandwidth and a 164 nm FSR. The nine outputs (λ1 to λ9 ) are spaced at 10 GHz (i.e., 90 GHz total bandwidth) and are coupled to the AMZI array through the 9 × 64 splitter. In a device without phase errors sðf Þ is recovered using an inverse DCT of P, which is a vector containing the P k values. The output is discrete and represented by the vector s with si ¼ sðΔf ði − 1Þ þ f 0 Þ. The frequency step, Δf , or spectral resolution, is equal to c=½2ΔLnðN − 1Þ. To account for phase errors, the retrieval algorithm relates s to P through an N×N matrix, M, by discretizing Eq. (1) across the measurement range. Each element is M i;k ¼ cosðπ=Nði − 1Þðk − 1Þ þ ϕk Þ. The matrix form allows retrieval of sðf Þ in a device with phase errors through s ¼ M −1 P in the data processing stage. For transmission measurements we use a swept frequency interferometer with high-resolution (500 MHz) and a rapid update rate (5 Hz) [9]. To collect light, a single-mode fiber is scanned across the 128 outputs. Figure 2(a) shows the transmission of the k ¼ 35 output, which has the shape of both the selection filter and the cosine shape of the AMZI. Figure 2(b) shows the transmission of the AMZI with the longest path-length difference. Since the selection filter is coupled to the AMZIs through its nine outputs through the power splitter, its shape is slightly different for each arm and contains some spectral dips. However, its 90 GHz bandwidth is still larger than the 64 GHz measurement range. All the AMZIs
3125
-1
(e)
1
10
20
30 40 Arm Number (k+1)
50
60 64
Fig. 2. (Color online) Transmission measurements of AMZI ðþÞ ð−Þ outputs H k ðωÞ (blue) and H k ðωÞ (red) for (a) k ¼ 35 and (b) k ¼ 64. (c) H k ðωÞ (blue) compared to a cosine fit (gray). (d) H k ðωÞ for all AMZI and (e) the measured phase errors.
obtain >15 dB extinction between the nulls and peaks, indicating that the AMZIs are power balanced. The phase errors, ϕk , are extracted by fitting a cosine function to the normalized transmission, H k ðωÞ ¼ ðþÞ ð−Þ ðþÞ ð−Þ ½H k ðωÞ − H k ðωÞ=½H k ðωÞ þ H k ðωÞ. Figure 2(c) shows the cosine fit and H 35 ðωÞ. Figure 2(d) shows the measured normalized transmission for all 64 AMZIs (columns). Fitting cosine functions to all H k ðωÞ enables calculation of the phase errors [Fig. 2(e)]. Since the fits are accurate across the FSR, there are no wavelengthdependent phase errors within the FSR. The accuracy and stability of the phase-error measurement depends on the measurement technique and temperature stability (stabilized to 20 °C) of the device as each transmission is measured (128 outputs). Yet, independent measurements completed on separate days show variations of 0:1 rad. Figure 3 shows spectral measurements of a singlefrequency laser measured in 0:1 nm increments across the entire measurement range between 1549.9 and 1550:4 nm. Separately measuring all 128 channels requires approximately 20 minutes and introduces an unknown coupling error and a time-dependent error to each P k . Figures 3(a) and 3(c) show the raw measurements of the power coupled into the output fiber of all 128 outputs for 1550.35 and 1549:95 nm. The nonuniformity of the output indicates that the input light is spread unevenly across the different input apertures. Figures 3(b) and 3(d) show the normalized coefficient vector, P,
1
(e)
−1 1 (f) 0
1550.35 nm
0
0 1 (g)
1550.25 nm
−0.5 1 10 20 30 40 50 Arm Number
64 0 Power (a.u.)
Power (µW)
(c) 1549.95 nm
1
0
1 (h) 1550.15 nm
0 1 (i) 1550.05 nm
(d) Normalized Coefficients
Power (a.u.)
Pk
0.5 0
−0.5 1 10 20 30 40 50 Arm Number
(b)
1 (a)
0 Frequency (5 GHz/div)
(c) Wavelength (0.1 nm/div)
Frequency (5 GHz/div)
Fig. 4. (Color online) Two-line results with (a) 10 GHz separation and (b) 2 GHz separation. Inset, measurement with OSA.
(b) Normalized Coefficients
0.5 Pk
1550.35 nm No Phase Error Correction
0
1
Power (a.u.)
Power (µW)
(a) 1550.35 nm
Power (a.u.)
OPTICS LETTERS / Vol. 36, No. 16 / August 15, 2011 Power (a.u.)
3126
0 1 (j) 1549.95 nm
64 0 Frequency (5 GHz/div)
Fig. 3. (Color online) Single-frequency spectrum measurements. (a),(c) single-ended coefficients pk (blue) and qk (red). (b),(d) Normalized coefficients. Retrieval of 1550:35 nm line (e) without and (f) with phase-error correction. (g),(h),(i),(j) Additional measurements. In (e),(f) dots are discrete spectral data, and lines are Fourier interpolated.
which includes correction for the uneven input coupling as indicated by Eq. (1). In a device without phase errors, a single-frequency input should produce a set of P k with a perfect sinusoidal shape versus k. To illustrate the effectiveness of an SHS device with significant phase errors, we compare the spectrum of a 1550:35 nm line recovered with and without including phase-error correction [Figs. 3(e) and 3(f)]. The recovered discrete spectra, s, are Fourier interpolated by zero padding in the temporal domain to improve the visual appearance of the curves. Including phase errors enables recovery of a clean single-frequency line at the correct frequency location, whereas neglecting the phase errors results in an incorrect spectrum with energy spread across the entire window. Figures 3(e) and 3(j) present additional measurements of the single-frequency laser as it is tuned across the entire measurement range. The line is strong and located at the correct frequency, which verifies measurement fidelity across the measurement range. Figure 4 shows two-line measurements that include phase-error correction to verify the 1 GHz spectral resolution. A high-extinction Mach–Zehnder modulator
biased at its null point and driven by a sinusoid generates a two-line spectrum with precise and adjustable spacing. Figure 4(a) shows measurement of a 10 GHz spaced twoline spectrum showing two lines with the nearly equal power and the correct frequency spacing. Figure 4(b) shows measurement of a two-line spectrum with 2 GHz spacing. The SHS cleanly resolves the two lines and the null between the lines, and therefore obtains 1 GHz resolution. For comparison, the inset shows an independent measurement using a high-resolution optical spectrum analyzer (OSA) (0:02 nm resolution). In conclusion, we demonstrated a planar SHS spectrometer with 64 GHz measurement range and 1 GHz resolution. Future experimental modifications are expected to greatly improve the performance. For instance, using a detector array to simultaneously measure all outputs will reduce temporal variations across P and coupling errors from the manual fiber scanning, which will improve the normalization of each P k [8]. Use of multimode input collection fiber, interference selection filter rather than an AWG, and possibly a photonic lantern is expected to greatly increase the étendue of the system. This type of integrated high-resolution spectrometer can offer solutions for environmental sensing, space applications, and optical performance monitoring due to its compact size and relatively inexpensive fabrication. References 1. J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, and R. R. Conway, Appl. Opt. 41, 1343 (2002). 2. J. M. Harlander, J. E. Lawler, J. Corliss, F. L. Roesler, and W. M. Harris, Opt. Express 18, 6205 (2010). 3. P. Cheben, I. Powell, S. Janz, and D.-X. Xu, Opt. Lett. 30, 1824 (2005). 4. M. Florjanczyk, P. Cheben, S. Janz, A. Scott, B. Solheim, and D.-X. Xu, Opt. Express 15, 18176 (2007). 5. K. Okamoto, H. Aoyagi, and K. Takada, Opt. Lett. 35, 2103 (2010). 6. N. K. Fontaine, K. Okamoto, T. Su, and S. J. B. Yoo, in Optical Fiber Communications Conference (Optical Society of America, 2011), p. OWM2. 7. D. Noordegraaf, P. M. W. Skovgaard, M. D. Maack, J. BlandHawthorn, R. Haynes, and J. Lægsgaard, Opt. Express 18, 4673 (2010). 8. C. R. Englert and J. M. Harlander, Appl. Opt. 45, 4583 (2006). 9. G. D. VanWiggeren and D. M. Baney, IEEE Photon. Technol. Lett. 15, 1267 (2003).
