The Surprisingly Swift Decline of U.S. Manufacturing Employment
Summary (2 min read)
1. INTRODUCTION
- Mode locking is a common technique employed to produce ultrashort optical pulses from lasers over a wide range of wavelengths.
- Such lasers serve as reliable sources of picosecond and subpicosecond pulses.
- This theory revealed spectral characteristics that are commonly referred to as a spike and a pair of pedestals, with the spike resulting from a delta-function-like shape at each harmonic owing to the external locking source.
2. MODEL
- The authors employ the technique of radio-frequency spectrum analysis to investigate random fluctuations in trains of 1997 Optical Society of America ultra-short pulses.
- As typically implemented, this technique is based on recording the power spectrum of the laser intensity by use of a fast photodiode and an electronic spectrum analyzer.
- Without any loss of generality, the authors can assume that the individual event fn(t) occurs over a short time compared with the observation period.
3. TIMING-JITTER FLUCTUATIONS
- Random variations of the time interval between successive pulses in the train are given by Tn 5 nT 1 dTn , (7) where T represents the average pulse repetition period and dTn is a random variable describing the fluctuations relative to the time nT of the nth pulse in the train.
- In what follows, the authors use these properties to give an analytical form for the spectra at different harmonics of the power spectrum.
- The second case is of long correlation time (t t @ T).
4. CORRELATION TIME tt
- The correlation time tt results, most likely, from relaxation processes in the mode-locked laser, which are responsible for timing-jitter fluctuations.
- One of these processes (e.g., a random process, such as spontaneous emission or gain profile fluctuation) results in a change of the central optical frequency through the action of the gain on the optical spectra.
- The timing-jitter fluctuations were found to have a behavior similar to that described in Eq. (20).
- Equation (23) shows that, besides the dependence on gain properties, the relaxation time depends on the pulse width.
- GAp2, (24) where g is the effective saturable absorber action and Ap is the pulse electric field amplitude.
5. AMPLITUDE FLUCTUATIONS
- Whenever the amplitude fluctuations are small relative to the mean amplitude intensity the power spectrum is influenced mainly by the timing-jitter noise and the results of Section 3 are applicable.
- The main influence of strong amplitude fluctuations appears whenever T/ta ; (^DT 2&)1/2/T.
- The dotted, dashed, and dotted–dashed curves represent the normalized spectra [the normalized outer parentheses of the summation in Eq. (28) are proportional to the normalized spectra] for (T/ta)/(2v 2^DT2&)1/2 equal to 1, 2, and 10, respectively, and ^dA2&/A2 5 1.
- This theory permits one to find the timing-jitter rms fluctuations from the shape and the width of the spectra for different harmonics of the experimental results and to estimate the correlation time tt for nonstationary timing fluctuations.
6. EXPERIMENTAL RESULTS
- Experimental measurements of noise have been made.
- 6,7 In Fig. 4 the two-section laser with an external cavity is shown.
- Therefore the timing-jitter fluctuations are damped slowly with relaxation time t t /T .
7. CONCLUSION
- The authors have presented an analysis of the power spectrum of optical pulse trains subject to nonstationary timing-jitter fluctuations.
- It is shown that the discrete lines and the v2 increase of the side-band peak values (characteristic of the low-frequency power spectrum for stationary timing-jitter fluctuations, as in actively mode-locked lasers) are not valid in this case.
- When timing-jitter fluctuations between successive neighboring pulses are uncorrelated in time, Lorentzianshaped spectra at different harmonics with FWHM proportional to the square of the harmonic number will result.
- The connection between the correlation time and the relaxation time that results from the coupling between the modes was discussed briefly.
- Small amplitude fluctuations or strong fluctuations with long or short amplitude correlation times both have little effect on the shape of the spectra.
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Frequently Asked Questions (7)
Q2. What are the future works mentioned in the paper "Nber working paper series the surprisingly swift decline of u.s. manufacturing employment" ?
This paper documents a strong relationship between the sharp decline in U. S. manufacturing employment beginning in 2001 and the United States ' conferral of permanent normal trade relations on China, a policy that is notable for eliminating the possibility of future tari increases rather than reducing the tari s actually applied to Chinese goods. The authors hope to bring additional data to bear on these questions in future research.
Q3. What is the significance of the coe cients for capital and skill intensity?
Coe cients for capital and skill intensity are mostly positive and negative, respectively, indicating that higher capital intensity is associated with higher employment growth, while higher skill intensity is associated with lower employment growth.
Q4. What is the important factor in the agglomeration patterns of U.S.?
Ellison, Glaeser and Kerr (2010) show that proximity to input suppliers and nal customers is the most important factor in the agglomeration patterns of U.S. manufacturing industries.
Q5. What is the reason for the differences in the NTR gap?
Another explanation for their results is that they are driven by labor-saving technical changes, such as automation, which are spuriously correlated with the NTR gap.
Q6. What does the President have to do to grant tari to non-market economies?
Act of 1974 allows the President to grant NTR tari rates to nonmarket economies on a temporary basis subject to Congressional approval.
Q7. What is the effect of PNTR on the growth rate of production hours?
The estimates in column 4 indicate that PNTR also had a substantial (-18.7 percentage points) negative e ect on the growth rate of production hours, con rming that the decline in employment can not be solely attributed to an increase in the number of hours worked per employee.