Group- and phase-velocity-mismatch fringes in triple sum-frequency spectroscopy

Darien J. Morrow, Daniel D. Kohler, and John C. Wright

Phys. Rev. A 96, 063835 – Published 26 December 2017

Abstract

The effects of group- and phase-velocity mismatch are well known in optical harmonic generation, but the nondegenerate cases remain unexplored. In this work we develop an analytic model which predicts velocity mismatch effects in nondegenerate triple sum-frequency mixing, TSF. We verify this model experimentally using two tunable, ultrafast, short-wave IR lasers to demonstrate spectral fringes in the TSF output from a 500- $μ m$ -thick sapphire plate. We find the spectral dependence of the TSF depends strongly on both the phase-velocity and the group-velocity differences between the input and output fields. We define practical strategies for mitigating the impact of velocity mismatches.

Received 29 September 2017
Revised 2 December 2017

DOI:https://doi.org/10.1103/PhysRevA.96.063835

Physics Subject Headings (PhySH)

Classical optics Laser spectroscopy Nonlinear optics Optical coherence Ultrafast optics

Atomic, Molecular & Optical

Authors & Affiliations

Darien J. Morrow, Daniel D. Kohler, and John C. Wright^*

Department of Chemistry, University of Wisconsin – Madison, 1101 University Ave., Madison, Wisconsin 53706, USA

^*wright@chem.wisc.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 6 — December 2017

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Pulsed excitation model for degenerate excitation ( ${\bar{ν}}_{1} = {\bar{ν}}_{2} = {\bar{ν}}_{3} = 7700 {cm}^{- 1}$ ) in sapphire with sample lengths up to $500 μ m$ . (a) Frequency distribution of the output against sapphire sample length. The frequency axis is referenced to the TSF frequency center, $ω_{4} = ω_{1} + ω_{2} + ω_{3}$ . (b) The temporal envelope of the output against sapphire sample length. The time axis is referenced relative to when a TSF pulse which was generated at the front of the sample leaves the sample. In both plots, the small plots overhead show frequency and time cross sections of $L = 10 μ m$ (dotted orange) and $L = 400 μ m$ (solid dark pink). The driving fields have widths of $σ = 160 {cm}^{- 1}$ .
Reuse & Permissions
Figure 2
TSF amplitude at multiple combinations of pump colors—a juxtaposition between experiment and model. Experimental spectra (a and b) are represented as the square root of the detected intensity. These spectra go to zero near the edges due to a lack of driving laser intensity—see Figs. 5 and 5. We note that (b) has been lightly smoothed. (c) Our model's prediction assuming $ω = ω_{1} + 2 ω_{2}$ with effectively no spectral bandwidth of resolution. (d) Comparison of a color and linestyle-coded trace from each of (a, b, and c).
Reuse & Permissions
Figure 3
TSF amplitude for multiple combinations of pump and monochromator color. The experimental spectrum (a) is represented as the square root of the detected intensity. Subplot (a) shows experiment while subplot (b) shows our model's prediction.
Reuse & Permissions
Figure 4
Phase and group velocities ( $v_{p}$ and $v_{g}$ , respectively) in sapphire. Calculated from refractive index data measured by [24]. The salmon- and magenta-colored regions represent the experimental colors explored in this work by our pump lasers (labeled $ω_{1}, ω_{2}$ ) and TSF output (labeled $ω_{TSF}$ ), respectively.
Reuse & Permissions
Figure 5
OPA output characterization and correction for different colors of pump light. The left-hand column corresponds to $ω_{1}$ and the right-hand column corresponds to $ω_{2}$ . Subplots (a) and (b) were acquired by measuring the filtered NIR output of the OPAs with a thermopile [slight smoothing has been applied]. Subplots (c) and (d) were acquired using a monochromator and array detector to spectrally resolve the NIR output of each OPA. Subplots (e) and (f) were acquired by measuring the TSF output of sapphire in transmissive geometry with a PMT and scanning monochromator.
Reuse & Permissions
Figure 6
Determination of pulse bandwidth. Data are blue points while fit is the orange line.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information