If this is for your Alaska landscapes, you don't want an ultra-wide like Chg_Canon's suggestions. Here's why:
https://www.uglyhedgehog.com/t-546747-1.html

In a nutshell, anything distant will look even further away and very small.

I found the Canon EF-S 18-135 mm to be highly versatile and have many landscape photos on UHH shot with that lens. I often do playful pp, but here are some with relatively normal processing

I recently posted sample pictures taken with my 12 year old Sigma lens and received some great advice. Even so, I think I may be forced to buy a new wide angle lens to avoid quality disappointment. Two suggestions have been made. The Tamron 18-200 and the Canon 18-135. My question is if I want quality nearly equivalent to my Canon 100-400 L lens, do I need to buy another L lens? I am really not anxious to make another major investment of say more than $500. I am shooting a Canon Rebel SL1 and although I know I could upgrade my camera, so far I don’t really see the need. I’d really appreciate your suggestions. Thanks for your time.

Note that many are responding with recommendations for zooms and not primes. I agree that the 17-40 is a good choice for a carry-around wide angle zoom. I'm a newcomer to DSLR's having used film through January 2018. I bought a nice used Canon 5D Mark ii which came with a 50mm 1.8, and the only lens I bought was a used 17-40 after reading all the reviews. It's pretty good at most focal lengths, although compared to wide angle primes, it falls a little short in image quality and color rendition. I like the Zeiss Distagon 25mm 2.8 for a prime wide. The Buddha was taken with the Canon zoom and the group picture with the Zeiss. About 80% of the group pic was cropped out, it was JPEG, the image was downgraded by Facebook's software and maybe this site's too. The original is amazing.

I recently posted sample pictures taken with my 12 year old Sigma lens and received some great advice. Even so, I think I may be forced to buy a new wide angle lens to avoid quality disappointment. Two suggestions have been made. The Tamron 18-200 and the Canon 18-135. My question is if I want quality nearly equivalent to my Canon 100-400 L lens, do I need to buy another L lens? I am really not anxious to make another major investment of say more than $500. I am shooting a Canon Rebel SL1 and although I know I could upgrade my camera, so far I don’t really see the need. I’d really appreciate your suggestions. Thanks for your time.

I recommended some lenses at your other post. To reiterate:

Tamron 18-200mm will feel and perform junk... compared to your 100-400L. Canon makes an EF-S 18-200mm that's a little better, but still not all that great.

Canon EF-S 18-135mm... there are three versions: The latest 18-135mm "USM" is a decent lens optically and for general performance: $600. The "STM" version is the same, but slower focusing: $400. The one that's neither STM nor USM is an older design that's not as good optically: $400. These lenses are capable, but clearly not "L quality". More like "high grade kit lens" quality. If you want a lens that's a better match to what your 100-400mm can do, I'd recommend:

Thank you SO much for the comprehensive response. The very last thing I want to do is buy another lens that doesn’t give good results. I feel like I wasted the money on the 100-300mm Canon lens I bought. It was good if I took it down an f-stop or two and If I didn’t shoot at more than 200mm.

Canon EF-S 15-85mm IS USM has "L like" image quality, as well as very good overall performance: $800. 15mm at the wide end of the zoom, it's also wider than most lenses of this type. And there isn't much gap between 85mm and your 100-400mm lens' shortest focal length.

Canon EF-S 17-55mm f/2.8 IS USM also has "L like" image quality and overall top performance... plus a bigger max aperture: $800. The trade-off to get f/2.8 is a narrower range of focal lengths... only 17 to 55mm. Not as wide nor as telephoto as the 15-85mm. Still, it would complement your 100-400mm well.

Neither of those zooms are an L-series lens. This IS NOT because they aren't capable. It's because no EF-S "crop only" lens can ever be an L, due to Canon's definition of what constitutes an "L". One of their main criteria for a lens to get a red ring painted on it is that it "must be compatible and work with all EOS cameras past, present and future". Since that's not the case with EF-S lenses, since they cannot be used on EOS film cameras or on full frame or APS-H DSLRs, no EF-S lens will ever qualify for the "L" label.

BUT that doesn't mean some EF-S lenses aren't just as capable, or even more-so than some L-series! For example, for someone with an APS-C camera the EF-S 17-55mm f/2.8 IS USM is clearly better choice than an EF 17-40mm f/4L USM. The EF-S lens is a stop faster, has image stabilization, offers a wider range of focal lengths AND has better image quality. A Canon EF 16-35mm f/4L IS USM or EF 16-35mm f/2.8L USM III would offer similar image quality to the 17-55mm... but are both have less focal length range more expensive than the EF-S lens. The 16-35mm f/4 has IS, like the 17-55mm... but is a stop slower. The 16-35mm f/2.8 has the same max aperture, but lacks IS. Since your camera can use an EF-S lens like the 17-55mm, that would be a better choice than any of those L-series.

There is no L-series comparable to the EF-S 15-85mm. The EF 24-105mm L IS USM II is the closest, slightly longer but not nearly as wide. And it costs $300 more... and doesn't offer any better image quality or better performance in any other ways.

The L-series... designed to cover a larger full frame sensor.... also will tend to be larger and heavier than comparable EF-S lenses.

Since you are using an APS-C camera (SL1), you can take advantage of EF-S lenses... spending less money for a lens that will likely be smaller, lighter and perform just as well... possibly even better... than many L-series.

My recommendation... if you don't need the f/2.8 aperture (for low light shooting, night photography), shop for a used EF-S 15-85mm IS USM. A new one is over your budget... a used one would be closer to what you want to spend. KEH.com, B&H Photo, Adorama are reliable sources of used gear (and all three currently have used copies of this lens in stock.... priced between $400 and $450). You also might watch the Canon USA online store for refurbished (there's none there now, but if there were, Canon's refurbs have the same warranty as new... while used gear from the above stores typically have 3 month warranty.)

If you want or need f/2.8 and don't mind the narrower range of focal lengths, the EF-S 17-55mm can also be found used for somewhat less than the price it sells for new. However, used ones appear to bring higher price than the 15-85mm, though.

Sold separately with Canon lenses other than L-series, I also recommend getting EW-78E lens hood for the 15-85mm... or the EW-83J lens hood for the 17-55mm (if not included with a used lens). The Canon OEM hoods are rather pricey at $30 to $50... there are cheaper 3rd party like Vello, typically about $20, that probably work just as well.

For landscape photography, I also highly recommend a high quality, multi-coated circular polarizer. B+W MRC, F-Pro or XS-Pro are usually the most reasonably priced among top quality C-Pol. The 15-85mm uses 72mm filters ($75 to $85 approx.) The 17-55mm lens uses 77mm filters (same size as your 100-400mm... $100 to $110 approx.)

I recently posted sample pictures taken with my 12 year old Sigma lens and received some great advice. Even so, I think I may be forced to buy a new wide angle lens to avoid quality disappointment. Two suggestions have been made. The Tamron 18-200 and the Canon 18-135. My question is if I want quality nearly equivalent to my Canon 100-400 L lens, do I need to buy another L lens? I am really not anxious to make another major investment of say more than $500. I am shooting a Canon Rebel SL1 and although I know I could upgrade my camera, so far I don’t really see the need. I’d really appreciate your suggestions. Thanks for your time.